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Logic, from the Greek λογικός (logikos)[1] is the study of reasoning.[2] Logic is used in most intellectual activity, but is studied primarily in the disciplines of philosophy, mathematics, and computer science. Logic examines general forms which arguments may take, which forms are valid, and which are fallacies. It is one kind of critical thinking. In philosophy, the study of logic falls in the area of epistemology, which asks: "How do we know what we know?" In mathematics, it is the study of valid inferences within some formal language.[3]
As a discipline, logic dates back to Aristotle, who established its fundamental place in philosophy. The study of logic is part of the classical trivium.
Averroes defined logic as "the tool for distinguishing between the true and the false"[4]; Richard Whately, '"the Science, as well as the Art, of reasoning"; and Frege, "the science of the most general laws of truth". The article Definitions of logic provides citations for these and other definitions.
Logic is often divided into two parts, inductive reasoning and deductive reasoning. The first is drawing general conclusions from specific examples, the second drawing logical conclusions from definitions and axioms. A similar dichotomy, used by Aristotle, is analysis and synthesis. Here the first takes an object of study and examines its component parts, the second considers how parts can be combined to form a whole.
Logic is also studied in argumentation theory.[5]

Contents

Nature of logic

The concept of logical form is central to logic, it being held that the validity of an argument is determined by its logical form, not by its content. Traditional Aristotelian syllogistic logic and modern symbolic logic are examples of formal logics.
  • Informal logic is the study of natural language arguments. The study of fallacies is an especially important branch of informal logic. The dialogues of Plato[6] are good examples of informal logic.
  • Formal logic is the study of inference with purely formal content. An inference possesses a purely formal content if it can be expressed as a particular application of a wholly abstract rule, that is, a rule that is not about any particular thing or property. The works of Aristotle contain the earliest known formal study of logic. Modern formal logic follows and expands on Aristotle.[7] In many definitions of logic, logical inference and inference with purely formal content are the same. This does not render the notion of informal logic vacuous, because no formal logic captures all of the nuance of natural language.
  • Symbolic logic is the study of symbolic abstractions that capture the formal features of logical inference.[8][9] Symbolic logic is often divided into two branches, propositional logic and predicate logic.
  • Mathematical logic is an extension of symbolic logic into other areas, in particular to the study of model theory, proof theory, set theory, and recursion theory.

Logical form

Logic is generally accepted to be formal, in that it aims to analyse and represent the form (or logical form) of any valid argument type. The form of an argument is displayed by representing its sentences in the formal grammar and symbolism of a logical language to make its content usable in formal inference. If one considers the notion of form to be too philosophically loaded, one could say that formalizing is nothing else than translating English sentences in the language of logic.
This is known as showing the logical form of the argument. It is necessary because indicative sentences of ordinary language show a considerable variety of form and complexity that makes their use in inference impractical. It requires, first, ignoring those grammatical features which are irrelevant to logic (such as gender and declension if the argument is in Latin), replacing conjunctions which are not relevant to logic (such as 'but') with logical conjunctions like 'and' and replacing ambiguous or alternative logical expressions ('any', 'every', etc.) with expressions of a standard type (such as 'all', or the universal quantifier ∀).
Second, certain parts of the sentence must be replaced with schematic letters. Thus, for example, the expression 'all As are Bs' shows the logical form which is common to the sentences 'all men are mortals', 'all cats are carnivores', 'all Greeks are philosophers' and so on.
That the concept of form is fundamental to logic was already recognized in ancient times. Aristotle uses variable letters to represent valid inferences in Prior Analytics, leading Jan Łukasiewicz to say that the introduction of variables was 'one of Aristotle's greatest inventions'.[10] According to the followers of Aristotle (such as Ammonius), only the logical principles stated in schematic terms belong to logic, and not those given in concrete terms. The concrete terms 'man', 'mortal', etc., are analogous to the substitution values of the schematic placeholders 'A', 'B', 'C', which were called the 'matter' (Greek 'hyle') of the inference.
The fundamental difference between modern formal logic and traditional or Aristotelian logic lies in their differing analysis of the logical form of the sentences they treat.
  • In the traditional view, the form of the sentence consists of (1) a subject (e.g. 'man') plus a sign of quantity ('all' or 'some' or 'no'); (2) the copula which is of the form 'is' or 'is not'; (3) a predicate (e.g. 'mortal'). Thus: all men are mortal. The logical constants such as 'all', 'no' and so on, plus sentential connectives such as 'and' and 'or' were called 'syncategorematic' terms (from the Greek 'kategorei' – to predicate, and 'syn' – together with). This is a fixed scheme, where each judgement has an identified quantity and copula, determining the logical form of the sentence.
  • According to the modern view, the fundamental form of a simple sentence is given by a recursive schema, involving logical connectives, such as a quantifier with its bound variable, which are joined to by juxtaposition to other sentences, which in turn may have logical structure.
  • The modern view is more complex, since a single judgement of Aristotle's system will involve two or more logical connectives. For example, the sentence "All men are mortal" involves in term logic two non-logical terms "is a man" (here M) and "is mortal" (here D): the sentence is given by the judgement A(M,D). In predicate logic the sentence involves the same two non-logical concepts, here analysed as m(x) and d(x), and the sentence is given by \forall x. (m(x) \rightarrow d(x)), involving the logical connectives for universal quantification and implication.
  • But equally, the modern view is more powerful: medieval logicians recognised the problem of multiple generality, where Aristotelean logic is unable to satisfactorily render such sentences as "Some guys have all the luck", because both quantities "all" and "some" may be relevant in an inference, but the fixed scheme that Aristotle used allows only one to govern the inference. Just as linguists recognise recursive structure in natural languages, it appears that logic needs recursive structure.

Deductive and inductive reasoning

Deductive reasoning concerns what follows necessarily from given premises (if a, then b). However, inductive reasoning—the process of deriving a reliable generalization from observations—has sometimes been included in the study of logic. Correspondingly, we must distinguish between deductive validity and inductive validity (called "cogency"). An inference is deductively valid if and only if there is no possible situation in which all the premises are true and the conclusion false. An inductive argument can be neither valid nor invalid; its premises give only some degree of probability, but not certainty, to its conclusion.
The notion of deductive validity can be rigorously stated for systems of formal logic in terms of the well-understood notions of semantics. Inductive validity on the other hand requires us to define a reliable generalization of some set of observations. The task of providing this definition may be approached in various ways, some less formal than others; some of these definitions may use mathematical models of probability. For the most part this discussion of logic deals only with deductive logic.

Consistency, validity, soundness, and completeness

Among the important properties that logical systems can have:
  • Consistency, which means that no theorem of the system contradicts another.[11]
  • Validity, which means that the system's rules of proof will never allow a false inference from true premises.[11]
  • Soundness, which means that the system's rules of proof will never allow a false inference from true premises, and the premises prove true. Soundness results from both validity and true premises. If a system is sound and its axioms are true then its theorems are also guaranteed to be true.[11]
  • Completeness, which means that if a theorem is true, it can be proven.
Some logical systems do not have all three properties. As an example, Kurt Gödel's incompleteness theorems show that no standard formal system of arithmetic can be consistent and complete.[9] At the same time his theorems for first-order predicate logics not extended by specific axioms to be arithmetic formal systems with equality, show those to be complete and consistent.[12]

Rival conceptions of logic

Logic arose (see below) from a concern with correctness of argumentation. Modern logicians usually wish to ensure that logic studies just those arguments that arise from appropriately general forms of inference. For example, Thomas Hofweber writes in the Stanford Encyclopedia of Philosophy that logic "does not, however, cover good reasoning as a whole. That is the job of the theory of rationality. Rather it deals with inferences whose validity can be traced back to the formal features of the representations that are involved in that inference, be they linguistic, mental, or other representations".[3]
By contrast, Immanuel Kant argued that logic should be conceived as the science of judgment, an idea taken up in Gottlob Frege's logical and philosophical work, where thought (German: Gedanke) is substituted for judgment (German: Urteil). On this conception, the valid inferences of logic follow from the structural features of judgments or thoughts.

History of logic

The earliest sustained work on the subject of logic is that of Aristotle,[13] In contrast with other traditions, Aristotelian logic became widely accepted in science and mathematics, ultimately giving rise to the formally sophisticated systems of modern logic.
Several ancient civilizations have employed intricate systems of reasoning and asked questions about logic or propounded logical paradoxes. In India, the Nasadiya Sukta of the Rigveda (RV 10.129) contains ontological speculation in terms of various logical divisions that were later recast formally as the four circles of catuṣkoṭi: "A", "not A", "Neither A or not A", and "Both not A and not not A".[14] The Chinese philosopher Gongsun Long (ca. 325–250 BC) proposed the paradox "One and one cannot become two, since neither becomes two."[15] Also, the Chinese School of Names is recorded as having examined logical puzzles such as "A White Horse is not a Horse" as early as the fifth century BCE.[16] In China, the tradition of scholarly investigation into logic, however, was repressed by the Qin dynasty following the legalist philosophy of Han Feizi.
Logic in Islamic philosophy also contributed to the development of modern logic, which included the development of "Avicennian logic"[17] as an alternative to Aristotelian logic. Avicenna's system of logic was responsible for the introduction of hypothetical syllogism,[18] temporal modal logic,[19][20] and inductive logic.[21][22] The rise of the Asharite school, however, limited original work on logic in Islamic philosophy, though it did continue into the 15th century and had a significant influence on European logic during the Renaissance.
In India, innovations in the scholastic school, called Nyaya, continued from ancient times into the early 18th century, though it did not survive long into the colonial period. In the 20th century, Western philosophers like Stanislaw Schayer and Klaus Glashoff have tried to explore certain aspects of the Indian tradition of logic.
During the later medieval period, major efforts were made to show that Aristotle's ideas were compatible with Christian faith. During the later period of the Middle Ages, logic became a main focus of philosophers, who would engage in critical logical analyses of philosophical arguments.
The syllogistic logic developed by Aristotle predominated until the mid-nineteenth century when interest in the foundations of mathematics stimulated the development of symbolic logic (now called mathematical logic). In 1854, George Boole published An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, introducing symbolic logic and the principles of what is now known as Boolean logic. In 1879 Frege published Begriffsschrift which inaugurated modern logic with the invention of quantifier notation. From 1910-13 Alfred North Whitehead and Bertrand Russell published Principia Mathematica[8] on the foundations of mathematics, attempting to derive mathematical truths from axioms and inference rules in symbolic logic. In 1931 Gödel raised serious problems with the foundationalist program and logic ceased to focus on such issues.
The development of logic since Frege, Russell and Wittgenstein had a profound influence on the practice of philosophy and the perceived nature of philosophical problems (see Analytic philosophy), and Philosophy of mathematics. Logic, especially sentential logic, is implemented in computer logic circuits and is fundamental to computer science. Logic is commonly taught by university philosophy departments often as a compulsory discipline.

Topics in logic

Syllogistic logic

The Organon was Aristotle's body of work on logic, with the Prior Analytics constituting the first explicit work in formal logic, introducing the syllogistic. The parts of syllogistic logic, also known by the name term logic, were the analysis of the judgements into propositions consisting of two terms that are related by one of a fixed number of relations, and the expression of inferences by means of syllogisms that consisted of two propositions sharing a common term as premise, and a conclusion which was a proposition involving the two unrelated terms from the premises.
Aristotle's work was regarded in classical times and from medieval times in Europe and the Middle East as the very picture of a fully worked out system. It was not alone: the Stoics proposed a system of propositional logic that was studied by medieval logicians; nor was the perfection of Aristotle's system undisputed; for example the problem of multiple generality was recognised in medieval times. Nonetheless, problems with syllogistic logic were not seen as being in need of revolutionary solutions.
Today, some academics claim that Aristotle's system is generally seen as having little more than historical value (though there is some current interest in extending term logics), regarded as made obsolete by the advent of propositional logic and the predicate calculus. Others use Aristotle in argumentation theory to help develop and critically question argumentation schemes that are used in artificial intelligence and legal arguments.

Sentential (propositional) logic

A propositional calculus or logic (also a sentential calculus) is a formal system in which formulae representing propositions can be formed by combining atomic propositions using logical connectives, and a system of formal proof rules allows certain formulæ to be established as "theorems".

Predicate logic

Predicate logic is the generic term for symbolic formal systems such as first-order logic, second-order logic, many-sorted logic, and infinitary logic.
Predicate logic provides an account of quantifiers general enough to express a wide set of arguments occurring in natural language. Aristotelian syllogistic logic specifies a small number of forms that the relevant part of the involved judgements may take. Predicate logic allows sentences to be analysed into subject and argument in several additional ways, thus allowing predicate logic to solve the problem of multiple generality that had perplexed medieval logicians.
The development of predicate logic is usually attributed to Gottlob Frege, who is also credited as one of the founders of analytical philosophy, but the formulation of predicate logic most often used today is the first-order logic presented in Principles of Mathematical Logic by David Hilbert and Wilhelm Ackermann in 1928. The analytical generality of predicate logic allowed the formalisation of mathematics, drove the investigation of set theory, and allowed the development of Alfred Tarski's approach to model theory. It provides the foundation of modern mathematical logic.
Frege's original system of predicate logic was second-order, rather than first-order. Second-order logic is most prominently defended (against the criticism of Willard Van Orman Quine and others) by George Boolos and Stewart Shapiro.

Modal logic

In languages, modality deals with the phenomenon that sub-parts of a sentence may have their semantics modified by special verbs or modal particles. For example, "We go to the games" can be modified to give "We should go to the games", and "We can go to the games"" and perhaps "We will go to the games". More abstractly, we might say that modality affects the circumstances in which we take an assertion to be satisfied.
The logical study of modality dates back to Aristotle, who was concerned with the alethic modalities of necessity and possibility, which he observed to be dual in the sense of De Morgan duality.[citation needed] While the study of necessity and possibility remained important to philosophers, little logical innovation happened until the landmark investigations of Clarence Irving Lewis in 1918, who formulated a family of rival axiomatizations of the alethic modalities. His work unleashed a torrent of new work on the topic, expanding the kinds of modality treated to include deontic logic and epistemic logic. The seminal work of Arthur Prior applied the same formal language to treat temporal logic and paved the way for the marriage of the two subjects. Saul Kripke discovered (contemporaneously with rivals) his theory of frame semantics which revolutionised the formal technology available to modal logicians and gave a new graph-theoretic way of looking at modality that has driven many applications in computational linguistics and computer science, such as dynamic logic.

Informal reasoning

The motivation for the study of logic in ancient times was clear: it is so that one may learn to distinguish good from bad arguments, and so become more effective in argument and oratory, and perhaps also to become a better person. Half of the works of Aristotle's Organon treat inference as it occurs in an informal setting, side by side with the development of the syllogistic, and in the Aristotelian school, these informal works on logic were seen as complementary to Aristotle's treatment of rhetoric.
This ancient motivation is still alive, although it no longer takes centre stage in the picture of logic; typically dialectical logic will form the heart of a course in critical thinking, a compulsory course at many universities.
Argumentation theory is the study and research of informal logic, fallacies, and critical questions as they relate to every day and practical situations. Specific types of dialogue can be analyzed and questioned to reveal premises, conclusions, and fallacies. Argumentation theory is now applied in artificial intelligence and law.

Mathematical logic

Mathematical logic really refers to two distinct areas of research: the first is the application of the techniques of formal logic to mathematics and mathematical reasoning, and the second, in the other direction, the application of mathematical techniques to the representation and analysis of formal logic.[23]
The earliest use of mathematics and geometry in relation to logic and philosophy goes back to the ancient Greeks such as Euclid, Plato, and Aristotle.[24] Many other ancient and medieval philosophers applied mathematical ideas and methods to their philosophical claims.[25]
One of the boldest attempts to apply logic to mathematics was undoubtedly the logicism pioneered by philosopher-logicians such as Gottlob Frege and Bertrand Russell: the idea was that mathematical theories were logical tautologies, and the programme was to show this by means to a reduction of mathematics to logic.[8] The various attempts to carry this out met with a series of failures, from the crippling of Frege's project in his Grundgesetze by Russell's paradox, to the defeat of Hilbert's program by Gödel's incompleteness theorems.
Both the statement of Hilbert's program and its refutation by Gödel depended upon their work establishing the second area of mathematical logic, the application of mathematics to logic in the form of proof theory.[26] Despite the negative nature of the incompleteness theorems, Gödel's completeness theorem, a result in model theory and another application of mathematics to logic, can be understood as showing how close logicism came to being true: every rigorously defined mathematical theory can be exactly captured by a first-order logical theory; Frege's proof calculus is enough to describe the whole of mathematics, though not equivalent to it. Thus we see how complementary the two areas of mathematical logic have been.[citation needed]
If proof theory and model theory have been the foundation of mathematical logic, they have been but two of the four pillars of the subject. Set theory originated in the study of the infinite by Georg Cantor, and it has been the source of many of the most challenging and important issues in mathematical logic, from Cantor's theorem, through the status of the Axiom of Choice and the question of the independence of the continuum hypothesis, to the modern debate on large cardinal axioms.
Recursion theory captures the idea of computation in logical and arithmetic terms; its most classical achievements are the undecidability of the Entscheidungsproblem by Alan Turing, and his presentation of the Church-Turing thesis.[27] Today recursion theory is mostly concerned with the more refined problem of complexity classes — when is a problem efficiently solvable? — and the classification of degrees of unsolvability.[28]

Philosophical logic

Philosophical logic deals with formal descriptions of natural language. Most philosophers assume that the bulk of "normal" proper reasoning can be captured by logic, if one can find the right method for translating ordinary language into that logic. Philosophical logic is essentially a continuation of the traditional discipline that was called "Logic" before the invention of mathematical logic. Philosophical logic has a much greater concern with the connection between natural language and logic. As a result, philosophical logicians have contributed a great deal to the development of non-standard logics (e.g., free logics, tense logics) as well as various extensions of classical logic (e.g., modal logics), and non-standard semantics for such logics (e.g., Kripke's technique of supervaluations in the semantics of logic).
Logic and the philosophy of language are closely related. Philosophy of language has to do with the study of how our language engages and interacts with our thinking. Logic has an immediate impact on other areas of study. Studying logic and the relationship between logic and ordinary speech can help a person better structure their own arguments and critique the arguments of others. Many popular arguments are filled with errors because so many people are untrained in logic and unaware of how to correctly formulate an argument.

Logic and computation

Logic cut to the heart of computer science as it emerged as a discipline: Alan Turing's work on the Entscheidungsproblem followed from Kurt Gödel's work on the incompleteness theorems, and the notion of general purpose computers that came from this work was of fundamental importance to the designers of the computer machinery in the 1940s.
In the 1950s and 1960s, researchers predicted that when human knowledge could be expressed using logic with mathematical notation, it would be possible to create a machine that reasons, or artificial intelligence. This turned out to be more difficult than expected because of the complexity of human reasoning. In logic programming, a program consists of a set of axioms and rules. Logic programming systems such as Prolog compute the consequences of the axioms and rules in order to answer a query.
Today, logic is extensively applied in the fields of artificial intelligence, and computer science, and these fields provide a rich source of problems in formal and informal logic. Argumentation theory is one good example of how logic is being applied to artificial intelligence. The ACM Computing Classification System in particular regards:
Furthermore, computers can be used as tools for logicians. For example, in symbolic logic and mathematical logic, proofs by humans can be computer-assisted. Using automated theorem proving the machines can find and check proofs, as well as work with proofs too lengthy to be written out by hand.

Controversies in logic

Just as we have seen there is disagreement over what logic is about, so there is disagreement about what logical truths there are.

Bivalence and the law of the excluded middle

The logics discussed above are all "bivalent" or "two-valued"; that is, they are most naturally understood as dividing propositions into true and false propositions. Non-classical logics are those systems which reject bivalence.
Hegel developed his own dialectic logic that extended Kant's transcendental logic but also brought it back to ground by assuring us that "neither in heaven nor in earth, neither in the world of mind nor of nature, is there anywhere such an abstract 'either–or' as the understanding maintains. Whatever exists is concrete, with difference and opposition in itself".[29]
In 1910 Nicolai A. Vasiliev rejected the law of excluded middle and the law of contradiction and proposed the law of excluded fourth and logic tolerant to contradiction.[citation needed] In the early 20th century Jan Łukasiewicz investigated the extension of the traditional true/false values to include a third value, "possible", so inventing ternary logic, the first multi-valued logic.[citation needed]
Logics such as fuzzy logic have since been devised with an infinite number of "degrees of truth", represented by a real number between 0 and 1.[30]
Intuitionistic logic was proposed by L.E.J. Brouwer as the correct logic for reasoning about mathematics, based upon his rejection of the law of the excluded middle as part of his intuitionism. Brouwer rejected formalisation in mathematics, but his student Arend Heyting studied intuitionistic logic formally, as did Gerhard Gentzen. Intuitionistic logic has come to be of great interest to computer scientists, as it is a constructive logic, and is hence a logic of what computers can do.
Modal logic is not truth conditional, and so it has often been proposed as a non-classical logic. However, modal logic is normally formalised with the principle of the excluded middle, and its relational semantics is bivalent, so this inclusion is disputable.

Is logic empirical?

What is the epistemological status of the laws of logic? What sort of argument is appropriate for criticizing purported principles of logic? In an influential paper entitled "Is logic empirical?"[31] Hilary Putnam, building on a suggestion of W.V. Quine, argued that in general the facts of propositional logic have a similar epistemological status as facts about the physical universe, for example as the laws of mechanics or of general relativity, and in particular that what physicists have learned about quantum mechanics provides a compelling case for abandoning certain familiar principles of classical logic: if we want to be realists about the physical phenomena described by quantum theory, then we should abandon the principle of distributivity, substituting for classical logic the quantum logic proposed by Garrett Birkhoff and John von Neumann.[32]
Another paper by the same name by Sir Michael Dummett argues that Putnam's desire for realism mandates the law of distributivity.[33] Distributivity of logic is essential for the realist's understanding of how propositions are true of the world in just the same way as he has argued the principle of bivalence is. In this way, the question, "Is logic empirical?" can be seen to lead naturally into the fundamental controversy in metaphysics on realism versus anti-realism.

Implication: strict or material?

It is obvious that the notion of implication formalised in classical logic does not comfortably translate into natural language by means of "if… then…", due to a number of problems called the paradoxes of material implication.
The first class of paradoxes involves counterfactuals, such as "If the moon is made of green cheese, then 2+2=5", which are puzzling because natural language does not support the principle of explosion. Eliminating this class of paradoxes was the reason for C. I. Lewis's formulation of strict implication, which eventually led to more radically revisionist logics such as relevance logic.
The second class of paradoxes involves redundant premises, falsely suggesting that we know the succedent because of the antecedent: thus "if that man gets elected, granny will die" is materially true if granny happens to be in the last stages of a terminal illness, regardless of the man's election prospects. Such sentences violate the Gricean maxim of relevance, and can be modelled by logics that reject the principle of monotonicity of entailment, such as relevance logic.

Tolerating the impossible

Hegel was deeply critical of any simplified notion of the Law of Non-Contradiction. It was based on Leibniz's idea that this law of logic also requires a sufficient ground in order to specify from what point of view (or time) one says that something cannot contradict itself, a building for example both moves and does not move, the ground for the first is our solar system for the second the earth. In Hegelian dialectic the law of non-contradiction, of identity, itself relies upon difference and so is not independently assertable.
Closely related to questions arising from the paradoxes of implication comes the suggestion that logic ought to tolerate inconsistency. Relevance logic and paraconsistent logic are the most important approaches here, though the concerns are different: a key consequence of classical logic and some of its rivals, such as intuitionistic logic, is that they respect the principle of explosion, which means that the logic collapses if it is capable of deriving a contradiction. Graham Priest, the main proponent of dialetheism, has argued for paraconsistency on the grounds that there are in fact, true contradictions.[34]

Rejection of logical truth

The philosophical vein of various kinds of skepticism contains many kinds of doubt and rejection of the various bases upon which logic rests, such as the idea of logical form, correct inference, or meaning, typically leading to the conclusion that there are no logical truths. Observe that this is opposite to the usual views in philosophical skepticism, where logic directs skeptical enquiry to doubt received wisdoms, as in the work of Sextus Empiricus.
Friedrich Nietzsche provides a strong example of the rejection of the usual basis of logic: his radical rejection of idealisation led him to reject truth as a mobile army of metaphors, metonyms, and anthropomorphisms—in short ... metaphors which are worn out and without sensuous power; coins which have lost their pictures and now matter only as metal, no longer as coins[35]. His rejection of truth did not lead him to reject the idea of either inference or logic completely, but rather suggested that logic [came] into existence in man's head [out] of illogic, whose realm originally must have been immense. Innumerable beings who made inferences in a way different from ours perished[36]. Thus there is the idea that logical inference has a use as a tool for human survival, but that its existence does not support the existence of truth, nor does it have a reality beyond the instrumental: Logic, too, also rests on assumptions that do not correspond to anything in the real world[37].

See also

Notes

  1. ^ "possessed of reason, intellectual, dialectical, argumentative", also related to λόγος (logos), "word, thought, idea, argument, account, reason, or principle" (Liddell & Scott 1999; Online Etymology Dictionary 2001).
  2. ^ Welton, James (1896). A manual of logic. University tutorial series. 1 (2nd ed.). W.B. Clive. http://books.google.com/books?id=KaAZAAAAMAAJ&pg=PA12&lpg=PA12&dq=%22art+and+science+of+reasoning%22. 
  3. ^ a b Hofweber, T. (2004). "Logic and Ontology". in Zalta, Edward N. Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/logic-ontology. 
  4. ^ Averroes, In Arist. Physicam I, textus 35, ed. Juntina, IV, fol. 11vb.
  5. ^ Cox, J. Robert; Willard, Charles Arthur, eds (1983). Advances in Argumentation Theory and Research. Southern Illinois University Press. ISBN 978-0809310500. 
  6. ^ Plato (1976). Buchanan, Scott. ed. The Portable Plato. Penguin. ISBN 0-14-015040-4. 
  7. ^ Aristotle (2001). "Posterior Analytics". in Mckeon, Richard. The Basic Works. Modern Library. ISBN 0-375-75799-6. 
  8. ^ a b c Whitehead, Alfred North; Russell, Bertrand (1967). Principia Mathematica to *56. Cambridge University Press. ISBN 0-521-62606-4. 
  9. ^ a b For a more modern treatment, see Hamilton, A. G. (1980). Logic for Mathematicians. Cambridge University Press. ISBN 0-521-29291-3. 
  10. ^ Łukasiewicz, Jan (1957). Aristotle's syllogistic from the standpoint of modern formal logic (2nd ed.). Oxford University Press. p. 7. ISBN 978-0198241447. 
  11. ^ a b c Bergmann, Merrie, James Moor, and Jack Nelson. The Logic Book fifth edition. New York, NY: McGraw-Hill, 2009.
  12. ^ Mendelson, Elliott (1964). "Quantification Theory: Completeness Theorems". Introduction to Mathematical Logic. Van Nostrand. ISBN 0412808307. 
  13. ^ E.g., Kline (1972, p.53) wrote "A major achievement of Aristotle was the founding of the science of logic".
  14. ^ Kak, S. (2004). The Architecture of Knowledge. Delhi: CSC. 
  15. ^ The four Catuṣkoṭi logical divisions are formally very close to the four opposed propositions of the Greek tetralemma, which in turn are analogous to the four truth values of modern relevance logic Cf. Belnap (1977); Jayatilleke, K. N., (1967, The logic of four alternatives, in Philosophy East and West, University of Hawaii Press).
  16. ^ "School of Names". Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/school-names/. Retrieved 5 September 2008. 
  17. ^ Goodman, Lenn Evan (1992). Avicenna. Routledge. p. 184. ISBN 978-0415019293. 
  18. ^ Goodman, Lenn Evan (2003). Islamic Humanism. Oxford University Press. p. 155. ISBN 0195135806. 
  19. ^ "History of logic: Arabic logic". Encyclopædia Britannica. http://www.britannica.com/EBchecked/topic/346217/history-of-logic/65928/Arabic-logic. 
  20. ^ Nabavi, Lotfollah. "Sohrevardi's Theory of Decisive Necessity and kripke's QSS System". Journal of Faculty of Literature and Human Sciences. Archived from the original on 26 January 2008. http://web.archive.org/web/20080126100838/http://public.ut.ac.ir/html/fac/lit/articles.html. 
  21. ^ "Science and Muslim Scientists". Islam Herald. Archived from the original on 17 December 2007. http://web.archive.org/web/20071217150016/http://www.islamherald.com/asp/explore/science/science_muslim_scientists.asp. 
  22. ^ Hallaq, Wael B. (1993). Ibn Taymiyya Against the Greek Logicians. Oxford University Press. p. 48. ISBN 0198240430. 
  23. ^ Stolyar, Abram A. (1983). Introduction to Elementary Mathematical Logic. Dover Publications. p. 3. ISBN 0-486-64561-4. 
  24. ^ Barnes, Jonathan (1995). The Cambridge Companion to Aristotle. Cambridge University Press. p. 27. ISBN 0-521-42294-9. 
  25. ^ Aristotle (1989). Prior Analytics. Hackett Publishing Co.. p. 115. ISBN 978-0872200647. 
  26. ^ Mendelson, Elliott (1964). "Formal Number Theory: Gödel's Incompleteness Theorem". Introduction to Mathematical Logic. Monterey, Calif.: Wadsworth & Brooks/Cole Advanced Books & Software. OCLC 13580200. 
  27. ^ Brookshear, J. Glenn (1989). "Computability: Foundations of Recursive Function Theory". Theory of computation: formal languages, automata, and complexity. Redwood City, Calif.: Benjamin/Cummings Pub. Co.. ISBN 0805301437. 
  28. ^ Brookshear, J. Glenn (1989). "Complexity". Theory of computation: formal languages, automata, and complexity. Redwood City, Calif.: Benjamin/Cummings Pub. Co.. ISBN 0805301437. 
  29. ^ Hegel, G. W. F (1971) [1817]. Philosophy of Mind. Encyclopedia of the Philosophical Sciences. trans. William Wallace. Oxford: Clarendon Press. p. 174. ISBN 0198750145. 
  30. ^ Hájek, Petr (2006). "Fuzzy Logic". in Zalta, Edward N.. Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/logic-fuzzy/. 
  31. ^ Putnam, H. (1969). "Is Logic Empirical?". Boston Studies in the Philosophy of Science 5. 
  32. ^ Birkhoff, G.; von Neumann, J. (1936). "The Logic of Quantum Mechanics". Annals of Mathematics 37: 823–843. 
  33. ^ Dummett, M. (1978). "Is Logic Empirical?". Truth and Other Enigmas. ISBN 0-674-91076-1. 
  34. ^ Priest, Graham (2008). "Dialetheism". in Zalta, Edward N.. Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/dialetheism. 
  35. ^ Nietzsche, 1873, On Truth and Lies in a Nonmoral Sense.
  36. ^ Nietzsche, 1882, The Gay Science.
  37. ^ Nietzsche, 1878, Human, All Too Human

References

External links and further reading


Quotes

Up to date as of January 14, 2010

From Wikiquote

Quotes about logic, rationality, and logical fallacies.

Contents

Sourced

Logic and rationality

  • Logic is a systematic method of coming to the wrong conclusion with confidence.
  • Logic hasn't wholly dispelled the society of witches and prophets and sorcerers and soothsayers.
  • Logic is a large drawer, containing some useful instruments, and many more that are superfluous. A wise man will look into it for two purposes, to avail himself of those instruments that are really useful, and to admire the ingenuity with which those that are not so, are assorted and arranged.
  • Logic is one thing and commonsense another.
  • The want of logic annoys. Too much logic bores. Life eludes logic, and everything that logic alone constructs remains artificial and forced.
  • Logic, like whiskey, loses its beneficial effect when taken in too large quantities.
    • Edward John Moreton Drax Plunkett, Lord Dunsany, "Weeds & Moss", My Ireland
  • Metaphysics may be, after all, only the art of being sure of something that is not so, and logic only the art of going wrong with confidence.
    • Joseph Wood Krutch, The Modern Temper (1929)
  • These, briefly, are the key elements of the stereotype: logic cripples and constrains; it forces one into narrow and mechanical modes of thought that cut one off from a vast range of superior thoughts, feelings and perceptions; logic is an enemy of wit and humor (Mr. Spock's face was always an impassive mask); logic makes us dull and pedantic (Mr. Spock always spoke in a monotone); logic presupposes a simple-minded, black-and-white, yes-no conception of the world. ... Logic misses the point of half the things we ordinarily say and cannot match the insight of the humblest person's common sense.
    • John M. Dolan, Inference and Imagination
  • One cannot use one's logic to explain actions driven by others' logic.
    • Sir. Acel Quailin KBE
  • Logic and mathematics seem to be the only domains where self-evidence manages to rise above triviality; and this it does, in those domains, by a linking of self-evidence on to self-evidence in the chain reaction known as proof.
  • "Contrariwise," continued Tweedledee, "if it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic."
  • ...logicians tell us that a system of ideas containing a contradiction can be used to deduce any statement whatsoever, no matter how absurd.
    • What is Your Dangerous Idea? (2007), John Brockman, ed., "Introduction," Steven Pinker, p. xxix
  • "Listen, Learn, Logic"
    • (2009), Steven Schaerer, Chemist

Logical fallacies

Appeal to authority

  • This fallacy [appeal to authority] is not in itself an error; it is impossible to learn much in today’s world without letting somebody else crunch the numbers and offer us explanations. And teachers are sources of necessary information. But how we choose our "authorities" and place a value on such information, is just another skill rarely taught in our education systems. It’s little wonder that to most folk, sound bites and talking heads are enough to count as experts. […] Teaching is reinforcing the appeal to authority, where anybody who seems more intelligent than you must ultimately be right. […] We educators must simply role-model critical thinking. […] Educators themselves have to be prepared to show that “evidence” and “answers” are two separate things by firmly believing that, themselves.
    • Mike McRae, Australian teacher and guest columnist, "Educating Future Critical Thinkers", Swift: Online Newsletter of the JREF, 31 March 2006

Unsourced

  • A good notation has a subtlety and suggestiveness which at times make it seem almost like a live teacher... ~ Bertrand Russell
  • A mind all logic is like a knife all blade. It cuts the hand that wields it. ~ Rabindranath Tagore
  • ... all traits of reality worthy of the name can be set down in an idiom of this form if in any idiom. ~ Willard van Orman Quine
  • If the world were a logical place, men would ride side saddle. ~ Rita Mae Brown
  • Instinct leads, logic does but follow. — William James
  • Logic: The art of thinking and reasoning in strict accordance with the limitations and incapacities of the human misunderstanding. ~ Ambrose Bierce
  • No, no, you're not thinking; you're just being logical. ~ Niels Bohr
  • Roughly speaking: to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing. ~ Ludwig Wittgenstein
  • All men are mortal. Socrates was mortal. Therefore, all men are Socrates. ~ Woody Allen
  • If you can't tell logical reasoning from brainwashing, you might get brainwashed. If you can, you might have already been brainwashed. ~

External links

Wikipedia
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Look up logic in Wiktionary, the free dictionary

1911 encyclopedia

Up to date as of January 14, 2010

From LoveToKnow 1911

LOGIC (Xoyu , sc. r xvr i, the art of reasoning), the name given to one of the four main departments of philosophy, though its sphere is very variously delimited. .The present article is divided into The Problems of Logic, History.^ The Future According to Madame Rhue by Randall L. Whipkey Madame Rhue gazes into her crystal ball to get answers to important questions in today's medium Logic Problem.
  • CRpuzzles Logic Problems Index 6 January 2010 10:47 UTC crpuzzles.com [Source type: General]

^ "Mathematical logic is traditionally divided into four parts: model theory, set theory, recursion theory and proof theory.
  • Readings in Logic 6 January 2010 10:47 UTC orcmid.com [Source type: Academic]

^ ARTICLE from the Encyclopædia Britannica the history of the discipline from its origins among the ancient Greeks to the present time.
  • history of logic -- Britannica Online Encyclopedia 6 January 2010 10:47 UTC www.britannica.com [Source type: Reference]

The Problems of Logic. Introduction. - .Logic
is the science of the processes of inference.^ And we said, finally, that there are three mental acts that make up the logical process: simple apprehension, judgement and deductive inference .

^ Logic is the science and art which so directs the mind in the process of reasoning and subsidiary processes as to enable it to attain clearness, consistency, and validity in those processes.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ The aim of logic is to secure clearness in the definition and arrangement of our ideas and other mental images, consistency in our judgments, and validity in our processes of inference.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

What, then, is inference ? .It is that mental operation which proceeds by combining two premises so as to cause a consequent conclusion.^ At the most fundamental level, the difference between the two is that, in a valid deductive argument, the conclusion asserts no more than what is contained in the premises, while, in an inductive argument, more is asserted in the conclusion than is contained in the premises.

^ I n the usual case, a valid argument consists of true propositions — true premises combining with true inferences leading to a true conclusion.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ The rules of natural deduction describe how we may proceed from valid premises to valid conclusions, where the premises and conclusions are expressions in predicate logic .
  • Logic Definition | Definition of Logic at Dictionary.com 6 January 2010 10:47 UTC dictionary.reference.com [Source type: Reference]

.Some suppose that we may infer from one premise by a so-called " immediate inference."^ Good, sound reasoning occurs when a person infers a conclusion from true, meaningful premises, and when we evaluate the inference or act of reasoning we see that it hangs together properly.
  • Can Logic Be Taught on Campus? 6 January 2010 10:47 UTC www.lewrockwell.com [Source type: Original source]

^ At least one of these statements is called the argument's premise(s) .
  • Can Logic Be Taught on Campus? 6 January 2010 10:47 UTC www.lewrockwell.com [Source type: Original source]

^ This is not to say that one should expect to find in A some direct and immediate duplication of not-A .

.But one premise can only reproduce itself in another form, e.g. all men are some animals; therefore some animals are men.^ Therefore, all dogs are animals.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ Therefore, some animals are rational.

^ Therefore, all animals are terriers.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

.It requires the combination of at least two premises to infer a conclusion different from both.^ C may require a different conclusion .
  • Formal Logic 22 September 2009 20:020 UTC www.plu.edu [Source type: Original source]

^ Good, sound reasoning occurs when a person infers a conclusion from true, meaningful premises, and when we evaluate the inference or act of reasoning we see that it hangs together properly.
  • Can Logic Be Taught on Campus? 6 January 2010 10:47 UTC www.lewrockwell.com [Source type: Original source]

^ Between this and the clear-cut Aristotelean syllogism, with its major and minor premises and conclusion, there is all the difference that exists between the Oriental and the Greek mode of thinking.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

.There are as many kinds of inference as there are different ways of combining premises, and in the main three types: 1. Analogical Inference, from particular to particular: e.g. border-war between Thebes and Phocis is evil; border-war between Thebes and Athens is similar to that between Thebes and Phocis; therefore, border-war between Thebes and Athens is evil.^ There are three types of jellyfish in the world.
  • Logic - Uncyclopedia, the content-free encyclopedia 6 January 2010 10:47 UTC uncyclopedia.wikia.com [Source type: Original source]

^ There are many ways to handle such prioritized sets of premises.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ There are, indeed, many different logics."
  • AITopics / Logic 6 January 2010 10:47 UTC www.aaai.org [Source type: Reference]

.2. Inductive Inference, from particular to universal: e.g. border-war between Thebes and Phocis is evil; all border-war is like that between Thebes and Phocis; therefore, all borderwar is evil.^ And stringing all the steps together into one movement is like deductive inference—we move from one place to another.

^ If we now put this all together, keeping our distinction between mental acts and verbal expressions, it would look like this: .

^ For example the problem how a universal relates to a particular that has it (assuming there are universals and particulars), or the problem how an event like John eating a cookie relate to the particulars John and the cookie, and the relation of eating, assuming there are events, particulars and relations.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.3. Deductive or Syllogistic Inference, from universal to particular, e.g. all border-war is evil; border-war between Thebes and Athens is border-war; therefore border-war between Thebes and Athens is evil.^ A deductive argument provides conclusive proof of its conclusions by presenting all the supporting evidence and reasoning for the premises and the inferences.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ Against relativism it is claimed that there exists a universal difference between rational and irrational beliefs or rational and irrational actions common to all cultures.
  • 20th WCP: The Classical Conception Of Rationality 18 September 2009 17:23 UTC www.bu.edu [Source type: FILTERED WITH BAYES]

^ And stringing all the steps together into one movement is like deductive inference—we move from one place to another.

.In each of these kinds of inference there are three mental judgments capable of being expressed as above in three linguistic propositions; and the two first are the premises which are combined, while the third is the conclusion which is consequent on their combination.^ The first two statements are premises and the last is the conclusion.

^ We term the combination of the two a proposition.

^ In the argument above, there are three propositions expressed.

.Each proposition consists of two terms, the subject and its predicate, united by the copula.^ We term the combination of the two a proposition.

^ "There are two main branches of formal logic today -- propositional calculus and predicate calculus.

^ "This glossary is limited to basic set theory, basic recursive function theory, two branches of logic (truth-functional propositional logic and first-order predicate logic) and their metatheory."
  • AITopics / Logic 6 January 2010 10:47 UTC www.aaai.org [Source type: Reference]

.Each inference contains three terms.^ Every syllogism contains three terms.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

.In syllogistic inference the subject of the conclusion is the minor term, and its predicate the major term, while between these two extremes the term common to the two premises is the middle term, and the premise containing the middle and major terms is the major premise, the premise containing the middle and minor terms the minor premise.^ The two premises always share a common term which does not appear in the conclusion.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ We said also that all arguments must contain two premises and a conclusion.

^ "The subject and the predicate of the conclusion each occur in one of the premises, together with a third term (the middle) that is found in both premises, but not in the conclusion.

.Thus in the example of syllogism given above, " border-war between Thebes and Athens " is the minor term, " evil " the major term, and " border-war " the middle term.^ Indeed, this is really the only example I’ve ever found of an Aristotelian syllogism that is at once useful and interesting from a practical perspective, and relatively transparent when the terms are interpreted.

^ Formal logic was once termed minor (or lesser) logic, while material logic usually went by the name of major (or greater) logic—a measure of how important classical thinkers considered them.
  • Memoria Press - Material Logic: A Traditional Approach to Thinking Skills 6 January 2010 10:47 UTC www.memoriapress.com [Source type: FILTERED WITH BAYES]

^ In our real estate example, the middle term is , i.e., that which increases in value.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

.Using S for minor, P for major and M for middle, and preserving these signs for corresponding terms in analogical and inductive inferences, we obtain the following formula of the three inferences: Inductive.^ For example, we noted earlier that the sign ‘ v ‘ is used analogously to ‘or’ in the inclusive sense, which means that language PL has no simple sign for ‘or’ in the exclusive sense .
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ The mental act involved in the third of these three logical processes is called deductive inference .

^ It would also be possible to reduce all truth-functional operators down to a single primitive by making use of a sign ‘↓’, treating it as roughly equivalent to the English expression, “neither … nor …”, so that the corresponding chart would be drawn as follows: .
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

Deductive or Syllogistic.
Every M is P S is M. S 2 is P.
.The love of unity has often made logicians attempt to resolve these three processes into one.^ The one has become divided into three.
  • The Limitation of Rationality and the Universal Thought 18 September 2009 17:23 UTC www.dreammanifesto.com [Source type: Original source]

^ The obvious retort to this criticism is that although expectations are inherently immeasurable, there have been numerous attempts made to incorporate them into econometric models and to test their validity in these models.
  • http://www.maths.tcd.ie/pub/econrev/ser/html/rationality.html 18 September 2009 17:23 UTC www.maths.tcd.ie [Source type: FILTERED WITH BAYES]

^ Any attempt to do so would demote these general terms and would thus turn these allegedly "general features of reality" into abstract particulars (as we saw in Essay Three ) --, at the same time as robbing language of its capacity to express generality (by turning predicates into singular terms).

But each process has a peculiarity of its own; they are similar, not the same. .Analogical and inductive inference alike begin with a particular premise containing one or more instances; but the former adds a particular premise to draw a particular conclusion, the latter requires a universal premise to draw a universal conclusion.^ Each of the premises and the conclusion is of one of four types: .
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ Induction reasons from repeated particular observations (which are usually observable) to more general truths through statistical generalizations and analogies which are sometimes unobserved (and which are considered stronger by virtue of the number of confirming instances that are appealed to in the premises.

^ These are reasoning gone wrong somewhere (although not always, as we’ll see), where the premises and conclusion(s) may seem plausible but where one or more mistakes have crept in (deliberately or otherwise).

.A citizen of Athens, who had known the evils of the border-war between Thebes and Phocis, would readily perceive the analogy of a similar war between Thebes and Athens, and conclude analogously that it would be evil; but he would have to generalize the similarity of all border-wars in order to draw the inductive conclusion that all alike are evil.^ In this way, Spock taught the concept of logic to a vast generation of hippies who would otherwise never have heard of it.
  • Logic - Uncyclopedia, the content-free encyclopedia 6 January 2010 10:47 UTC uncyclopedia.wikia.com [Source type: Original source]

^ At the most fundamental level, the difference between the two is that, in a valid deductive argument, the conclusion asserts no more than what is contained in the premises, while, in an inductive argument, more is asserted in the conclusion than is contained in the premises.

^ Between this and the clear-cut Aristotelean syllogism, with its major and minor premises and conclusion, there is all the difference that exists between the Oriental and the Greek mode of thinking.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

.Induction and deduction differ still more, and are in fact opposed, as one makes a particular premise the evidence of a universal conclusion, the other makes a universal premise evidence of a particular conclusion.^ Each of the premises and the conclusion is of one of four types: .
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ Induction reasons from repeated particular observations (which are usually observable) to more general truths through statistical generalizations and analogies which are sometimes unobserved (and which are considered stronger by virtue of the number of confirming instances that are appealed to in the premises.

^ These are reasoning gone wrong somewhere (although not always, as we’ll see), where the premises and conclusion(s) may seem plausible but where one or more mistakes have crept in (deliberately or otherwise).

.Yet they are alike in requiring the generalization of the universal and the belief that there are classes which are whole numbers of similars.^ Is it possible that 1/0 is not really undefined, but is in fact the key to a whole new class of numbers, much as the imaginary unit i led to the development of complex numbers?
  • Math Forum - Ask Dr. Math Archives: Middle School Logic 6 January 2010 10:47 UTC mathforum.org [Source type: FILTERED WITH BAYES]

^ Since robust rationality is rarely (if ever) completely attained, there have been many attempts to ëhumanizeí the constitutive constraints on belief by claiming that they only require that we treat those we interpret as believing what a ëtypicalí person would if she were in their situation.
  • Belief, Rationality and Psychophysical Laws 18 September 2009 17:23 UTC www.yorku.ca [Source type: Original source]

^ However, as researchers turned to generalizations of alethic modal logic, they began considering wider classes of modal logics, including ones where the necessity operator was not truth-implicating.
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

.On this point both differ from inference by analogy, which proceeds entirely from particular premises to a particular conclusion.^ Good, sound reasoning occurs when a person infers a conclusion from true, meaningful premises, and when we evaluate the inference or act of reasoning we see that it hangs together properly.
  • Can Logic Be Taught on Campus? 6 January 2010 10:47 UTC www.lewrockwell.com [Source type: Original source]

^ At the most fundamental level, the difference between the two is that, in a valid deductive argument, the conclusion asserts no more than what is contained in the premises, while, in an inductive argument, more is asserted in the conclusion than is contained in the premises.

^ I n the usual case, a valid argument consists of true propositions — true premises combining with true inferences leading to a true conclusion.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

.Hence we may redivide inference into particular inference by analogy and universal inference by induction and deduction.^ And stringing all the steps together into one movement is like deductive inference—we move from one place to another.

^ The contrast between deductive and ampliative inferences may be illustrated in the following examples.
  • logic -- Britannica Online Encyclopedia 6 January 2010 10:47 UTC www.britannica.com [Source type: Reference]

.Universal inference is what we call reasoning; and its two species are very closely connected, because universal conclusions of induction become universal premises of deduction.^ In teaching logic, after setting out a number of basic definitions ( argument itself, premise , conclusion , deduction , inference , valid , and so on) and explaining what they refer to, I turned to the Square of Opposition, which stands at the foundation of classical deductive logic.
  • Can Logic Be Taught on Campus? 6 January 2010 10:47 UTC www.lewrockwell.com [Source type: Original source]

^ Good, sound reasoning occurs when a person infers a conclusion from true, meaningful premises, and when we evaluate the inference or act of reasoning we see that it hangs together properly.
  • Can Logic Be Taught on Campus? 6 January 2010 10:47 UTC www.lewrockwell.com [Source type: Original source]

^ At the most fundamental level, the difference between the two is that, in a valid deductive argument, the conclusion asserts no more than what is contained in the premises, while, in an inductive argument, more is asserted in the conclusion than is contained in the premises.

.Indeed, we often induce in order to deduce, ascending from particular to universal and descending from universal to particular in one act as it were; so that we may proceed either directly from particular to particular by analogical inference, or indirectly from particular through universal to particular by an inductivedeductive inference which might be called " perduction."^ Indeed, that word is said to have unspecified universal inadequacies, which 'shortcomings' must of necessity feature in the very act of pointing this alleged fact out -- nullifying that criticism.

^ There are two ways for us to know: either directly or by inference.
  • Is Sherlock Holmes 11 September 2009 7:35 UTC plato.ucs.mun.ca [Source type: Original source]

^ Given that assumption , you may be able to prove the speaker is a knight; you may be able to prove the speaker is a knave; you might not be able to prove either; or you might be able to derive a contradiction, thus disproving the assumptions of the puzzle .
  • I Had A Dream 11 September 2009 7:35 UTC www.eblong.com [Source type: Original source]

.On the whole, then, analogical, inductive and deductive inferences are not the same but three similar and closely connected processes.^ Such relations are the subject matter of the general theory of rational argument or inference, whether deductive or inductive.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ The mental act involved in the third of these three logical processes is called deductive inference .

^ It studies the two kinds of reasoning, deductive and inductive , so as to direct the mind to use these processes validly.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

.The three processes of inference, though different from one another, rest on a common principle of similarity of which each is a different application.^ If you patronize small forum communities, I’m sure you have run into that application in one site or another.
  • Logician.org 11 September 2009 7:35 UTC www.logician.org [Source type: General]

^ Here I have an application full of RESTful controllers where the code is pretty similar, then I have this UserSessionsController thats different.
  • Binary Logic - Ben Johnson’s thoughts and programming techniques 6 January 2010 10:47 UTC www.binarylogic.com [Source type: General]

^ As was also argued in Essay Three Part One , if sentences were composed solely of names (or singular terms), they would be no different from lists .

.Analogical inference requires that one particular is similar to another, induction that a whole number or class is similar to its particular instances, deduction that each particular is similar to the whole number or class.^ Induction reasons from repeated particular observations (which are usually observable) to more general truths through statistical generalizations and analogies which are sometimes unobserved (and which are considered stronger by virtue of the number of confirming instances that are appealed to in the premises.

^ The subject has origins in philosophy, and indeed it is only by nonmathematical argument that one can show the usual rules for inference and deduction (law of excluded middle; cut rule; etc.
  • 03: Mathematical logic and foundations 6 January 2010 10:47 UTC www.math.niu.edu [Source type: Academic]

^ This observation indicates that the analysis of language had developed to the point of investigating the internal structures of statements, in addition to the relations of statements as a whole to one another.
  • history of logic -- Britannica Online Encyclopedia 6 January 2010 10:47 UTC www.britannica.com [Source type: Reference]

.Not that these inferences require us to believe, or assume, or premise or formulate this principle either in general, or in its applied forms: the premises are all that any inference needs the mind to assume.^ At bottom, Stove shows, his authors embrace irrationalism because of ‘a certain extreme belief, by which their minds are dominated, about what is required for one proposition to be a reason to believe another.’ They all acknowledge that absolute certainty is impossible; but they assume that only absolute certainty will do as a warrant for rational belief.
  • Science and Rationality 18 September 2009 17:23 UTC home.comcast.net [Source type: Original source]

^ The problem with these formulations, however they may play themselves out politically and ethically, is that in the first place we are not as rational as all that, and secondly the "Natives", whose irrationalities are generally different from our own, possess their own habits of mind which we have no right to disparage.
  • Rationality and Culture Difference 18 September 2009 17:23 UTC www.chass.toronto.edu [Source type: FILTERED WITH BAYES]

^ There are two ways for us to know: either directly or by inference.
  • Is Sherlock Holmes 11 September 2009 7:35 UTC plato.ucs.mun.ca [Source type: Original source]

.The principle of similarity is used, not assumed by the inferring mind, which in accordance with the similarity of things and the parity of inference spontaneously concludes in the form that similars are similarly determined (" similia similibus convenire ").^ Strictly speaking, rules of replacement differ from inference rules, because, in a sense, when a rule of replacement is used, one is not inferring something new but merely stating what amounts to the same thing using a different combination of symbols.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ Over time, economic agents learn what the process determining a variable is and they will use this knowledge to form expectations of that variable.
  • http://www.maths.tcd.ie/pub/econrev/ser/html/rationality.html 18 September 2009 17:23 UTC www.maths.tcd.ie [Source type: FILTERED WITH BAYES]

^ Many of the above sentences are somewhat stilted because they have been deliberately tailored to use the words "this" and "that" (i.e., the form of words that Rees employed to caricature the vernacular) in order to show that "things and ideas" are not "assumed" to be stable -- contrary to Rees's assertion.

.In applying this principle of similarity, each of the three processes in its own way has to premise both that something is somehow determined and that something is similar, and by combining these premises to conclude that this is similarly determined to that.^ Mathematics is also applied to logic itself: probability theory is a way to model reasoning with quantifiable uncertainty , formal mathematical logic approaches qualitative reasoning as a computational process.
  • logic@Everything2.com 6 January 2010 10:47 UTC www.everything2.com [Source type: Original source]

^ How this is done depends on whether the step is a premise, an axiom, or a result of modus ponens , and depending on which it is, applying one of the three procedures sketched in the proof above.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ In order to give ourselves a mental picture of these three logical processes, let us think of a man walking.

.Thus the very principle of inference by similarity requires it to be a combination of premises in order to draw a conclusion.^ Thus, if the premises and inferences are true, then probably the conclusion is as well.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ I n the usual case, a valid argument consists of true propositions — true premises combining with true inferences leading to a true conclusion.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ Thus in order to formalize the notion of a correct inference, one first needs to define what constitutes well-formed sentences.

.The three processes, as different applications of the principle of similarity, consisting of different combinations of premises, cause different degrees of cogency in their several conclusions.^ I n the usual case, a valid argument consists of true propositions — true premises combining with true inferences leading to a true conclusion.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ Between this and the clear-cut Aristotelean syllogism, with its major and minor premises and conclusion, there is all the difference that exists between the Oriental and the Greek mode of thinking.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ Here I have an application full of RESTful controllers where the code is pretty similar, then I have this UserSessionsController thats different.
  • Binary Logic - Ben Johnson’s thoughts and programming techniques 6 January 2010 10:47 UTC www.binarylogic.com [Source type: General]

Analogy hardly requires as much evidence as induction. .Men speculate about the analogy between Mars and the earth, and infer that it is inhabited, without troubling about all the planets.^ I don't know what I have to say about all that inbreeding that will never go on between ignorant agrrogant people, but...
  • Who Has Time For This?: Limits of Rationality: Beware the Paralimbic Cortex 18 September 2009 17:23 UTC whohastimeforthis.blogspot.com [Source type: General]

^ How, after all, does one go about "subduing the earth?"

^ Nevertheless, it is clear from this, as it is from Aristotle's other writings, that he continually switches back and forth without warning between talk about talk and talk about things.

.Induction has to consider more instances, and the similarity of a whole number or class.^ Induction reasons from repeated particular observations (which are usually observable) to more general truths through statistical generalizations and analogies which are sometimes unobserved (and which are considered stronger by virtue of the number of confirming instances that are appealed to in the premises.

^ Her whole class schedule has changed and shes still trying to remember it...Determine what subject Sally had in each Period, and the building, floor, and classroom number where each class was held.

.Even so, however, it starts from a particular premise which only contains many instances, and leaves room to doubt the universality of its conclusions.^ In the process of deduction, we derive the conclusion by reasoning: the conclusion follows necessarily from (and is entailed by) the (general or universal) premises.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ At the most fundamental level, the difference between the two is that, in a valid deductive argument, the conclusion asserts no more than what is contained in the premises, while, in an inductive argument, more is asserted in the conclusion than is contained in the premises.

^ For instance in a list of "best-selling books" the ranking can only be determined by how many people bought each book, not by whether it's considered a good book or not.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

.But deduction, starting from a premise about all the members of a class, compels a conclusion about every and each of necessity.^ This breaks the boundary between the premises which deal with the mechanics of the language and the conclusion which is about the subject-matter of the language.
  • Logic on the Web -- Web architecture 6 January 2010 10:47 UTC www.w3.org [Source type: FILTERED WITH BAYES]

^ Now, recalling that “A” stands for “All” we can read off what the second premise says from our previous interpretations: “All Rights that exist are Mentioned in the Constitution.” This is now a logically valid argument, and if both premises are true, then the conclusion follows by necessity.

^ At the most fundamental level, the difference between the two is that, in a valid deductive argument, the conclusion asserts no more than what is contained in the premises, while, in an inductive argument, more is asserted in the conclusion than is contained in the premises.

.One border-war may be similar to another, and the whole number may be similar, without being similarly evil; but if all alike are evil, each is evil of necessity.^ This observation indicates that the analysis of language had developed to the point of investigating the internal structures of statements, in addition to the relations of statements as a whole to one another.
  • history of logic -- Britannica Online Encyclopedia 6 January 2010 10:47 UTC www.britannica.com [Source type: Reference]

^ We may seek to employ,e.g., the doctrine of divine sovereignty, in contexts similar to those in which the biblical writers used it, without necessarily being able to reconcile it with human responsibility.

^ But what may be part of the technical culture of one group may belong to another level of culture of another.
  • Pluralism and Rationality: the limits of tolerance 18 September 2009 17:23 UTC www.newfoundations.com [Source type: Original source]

.Deduction or syllogism is superior to analogy and induction in combining premises so as to involve or contain the conclusion.^ At the most fundamental level, the difference between the two is that, in a valid deductive argument, the conclusion asserts no more than what is contained in the premises, while, in an inductive argument, more is asserted in the conclusion than is contained in the premises.

^ I n the usual case, a valid argument consists of true propositions — true premises combining with true inferences leading to a true conclusion.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ Between this and the clear-cut Aristotelean syllogism, with its major and minor premises and conclusion, there is all the difference that exists between the Oriental and the Greek mode of thinking.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

.For this reason it has been elevated by some logicians above all other inferences, and for this very same reason attacked by others as no inference at all.^ I see no reason why theologians should not attempt to resolve these as they have resolved the others.

^ No general theory of argument or inference would be complete without an account of the various fallacies and paradoxes which beset our attempts to reason from premise to conclusion.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ With reasoning like that you might as well argue that if a metre rule, say, has been made incorrectly the same must be true of all it measures!

.The truth is that, though the premises contain the conclusion, neither premise alone contains it, and a man who knows both but does not combine them does not draw the conclusion; it is the synthesis of the two premises which at once contains the conclusion and advances our knowledge; and as syllogism consists, not indeed in the discovery, but essentially in the synthesis of two premises, it is an inference and an advance on each premise and on both taken separately.^ The truth of the premises guarantees the truth of the conclusions.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ It does not address the truth of either the premises or the conclusion.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ Furthermore, the order of the two premises in a syllogism does not matter.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

.As again the synthesis contains or involves the conclusion, syllogism has the advantage of compelling assent to the consequences of the premises.^ Between this and the clear-cut Aristotelean syllogism, with its major and minor premises and conclusion, there is all the difference that exists between the Oriental and the Greek mode of thinking.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ An argument is logically valid if and only if its conclusion is a logical consequence of its premises.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ By metatheoretic result 2, we can remove from each of these sets of premises either p n or ¬p n , depending on which it contains, and make it an antecedent of a conditional in which α is consequent, and the result will be provable without using p n or ¬p n as a premise.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

.Inference in general is a combination of premises to cause a conclusion; deduction is such a combination as to compel a conclusion involved in the combination, and following from the premises of necessity.^ The nature of an argument is such that if the premises are true, then the conclusion that follows from them must also be true.
  • logic@Everything2.com 6 January 2010 10:47 UTC www.everything2.com [Source type: Original source]

^ And when an inference is formally valid then the conclusion logically follows from the premises.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ In teaching logic, after setting out a number of basic definitions ( argument itself, premise , conclusion , deduction , inference , valid , and so on) and explaining what they refer to, I turned to the Square of Opposition, which stands at the foundation of classical deductive logic.
  • Can Logic Be Taught on Campus? 6 January 2010 10:47 UTC www.lewrockwell.com [Source type: Original source]

.Nevertheless, deduction or syllogism is not independent of the other processes of inference.^ Over-estimation of the syllogism, as compared to other forms of deductive argument.
  • The Development of Laws of Formal Logic of Aristotle 22 September 2009 20:020 UTC uweb.superlink.net [Source type: Original source]

^ When we verbally express this in an argument, we have put this deductive inference in the form of a syllogism.

^ The lower limit logic, AN , validates disjunctive syllogism and all other analysing inferences (specified in the paper).
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

.It is not the primary inference of its own premises, but constantly converts analogical and inductive conclusions into its particular and universal premises.^ Good, sound reasoning occurs when a person infers a conclusion from true, meaningful premises, and when we evaluate the inference or act of reasoning we see that it hangs together properly.
  • Can Logic Be Taught on Campus? 6 January 2010 10:47 UTC www.lewrockwell.com [Source type: Original source]

^ At the most fundamental level, the difference between the two is that, in a valid deductive argument, the conclusion asserts no more than what is contained in the premises, while, in an inductive argument, more is asserted in the conclusion than is contained in the premises.

^ I n the usual case, a valid argument consists of true propositions — true premises combining with true inferences leading to a true conclusion.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

.Of itself it causes a necessity of consequence, but only a hypothetical necessity; if these premises are true, then this conclusion necessarily follows.^ The nature of an argument is such that if the premises are true, then the conclusion that follows from them must also be true.
  • logic@Everything2.com 6 January 2010 10:47 UTC www.everything2.com [Source type: Original source]

^ In reasoning, whether premises are true or false, conclusions can follow (validly).
  • Is Sherlock Holmes 11 September 2009 7:35 UTC plato.ucs.mun.ca [Source type: Original source]

^ Good, sound reasoning occurs when a person infers a conclusion from true, meaningful premises, and when we evaluate the inference or act of reasoning we see that it hangs together properly.
  • Can Logic Be Taught on Campus? 6 January 2010 10:47 UTC www.lewrockwell.com [Source type: Original source]

.To eliminate this " if " ultimately requires other inferences before deduction.^ From a foundational perspective rational justification ultimately requires both premises and rules that can be justified without appealing to other premises and rules.
  • 20th WCP: The Classical Conception Of Rationality 18 September 2009 17:23 UTC www.bu.edu [Source type: FILTERED WITH BAYES]

^ Indeed, Loar considers it a virtue of his theory that the L-constraints neither "imply that the set of a person's beliefs is deductively closed", nor "require that one is proficient at making inferences."
  • Belief, Rationality and Psychophysical Laws 18 September 2009 17:23 UTC www.yorku.ca [Source type: Original source]

^ Rational knowledge conceived as a deductive system should meet the requirement of consistency: two propositions which are inconsistent with each other are not allowed to belong to one system of knowledge.
  • 20th WCP: The Classical Conception Of Rationality 18 September 2009 17:23 UTC www.bu.edu [Source type: FILTERED WITH BAYES]

Especially, induction to universals is the warrant and measure of deduction from universals. .So far as it is inductively true that all border-war is evil, it is deductively true that a given border-war is therefore evil.^ For any given argument, a deduction of the conclusion from the premises conducted in PC is likely to be far longer and less psychologically natural than one carried out in a natural deduction system.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ Bill Bailey Therefore, following all of the above: being an omnivore or being a vegan is fine, but anything in-between is evil.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ An inference is deductively valid if and only if there is no possible situation in which all the premises are true and the conclusion false.
  • Logic - encyclopedia article - Citizendium 6 January 2010 10:47 UTC en.citizendium.org [Source type: FILTERED WITH BAYES]

.Now, as an inductive combination of premises does not necessarily involve the inductive conclusion, induction normally leads, not to a necessary, but to a probable conclusion; and whenever its probable conclusions become deductive premises, the deduction only involves a probable conclusion.^ Therefore, we concluded, while the conclusion of a deductive argument is conclusive , the conclusion of an inductive argument is only probable .

^ That is why, in a valid deductive argument, the truth of the premises guarantees the truth of the conclusion, while, in a valid inductive argument, the truth of the premises only makes the conclusion probable .

^ Students learn the mental steps involved in logical thinking and are taught to identify the common errors in reasoning which lead to faulty conclusions.
  • Memoria Press: Traditional Logic I 6 January 2010 10:47 UTC www.memoriapress.com [Source type: General]

Can we then infer any certainty at all? .In order to answer this question we must remember that there are many degrees of probability, and that induction, and therefore deduction, draw conclusions more or less probable, and rise to the point at which probability becomes moral certainty, or that high degree of probability which is sufficient to guide our lives, and even condemn murderers to death.^ There are many ways we can answer this question.
  • Domain Logic and SQL 6 January 2010 10:47 UTC www.martinfowler.com [Source type: FILTERED WITH BAYES]

^ Therefore, we concluded, while the conclusion of a deductive argument is conclusive , the conclusion of an inductive argument is only probable .

^ In this particular problem there is sufficient information to be able to draw the correct conclusion.

But can we rise still higher and infer real necessity ? .This is a difficult question, which has received many answers.^ There are many ways we can answer this question.
  • Domain Logic and SQL 6 January 2010 10:47 UTC www.martinfowler.com [Source type: FILTERED WITH BAYES]

^ In order to boldly answer these questions, and as a reaction against formalism, many researchers in axiomatic set theory have subscribed to what is known as set-theoretical Platonism .
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ I f the writer demands or suggests that there is only one answer to a complex question, or insists on a single answer to a multi-part questions, then s/he is using the fallacy of many questions .
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

.Some noOlogists suppose a mental power of forming necessary principles of deduction a priori; but fail to show how we can apply principles of mind to things beyond mind.^ Titled, Some Problems of Philosophy , it shows to what extent James moved beyond pragmatism, and how closely he approached a new quantum philosophy.
  • The Prodigy Review - Bio: Life of William James Sidis 18 September 2009 8:08 UTC www.quantonics.com [Source type: General]

^ Some things are beyond the call of duty or supererogatory (e.g., volunteering for a costly or risky good endeavor where others are equally qualified and no one person is obligated).
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

^ Suppose that you would be immediately rewarded upon forming the intention to later drink a mild toxin that would cause you some discomfort.
  • Global Rationality 18 September 2009 17:23 UTC docs.google.com [Source type: Original source]

.Some empiricists, on the other hand, suppose that induction only infers probable conclusions which are premises of probable deductions; but they give up all exact science.^ As a result, some statements will only be seen to be derivable from the premises after other statements have been derived.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ In teaching logic, after setting out a number of basic definitions ( argument itself, premise , conclusion , deduction , inference , valid , and so on) and explaining what they refer to, I turned to the Square of Opposition, which stands at the foundation of classical deductive logic.
  • Can Logic Be Taught on Campus? 6 January 2010 10:47 UTC www.lewrockwell.com [Source type: Original source]

^ So you might want to give it some time and let the early adopters report all the bugs and installation issues and shout #FAIL all over Twitter.

.Between these extremes there is room for a third theory, empirical yet providing a knowledge of the really necessary.^ The goal of this preliminary material is to serve as a contrast between what "standard" game theory wisdom suggests about certain games and the way these games are played in practice.
  • Feature Column from the AMS 18 September 2009 17:23 UTC www.ams.org [Source type: FILTERED WITH BAYES]

^ These choices must be fundamental enough to produce significant differences between people in their attitudes and outlook on the world, yet no so fundamental that they are divisive.
  • Pluralism and Rationality: the limits of tolerance 18 September 2009 17:23 UTC www.newfoundations.com [Source type: Original source]

^ But there is also another, seemingly opposite fact that must be noted about the relation between Scripture and sanctification: not only is Scripture necessary to our sanctification, but sanctification is necessary for a right use of Scripture.

In some cases of induction concerned with objects capable of abstraction and simplification, we have a power of identification, by which, not a priori but in the act of inducing a conclusion, we apprehend that the things signified ..SisP.
Analogical. S i is P S 2 is similar to S1 S is P Every M is similar to S. . Every M is P.
by its subject and predicate are one and the same thing which cannot exist apart from itself. .Thus by combined induction and identification we apprehend that one and one are the same as two, that there is no difference between a triangle and a three-sided rectilineal figure, that a whole must be greater than its part by being the whole, that inter-resisting bodies necessarily force one another apart, otherwise they would not be interresisting but occupy the same place at the same moment.^ Thus two sets are identical if and only if they have the same elements.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ A moving body is at a particular place, and at the same time it is not there ."

^ So there is no difference between them."
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

.Necessary principles, discovered by this process of induction and identification, become premises of deductive demonstration to conclusions which are not only necessary consequents on the premises, but also equally necessary in reality.^ An argument is logically valid if and only if its conclusion is a logical consequence of its premises.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ At the most fundamental level, the difference between the two is that, in a valid deductive argument, the conclusion asserts no more than what is contained in the premises, while, in an inductive argument, more is asserted in the conclusion than is contained in the premises.

^ Corollary 5.4: There is a derivation of the wff β with α 1 , …, α n as premises in the Propositional Calculus if and only if β is a logical consequence of α 1 , …, α n , according to their combined truth table.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

.Induction thus is the source of deduction, of its truth, of its probability, of its moral certainty; and induction, combined with identification, is the origin of the necessary principles of demonstration or deduction to necessary conclusions.^ The transmissibility capacity of truth and probability led, historically, to the general assumption that intellectual respectability is transmissible from premises to conclusion.
  • Bartley's 1964 paper on Rationality and the theory of rationality. 18 September 2009 17:23 UTC www.the-rathouse.com [Source type: Original source]

^ If a necessary truth should be the conclusion of an argument, then that argument is always valid because the conclusion can never be false in any possible world.
  • logic@Everything2.com 6 January 2010 10:47 UTC www.everything2.com [Source type: Original source]

^ That is why, in a valid deductive argument, the truth of the premises guarantees the truth of the conclusion, while, in a valid inductive argument, the truth of the premises only makes the conclusion probable .

Analogical inference in its turn is as closely allied with induction. .Like induction, it starts from a particular premise, containing one or more examples or instances; but, as it is easier to infer a particular than a universal conclusion, it supplies particular conclusions which in their turn become further particular premises of induction.^ Each of the premises and the conclusion is of one of four types: .
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ Induction reasons from repeated particular observations (which are usually observable) to more general truths through statistical generalizations and analogies which are sometimes unobserved (and which are considered stronger by virtue of the number of confirming instances that are appealed to in the premises.

^ This example commits one of our earlier blunders as well – by simply ignoring scientists who question the premise that the earth is really heating up.
  • Can Logic Be Taught on Campus? 6 January 2010 10:47 UTC www.lewrockwell.com [Source type: Original source]

.Its second premise is indeed merely a particular apprehension that one particular is similar to another, whereas the second premise of induction is a universal apprehension that a whole number of particulars is similar to those from which the inference starts; but at bottom these two apprehensions of similarity are so alike as to suggest that the universal premise of induction has arisen as a generalized analogy.^ Induction reasons from repeated particular observations (which are usually observable) to more general truths through statistical generalizations and analogies which are sometimes unobserved (and which are considered stronger by virtue of the number of confirming instances that are appealed to in the premises.

^ This observation indicates that the analysis of language had developed to the point of investigating the internal structures of statements, in addition to the relations of statements as a whole to one another.
  • history of logic -- Britannica Online Encyclopedia 6 January 2010 10:47 UTC www.britannica.com [Source type: Reference]

^ In this case, no one would be seeking to correct or revise its meaning, nor suggest that it was universally inadequate.

.It seems likely that man has arrived at the apprehension of a whole individual, e.g. a whole animal including all its parts, and thence has inferred by analogy a whole number, or class, e.g. of animals including all individual animals; and accordingly that the particular analogy of one individual to another has given rise to the general analogy of every to each individual in a class, or whole number of individuals, contained in the second premise of induction.^ In general, if is any individual whatsoever, then is the assertion that is a man.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ Induction reasons from repeated particular observations (which are usually observable) to more general truths through statistical generalizations and analogies which are sometimes unobserved (and which are considered stronger by virtue of the number of confirming instances that are appealed to in the premises.

^ This observation indicates that the analysis of language had developed to the point of investigating the internal structures of statements, in addition to the relations of statements as a whole to one another.
  • history of logic -- Britannica Online Encyclopedia 6 January 2010 10:47 UTC www.britannica.com [Source type: Reference]

In this case, analogical inference has led to induction, as induction to deduction. Further, analogical inference from particular to particular suggests inductivedeductive inference from particular through universal to particular.
.Newton, according to Dr Pemberton, thought in 1666 that the moon moves so like a falling body that it has a similar centripetal force to the earth, 20 years before he demonstrated this conclusion from the laws of motion in the Principia. In fact, analogical, inductive and deductive inferences, though different processes of combining premises to cause different conclusions, are so similar and related, so united in principle and interdependent, so consolidated into a system of inference, that they cannot be completely investigated apart, but together constitute a single subject of science.^ The following constitutes a derivation in system PC of the conclusion from the premises: .
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ This breaks the boundary between the premises which deal with the mechanics of the language and the conclusion which is about the subject-matter of the language.
  • Logic on the Web -- Web architecture 6 January 2010 10:47 UTC www.w3.org [Source type: FILTERED WITH BAYES]

^ The parts of syllogistic, also known by the name term logic , were the analysis of the judgements into propositions consisting of two terms that are related by one of a fixed number of relations, and the expression of inferences by means of syllogisms that consisted of two propositions sharing a common term as premise, and a conclusion which was a proposition involving the two unrelated terms from the premises.
  • Logic - encyclopedia article - Citizendium 6 January 2010 10:47 UTC en.citizendium.org [Source type: FILTERED WITH BAYES]

.This science of inference in general is logic.^ Thus logic is the science of necessary inference.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ In this sense logic is different from biology, since it is more general, but it is also similar to biology in that it is a science that aims to capture a certain body of truths.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Naturally, logic has moved on considerably since Aristotle's day, as have mathematics and science in general.

.Logic, however, did not begin as a science of all inference.^ Thus logic is the science of necessary inference.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ However, once this misbegotten 'ontological' interpretation of FL is abandoned, the temptation to identify logic with science (or with the " Laws of Thought ") loses whatever superficial plausibility it ever seemed to have.

^ As I said earlier, the power of formal logic, its common to all sciences, based on its four laws, rather than on different types of syllogism.
  • The Development of Laws of Formal Logic of Aristotle 22 September 2009 20:020 UTC uweb.superlink.net [Source type: Original source]

.Rather it began as a science of reasoning (Xbyos), of syllogism (vvXXoycvA6s), of deductive inference.^ As I said earlier, the power of formal logic, its common to all sciences, based on its four laws, rather than on different types of syllogism.
  • The Development of Laws of Formal Logic of Aristotle 22 September 2009 20:020 UTC uweb.superlink.net [Source type: Original source]

^ A deductive argument provides conclusive proof of its conclusions by presenting all the supporting evidence and reasoning for the premises and the inferences.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ Logic is the science of formal principles of reasoning or correct inference.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

Aristotle was its founder. .He was anticipated of course by many generations of spontaneous thinking (logica naturalis). Many of the higher animals infer by analogy: otherwise we cannot explain their thinking.^ Other inductive argument forms include enumerations, analogies, inferences to the next case and many scientific generalizations.
  • Can Logic Be Taught on Campus? 6 January 2010 10:47 UTC www.lewrockwell.com [Source type: Original source]

^ I could think of so many things to say about this, and how it explains who gives to charity and who...
  • EconLog: Behavioral Economics and Rationality Archives 18 September 2009 17:23 UTC econlog.econlib.org [Source type: General]

.Man so infers at first: otherwise we cannot explain the actions of young children, who before they begin to speak give no evidence of universal thinking.^ From this we conclude that it is not a doctrine that must first be learned in school, but one of which each of us is master from his mother's womb and which nature itself permits no man to forget.
  • Theism, Atheism, and Rationality 18 September 2009 17:23 UTC www.origins.org [Source type: Original source]

^ If A is A, it follows, according to formal thinking that A cannot be non-A. Thus the second law of formal logic, the law of contradiction forms the essential supplement to the first law.

^ Moreover, if a student begins a sentence with, "Well, I just feel that " – a professor who is thinking logically has no choice but to respond, "This course is not about your feelings ."
  • Can Logic Be Taught on Campus? 6 January 2010 10:47 UTC www.lewrockwell.com [Source type: Original source]

.It is likely that man began with particular inference and with particular language; and that, gradually generalizing thought and language, he learnt at last to think and say " all," to infer universally, to induce and deduce, to reason, in short, and raise himself above other animals.^ He, like his predecessors, though in a different way, was misled by respect for Aristotle" (p.199) Rather than to say that even outside of logic and pure mathematics, four of law of formal logic, without any doubt remained valid, he emphasizes on the syllogisms that do not constitute the essence of formal logic and for this reason are not general to all science.
  • The Development of Laws of Formal Logic of Aristotle 22 September 2009 20:020 UTC uweb.superlink.net [Source type: Original source]

^ And at the graduate level there is plenty formal semantics of natural languages -- I would even say that that is the main business of the department, if it has one.
  • LogBlog: Formal Logic and Philosophy III | Richard Zach | Philosophy | University of Calgary 22 September 2009 20:020 UTC www.ucalgary.ca [Source type: Academic]

^ The science or art of exact reasoning, or of pure and formal thought, or of the laws according to which the processes of pure thinking should be conducted; the science of the formation and application of general notions; the science of generalization, judgment, classification, reasoning, and systematic arrangement; correct reasoning.
  • logic@Everything2.com 6 January 2010 10:47 UTC www.everything2.com [Source type: Original source]

.In ancient times, and especially in Egypt, Babylon and Greece, he went on to develop reason into science or the systematic investigation of definite subjects, e.g. arithmetic of number, geometry of magnitude, astronomy of stars, politics of government, ethics of goods.^ He got the idea after a time trip with Mr. Spock during which his dog Fuzzy went into the washing and drying machine and became all fuzzy.
  • Logic - Uncyclopedia, the content-free encyclopedia 6 January 2010 10:47 UTC uncyclopedia.wikia.com [Source type: Original source]

^ But in science, formal reasoning has seen immense progress: mathematical reasoning has advanced far beyond the simple geometry and calculus known to the Greeks.
  • logic@Everything2.com 6 January 2010 10:47 UTC www.everything2.com [Source type: Original source]

^ While logic often seems to provide its own motivations, the subject develops most healthily when the reason for our interest is made clear.
  • Logic - encyclopedia article - Citizendium 6 January 2010 10:47 UTC en.citizendium.org [Source type: FILTERED WITH BAYES]

.In Greece he became more and more reflective and conscious of himself, of his body and soul, his manners and morals, his mental operations and especially his reason.^ In like manner the definitions which fail to distinguish between logic and psychology , defining logic as "the science of mental processes", or "the science of the operations of the mind ", are too wide.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

.One of the characteristics of Greek philosophers is their growing tendency, in investigating any subject, to turn round and ask themselves what should be the method of investigation.^ These kinds of problems quickly turn into metaphysics more generally, which is the philosophical discipline that encompasses ontology as one of its parts.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ It is a process that is very hard to achieve if one is subjected to the influence of mainstream philosophers.
  • Bartley's 1964 paper on Rationality and the theory of rationality. 18 September 2009 17:23 UTC www.the-rathouse.com [Source type: Original source]

^ Most philosophers assume that the bulk of "normal" proper reasoning can be captured by logic, if one can find the right method for translating ordinary language into that logic.
  • Logic - encyclopedia article - Citizendium 6 January 2010 10:47 UTC en.citizendium.org [Source type: FILTERED WITH BAYES]

.In this way the Presocratics and Sophists, and still more Socrates and Plato, threw out hints on sense and reason, on inferential processes and scientific methods which may be called anticipations of logic.^ Mathematics is also applied to logic itself: probability theory is a way to model reasoning with quantifiable uncertainty , formal mathematical logic approaches qualitative reasoning as a computational process.
  • logic@Everything2.com 6 January 2010 10:47 UTC www.everything2.com [Source type: Original source]

^ If you have not studied logic you may still be familiar with the philosophy of the Vulcan race from the TV show 'Star Trek'.
  • AKRI : Artificial Intelligence : From Logic To Fuzzy Logic 6 January 2010 10:47 UTC www.akri.org [Source type: FILTERED WITH BAYES]

^ Socrates wielded an argument of this kind against the relativism of the great sophist Protagoras with great skill in one of the most important of Plato's dialogues, the Thaeatetus .
  • Can Logic Be Taught on Campus? 6 January 2010 10:47 UTC www.lewrockwell.com [Source type: Original source]

.But Aristotle was the first to conceive of reasoning itself as a definite subject of a special science, which he called analytics or analytic science, specially designed to analyse syllogism and especially demonstrative syllogism, or science, and to be in fact a science of sciences.^ If I am sworn to honesty, then the fact that I believe that P may itself provide a reason for me to assert that P. 5 I leave open the question whether such value is impersonal or agent-relative.
  • Global Rationality 18 September 2009 17:23 UTC docs.google.com [Source type: Original source]

^ Aristotle , the founder of the science , designates it as "analytic", and the Epicureans use the term canonic .
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ Aristotle would have denied it was a legitimate syllogism in view of the fact that it has a particular middle premiss which is not governed by a what we would now call a quantifier expression (e.g., "Some", "All", "Every", and "No"), but concerns a named individual .

He was therefore the founder of the science of logic.
Among the Aristotelian treatises we have the following, which together constitute this new science of reasoning: i. .The Categories, or names signifying things which can become predicates; 2. The De Interpretatione, or the enumeration of conceptions and their combinations by (I) nouns and verbs (names), (2) enunciations (propositions); 3. The Prior Analytics, on syllogism; 4. The Posterior Analytics, on demonstrative syllogism, or science; 5. The Topics, on dialectical syllogism; or argument; 6. The Sophistical Elenchi, on sophistical or contentious syllogism, or sophistical fallacies.^ The names dialectic and analytic are also used.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ They included in it dialectic and rhetoric, or the science of argumentation and the science of persuasion.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ By strict standards, fallacies don't address the truth of the premises or syllogism; they only address to the validity of the logic , and as the final section of this page demonstrates, "truth" and "validity" are not the same thing when speaking of formal logic.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

.So far as we know, Aristotle had no one name for all these investigations.^ This fallacy, combined with Reification, is the reason that one of the classic "paradoxes" is not really a paradox at all, namely, "If God can do anything, can he make a stone so big he can't lift it?"
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ The disciplines of mathematics and logic, far from consisting of truisms, are riddled with controversy[66].  (d) No one has succeeded In justifying induction from within the discipline of logic; yet all non-deductive reasoning presupposes it[67].

^ Thus if most but not all P are Q , these logics enable one to predict Qa from Pa – remark that ( x )( Px Qx ) is not inductively derivable in this case.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

." Analytics " is only applied to the Prior and Posterior Analytics, and " logical," which he opposed to " analytical," only suits the Topics and at most the Sophistical Elenchi; secondly, while he analyzed syllogism into premises, major and minor, and premises into terms, subject and predicate, he attempted no division of the whole science; thirdly, he attempted no order and arrangement of the treatises into a system of logic, but only of the Analytics, Topics and Sophistical Elenchi into a system of syllogisms.^ Of these treatises, the Prior Analytics contains the most systematic discussion of formal logic.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ The predicate of the conclusion is the major term; the premise in which it is contained is the major premise; the subject of the conclusion is the minor term; and the premise in which it is contained is the minor premise.

^ Frege's original system of predicate logic was not first-, but second-order.
  • Logic - encyclopedia article - Citizendium 6 January 2010 10:47 UTC en.citizendium.org [Source type: FILTERED WITH BAYES]

.Nevertheless, when his followers had arranged the treatises into the Organon, as they called it to express that it is an instrument of science, then there gradually emerged a system of syllogistic logic, arranged in the triple division - terms, propositions and syllogisms - which has survived to this day as technical logic, and has been the foundation of all other logics, even of those which aim at its destruction.^ In the argument above, there are three propositions expressed.

^ It is the Holy of Holies of Logic, and not to be called into question.

^ And there are other notions of ‘logic’ as well.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.The main problem which Aristotle set before him was the analysis of syllogism, which he defined as " reasoning in which certain things having been posited something different from them of necessity follows by their being those things " (Prior Analytics, i. z).^ The difference between good, informative genus-and-difference definitions (my initial definition of logic exemplifies this method of defining) and merely pointing and saying, "That's what one of those things looks like," fell into place.
  • Can Logic Be Taught on Campus? 6 January 2010 10:47 UTC www.lewrockwell.com [Source type: Original source]

^ This fallacy ignores the possibility that the two things might be unrelated, having different causes, and that their simultaneous appearance was coincidence.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ He has high hopes for his business being successful as there's a number of large companies in the area that he can cater to....Each day he chose something different to eat, drink, and snack on.

.What then did he mean by reasoning, or rather by the Greek word Xiryos of which " reasoning " is an approximate rendering?^ The Greek word logos , meaning "reason", is the origin of the term logic--logike ( techen, pragmateia, or episteme , understood), as the name of a science or art, first occurs in the writings of the Stoics .
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ First is the idea that words indeed do have reasonably precise meanings and that there are definite cognitive rights and wrongs.
  • Can Logic Be Taught on Campus? 6 January 2010 10:47 UTC www.lewrockwell.com [Source type: Original source]

It was meant (cf. Post. An. i. 10) to be both internal, in the soul (6 g o-co ?6yos, Ev T 71 ikvx fj), and external, in language (6 g 5w X6yos): hence after Aristotle the Stoics distinguished X6yos EvScfiO€ros and 7rp040pcK6s. It meant, then, both reason and discourse of reason (cf. Shakespeare, Hamlet, i. 2). On its mental side, as reason it meant combination of thoughts. .On its linguistic side, as discourse it was used for any combination of names to form a phrase, such as the definition " rational animal," or a book, such as the Iliad. It had also the mathematical meaning of ratio; and in its use for definition it is sometimes transferred to essence as the object of definition, and has a mixed meaning, which may be expressed by " account."^ On this view, then, the true logical form of 'Mars exists' is 'There is at least one object, x , such that x is identical with Mars'.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ Thus, phrases like "The concept green" cannot designate the concepts they were perhaps intended to designate without seeming to transform them into 'objects' 'named' by singular terms, which then prevents such phrases from designating their intended target , since concepts are not objects!

^ Calling such a language, L , the object language , Tarski undertook to provide a recursive definition of truth-in- L , the definition being formulated in an appropriate metalanguage .
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

.In all its uses, however, the common meaning is combination.^ However, we have been able to adapt quite well by printing orders, retrieving results over the hospital systems’ network, and by using a combination of scanning and hand data entry as needed.
  • http://www.crmef.org/curriculum/LogicianEMR/LogicianMSR.htm 11 September 2009 7:35 UTC www.crmef.org [Source type: FILTERED WITH BAYES]

^ These were afterwards given the title of "Organon", or "Instrument of Knowledge"; this designation, however, did not come into common use until the fifteenth century.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ Now, if would-be critics want to revise a word in common use, all well and good; but this cannot affect the ordinary meaning of that word .

.When Aristotle called syllogism X6yos, he meant that it is a combination of premises involving a conclusion of necessity.^ I n the usual case, a valid argument consists of true propositions — true premises combining with true inferences leading to a true conclusion.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ Between this and the clear-cut Aristotelean syllogism, with its major and minor premises and conclusion, there is all the difference that exists between the Oriental and the Greek mode of thinking.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ A proposition can only be called a premise, an inference, or a conclusion with respect to its particular argument, to that particular context.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

Moreover, he tended to confine the term X6yos to syllogistic inference. Not that he omitted other inferences (irio-mcs). On the contrary, to him (cf. Prior Analytics, ii. .24) we owe the triple distinction into inference from particular to particular (irapf16ecy i ug, example, or what we call " analogy "), inference from particular to universal (i raywy17, induction), and inference from universal to particular (ouXXoyco-Os, syllogism, or deduction).^ For example the problem how a universal relates to a particular that has it (assuming there are universals and particulars), or the problem how an event like John eating a cookie relate to the particulars John and the cookie, and the relation of eating, assuming there are events, particulars and relations.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ A proposition can only be called a premise, an inference, or a conclusion with respect to its particular argument, to that particular context.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ For example, the concept of elliptical orbit can unite all observational data of Mars into a coherent whole; this Whewell calls "the colligation of facts by means of a concept."
  • Sherlock Holmes and Probabilistic Induction 11 September 2009 7:35 UTC philsci-archive.pitt.edu [Source type: Original source]

.But he thought that inferences other than syllogism are imperfect; that analogical inference is rhetorical induction; and that induction, through the necessary preliminary of syllogism and the sole process of ascent from sense, memory and experience to the principles of science, is itself neither reasoning nor science.^ Logic is the science of formal principles of reasoning or correct inference.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ In this paper I will argue that as economists we need to pay great attention to inductive reasoning; that it makes excellent sense as an intellectual process; and that it is not hard to model.
  • Inductive Reasoning and Bounded Rationality 18 September 2009 17:23 UTC www.santafe.edu [Source type: FILTERED WITH BAYES]

^ "The reason for mistrusting the induction principle is that it involves an impredicative concept of number.
  • Readings in Logic 6 January 2010 10:47 UTC orcmid.com [Source type: Academic]

.To be perfect he thought that all inference must be reduced to syllogism of the first figure, which he regarded as the specially scientific inference.^ There are three reasons for discussing mathematics in a volume on general philosophy: Mathematics has always played a special role in scientific thought.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ As noted above, this 'inference' encourages the additional (and traditional) idea that ordinary language must be "defective" if it prevents 'profound' 'scientific/philosophical' moves like this from being made.

^ If all that is real is indeed rational, then the identification of rules of inference with the "rules of thought" -- and with metaphysical truths about "Being" -- becomes more all the more natural.

.Accordingly, the syllogism appeared to him to be the rational process (wet X6yov), and the demonstrative syllogism fran inductively discovered principles to be science (Eirurrr7un).^ The cold-cognition challenge to scientific rationality would be that people's cognitive processes are such that it is difficult or impossible for them to reason in ways that promote the aims of science.
  • Rationality and Science 18 September 2009 17:23 UTC cogsci.uwaterloo.ca [Source type: FILTERED WITH BAYES]

^ This conflict is usually occasioned by the existence of another conflict within the theory of rationality itself, a conflict that appears when it is discovered that according to one’s theory of rationality, rationality is impossible.
  • Bartley's 1964 paper on Rationality and the theory of rationality. 18 September 2009 17:23 UTC www.the-rathouse.com [Source type: Original source]

^ Karl Popper’s Falsifiability Principle is False Many technicists conflate science with rationality.
  • Science and Rationality 18 September 2009 17:23 UTC home.comcast.net [Source type: Original source]

.Hence, without his saying it in so many words, Aristotle's logic perforce became a logic of deductive reasoning, or syllogism.^ This he attempted to do in his "Novum Organum", which was to introduce a new logic, an inductive logic, to take the place of the deductive logic of Aristotle and the Schoolmen .
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ This is one of the reasons why the predicative level is considered extremely important, even if, for many adaptive logics, the basic features of the dynamics are already present at the propositional level.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ "If pressed to [provide] a discursive definition of [deductive logic], I would say that logic is the systematic study of the logical truths.
  • Readings in Logic 6 January 2010 10:47 UTC orcmid.com [Source type: Academic]

As it happened this deductive tendency helped the development of logic. .The obscurer premises of analogy and induction, together with the paucity of experience and the backward state of physical science in Aristotle's time would have baffled even his analytical genius.^ Aristotle , the founder of the science , designates it as "analytic", and the Epicureans use the term canonic .
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ Wittgenstein dreamed of developing a 'formal language' for every science -- physics, biology, even psychology.

^ But whereas we can say of Harry that he values a good cup of coffee even when he is asleep at the time of our so saying, we would not say of him that he wants or desires a cup of coffee at that time.
  • Pluralism and Rationality: the limits of tolerance 18 September 2009 17:23 UTC www.newfoundations.com [Source type: Original source]

.On the other hand, the demonstrations of mathematical sciences of his time, and the logical forms of deduction evinced in Plato's dialogues, provided him with admirable examples of deduction, which is also the inference most capable of analysis.^ Examples of such necessity are provided again by mathematics and logic.
  • 20th WCP: The Classical Conception Of Rationality 18 September 2009 17:23 UTC www.bu.edu [Source type: FILTERED WITH BAYES]

^ Thus logic is the science of necessary inference.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ Mathematics and logic provide paradigm examples for rational decisions.
  • 20th WCP: The Classical Conception Of Rationality 18 September 2009 17:23 UTC www.bu.edu [Source type: FILTERED WITH BAYES]

.Aristotle's analysis of the syllogism showed man how to advance by combining his thoughts in trains of deductive reasoning.^ This view of the question led naturally to an analysis of the methods of thinking, and to the construction of a type of reasoning which bears a remote resemblance to the syllogism.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ Molyneux failed to show how a single syllogism follows from these illusory principles.

^ The question is, how can we know in advance which reasons, and which assertions will be selected for, when selection is only recognized after the fact?
  • Science and Rationality 18 September 2009 17:23 UTC home.comcast.net [Source type: Original source]

.Nevertheless, the wider question remained for logic: what is the nature of all inference, and the special form of each of its three main processes?^ The following form the main branches of logic: .
  • Logic - encyclopedia article - Citizendium 6 January 2010 10:47 UTC en.citizendium.org [Source type: FILTERED WITH BAYES]

^ The crucial concept of form is central to discussions of the nature of logic, and it complicates exposition that 'formal' in "formal logic" is commonly used ambiguously.
  • Logic - encyclopedia article - Citizendium 6 January 2010 10:47 UTC en.citizendium.org [Source type: FILTERED WITH BAYES]

^ Although maintaining a weak form of the "psychic unity" hypothesis, Durkheim and Mauss took seriously the question of cognitive difference, which they framed in terms of classification (of space, time, natural species, etc.
  • Rationality and Culture Difference 18 September 2009 17:23 UTC www.chass.toronto.edu [Source type: FILTERED WITH BAYES]

.As then the reasoning of the syllogism was the main problem of Aristotle's logic, what was his analysis of it?^ Problems of logical analysis .
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ It was not alone: the Stoics proposed a system of propositional logic that was studied by medieval logicians; nor was the perfection of Aristotle's system undisputed; for example the problem of multiple generality was recognised in medieval times.
  • Logic - encyclopedia article - Citizendium 6 January 2010 10:47 UTC en.citizendium.org [Source type: FILTERED WITH BAYES]

^ This view of the question led naturally to an analysis of the methods of thinking, and to the construction of a type of reasoning which bears a remote resemblance to the syllogism.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

.In distinguishing inner and outer reason, or reasoning and discourse, he added that it is not to outer reason but to inner reason in the soul that demonstration and syllogism are directed (Post.^ But as he has demonstrated over and over again his kind of reasoning can be applied to all kinds of situations in which we want to uncover knowledge of things to which we do not have direct access.
  • Is Sherlock Holmes 11 September 2009 7:35 UTC plato.ucs.mun.ca [Source type: Original source]

An.
i. ro). .One would expect, then, an analysis of mental reasoning into mental judgments as premises and conclusion.^ Each of the premises and the conclusion is of one of four types: .
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ In the process of deduction, we derive the conclusion by reasoning: the conclusion follows necessarily from (and is entailed by) the (general or universal) premises.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ An internal dynamics: a conclusion may be withdrawn in view of the better understanding of the premises provided by a continuation of the reasoning.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

.In point of fact, he analysed it into premises, but then analysed a premise into terms, which he divided into subject and predicate, with the addition of the copula " is " or " is not."^ In a very broad sense of the term 'name', names traditionally divide into two classesproper names and common names, these being species of singular and general terms respectively.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ The main point here is that, in the predicate calculus, a subject is always an individual entity, never a class of entities.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ The traditional mode of dividing logic, into "formal" and "material", is maintained in many modern treatises on the subject.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

.This analysis, regarded as a whole and as it is applied in the Analytics and in the other logical treatises, was evidently intended as a linguistic analysis.^ Of these treatises, the Prior Analytics contains the most systematic discussion of formal logic.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ Mathematical logic really refers to two distinct areas of research: the first is the application of the techniques of formal logic to mathematics and mathematical reasoning, and the second, in the other direction, the application of mathematical techniques to the representation and analysis of formal logic.
  • Logic - encyclopedia article - Citizendium 6 January 2010 10:47 UTC en.citizendium.org [Source type: FILTERED WITH BAYES]

^ On both conceptions of logic we deal with logical constants, the difference is that one deals with a system of mental representations, the other with a system of linguistic representations.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.So in the Categories, he first divided things said 0ra XEy6 i 1Eva) into uncombined and combined, or names and propositions, and then divided the former into categories; and in the De interpretatione he expressly excluded mental conceptions and their combinations, and confined himself to nouns and verbs and enunciations, or, as we should say, to names and propositions.^ In a very broad sense of the term 'name', names traditionally divide into two classesproper names and common names, these being species of singular and general terms respectively.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ First, it is not clear what should be said about true sentences containing no demonstrative element, such as 'Horses are mammals'.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ Theories of reference are primarily concerned with the relationships between sub-propositional or sub-sentential parts of thought or speech and extra-mental or extra-linguistic entitiesfor instance, with the relationship between names and things named, and with the relationship between predicates and the properties they express or the items to which they apply.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

.Aristotle apparently intended, or at all events has given logicians in general the impression, that he intended to analyse syllogism into propositions as premises, and premise into names as terms.^ In a very broad sense of the term 'name', names traditionally divide into two classesproper names and common names, these being species of singular and general terms respectively.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ Between this and the clear-cut Aristotelean syllogism, with its major and minor premises and conclusion, there is all the difference that exists between the Oriental and the Greek mode of thinking.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ As for the question of how, if at all, we can analyse modal propositions, opinions vary between those who regard modal notions as fundamental and irreducible and those who regard them as being explicable in other termsnotably, in terms of possible worlds , conceived as 'ways the world might have been'.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

.His logic therefore exhibits the curious paradox of being an analysis of mental reasoning into linguistic elements.^ Therefore, here we will examine the simple basics of logical argument, some of the types of argument, and finally some of the mistakes we are likely to see when we use logic incorrectly (called fallacies or fallacious reasoning).
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ Interestingly, a first college course in logic will typically be taught in the philosophy department--logic being, of course, the foundation of reasoning and reasoning being the foundation of most precisely communicable human understanding.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

^ Logic deals with mental processes in relation to truth or, more particularly, in relation to the attainment and exposition of truth by processes which aim at being valid, clear, orderly, and consistent.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

.The explanation is that outer speech is more obvious than inner thought, and that grammar and poetic criticism, rhetoric and dialectic preceded logic, and that out of those arts of language arose the science of reasoning.^ More briefly "Logic is the art of reasoning."
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ Logic is the science of correct reasoning.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ Natural logic is that native power of the mind by which most persons are competent to judge correctly and reason validly about the affairs and interests of everyday life; it is contrasted with scientific logic, which is logic as a science and cultivated art.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

.The sophist Protagoras had distinguished various kinds of sentences, and Plato had divided the sentence into noun and verb, signifying a thing and the action of a thing.^ For example, Protagoras is reported to have been the first to distinguish different kinds of sentences : questions, answers, prayers, and injunctions.
  • history of logic -- Britannica Online Encyclopedia 6 January 2010 10:47 UTC www.britannica.com [Source type: Reference]

^ In the Sophist , he distinguished affirmation from negation and made the important distinction between verbs and names (including both nouns and adjectives).
  • history of logic -- Britannica Online Encyclopedia 6 January 2010 10:47 UTC www.britannica.com [Source type: Reference]

^ It is useful to distinguish the set of possible input values D from the set of possible output values R as they may be quite different kinds of things.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

.Rhetoricians had enumerated various means of persuasion, some of which are logical forms, e.g. probability and sign, example and enthymeme.^ (C → Satirical comment on the Greek taxation system) Another form of syllogistic logic is the metaphor , which actually uses a logical fallacy created by improperly associated syllogisms, as in this example: .
  • Logic - Uncyclopedia, the content-free encyclopedia 6 January 2010 10:47 UTC uncyclopedia.wikia.com [Source type: Original source]

^ That a logic assigns the trivial consequence set to some set of premises means that, in semantic terms, the set of premises has no models or that its only model is the trivial one.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ I have illustrated this with the example of indirect utilitarianism, but the general principle will apply whenever some end is best achieved by imperfect agents when they pursue it by indirect means.
  • Global Rationality 18 September 2009 17:23 UTC docs.google.com [Source type: Original source]

.Among the dialecticians, Socrates had used inductive arguments to obtain definitions as data of deductive arguments against his opponents, and Plato had insisted on the processes of ascending to and descending from an unconditional principle by the power of giving and receiving argument.^ At the most fundamental level, the difference between the two is that, in a valid deductive argument, the conclusion asserts no more than what is contained in the premises, while, in an inductive argument, more is asserted in the conclusion than is contained in the premises.

^ But using arguments is not the same as studying them, and Parmenides never systematically formulated or studied principles of argumentation in their own right.
  • history of logic -- Britannica Online Encyclopedia 6 January 2010 10:47 UTC www.britannica.com [Source type: Reference]

^ Auxiliary assumptions are often highly theoretical; if we can’t verify A, we will not be able to falsify T by using the deductively valid argument form just described.
  • Science and Rationality 18 September 2009 17:23 UTC home.comcast.net [Source type: Original source]

.All these points about speech, eloquence and argument between man and man were absorbed into Aristotle's theory of reasoning, and in particular the grammar of the sentence consisting of noun and verb caused the logic of the proposition consisting of subject and predicate.^ These are common to all reasoning, and well known from usual logics.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ Basic propositions are the starting point for reasoning and reasons for acceptance of all other propositions.
  • 20th WCP: The Classical Conception Of Rationality 18 September 2009 17:23 UTC www.bu.edu [Source type: FILTERED WITH BAYES]

^ Logic since 1900 - Propositional and predicate logic .
  • history of logic -- Britannica Online Encyclopedia 6 January 2010 10:47 UTC www.britannica.com [Source type: Reference]

.At the same time, Aristotle was well aware that the science of reasoning is no art of language and must take up a different position towards speech as the expression of thought.^ The science or art of exact reasoning, or of pure and formal thought, or of the laws according to which the processes of pure thinking should be conducted; the science of the formation and application of general notions; the science of generalization, judgment, classification, reasoning, and systematic arrangement; correct reasoning.
  • logic@Everything2.com 6 January 2010 10:47 UTC www.everything2.com [Source type: Original source]

^ These choices must be fundamental enough to produce significant differences between people in their attitudes and outlook on the world, yet no so fundamental that they are divisive.
  • Pluralism and Rationality: the limits of tolerance 18 September 2009 17:23 UTC www.newfoundations.com [Source type: Original source]

^ Now, Aristotle certainly believed that during change something must remain the same (but precisely what that "something" was is subject to controversy among Aristotle scholars) -- for example, in Aristotle (1984e), p.1595.

In the Categories he classified names, not, however, as a grammarian by their structure, but as a logician by their signification. .In the De interpretatione, having distinguished the enunciation, or proposition, from other sentences as that in which there is truth or falsity, he relegated the rest to rhetoric or poetry, and founded the logic of the proposition, in which, however, he retained the grammatical analysis into noun and verb.^ And there are other notions of ‘logic’ as well.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ In the Sophist , he distinguished affirmation from negation and made the important distinction between verbs and names (including both nouns and adjectives).
  • history of logic -- Britannica Online Encyclopedia 6 January 2010 10:47 UTC www.britannica.com [Source type: Reference]

^ There are also “non-classical” propositional logics in which such possibilities as (i) a proposition’s having a truth-value other than truth or falsity, (ii) a proposition’s having an indeterminate truth-value or lacking a truth-value altogether, and sometimes even (iii) a proposition’s being both true and false, are considered.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

.In the Analytics he took the final step of originating the logical analysis of the proposition as premise into subject and predicate as terms mediated by the copula, and analysed the syllogism into these elements.^ The predicate of the conclusion is the major term; the premise in which it is contained is the major premise; the subject of the conclusion is the minor term; and the premise in which it is contained is the minor premise.

^ Logic since 1900 - Propositional and predicate logic .
  • history of logic -- Britannica Online Encyclopedia 6 January 2010 10:47 UTC www.britannica.com [Source type: Reference]

^ The parts of syllogistic, also known by the name term logic , were the analysis of the judgements into propositions consisting of two terms that are related by one of a fixed number of relations, and the expression of inferences by means of syllogisms that consisted of two propositions sharing a common term as premise, and a conclusion which was a proposition involving the two unrelated terms from the premises.
  • Logic - encyclopedia article - Citizendium 6 January 2010 10:47 UTC en.citizendium.org [Source type: FILTERED WITH BAYES]

.Thus did he become the founder of the logical but linguistic analysis of reasoning as discourse (o w into propositions and terms.^ The parts of syllogistic, also known by the name term logic , were the analysis of the judgements into propositions consisting of two terms that are related by one of a fixed number of relations, and the expression of inferences by means of syllogisms that consisted of two propositions sharing a common term as premise, and a conclusion which was a proposition involving the two unrelated terms from the premises.
  • Logic - encyclopedia article - Citizendium 6 January 2010 10:47 UTC en.citizendium.org [Source type: FILTERED WITH BAYES]

^ Mathematical logic really refers to two distinct areas of research: the first is the application of the techniques of formal logic to mathematics and mathematical reasoning, and the second, in the other direction, the application of mathematical techniques to the representation and analysis of formal logic.
  • Logic - encyclopedia article - Citizendium 6 January 2010 10:47 UTC en.citizendium.org [Source type: FILTERED WITH BAYES]

^ Thus it is evident that we do not find in human reason alone, even in logic, an infallible criterion of truth that might compete with Scripture as our ultimate covenant rule.

.Nevertheless, the deeper question remained, what is the logical but mental analysis of reasoning itself (6 g o-co Xoyos) into its mental premises and conclusion?^ It is the Holy of Holies of Logic, and not to be called into question.

^ The parts of syllogistic, also known by the name term logic , were the analysis of the judgements into propositions consisting of two terms that are related by one of a fixed number of relations, and the expression of inferences by means of syllogisms that consisted of two propositions sharing a common term as premise, and a conclusion which was a proposition involving the two unrelated terms from the premises.
  • Logic - encyclopedia article - Citizendium 6 January 2010 10:47 UTC en.citizendium.org [Source type: FILTERED WITH BAYES]

^ Mathematical logic really refers to two distinct areas of research: the first is the application of the techniques of formal logic to mathematics and mathematical reasoning, and the second, in the other direction, the application of mathematical techniques to the representation and analysis of formal logic.
  • Logic - encyclopedia article - Citizendium 6 January 2010 10:47 UTC en.citizendium.org [Source type: FILTERED WITH BAYES]

.Aristotle thus was the founder of logic as a science.^ Aristotle, the founder of logic .
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ Finally, formal logic is also taught in computer science departments, as computers are implemented in terms of logical operations; thus all theoretical models of computation reduce to the study of formal logic and formal systems.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

^ "The science of the laws of thought, formal logic, reached its highest point with Aristotle....

.But he laid too much stress on reasoning as syllogism or deduction, and on deductive science; and he laid too much stress on the linguistic analysis of rational discourse into proposition and terms.^ The parts of syllogistic, also known by the name term logic , were the analysis of the judgements into propositions consisting of two terms that are related by one of a fixed number of relations, and the expression of inferences by means of syllogisms that consisted of two propositions sharing a common term as premise, and a conclusion which was a proposition involving the two unrelated terms from the premises.
  • Logic - encyclopedia article - Citizendium 6 January 2010 10:47 UTC en.citizendium.org [Source type: FILTERED WITH BAYES]

^ This view of the question led naturally to an analysis of the methods of thinking, and to the construction of a type of reasoning which bears a remote resemblance to the syllogism.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ Rational knowledge conceived as a deductive system should meet the requirement of consistency: two propositions which are inconsistent with each other are not allowed to belong to one system of knowledge.
  • 20th WCP: The Classical Conception Of Rationality 18 September 2009 17:23 UTC www.bu.edu [Source type: FILTERED WITH BAYES]

.These two defects remain ingrained in technical logic to this day.^ It is an astonishing fact that the basic laws of formal logic worked out by Aristotle have remained fundamentally unchanged for over two thousand years."

^ To conflate these two concerns is to fall into the error of psychologism, much decried by Gottlob Frege, arguably the founding father of modern philosophical logic.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ We insist on an important grammatical or logical distinction between these two groups.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

.But in the course of the development of the science, logicians have endeavoured to correct those defects, and have diverged into two schools.^ Such attempts to squeeze science into such an ill-fitting dialectical corset will be considered in detail in Essay Three Part Six and Essay Thirteen Part Two.

.Some have devoted themselves to induction from sense and experience and widened logic till it has become a general science of inference and scientific method.^ Thus logic is the science of necessary inference.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ The suggestion is that dialectic is a science in its own right, or perhaps a general method for arriving at scientific conclusions in other fields.
  • history of logic -- Britannica Online Encyclopedia 6 January 2010 10:47 UTC www.britannica.com [Source type: Reference]

^ Models based on formal logic and probability theory have tended to be so remote from scientific practice that they encourage the inference that scientists are irrational.
  • Rationality and Science 18 September 2009 17:23 UTC cogsci.uwaterloo.ca [Source type: FILTERED WITH BAYES]

.Others have devoted themselves to the mental analysis of reasoning, and have narrowed logic into a science of conception, judgment and reasoning.^ Logic is the science of correct reasoning.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ Sherlock Holmes does a huge amount of reasoning, and he is careful and rigorous when he does, but things he can teach us about reasoning can likely be found in logic textbooks by other authors.
  • Is Sherlock Holmes 11 September 2009 7:35 UTC plato.ucs.mun.ca [Source type: Original source]

^ In recent times the word epistemology (science of knowledge ), meaning an inquiry into the value of knowledge , has come into general use, and designates that portion of philosophy which inquires into the objective value of our concepts, the import and value of judgments and reasoning, the criteria of truth , the nature of evidence, certitude, etc.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

.The former belong to the school of empirical logic, the latter to the school of conceptual and formal logic.^ Although philosophical logic should not be confused with the philosophy of logic, the latter must ultimately be responsive to considerations addressed by the former.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ Such ad hoc empirical adjustments to the conclusions of formal logic betray a 'primitive form of dialectical thinking.'"

^ The former is logic as a theoretical science ; the latter is logic as an applied art, practical logic.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

.Both have started from points which Aristotle indicated without developing them.^ This observation indicates that the analysis of language had developed to the point of investigating the internal structures of statements, in addition to the relations of statements as a whole to one another.
  • history of logic -- Britannica Online Encyclopedia 6 January 2010 10:47 UTC www.britannica.com [Source type: Reference]

^ At one point in their heated (and rather loud) debate, the man started to speak, and both women, simultaneously, turned on him and nearly said in unison: .
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ The analysis above was started from Row's point of view and indicated that there was a dominating row.
  • Feature Column from the AMS 18 September 2009 17:23 UTC www.ams.org [Source type: FILTERED WITH BAYES]

But we shall find that his true descendants are the empirical logicians.
Aristotle was the first of the empiricists. .He consistently maintained that sense is knowledge of particulars and the origin of scientific knowledge of universals.^ Lecture on the consistency of the continuum hypothesis (Brown University) [Gödel*1940a] In what sense is intuitionisstic logic constructive?
  • Readings in Logic 6 January 2010 10:47 UTC orcmid.com [Source type: Academic]

^ They maintained that it is an adjunct of physics, and that a knowledge of physical phenomena acquired through the senses is the only knowledge that is of value in the pursuit of happiness .
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

.In his view, sense is a congenital form of judgment (Suvaµcs Quµdiuros Kpo-uo), Post.^ For one, of course, there is an issue about what it means to say that judgments have a form, and whether they do in the relevant sense.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ In this sense we associate "form" neither with the representation that is involved in the judgment, nor with the proposition which is its content, but rather with the world that is judged about.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

An.
ii. .19); a sensation of each of the five senses is always true of its proper object; without sense there is no science; sense is the origin of induction, which is the origin of deduction and science.^ No philosopher of science can do without them entirely.
  • Science and Rationality 18 September 2009 17:23 UTC home.comcast.net [Source type: Original source]

^ And, he argues in (Yablo 1998), since there is no fact about this distinction, ontology, in the sense of (O2), rests on a mistake and is to be rejected, as Carnap did.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ On this view, then, the true logical form of 'Mars exists' is 'There is at least one object, x , such that x is identical with Mars'.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

The Analytics end (Post. An. ii. r9) with a detailed system of .empiricism, according to which sense is the primary knowledge of particulars, memory is the retention of a sensation, experience is the sum of many memories, induction infers universals, and intelligence is the true apprehension of the universal principles of science, which is rational, deductive, demonstrative, from empirical principles.^ According to empiricists, the rational authority lies in sense experience.
  • Bartley's 1964 paper on Rationality and the theory of rationality. 18 September 2009 17:23 UTC www.the-rathouse.com [Source type: Original source]

^ In conformity with the fundamental principle of his theory of knowledge , namely, that all our knowledge comes from experience, Aristotle recognizes the importance of inductive reasoning, that is to say, reasoning from particular instances to general principles.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ Karl Popper’s Falsifiability Principle is False Many technicists conflate science with rationality.
  • Science and Rationality 18 September 2009 17:23 UTC home.comcast.net [Source type: Original source]

.This empirical groundwork of Aristotle's logic was accepted by the Epicureans, who enunciated most distinctly the fundamental doctrine that all sensations are true of their immediate objects, and falsity begins with subsequent opinions, or what the moderns call " interpretation."^ On this view, then, the true logical form of 'Mars exists' is 'There is at least one object, x , such that x is identical with Mars'.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ Even if this definition of philosophical logic may be implicitly accepted by most of its current practitioners, no single way of dividing up its subject matter would be agreed upon by all them.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ [P]lease take the trouble to inform us just who following Aristotle analysed and systematized the subsequent progress of logic."

.Beneath deductive logic, in the logic of Aristotle and the canonic of the Epicureans, there already lay the basis of empirical logic: sensory experience is the origin of all inference and science.^ Thus logic is the science of necessary inference.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ Finally, our basis in formal logic entrains with it the intellectual depth of the philosophical discipline of logic and the mathematical models of the sciences.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

^ One of the devices of the opponents of scholasticism is to identify the Schoolmen and Aristotle with the advocacy of an exclusively deductive logic.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

.It remained for Francis Bacon to develop these beginnings into a new logic of induction.^ We shall also need to develop several new metatheoretic tools in order to obtain a decent formal control on adaptive logics.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ To conflate these two concerns is to fall into the error of psychologism, much decried by Gottlob Frege, arguably the founding father of modern philosophical logic.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ Logical expressions may be written using these new operators, or quantifiers.
  • AKRI : Artificial Intelligence : From Logic To Fuzzy Logic 6 January 2010 10:47 UTC www.akri.org [Source type: FILTERED WITH BAYES]

He did not indeed accept the infallibility of sense or of any other operation unaided. He thought, rather, that every operation becomes infallible by method. Following Aristotle in this order - sense, memory, intellect - he resolved the whole process of induction into three ministrations: r. The ministration to sense, aided by observation and experiment.
.2. The ministration to memory, aided by registering and arranging the data, of observation and experiment in tables of instances of agreement, difference and concomitant variations.^ Finally, to the Schoolmen logic owes the various memory-aiding contrivances by the aid of which the task of teaching or learning the technicalities of the science is greatly facilitated.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

.3. The ministration to intellect or reason, aided by the negative elimination by means of contradictory instances of whatever in the instances is not always present, absent and varying with the given subject investigated, and finally by the positive inference that whatever in the instances is always present, absent and varying with the subject is its essential cause.^ The leading idea here is that logical constants are those whose meaning can be given by proof-theoretic introduction and elimination rules.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ For example, we may call “ Instrumentalism ” the claim that we have reason to fulfill our own present desires, whatever they may be.
  • Global Rationality 18 September 2009 17:23 UTC docs.google.com [Source type: Original source]

^ We also can see clearly, that since objective reality is contingent and variable, that is, the new is always coming into being, that reason will not necessarily apply to future events.
  • Science and Rationality 18 September 2009 17:23 UTC home.comcast.net [Source type: Original source]

.Bacon, like Aristotle, was anticipated in this or that point; but, as Aristotle was the first to construct a system of deduction in the syllogism and its three figures, so Bacon was the first to construct a system of induction in three ministrations, in which the requisites of induction, hitherto recognized only in sporadic hints, were combined for the first time in one logic of induction.^ (C → Satirical comment on the Greek taxation system) Another form of syllogistic logic is the metaphor , which actually uses a logical fallacy created by improperly associated syllogisms, as in this example: .
  • Logic - Uncyclopedia, the content-free encyclopedia 6 January 2010 10:47 UTC uncyclopedia.wikia.com [Source type: Original source]

^ If you would like to use logic in any way, but are unsure of the implications, you should first contact him by wrapping your request in a brick and throwing it at him.
  • Logic - Uncyclopedia, the content-free encyclopedia 6 January 2010 10:47 UTC uncyclopedia.wikia.com [Source type: Original source]

^ (D→A=C) The first time logic became greatly publicized was in the TV show Bobobo-bo Bo-bobo.
  • Logic - Uncyclopedia, the content-free encyclopedia 6 January 2010 10:47 UTC uncyclopedia.wikia.com [Source type: Original source]

.Bacon taught men to labour in inferring from particular to universal, to lay as much stress on induction as on deduction, and to think and speak of inductive reasoning, inductive science, inductive logic.^ Deductive and inductive reasoning .
  • Logic - encyclopedia article - Citizendium 6 January 2010 10:47 UTC en.citizendium.org [Source type: FILTERED WITH BAYES]

^ Logic is the science of correct reasoning.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ The advantage of the former approach is that it conforms better with our ordinary reasoning and thinking habits; the advantage of the latter is that it simplifies the logical language, which makes certain interesting results regarding the deductive systems making use of the language easier to prove.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

Moreover, while Aristotle had the merit of discerning the triplicity of inference, to Bacon we owe the merit of distinguishing the three processes without reduction: - I. Inference from particular to particular by Experientia Literata, in piano; 2. Inference from particular to universal by Inductio, ascendendo; 3. Inference from universal to particular by Syllogism, descendendo.
.In short, the comprehensive genius of Bacon widened logic into a general science of inference.^ Thus logic is the science of necessary inference.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ The first four treatises contain, with occasional excursions into the domain of grammar and metaphysics , the science of formal logic essentially the same as it is taught at the present day.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ Naturally, logic has moved on considerably since Aristotle's day, as have mathematics and science in general.

.On the other hand, as Aristotle over-emphasized deduction so Bacon over-emphasized induction by contending that it is the only process of discovering universals (axiomata), which deduction only applies to particulars.^ "Caesar is a man" ( W1 ) does not say the particular is the universal, and can only be made to do so by imposing on it a grammatical theory that these two comrades failed to justify.

^ In the process of deduction, we derive the conclusion by reasoning: the conclusion follows necessarily from (and is entailed by) the (general or universal) premises.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ On the other hand, if it could be shown that the universe does have an underlying 'rational' structure, then the conclusion that nature is Mind (or that it has been constituted by Mind) would be difficult to resist.

.J. S. Mill in his Logic pointed out this defect, and without departing from Baconian principles remedied it by quoting scientific examples, in which deduction, starting from inductive principles, applies more general to less general universals, e.g. when the more general law of gravitation is shown to include the less general laws of planetary gravitation.^ If that cannot be ascertained, the next is to generalize the phenomenon, and include it, with others analogous to it, in the expression of some law, in the hope that its consideration, in a more advanced state of knowledge, may lead to the discovery of an adequate proximate cause.
  • Sherlock Holmes and Probabilistic Induction 11 September 2009 7:35 UTC philsci-archive.pitt.edu [Source type: Original source]

^ Indeed, that word is said to have unspecified universal inadequacies, which 'shortcomings' must of necessity feature in the very act of pointing this alleged fact out -- nullifying that criticism.

^ Again, it is worth pointing out that fundamental criticisms of FL (like these) advanced by DL-fans are seldom if ever substantiated with examples drawn from the work of a single logician.

.Mill's logic has the great merit of copiously exemplifying the principles of the variety of method according to subject-matter.^ Logic is a broad and ancient subject, and its exact definition remains, even today, a matter of controversy and discussion among philosophers.
  • Logic - encyclopedia article - Citizendium 6 January 2010 10:47 UTC en.citizendium.org [Source type: FILTERED WITH BAYES]

^ At least, he brought about a change in the method of teaching logic at the great English seats of learning.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ In discussing logic in a variety of forms, it has been possible to demonstrate the importance of the subject.
  • AKRI : Artificial Intelligence : From Logic To Fuzzy Logic 6 January 2010 10:47 UTC www.akri.org [Source type: FILTERED WITH BAYES]

.It teaches us that scientific method is sometimes induction, sometimes deduction, and sometimes the consilience of both, either by the inductive verification of previous deductions, or by the deductive explanation of previous inductions.^ Since others can sometimes discharge our obligations, either our obligations are not always obligations for us to do things, and thus personal obligations need not be agential or obligation fulfillment is more complex than has been previously realized, and perhaps both.
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

^ He erred in describing Aristotle's logic as exclusively deductive , and he erred in claiming for the inductive method the ability to direct the mind in scientific discovery and practical invention.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ When logicians read other logicians writing about scientific method they will want to know what their peers think about the problem of induction.
  • Is Sherlock Holmes 11 September 2009 7:35 UTC plato.ucs.mun.ca [Source type: Original source]

.It is also most interesting to notice that Aristotle saw further than Bacon in this direction.^ Further analysis of the character of this seductive appeal leads down a more epistemological path than we choose to pursue in this essay; we refer the interested reader to Kuhn.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

^ It's a convenient device, but it seems to me that most things that are actually interesting - and potentially value creating, occur in the process of moving, rather than in stasis.
  • Who Has Time For This?: Limits of Rationality: Beware the Paralimbic Cortex 18 September 2009 17:23 UTC whohastimeforthis.blogspot.com [Source type: General]

.The founder of logic anticipated the latest logic of science, when he recognized, not only the deduction of mathematics, but also the experience of facts followed by deductive explanations of their causes in physics.^ In this case, the logic will only be concerned with the fact that, .
  • AKRI : Artificial Intelligence : From Logic To Fuzzy Logic 6 January 2010 10:47 UTC www.akri.org [Source type: FILTERED WITH BAYES]

^ We merely assume such causes or laws, deduce particular consequences from them, and try to verify whether or not they hold (notice that, according to Mill, even a logical or mathematical truth must be verified ultimately by referring to experience).
  • Sherlock Holmes and Probabilistic Induction 11 September 2009 7:35 UTC philsci-archive.pitt.edu [Source type: Original source]

^ Finally, our basis in formal logic entrains with it the intellectual depth of the philosophical discipline of logic and the mathematical models of the sciences.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

The consilience of empirical and deductive processes was an Aristotelian discovery, elaborated by Mill against Bacon. .On the whole, however, Aristotle, Bacon and Mill, purged from their errors, form one empirical school, gradually growing by adapting itself to the advance of science; a school in which Aristotle was most influenced by Greek deductive Mathematics, Bacon by the rise of empirical physics at the Renaissance, and Mill by the Newtonian combination of empirical facts and mathematical principles in the Principia. From studying this succession of empirical logicians, we cannot doubt that sense, memory and experience are the real origin of inference, analogical, inductive and deductive.^ This is one of a series of labs written to be used with The Most Complex Machine: A Survey of Computers and Computing , an introductory computer science textbook by David Eck .
  • xLogicCircuits Lab 1 6 January 2010 10:47 UTC math.hws.edu [Source type: FILTERED WITH BAYES]

^ The long struggle of empiricism since Bacon had yielded a straightforward but powerful conception of science.
  • Science and Rationality 18 September 2009 17:23 UTC home.comcast.net [Source type: Original source]

^ When we think about inferences and implicature, we need to remember one very important point: the fact that a deductive argument is valid does not necessarily entail that its conclusion holds, or the fact that a deductive argument's conclusion is true does not necessarily mean that its premises are true as well.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

.The deepest problem of logic is the relation of sense and inference.^ Logic is the study of such inferences, and certain related concepts and topics, like formal invalidity, proof, consistency, and so on.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Characterization of an adaptive logic A general characteristic of the consequence relations mentioned in the previous section is that certain inferences are considered as correct iff certain formulas behave normally .
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ Both logic and ontology are diverse fields within philosophy, and partly because of this there is not one single philosophical problem about the relation between logic and ontology.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.But we must first consider the mental analysis of inference, and this brings us to conceptual and formal logic.^ Rather it deals with inferences whose validity can be traced back to the formal features of the representations that are involved in that inference, be they linguistic, mental, or other representations (Hofweber 2004).
  • Logic - encyclopedia article - Citizendium 6 January 2010 10:47 UTC en.citizendium.org [Source type: FILTERED WITH BAYES]

^ Models based on formal logic and probability theory have tended to be so remote from scientific practice that they encourage the inference that scientists are irrational.
  • Rationality and Science 18 September 2009 17:23 UTC cogsci.uwaterloo.ca [Source type: FILTERED WITH BAYES]

^ Mathematical logic really refers to two distinct areas of research: the first is the application of the techniques of formal logic to mathematics and mathematical reasoning, and the second, in the other direction, the application of mathematical techniques to the representation and analysis of formal logic.
  • Logic - encyclopedia article - Citizendium 6 January 2010 10:47 UTC en.citizendium.org [Source type: FILTERED WITH BAYES]

.Aristotle's logic has often been called formal logic; it was really a technical logic of syllogism analysed into linguistic elements, and of science rested on an empirical basis.^ It is the Holy of Holies of Logic, and not to be called into question.

^ This is what is meant by saying that logic is a formal science.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ Finally, our basis in formal logic entrains with it the intellectual depth of the philosophical discipline of logic and the mathematical models of the sciences.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

.At the same time his psychology, though maintaining his empiricism, contained some seeds of conceptual logic, and indirectly of formal logic.^ Some Nasty Problems in the Formal Logic of Ethics.” Noûs 1 : 345-360.
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

^ (For one thing, much of the time they say "logic" when they mean "rationality"; they aren't the same thing at all.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ I have known about Nature's Logic for some time, but could not get it very easily until recently.

.Intellectual development, which according to the logic of the Analytics consists of sense, memory, experience, induction and intellect, according to the psychology of the De Anima consists of sense, imagination and intellect, and one division of intellect is into conception of the undivided and combination of conceptions as one (De An. iii.^ Logic is the study of such inferences, and certain related concepts and topics, like formal invalidity, proof, consistency, and so on.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ In this wider sense, logically necessary truths are often identified with analytic truths (see above).
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ Corollary 5.4: There is a derivation of the wff β with α 1 , …, α n as premises in the Propositional Calculus if and only if β is a logical consequence of α 1 , …, α n , according to their combined truth table.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

6). .The De Interpretatione opens with a reference to this psychological distinction, implying that names represent conceptions, propositions represent combinations of conceptions.^ The distinction between concepts and objects (or rather, the distinction between concept expressions and singular terms) is needed, otherwise propositions would turn into mere lists.

^ TAUT combined with MP gives us the full inferential power of the Propositional Calculus (often referred to, including here, as “PC”).
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

.But the same passage relegates conceptions and their combinations to the De Anima, and confines the De Inter pretatione to names and propositions in conformity with the linguistic analysis which pervades the logical treatises of Aristotle, who neither brought his psychological distinction between conceptions and their combinations into his logic, nor advanced the combinations of conceptions as a definition of judgment (Kcp16cs), nor employed the mental distinction between conceptions and judgments as an analysis of inference, or reasoning, or syllogism: he was no conceptual logician.^ In his commentary on Aristotle's logical treatises (" In Post.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ Taking reason in its broadest sense, so as to include all the operations of the mind which are strictly cognitive, namely, the formation of mental images, judgment, and ratiocination, we may expand St. Thomas' definition and define logic as "the science and art which so directs the mind in the process of reasoning and subsidiary processes as to enable it to attain clearness (or order), consistency, and validity in those processes".
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ Combining those two sentences, we may render St. Thomas's definition as follows: "Logic is the science and art which directs the act of the reason, by which a man in the exercise of his reason is enabled to proceed without error , confusion, or unnecessary difficulty."
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

.The history of logic shows that the linguistic distinction between terms and propositions was the sole analysis of reasoning in the logical treatises of Aristotle; that the mental distinction between conceptions (g vvocac) and judgments (a uiwara in a wide sense) was imported into logic by the Stoics; and that this mental distinction became the logical analysis of reasoning under the authority of St Thomas Aquinas.^ In his commentary on Aristotle's logical treatises (" In Post.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ Taking reason in its broadest sense, so as to include all the operations of the mind which are strictly cognitive, namely, the formation of mental images, judgment, and ratiocination, we may expand St. Thomas' definition and define logic as "the science and art which so directs the mind in the process of reasoning and subsidiary processes as to enable it to attain clearness (or order), consistency, and validity in those processes".
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ Combining those two sentences, we may render St. Thomas's definition as follows: "Logic is the science and art which directs the act of the reason, by which a man in the exercise of his reason is enabled to proceed without error , confusion, or unnecessary difficulty."
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

.In his commentary on the De Interpretatione, St Thomas, after citing from the De Anima Aristotle's " duplex operatio intellectus," said, " Additur autem et tertia operatio, scilicet ratiocinandi," and concluded that, since logic is a rational science (rationalis scientia), its consideration must be directed to all these operations of reason.^ Naturally, logic has moved on considerably since Aristotle's day, as have mathematics and science in general.

^ These are common to all reasoning, and well known from usual logics.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ Taking reason in its broadest sense, so as to include all the operations of the mind which are strictly cognitive, namely, the formation of mental images, judgment, and ratiocination, we may expand St. Thomas' definition and define logic as "the science and art which so directs the mind in the process of reasoning and subsidiary processes as to enable it to attain clearness (or order), consistency, and validity in those processes".
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

.Hence arose conceptual logic; according to which conception is a simple apprehension of an idea without belief in being or not being, e.g. the idea of man or of running; judgment is a combination of conceptions, adding being or not being, e.g. man is running or not running; and reasoning is a combination of judgments: conversely, there is a mental analysis of reasoning into judgments, and judgment into conceptions, beneath the linguistic analysis of rational discourse into propositions, and propositions into terms.^ In a very broad sense of the term 'name', names traditionally divide into two classesproper names and common names, these being species of singular and general terms respectively.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ This would provide reasons that elude our rational grasp, being such that we ought to act unwittingly rather than by grasping the reason that underlies this very ‘ought’-fact.
  • Global Rationality 18 September 2009 17:23 UTC docs.google.com [Source type: Original source]

^ With the many conceptions of logic and the many different philosophical projects under the heading of ontology, there are many problems that are in the intersection of these areas.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.Logic, according to this new school, which has by our time become an old school, has to co-ordinate these three operations, direct them, and, beginning with conceptions, combine conceptions into judgments, and judgments into inference, which thus becomes a complex combination of conceptions, or, in modern parlance, an extension of our ideas.^ Thus logic is the science of necessary inference.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ Some old versions of Flash don't work well with our new chat application.
  • Play 3D Logic, a free online game on Kongregate 6 January 2010 10:47 UTC www.kongregate.com [Source type: FILTERED WITH BAYES]

^ New Line Cinema Corporate Ethical Lapses Enron, Worldcom- these qand other modern corporations have ethical problems resulting in jail time for its executive and denucniation by federal regulators, employees and the public By Werner Haas .

.Conceptual logicians were, indeed, from the first aware that sense supplies the data, and that judgment and therefore inference contains belief that things are or are not.^ If our universe contains some things that are A's but not B's, and other things that are B's but not A's, and nothing that is neither, then the first of these expressions will be false and the second true.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ Fourth, Scrip­ture itself contains any number of judgments, conclusions, and inferences that it calls us to accept.

.But they held, and still hold that sensation and conception are alike mere apprehensions, and that the belief that things are or are not arises somehow after sensation and conception in judgment, from which it passes into inference.^ But even when they get that much right, they still frequently fall into the errors listed below, or have their "logical" characters do so.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ And if one holds that one of the crucial features of logically valid inferences is that they preserve truth then one could argue that the logical laws are norms that apply to those who have beliefs.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ The premise: While guys like Lenin, Hitler, and Mao were hopelessly deluded about many things, their beliefs about how to win and hold power were probably correct.
  • EconLog: Behavioral Economics and Rationality Archives 18 September 2009 17:23 UTC econlog.econlib.org [Source type: General]

.At first, they were more sanguine of extracting from these unpromising beginnings some knowledge of things beyond ideas.^ One of these is constructivism , the idea that mathematical knowledge can be obtained by means of a series of purely mental constructions.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ In the first half of this article, we will review some of these.
  • Geometry.Net - Mathematical_Logic: Logics Admitting Inconsistency 11 October 2009 10:39 UTC www.algebraic.net [Source type: FILTERED WITH BAYES]

^ These are all problems in ontology in the sense that they deal with whether or not a certain thing, or more broadly entity, exists.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.But at length many of them became formal logicians, who held that logic is the investigation of formal thinking, or consistent conception, judgment and reasoning; that it shows how we infer formal truths of consistency without material truth of signifying things; that, as the science of the form or process, it must entirely abstract from the matter, or objects, of thought; and that it does not tell us how we infer from experience.^ And, of course, logic does not tell us how we ought to reason or infer in all particular cases.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ In formal logic the processes of thought are studied independently of, or without consideration of, their content.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

^ Logic tells us how we should reason.
  • Is Sherlock Holmes 11 September 2009 7:35 UTC plato.ucs.mun.ca [Source type: Original source]

.Thus has logic drifted further and further from the real and empirical logic of Aristotle the founder and Bacon the reformer of the science.^ Thus logic is the science of necessary inference.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ The long struggle of empiricism since Bacon had yielded a straightforward but powerful conception of science.
  • Science and Rationality 18 September 2009 17:23 UTC home.comcast.net [Source type: Original source]

^ Finally, formal logic is also taught in computer science departments, as computers are implemented in terms of logical operations; thus all theoretical models of computation reduce to the study of formal logic and formal systems.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

.The great merit of conceptual logic was the demand for a mental analysis of mental reasoning, and the direct analysis of reasoning into judgments which are the sole premises and conclusions of reasoning and of all mental inferences.^ And when an inference is formally valid then the conclusion logically follows from the premises.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ I n the usual case, a valid argument consists of true propositions — true premises combining with true inferences leading to a true conclusion.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ Nevertheless, the adaptive logics interprets the premises as normally as possible, and delivers all CL -consequences if the premises have CL -models (that is: are normal with respect to CL ).
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

Aristotle had fallen into the paradox of resolving a mental act into verbal elements. .The Schoolmen, however, gradually came to realize that the result to their logic was to make it a sermocionalis scientia, and to their metaphysics the danger of nominalism.^ However, the grammar of (6) looks decidedly odd at first sight, so much so that it is debatable whether (6) really makes sense at all.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ However, it should be clear that in order to take decisions from the results of fuzzy logic, some additional processing is required.
  • AKRI : Artificial Intelligence : From Logic To Fuzzy Logic 6 January 2010 10:47 UTC www.akri.org [Source type: FILTERED WITH BAYES]

.St Thomas made a great advance by making logic throughout a rationalis scientia; and logicians are now agreed that reasoning consists of judgments, discourse of propositions.^ When we reason we often make mistakes, the reason why we need this study we call logic.
  • Is Sherlock Holmes 11 September 2009 7:35 UTC plato.ucs.mun.ca [Source type: Original source]

^ This is so manifestly (and demonstrably) untrue that these two comrades have to ignore and distort the major advances that have been made in logic since the 1850s to make it 'work': .

^ The idea that human reason, or at least the "laws of logic," are a neutral, even infallible basis for human decision-making is an idea that dies hard.

.This distinction is, moreover, vital to the whole logic of inference, because we always think all the judgments of which our inference consists, but seldom state all the propositions by which it is expressed.^ I n the usual case, a valid argument consists of true propositions — true premises combining with true inferences leading to a true conclusion.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ Sometimes an argument does not use all the structure we can express with our notation.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ And this neutrality, or complete generality of logic, together with its normativity, is often put as "logic is about how we ought to think if we are to think at all" or "logic is the science of the laws that we ought to follow in our thinking no matter what we think about".
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

We omit propositions, curtail them, and even express a judgment by a single term, e.g. " Good ! " " Fire ! .". Hence the linguistic expression is not a true measure of inference; and to say that an inference consists of two propositions causing a third is not strictly true.^ I n the usual case, a valid argument consists of true propositions — true premises combining with true inferences leading to a true conclusion.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ With reasoning like that you might as well argue that if a metre rule, say, has been made incorrectly the same must be true of all it measures!

^ Inferences are the propositions that are entailed (i.e., logically must follow) if the premises are true.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

.But to say that it is two judgments causing a third is always true, and the very essence of inference, because we must think the two to conclude the third in " the sessions of sweet silent thought."^ A noteworthy axiom is which says: any three points equidistant from two distinct points must be collinear.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ Because α is β → γ , by the semantics for the sign ‘→’, the truth-value assignment must make either β false or γ true.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ Affirming the consequent : Claiming that because the result of something is true, the original statement must also be true.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

.Inference, in short., consists of actual judgments capable of being expressed in propositions.^ I n the usual case, a valid argument consists of true propositions — true premises combining with true inferences leading to a true conclusion.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ The aim of logic is to secure clearness in the definition and arrangement of our ideas and other mental images, consistency in our judgments, and validity in our processes of inference.
  • CATHOLIC ENCYCLOPEDIA: Logic 6 January 2010 10:47 UTC www.newadvent.org [Source type: FILTERED WITH BAYES]

Inference always consists of judgments. But judgment does not always consist of conceptions. .It is not a combination of conceptions; it does not arise from conceptions, nor even at first require conception.^ (Note that our description of the paper does not require the Stupid Logician to observe the paper -- even in this self-referential case.
  • I Had A Dream 11 September 2009 7:35 UTC www.eblong.com [Source type: Original source]

^ If one’s theory of rationality does not require one’s standards of rationality to be rationally justifiable, then the skeptic’s argument that it is impossible to do so loses its force even when it is admitted as correct.
  • Bartley's 1964 paper on Rationality and the theory of rationality. 18 September 2009 17:23 UTC www.the-rathouse.com [Source type: Original source]

Sense is the origin of judgment. .One who feels pained or pleased, who feels hot or cold or resisting in touch, who tastes the flavoured, who smells the odorous, who hears the sounding, who sees the coloured, or is conscious, already believes that something sensible exists before conception, before inference, and before language; and his belief is true of the immediate object of sense, the sensible thing, e.g. the hot felt in touch.^ We seek true beliefs, not justified ones.
  • Global Rationality 18 September 2009 17:23 UTC docs.google.com [Source type: Original source]

^ Though not strictly a fallacy, writers who ignore this principle run a risk: careful readers often feel that writers are trying to hide something if those readers see only implicit, rather than explicit, assumptions .
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ One first step to making progress on this question is to see if what we believe already rationally settles this question.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

But a belief in the existence of something is a judgment and a categorical judgment of existence. .Sense, then, outer and inner, or sensation and consciousness, is the origin of sensory judgments which are true categorical beliefs in the existence of sensible things; and primary judgments are such true categorical sensory beliefs that things exist, and neither require conception nor are combinations of conceptions.^ On this view, then, the true logical form of 'Mars exists' is 'There is at least one object, x , such that x is identical with Mars'.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ These are all problems in ontology in the sense that they deal with whether or not a certain thing, or more broadly entity, exists.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ If our universe contains some things that are A's but not B's, and other things that are B's but not A's, and nothing that is neither, then the first of these expressions will be false and the second true.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

.Again, since sense is the origin of memory and experience, memorial and experiential judgments are categorical and existential judgments, which so far as they report sensory judgments are always true.^ They are far from what the speaker of the original English sentence probably meant: there is something which is either not in a black hole or not lost forever, or something that is not both in a black hole and not lost.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ While persuasive, it's not always true, since while Hitler did a lot of evil things, he also was a massive advocate of animal rights (more so than Jewish, gay or Gypsy rights...
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ For one, of course, there is an issue about what it means to say that judgments have a form, and whether they do in the relevant sense.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.Finally, since sense, memory and experience are the origin of inference, primary inference is categorical and existential, starting from sensory, memorial and experiential judgments as premises, and proceeding to inferential judgments as conclusions, which are categorical and existential, and are true, so far as they depend on sense, memory and experience.^ If the premises are true and the conclusion false, the inference must be invalid.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ Thus, if the premises and inferences are true, then probably the conclusion is as well.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ If the premises are true and the inference valid, the conclusion must be true.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

.Sense, then, is the origin of judgment; and the consequence is that primary judgments are true, categorical and existential judgments of sense, and primary inferences are inferences from categorical and existential premises to categorical and existential conclusions, which are true so far as they arise from outer and inner sense, and proceed to things similar to sensible things.^ Thus, if the premises and inferences are true, then probably the conclusion is as well.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ The premises and conclusion can be true or false, but they are not called "sound" or "valid".
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ If the premises are true and the conclusion false, the inference must be invalid.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

.All other judgments and inferences about existing things, or ideas, or names, whether categorical or hypothetical, are afterthoughts, partly true and partly false.^ Other philosophers are 'actualists', maintaining that the only entities that exist at all are entities that actually exist.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ These are all problems in ontology in the sense that they deal with whether or not a certain thing, or more broadly entity, exists.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ What are true are certain statements; and the pursuit of truth is the endeavor to sort out the true statements from the others, which are false.
  • Readings in Logic 6 January 2010 10:47 UTC orcmid.com [Source type: Academic]

.Sense, then, because it involves a true belief in existence is fitted to be the origin of judgment.^ Affirming the consequent : Claiming that because the result of something is true, the original statement must also be true.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ In this sense we associate "form" neither with the representation that is involved in the judgment, nor with the proposition which is its content, but rather with the world that is judged about.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.Conception on the other hand is the simple apprehension of an idea, particular or universal, but without belief that anything is or is not, and therefore is unfitted to beget judgment.^ On the other hand, if it could be shown that the universe does have an underlying 'rational' structure, then the conclusion that nature is Mind (or that it has been constituted by Mind) would be difficult to resist.

^ As we saw in Essay Three , this is based on the idea that all words are really names, and on the belief that all concepts expressions are really singular terms (i.e., they are the names of abstract particulars -- or they 'designate' them in other ways).

^ The idea of dispensing with the justification of beliefs is often dismissed out of hand, on the grounds that this is the primary topic of philosophy.
  • Bartley's 1964 paper on Rationality and the theory of rationality. 18 September 2009 17:23 UTC www.the-rathouse.com [Source type: Original source]

.Nor could a combination of conceptions make a difference so fundamental as that between conceiving and believing.^ John Donne put it long ago, “The ends crowne our workes, but thou crown’st our ends...” Whether ‘thou’ is conceived as ‘God the Father’, as ‘Necessity’, or as the modern ‘Selection’, really makes no difference, it’s the same concept.
  • Science and Rationality 18 September 2009 17:23 UTC home.comcast.net [Source type: Original source]

^ Behavioral Economics and Rationality Bryan Caplan Arnold writes: It is not the scientific consensus that makes me believe that there is a link between smoking and cancer.
  • EconLog: Behavioral Economics and Rationality Archives 18 September 2009 17:23 UTC econlog.econlib.org [Source type: General]

^ Thus the difference between the testability theory and various probabilistic theories of confirmation can be defined by reference to the irreducible difference in the ways the two concepts are logically transmitted.
  • Bartley's 1964 paper on Rationality and the theory of rationality. 18 September 2009 17:23 UTC www.the-rathouse.com [Source type: Original source]

The most that it could do would be to cause an ideal judgment, e.g. that the idea of a centaur is the idea of a man-horse; and even here some further origin is needed for the addition of the copula " is." So far from being a cause, conception is not even a condition of all judgments; a sensation of hot is sufficient evidence that hot exists, before the idea of hot is either present or wanted. .Conception is, however, a condition of a memorial judgment: in order to remember being hot, we require an idea of hot.^ However, the idea of basing all of mathematics on one simple concept, sets, has exerted a powerful attraction.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

.Memory, however, is not that idea, but involves a judgment that there previously existed the hot now represented by the idea, which is about the sensible thing beyond the conceived idea; and the cause of this memorial judgment is past sense and present memory.^ An idea which is conceived of and which exists is better than one which is only imagined.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ However, rather then exploring the details of these and other rival systems, in the next section, we focus on proving things about the system PC, the axiomatic system treated at length above.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ Of course, even atomists will want to go beyond the present by including knowledge about the future in their decision procedure.
  • Global Rationality 18 September 2009 17:23 UTC docs.google.com [Source type: Original source]

.So sense, memory and experience, the sum of sense and memory, though requiring conception, are the causes of the experiential judgment that there exist and have existed many similar, sensible things, and these sensory, memorial and experiential judgments about the existence of past and present sensible things beyond conceived ideas become the particular premises of primary inference.^ An idea which is conceived of and which exists is better than one which is only imagined.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ However, rather then exploring the details of these and other rival systems, in the next section, we focus on proving things about the system PC, the axiomatic system treated at length above.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ With the many conceptions of logic and the many different philosophical projects under the heading of ontology, there are many problems that are in the intersection of these areas.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.Starting from them, inference is enabled to draw conclusions which are inferential judgments about the existence of things similar to sensible things beyond conceived ideas.^ Dialectical logic moves beyond formal logic by starting not with 'things' but with processes, processes of coming into being and passing out of being.

^ Third, Scripture commands actions which involve making judgments, conclusions, inferences: obeying, understanding the word, loving others as Jesus loved us, etc.

^ To accept these is in itself a rational activity, a forming of a judgment, conclusion, inference.

.In rising, however, from particular to universal inference, induction, as we have seen, adds to its particular premise, S is P, a universal premise, every M is similar to S, in order to infer the universal conclusion, every M is P. This universal premise requires a universal conception of a class or whole number of similar particulars, as a condition.^ In the process of deduction, we derive the conclusion by reasoning: the conclusion follows necessarily from (and is entailed by) the (general or universal) premises.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ I n the usual case, a valid argument consists of true propositions — true premises combining with true inferences leading to a true conclusion.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ "The reason for mistrusting the induction principle is that it involves an impredicative concept of number.
  • Readings in Logic 6 January 2010 10:47 UTC orcmid.com [Source type: Academic]

.But the premise is not that conception; it is a belief that there is a whole number of particulars similar to those already experienced.^ In particular, Quine rejects the idea that there could be truths which are the trivial internal statements, like "There are numbers", whose truth is a given once the framework of numbers has been adopted.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ That is to say, given that we have certain beliefs, do these beliefs already bring with them a rational commitment to an answer to such questions as ‘Are there numbers?’ If our beliefs bring with them a rational commitment to an answer to an ontological question about the existence of certain entities then we can say that we are committed to the existence of these entities.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ But if your beliefs are all true then there have to be numbers, if you are committed to numbers.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.The generalization of a class is not, as the conceptual logic assumes, the abstraction of a general idea, but an inference from the analogy of a whole individual thing, e.g. a whole man, to a whole number of similar individuals, e.g. the whole of men.^ In general, if is any individual whatsoever, then is the assertion that is a man.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ However, as researchers turned to generalizations of alethic modal logic, they began considering wider classes of modal logics, including ones where the necessity operator was not truth-implicating.
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

^ For example, an individual man can be treated as a subject, but the class of all men must be treated as a predicate.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

.The general idea of all men or the combination that the idea of all men is similar to the idea of particular men would not be enough; the universal premise that all men in fact are similar to those who have died is required to induce the universal conclusion that all men in fact die.^ Those who gain a refuge of safety for themselves through appeal to the limits of rationality thereby provide a similar refuge for all others whose commitments differ from theirs.
  • Bartley's 1964 paper on Rationality and the theory of rationality. 18 September 2009 17:23 UTC www.the-rathouse.com [Source type: Original source]

^ 'Men' is a conception of the same fact -- 'all men' -- but in respect of their multiplicity, the fact that no two of them are exactly alike.

^ Well,, it turns out that they are, in fact, biologically inclined to be angry and punitive toward those who they perceive to be not being...
  • EconLog: Behavioral Economics and Rationality Archives 18 September 2009 17:23 UTC econlog.econlib.org [Source type: General]

.Universal inference thus requires particular and universal conceptions as its condition; but, so far as it arises from sense, memory, experience, and involves generalization, it consists of judgments which do not consist of conceptions, but are beliefs in things existing beyond conception.^ And to this issue so central to the notion of instrumental rationality and the rationality of belief - why in a particular instance we should act on the most probable or believe the most probable will occur - the resources of rationality have thus far not provided a satisfactory answer .
  • Science and Rationality 18 September 2009 17:23 UTC home.comcast.net [Source type: Original source]

^ The Liar Paradox and Beyond Paraconsistency and Theology Though such a deprecation of consistency is a novelty for logicians, it is in a sense well familiar to theologians who have generally preferred biblical fidelity to logical consistency.
  • Geometry.Net - Mathematical_Logic: Logics Admitting Inconsistency 11 October 2009 10:39 UTC www.algebraic.net [Source type: FILTERED WITH BAYES]

^ Lecture on the consistency of the continuum hypothesis (Brown University) [Gödel*1940a] In what sense is intuitionisstic logic constructive?
  • Readings in Logic 6 January 2010 10:47 UTC orcmid.com [Source type: Academic]

.Inference then, so far as it starts from categorical and existential premises, causes conclusions, or inferential judgments, which require conceptions, but are categorical and existential judgments beyond conception.^ I n the usual case, a valid argument consists of true propositions — true premises combining with true inferences leading to a true conclusion.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ Sometimes, the writer hasn't strong premises or inferences and simply wants to "push" the conclusion on the unsuspecting readers anyway.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ This inference is logically correct, because the conclusion ``some real estate is a good investment'' necessarily follows once we accept the premises ``some real estate will increase in value'' and ``anything that will increase in value is a good investment''.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

.Moreover, as it becomes more deductive, and causes conclusions further from sensory experience, these inferential judgments become causes of inferential conceptions.^ For if concepts are viewed as abstract objects of some sort, then it becomes natural to jumble-together these two sorts of change.

^ Has anything been written on whether the study of happiness causes people to become more happy?
  • EconLog: Behavioral Economics and Rationality Archives 18 September 2009 17:23 UTC econlog.econlib.org [Source type: General]

^ To accept these is in itself a rational activity, a forming of a judgment, conclusion, inference.

.For example, from the evidence of molar changes due to the obvious parts of bodies, science first comes to believe in molecular changes due to imperceptible particles, and then tries to conceive the ideas of particles, molecules, atoms, electrons.^ However, if in the end materialists are to reject Hegelian Ontology -- as surely they must -- then the idea that FL is a part of science becomes much harder to sustain.

^ Now, Aristotle certainly believed that during change something must remain the same (but precisely what that "something" was is subject to controversy among Aristotle scholars) -- for example, in Aristotle (1984e), p.1595.

^ Trying to teach them a classical art form is difficult because they want to proceed directly to the post-modern part without learning the classical or the modern first.
  • Augean Stables » David Landau, Oslo Logician, Asks Condi Rice to “Rape” Israel 11 September 2009 7:35 UTC www.theaugeanstables.com [Source type: Original source]

.The conceptual logic supposes that conception always precedes judgment; but the truth is that sensory judgment begins and inferential judgment ends by preceding conception.^ Whatever one says about the possibility of proving the existence of an object purely with conceptual truths, many philosophers have maintained that at least logic has to be neutral about what there is.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ But this conception of their relationship assumes that the "general features of judgments" or "forms of judgment" which (L4) is concerned with deal with something like the logical constants in the language of thought.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Note that this guarantees that something is always obligatory (even if only logical truths).
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

The supposed triple order - conception, judgment, reasoning - is defective and false. The real order is sensation and sensory judgment, conception, memory and memorial judgment, experience and experiential judgment, inference, inferential judgment, inferential conception. .This is not all: inferential conceptions are inadequate, and finally fail.^ Naturally, that would fatally blur the distinction between concepts and objects, all the while failing to pick out the original concept intended.

.They are often symbolical; that is, we conceive one thing only by another like it, e.g. atoms by minute bodies not nearly small enough.^ They wander from one topic to another.
  • Geometry.Net - Mathematical_Logic: Logics Admitting Inconsistency 11 October 2009 10:39 UTC www.algebraic.net [Source type: FILTERED WITH BAYES]

^ (Often the payoffs in a zero-sum game are displayed with only one entry in each cell of the matrix.
  • Feature Column from the AMS 18 September 2009 17:23 UTC www.ams.org [Source type: FILTERED WITH BAYES]

^ One only needs to check the Guardian occasionally especially the cartoons - often they rival der Sturmer.
  • Augean Stables » David Landau, Oslo Logician, Asks Condi Rice to “Rape” Israel 11 September 2009 7:35 UTC www.theaugeanstables.com [Source type: Original source]

Often the symbol is not like. What idea can the physicist form of intraspatial ether ? What believer in God pretends to conceive Him as He really is ? .We believe many things that we cannot conceive; as Mill said, the inconceivable is not the incredible; and the point of science is not what we can conceive but what we should believe on evidence.^ And many more specific things could be said under the category of Formgeschichte.

^ The only difference is that they actually did know things that were worth knowing, like the movements of the heavenly bodies, something which cannot be said of modern logicians.

Conception is the weakest, judgment the strongest power of man's mind. Sense before conception is the original cause of judgment; and inference from sense enables judgment to continue after conception ceases. Finally, as there is judgment without conception, so there is conception without judgment. We often say " I understand, but do not decide." But this suspension of judgment is a highly refined act, unfitted to the beginning of thought. Conception begins as a condition of memory, and after a long continuous process of inference ends in mere ideation. .The conceptual logic has made the mistake of making ideation a stage in thought prior to judgment.^ This is so manifestly (and demonstrably) untrue that these two comrades have to ignore and distort the major advances that have been made in logic since the 1850s to make it 'work': .

^ One way to understand logic is as the study of the most general forms of thought or judgment, what we called (L4).
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ But this conception of their relationship assumes that the "general features of judgments" or "forms of judgment" which (L4) is concerned with deal with something like the logical constants in the language of thought.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.It was natural enough that the originators of conceptual logic, seeing that judgments can be expressed by propositions, and conceptions by terms, should fall into the error of supposing that, as propositions consist of terms, so judgments consist of conceptions, and that there is a triple mental order - conception, judgment, reasoning - parallel to the triple linguistic order - term, proposition, discourse.^ "There are obvious benefits to be gained from the study of logic: heightened ability to express ideas clearly and concisely, increased skill in defining one's terms, enlarged capacity to formulate arguments rigorously and to analyze them critically.
  • Readings in Logic 6 January 2010 10:47 UTC orcmid.com [Source type: Academic]

^ However, as we will see in other Essays posted at this site, not only is the above incorrect in general (in that it is the conceptual wealth expressed in the use of ordinary language which enables the depiction and comprehension of change (in nature and society)), it is misguided in particular.

^ Four terms fallacy : Using a standard 3-step proof-of-concept to prove your theory, but including one unconnected tenet which breaks the line of reasoning.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

.They overlooked the fact that man thinks long before he speaks, makes judgments which he does not express at all, or expresses them by interjections, names and phrases, before he uses regular propositions, and that he does not begin by conceiving and naming, and then proceed to believing and proposing.^ A writer begins an argument by making a proposition.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ In case I didn't make this point strongly enough before: though his post was sharp edged, I don't think there was any reason to resort to unnecessary name calling & personal attacks.
  • Who Has Time For This?: Limits of Rationality: Beware the Paralimbic Cortex 18 September 2009 17:23 UTC whohastimeforthis.blogspot.com [Source type: General]

^ Readers need to make note of the fact that this Essay does not represent my final view on any of the issues raised.

Feeling and sensation, involving believing or judging, come before conception and language. .As conceptions are not always present in judgment, as they are only occasional conditions, and as they are unfitted to cause beliefs or judgments, and especially judgments of existence, and as judgments both precede conceptions in sense and continue after them in inference, it follows that conceptions are not the constituents of judgment, and judgment is not a combination of conceptions.^ And if one holds that one of the crucial features of logically valid inferences is that they preserve truth then one could argue that the logical laws are norms that apply to those who have beliefs.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Moreover, both kinds of rules carry over the conditions from the formulas to which they are applied.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ Of course, it could always be argued that variables that relate to quantities (as they feature in mathematics) are not at all the same as the variables that relate to concepts, properties or qualities (as they are employed in FL).

Is there then any analysis of judgment ? .Paradoxical as it may sound, the truth seems to be that primary judgment, beginning as it does with the simplest feeling and sensation, is not a combination of two mental elements into one, but is a division of one sensible thing into the thing itself and its existence and the belief that it is determined as existing, e.g. that hot exists, cold exists, the pained exists, the pleased exists.^ And if one holds that one of the crucial features of logically valid inferences is that they preserve truth then one could argue that the logical laws are norms that apply to those who have beliefs.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ One idea to answer this is to employ the notion of a ‘constitutive aim of belief’, the idea that belief as such aims at something: the truth.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ But, such inferences have only ever been justified by nominalisations of this sort -- ones that conjure into existence objects at the drop of a noun.

.Such a judgment has a cause, namely sense, but no mental elements.^ First, it is not clear what should be said about true sentences containing no demonstrative element, such as 'Horses are mammals'.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

.Afterwards come judgments of complex sense, e.g. that the existing hot is burning or becoming more or less hot, &c.^ These are all problems in ontology in the sense that they deal with whether or not a certain thing, or more broadly entity, exists.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ The situation will be less transparent if the premises are more complex.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ The question then becomes, first how should we understand ‘form of judgement’ more precisely, and secondly, how does logic, as the discipline concerned with forms of judgments in the sense of (L4), relate to (L2)?
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.Thus there is a combination of sensations causing the judgment; but the judgment is still a division of the sensible thing into itself and its being, and a belief that it is so determined.^ Dialectical logic moves beyond formal logic by starting not with 'things' but with processes, processes of coming into being and passing out of being.

^ In that case, one is tempted to say that the idea that there is such a thing as 'commonsense' must be a "scientistic folk belief" itself , since it is not based on any clear evidence --, at least none that is not 'tainted' with the sorts of ideas many would include in 'commonsense', too.

^ Rather, it is equivalent to 'The property of being (identical with) Mars is instantiated', asserting that the property of being Mars has at least one instance, or that there is at least one thing possessing that property.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

Afterwards follow judgments arising from more complex causes, e.g. memory, experience, inference. .But however complicated these mental causes, there still remain these points common to all judgment: - (i) The mental causes of judgment are sense, memory, experience and inference; while conception is a condition of some judgments.^ In a very broad sense of the term 'name', names traditionally divide into two classesproper names and common names, these being species of singular and general terms respectively.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ With the many conceptions of logic and the many different philosophical projects under the heading of ontology, there are many problems that are in the intersection of these areas.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ But there nevertheless remains enormous latitude for the exercise of aesthetic judgment in the development of any given image.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

.(2) A judgment is not a combination either of its causes or of its conditions, e.g. it is not a combination of sensations any more than of ideas.^ For example, authorities would engage in torture or frame innocent persons whenever they believed that doing so would cause more good than harm.
  • Global Rationality 18 September 2009 17:23 UTC docs.google.com [Source type: Original source]

^ It combines ideas from the method of prefixes used in tableaux, and resolution ideas in such a way that some of the heuristics and optimizations devised in either field are applicable."
  • http://www.cs.mu.oz.au/482/biblio/Year/2001.complete.html 18 September 2009 8:08 UTC www.cs.mu.oz.au [Source type: Academic]

^ The three rectangular cells are jointly exhaustive and mutually exclusive: every proposition is either necessary, contingent, or impossible, but no proposition is more than one of these.
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

.(3) A judgment is a unitary mental act, dividing not itself but its object into the object itself and itself as determined, and signifying that it is so determined.^ Here the judgment as a mental act is assumed to operate on a mental representation that itself has syntactic structure.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.(¢) A primary judgment is a judgment that a sensible thing is determined as existing; but later judgments are concerned with either existing things, or with ideas, or with words, and signify that they are determined in all sorts of ways.^ One way to answer the first question is to understand "form of judgment" as not being concerned with the representation that might be involved in a judgment, but rather with the content of the judgment, i.e.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Due to the constraints of their cars, they listen to the books in a variety of ways...Determine the full name of each commuter, the title and genre of each book, and in what format each listens to their audio book.

^ These are all problems in ontology in the sense that they deal with whether or not a certain thing, or more broadly entity, exists.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.(5) When a judgment is expressed by a proposition, the proposition expresses the results of the division by two terms, subject and predicate, and by the copula that what is signified by the subject is what is signified by the predicate; and the proposition is a combination of the two terms; e.g. border war is evil.^ The truth-function for an operator can be represented as a table, each line of which expresses a possible combination of truth-values for the simpler statements to which the operator applies, along with the resulting truth-value for the complex statement formed using the operator.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ "The subject and the predicate of the conclusion each occur in one of the premises, together with a third term (the middle) that is found in both premises, but not in the conclusion.

^ The predicate of the conclusion is the major term; the premise in which it is contained is the major premise; the subject of the conclusion is the minor term; and the premise in which it is contained is the minor premise.

(6) A complex judgment is a combination of two judgments, and may be copulative, e.g. you and I are men, or hypothetical, or disjunctive, &c.
Empirical logic, the logic of Aristotle and Bacon, is on the right way. .It is the business of the logician to find the causes of the judgments which form the premises and the conclusions of inference, reasoning and science.^ I n the usual case, a valid argument consists of true propositions — true premises combining with true inferences leading to a true conclusion.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ Sometimes, the writer hasn't strong premises or inferences and simply wants to "push" the conclusion on the unsuspecting readers anyway.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ This inference is logically correct, because the conclusion ``some real estate is a good investment'' necessarily follows once we accept the premises ``some real estate will increase in value'' and ``anything that will increase in value is a good investment''.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

.What knowledge do we get by sense, memory and experience, the first mental causes of judgment?^ He takes one idea after another—the idea of God, of the soul, of memory, of other minds—and asks whether it can be justified by being derived from sense experience, which he regards as man’s only source of knowledge, or rational authority.
  • Bartley's 1964 paper on Rationality and the theory of rationality. 18 September 2009 17:23 UTC www.the-rathouse.com [Source type: Original source]

^ If we take the second requirement seriously, we will have to justify the first; but this cannot be done by sense experience, intellectual intuition, or any other rational authority ever proposed.
  • Bartley's 1964 paper on Rationality and the theory of rationality. 18 September 2009 17:23 UTC www.the-rathouse.com [Source type: Original source]

What is judgment, and what its various kinds? .What is inference, how does it proceed by combining judgments as premises to cause judgments as conclusions, and what are its various kinds?^ Happily, the derivation of the conclusion of the premises using our inference and replacement rules, while far from simple, is relatively less exhausting: .
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ I n the usual case, a valid argument consists of true propositions — true premises combining with true inferences leading to a true conclusion.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ No general theory of argument or inference would be complete without an account of the various fallacies and paradoxes which beset our attempts to reason from premise to conclusion.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

.How does inference draw conclusions more or less probable up to moral certainty?^ They talked about how in artificial vitamins the body does not get the whole vitamin complex and ...this may do more harm than good.

^ Behavioral Economics and Rationality Arnold Kling Tyler Cowen finds research suggesting that the more highly you think of your morals, the less altruistic you are.
  • EconLog: Behavioral Economics and Rationality Archives 18 September 2009 17:23 UTC econlog.econlib.org [Source type: General]

^ Happily, the derivation of the conclusion of the premises using our inference and replacement rules, while far from simple, is relatively less exhausting: .
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

.How does it by the aid of identification convert probable into necessary conclusions, which become necessary principles of demonstration?^ Controversy does arise, however, concerning certain conclusions which have been drawn from this principle.

^ First he commits an error of composition, extrapolating that into the general rule that anyone who does not drill a hole in their head will not become famous.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ The moment processes of change are fed into the equation it becomes necessary to deal with contradiction.

How is categorical succeeded by conditional inference? .What is scientific method as a system of inferences about definite subjects?^ However, when logic is applied to specific subject matter, it is important to note that not all logical inference constitutes a scientifically valid demonstration.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

.How does inference become the source of error and fallacy?^ First he commits an error of composition, extrapolating that into the general rule that anyone who does not drill a hole in their head will not become famous.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

.How does the whole process from sense to inference discover the real truth of judgments, which are true so far as they signify things known by sense, memory, experience and inference?^ They talked about how in artificial vitamins the body does not get the whole vitamin complex and ...this may do more harm than good.

^ In addition, the idea that truths about fundamental aspects of reality can be uncovered by an examination of how human beings reason is highly suspect in itself; but, like most things, so much depends on what allegedly follows from that assumption.

^ T he first statement is a statement of causality, really, not an argument, and the writer is asserting as truthful that a known problem with the spark plugs is the reason the car will not start.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

These are the fundamental questions of the science of inference. .Conceptual logic, on the other hand, is false from the start.^ On the other hand, some normative sentences do seem to follow from others, so deontic logic must be possible.
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

^ However, the truth table given above for the statements “P v Q” and “¬(P ↔ ¬Q)” show that they, on the other hand, are not logically equivalent, because they differ in truth-value for two of the four possible truth-value assignments.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ On the other hand, the class of logically valid formulas is known to be extremely complicated.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

.It is not the first business of logic to direct us how to form conceptions signified by terms, because sense is a prior cause of judgment and inference.^ So, no wonder that that dialecticians copy Hegel and talk about concepts developing , and how FL is hamstrung because of its fixation with 'fixed' concepts.

^ And, of course, logic does not tell us how we ought to reason or infer in all particular cases.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ However, in logic, the term is generally used to refer only to a form of technically incorrect argument, especially if that argument appears to be valid or convincing.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

.It is not the second business of logic to direct us how out of conceptions to form judgments signified by propositions, because the real causes of judgments are sense, memory, experience and inference.^ This proposition forms one basis of logic.

^ Perhaps the most well known form of non-truth-functional propositional logic is modal propositional logic .
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ So, no wonder that that dialecticians copy Hegel and talk about concepts developing , and how FL is hamstrung because of its fixation with 'fixed' concepts.

.It is, however, the main business of logic to direct us how out of judgments to form inferences signified by discourse; and this is the one point which conceptual logic has contributed to the science of inference.^ This proposition forms one basis of logic.

^ Thus logic is the science of necessary inference.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ One way to answer the first question is to understand "form of judgment" as not being concerned with the representation that might be involved in a judgment, but rather with the content of the judgment, i.e.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.But why spoil the further mental analysis of inference by supposing that conceptions are constituents of judgment and therefore of inference, which thus becomes merely a complex combination of conceptions, an extension of ideas?^ Change to objects thus becomes the exemplar that conceptual change is now modelled upon, but only because, in referring to concepts, it seems we have to nominalise them.

.The mistake has been to convert three operations of mind into three processes in a fixed order - conception, judgment, inference.^ According to this conception, different formal languages will be useful in modeling the inferences that are formally valid given different set of ‘logical constants’ or expressions whose meaning is kept fixed.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ This is because it supposedly operates with a "static" view of the world --, or at least with "fixed and immutable" concepts.

^ "Reasoning," then, will be the process of forming those judgments, conclusions, inferences.

.Conception and judgment are decisions: inference alone is a process, from decisions to decision, from judgments to judgment.^ As with practical judgments of emotional coherence in practical decision making, we have no direct conscious access to the cognitive processes by which we judge some hypotheses to be more coherent than others.
  • Rationality and Science 18 September 2009 17:23 UTC cogsci.uwaterloo.ca [Source type: FILTERED WITH BAYES]

^ "Reasoning," then, will be the process of forming those judgments, conclusions, inferences.

Sense, not conception, is the origin of judgment. .Inference is the process which from judgments about sensible things proceeds to judgments about things similar to sensible things.^ The form of a judgment could be understood along the lines we understood the form of a linguistic representation when we talked about formally valid inferences.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ God cares that we make the right judgments, conclusions, inferences; he cares about this because he cares about our obedience.

^ "Reasoning," then, will be the process of forming those judgments, conclusions, inferences.

.Though some conceptions are its conditions and some judgments its causes, inference itself in its conclusions causes many more judgments and conceptions.^ As with practical judgments of emotional coherence in practical decision making, we have no direct conscious access to the cognitive processes by which we judge some hypotheses to be more coherent than others.
  • Rationality and Science 18 September 2009 17:23 UTC cogsci.uwaterloo.ca [Source type: FILTERED WITH BAYES]

^ This inference is logically correct, because the conclusion ``some real estate is a good investment'' necessarily follows once we accept the premises ``some real estate will increase in value'' and ``anything that will increase in value is a good investment''.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ Third, Scripture commands actions which involve making judgments, conclusions, inferences: obeying, understanding the word, loving others as Jesus loved us, etc.

.Finally, inference is an extension, not of ideas, but of beliefs, at first about existing things, afterwards about ideas, and even about words; about anything in short about which we think, in what is too fancifully called " the universe of discourse."^ (This theorem demonstrates that, for any 'sufficiently powerful' formal system, there exist statements that are neither inconsistent with the system nor provable or disprovable within the system; in short, the system has nothing to say about them.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

^ Formal ontologies could also only have axioms that state how the things the theory is about, whatever they may be, relate to each other, but no axioms that state that certain things exist.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Here, the second component's universal claim about logicians guarantees that it covers the creatures referred to by the first component's existential claim, even though different variables and quantifiers are used.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

.Formal logic has arisen out of the narrowness of conceptual logic.^ We can then view our elaborate logical formalisms and derivations as simply selectors that choose for one out of a truly vast, but finite, set of possible outcomes.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

^ Dialectical logic moves beyond formal logic by starting not with 'things' but with processes, processes of coming into being and passing out of being.

^ It is an astonishing fact that the basic laws of formal logic worked out by Aristotle have remained fundamentally unchanged for over two thousand years."

.The science of inference no doubt has to deal primarily with formal truth or the consistency of premises and conclusion.^ The truth of the premises guarantees the truth of the conclusions.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ And when an inference is formally valid then the conclusion logically follows from the premises.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ I n the usual case, a valid argument consists of true propositions — true premises combining with true inferences leading to a true conclusion.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

.But as all truth, real as well as formal, is consistent, formal rules .of consistency become real rules of truth, when the premises are true and the consistent conclusion is therefore true.^ The idea is that if the premises are true, then the conclusion must also be true as well.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ The truth of the premises guarantees the truth of the conclusions.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ Thus, if the premises and inferences are true, then probably the conclusion is as well.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

.The science of inference again rightly emphasizes the formal thinking of the syllogism in which the combination of premises involves the conclusion.^ And when an inference is formally valid then the conclusion logically follows from the premises.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ I n the usual case, a valid argument consists of true propositions — true premises combining with true inferences leading to a true conclusion.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ When we think about inferences and implicature, we need to remember one very important point: the fact that a deductive argument is valid does not necessarily entail that its conclusion holds, or the fact that a deductive argument's conclusion is true does not necessarily mean that its premises are true as well.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

.But the combinations of premises in analogical and inductive inference, although the combination does not involve the conclusion, yet causes us to infer it, and in so similar a way that the science of inference is not complete without investigating all the combinations which characterize different kinds of inference.^ I n the usual case, a valid argument consists of true propositions — true premises combining with true inferences leading to a true conclusion.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ Analogously, we can imagine in science and other organizations a kind of "tragedy of consensus", in which the individuals all reach similar conclusions about what to believe, stifling creative growth.
  • Rationality and Science 18 September 2009 17:23 UTC cogsci.uwaterloo.ca [Source type: FILTERED WITH BAYES]

^ No general theory of argument or inference would be complete without an account of the various fallacies and paradoxes which beset our attempts to reason from premise to conclusion.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

.The question of logic is how we infer in fact, as well as perfectly; and we cannot understand inference unless we consider inferences of probability of all kinds.^ And, of course, logic does not tell us how we ought to reason or infer in all particular cases.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Models based on formal logic and probability theory have tended to be so remote from scientific practice that they encourage the inference that scientists are irrational.
  • Rationality and Science 18 September 2009 17:23 UTC cogsci.uwaterloo.ca [Source type: FILTERED WITH BAYES]

^ Now, if would-be critics want to revise a word in common use, all well and good; but this cannot affect the ordinary meaning of that word .

.Moreover, the study of analogical and inductive inference is necessary to that of the syllogism itself, because they discover the premises of syllogism.^ Yet this same inference may not be a demonstration of its conclusion, because one or both of the premises may be faulty.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ This is because a premise of some priority level will itself be marked in view of formulas that have a higher priority.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ This inference is logically correct, because the conclusion ``some real estate is a good investment'' necessarily follows once we accept the premises ``some real estate will increase in value'' and ``anything that will increase in value is a good investment''.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

.The formal thinking of syllogism alone is merely necessary consequence; but when its premises are necessary principles, its conclusions are not only necessary consequents but also necessary truths.^ The truth of the premises guarantees the truth of the conclusions.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ That a logic assigns the trivial consequence set to some set of premises means that, in semantic terms, the set of premises has no models or that its only model is the trivial one.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ For example, a realistic adaptive logic of induction should not only extend the CL -consequences of the premises, but should also be able to handle inconsistent background theories.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

.Hence the manner in which induction aided by identification discovers necessary principles must be studied by the logician in order to decide when the syllogism can really arrive at necessary conclusions.^ They must do if they believe that logicians study how people in fact think.

^ In order to classify the various types of syllogisms, one must take account of certain symmetries.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ In order to justify the original conclusion, it appears that one must eventually stop at something not open to question, for which one need not provide reasons when demanded.
  • Bartley's 1964 paper on Rationality and the theory of rationality. 18 September 2009 17:23 UTC www.the-rathouse.com [Source type: Original source]

.Again, the science of inference has for its subject the form, or processes, of thought, but not its matter or objects.^ Such relations are the subject matter of the general theory of rational argument or inference, whether deductive or inductive.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ Follow this rule: when order matters, the first quantifier quantifies the subject of the sentence; the others quantify the objects of the verb.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ Logicians investigate the activities of the thought process which goes on in human heads and formulate the laws, forms and interrelations of those mental processes."

.But it does not follow that it can investigate the former without the latter.^ These hardly look like the same things (for example, the latter notion calls for an agent, the former does not).
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

.Formal logicians say that, if they had to consider the matter, they must either consider all things, which would be impossible, or select some, which would be arbitrary.^ Formal logic has said all that it has to say.

^ It would affirm the nihilistic philosophy of fatalism, and undermine the basis of human morality: that we have a choice in matters, and that what we choose to do--and not to do--makes some kind of a difference.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

^ An actor, in forethought, has a contract made that says either they play a certain role in a future film, and are paid accordingly, or they are paid anyway to not take the role.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

.But there is an intermediate alternative, which is neither impossible nor arbitrary; namely, to consider the general distinctions and principles of all things; and without this general consideration of the matter the logician cannot know the form of thought, which consists in drawing inferences about things on these general principles.^ (This theorem demonstrates that, for any 'sufficiently powerful' formal system, there exist statements that are neither inconsistent with the system nor provable or disprovable within the system; in short, the system has nothing to say about them.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

^ There are useful notes by Stephen Kleene on achieving consistency of the λ-calculus and Gödel's gradual acceptance of Church's Thesis in the form of Turing computable functions.
  • Readings in Logic 6 January 2010 10:47 UTC orcmid.com [Source type: Academic]

^ In a very broad sense of the term 'name', names traditionally divide into two classesproper names and common names, these being species of singular and general terms respectively.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

.Lastly, the science of inference is not indeed the science of sensation, memory and experience, but at the same time it is the science of using those mental operations as data of inference; and, if logic does not show how analogical and inductive inferences directly, and deductive inferences indirectly, arise from experience, it becomes a science of mere thinking without knowledge.^ Thus logic is the science of necessary inference.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ We may seek to employ,e.g., the doctrine of divine sovereignty, in contexts similar to those in which the biblical writers used it, without necessarily being able to reconcile it with human responsibility.

^ Since the payoff to Row in this case will be the same whatever Column does, let us first compute the payoff to Row when Column plays column 1 all of the time.
  • Feature Column from the AMS 18 September 2009 17:23 UTC www.ams.org [Source type: FILTERED WITH BAYES]

.Logic is related to all the sciences, because it considers the common inferences and varying methods used in investigating different subjects.^ This example of logic is used by Heroic Sociopath Belkar Bitterleaf in this strip of The Order of the Stick Belkar: See, now that's what being on a team is all about.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ But when Hegel, for example, uses ‘logic’, or better ‘Logik’, he means something quite different than what is meant by the word in much of the contemporary philosophical scene.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ The matter is different for the adaptive logic of induction that was used as an example before.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

.But it is most closely related to the sciences of metaphysics and psychology, which form with it a triad of sciences.^ The notion of broadly logical necessity is closely related to that of metaphysical necessity.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ (O2) the study of what there is, (O3) the study of the most general features of what there is, and how the things there are relate to each other in the metaphysically most general ways, (O4) the study of meta-ontology, i.e.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.Metaphysics is the science of being in general, and therefore of the things which become objects apprehended by our minds.^ They are, at basis, an expression of our " species being " and are intimately connected with our relationship with the world, with one another and with previous generations.

^ If all that is real is indeed rational, then the identification of rules of inference with the "rules of thought" -- and with metaphysical truths about "Being" -- becomes more all the more natural.

^ Metaphysics 2 The Metaphysics is Aristotle's treatise on the science of existence, i.e., being as such.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

.Psychology is the science of mind in general, and therefore of the mental operations, of which inference is one.^ However, as researchers turned to generalizations of alethic modal logic, they began considering wider classes of modal logics, including ones where the necessity operator was not truth-implicating.
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

^ In psychology this is generally related to cognitive dissonance theory, which is basically the idea that when people think of themselves one way, but act in another way they will try to rationalize it.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ Therefore the question of the rationality of science can be raised for groups as well as individuals: What is it for a group of scientists to be collectively rational, and are such groups generally rational?
  • Rationality and Science 18 September 2009 17:23 UTC cogsci.uwaterloo.ca [Source type: FILTERED WITH BAYES]

.Logic is the science of the processes of inference.^ As a practitioner of the new process, I will attempt to illuminate both its specific concerns and the significance of its links to the fields of formal logic, the natural sciences, and computer science.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

.These three sciences, of the objects of mind, of the operations of mind, of the processes used in the inferences of mind, are differently, but closely related, so that they are constantly confused.^ If they are higher order properties or functions that are members of these propositions alongside other objects and properties then presumably the logical constants have content.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ As was also argued in Essay Three Part One , if sentences were composed solely of names (or singular terms), they would be no different from lists .

^ According to this conception, different formal languages will be useful in modeling the inferences that are formally valid given different set of ‘logical constants’ or expressions whose meaning is kept fixed.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.The real point is their interdependence, which is so intimate that one sign of great philosophy is a consistent metaphysics, psychology and logic.^ The inconsistency of Frege's original formulation of his position sometimes has been taken to show this, but since consistent formulations of Frege's philosophy of arithmetic have surfaced this last point is moot.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Main areas of research: metaphysics, philosophy of mind, philosophical logic, and the history of early modern philosophy.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ Both logic and ontology are diverse fields within philosophy, and partly because of this there is not one single philosophical problem about the relation between logic and ontology.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.If the world of things is known to be partly material and partly mental, then the mind must have powers of sense and inference enabling it to know these things, and there must be processes of inference carrying us from and beyond the sensible to the insensible world of matter and mind.^ So, there must be an i -acceptable world, say j , where OB p is true, but p is false.
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

^ These are all problems in ontology in the sense that they deal with whether or not a certain thing, or more broadly entity, exists.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Dialectical logic moves beyond formal logic by starting not with 'things' but with processes, processes of coming into being and passing out of being.

If the whole world of things is matter, operations and processes of mind are themselves material. .If the whole world of things is mind, operations and processes of mind have only to recognize their like all the world over.^ FL has not only contributed to the evolution of software and of computer languages, the principles of Propositional Calculus govern the operation of all standard processors (etc.

^ The dog recognizes a good thing :) Looks like the old food is headed out for the local wildlife.

^ The only difference is that they actually did know things that were worth knowing, like the movements of the heavenly bodies, something which cannot be said of modern logicians.

It is clear then that a man's metaphysics and psychology must colour his logic. .It is accordingly necessary to the logician to know beforehand the general distinctions and principles of things in metaphysics, and the mental operations of sense, conception, memory and experience in psychology, so as to discover the processes of inference from experience about things in logic.^ In this sense, the concept of logical validity is too general and too intractable to be analyzed thoroughly.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ For that we need some distinctive principles governing our deontic operator, and in particular, to generate the alternative equivalences that reflect the alternative definitional schemes alluded to above, we need what is perhaps the most fundamental and least controversial rule of inference in deontic logic, and the one characteristic of “classical modal logics” (Chellas 1980): .
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

^ Logically necessary truths in these narrower senses are, it seems, knowable a priori, but Kripke argues that metaphysical necessity is, typically, only discoverable a posteriorithat is, on the basis of empirical evidence.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

The interdependence of this triad of sciences has sometimes led to their confusion. .Hegel, having identified being with thought, merged metaphysics in logic.^ However, once this misbegotten 'ontological' interpretation of FL is abandoned, the temptation to identify logic with science (or with the " Laws of Thought ") loses whatever superficial plausibility it ever seemed to have.

^ "It is impossible to understand Marx's Capital, and especially its first chapter, without having thoroughly studied and understood the whole of Hegel's Logic.

^ If all that is real is indeed rational, then the identification of rules of inference with the "rules of thought" -- and with metaphysical truths about "Being" -- becomes more all the more natural.

.But he divided logic into objective and subjective, and thus practically confessed that there is one science of the objects and another of the pro cesses of thought.^ Thus, one might argue, logic is not neutral with respect to what there is.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Thus for a believer in logical objects there can be no empty domain.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ This debate thus concerns whether there is one and only one set of logical constants for a system of representations, and if so, which ones are the logical ones.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.Psychologists, seeing that inference is a mental operation, often extemporize a theory of inference to the neglect of logic.^ Models based on formal logic and probability theory have tended to be so remote from scientific practice that they encourage the inference that scientists are irrational.
  • Rationality and Science 18 September 2009 17:23 UTC cogsci.uwaterloo.ca [Source type: FILTERED WITH BAYES]

^ This often offers a clue on the conditions (see the section on the dynamic proof theory ) that govern the derivation of the supplementary formulas.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ But it also cannot proceed in terms of a monotonic paraconsistent logic [1] because such logics assign to the theory a consequence set that is too weak (see the next two paragraphs).
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

But we have a double consciousness of inference. .We are conscious of it as one operation among many, and of its omnipresence, so to speak, to all the rest.^ Although all of the above operators are generally deemed definable in terms of any one of the first four, the necessity operator is typically taken as basic and the rest defined accordingly: .
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

^ In many cases, the premises are all pushed into one sentence, or even, are simply implied.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ If the English operator has multiple meanings, one truth-functional and others not, then only translate it with one of our operator symbols if you want the truth-functional core of meaning and are willing to discard the rest.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

But we are also conscious of the processes of the operation of inference. .To a certain extent this second consciousness applies to other operations: for example, we are conscious of the process of association by which various mental causes recall ideas in the imagination.^ But on the other hand, the second quantifier is unnecessary in this case, provided the second component uses the variables of the first and is put within the scope of the first quantifier: "(x)[(Cx É Mx) · (Cx É ~Bx)]".
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ To wit: Man can think some thoughts and imagine some ideas which are greater than others.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

.But how little does the psychologist know about the association of ideas, compared with what the logician has discovered about the processes of inference!^ They talked about how in artificial vitamins the body does not get the whole vitamin complex and ...this may do more harm than good.

^ If, however, no one knows what "change" really means (or if it has unspecified shortcomings), then no one would know precisely what was being corrected, or how to go about it.

^ And how does Plekhanov counter the garbled ideas he attributes to FL? .

.The fact is that our primary consciousness of all mental operations is hardly equal to our secondary consciousness of the processes of the one operation of inference from premises to conclusions permeating long trains and pervading whole sciences.^ Each of the premises and the conclusion is of one of four types: .
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ I n the usual case, a valid argument consists of true propositions — true premises combining with true inferences leading to a true conclusion.
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ The writer begins with a general statement (the premise) and then draws specific conclusions (by the processes of implicature and entailment).
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

.This elaborate consciousness of inferential process is the justification of logic as a distinct science, and is the first step in its method.^ As a practitioner of the new process, I will attempt to illuminate both its specific concerns and the significance of its links to the fields of formal logic, the natural sciences, and computer science.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

^ In this way we limit the scope of logic, maintaining a sharp distinction between logic and the other sciences.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ Certainly as the logical process is worked in my mind I distinguish first one pole, then the other of the separation and then their conjunction .

.But it is not the whole method of logic, which also and rightly considers the mental process necessary to language, without substituting linguistic for mental distinctions.^ The use of the process would not be sustainable without an environmentally safe method of disposal, and better still preferably a ‘beneficial use’ of the output from digestion.

^ On both conceptions of logic we deal with logical constants, the difference is that one deals with a system of mental representations, the other with a system of linguistic representations.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ "It is impossible to understand Marx's Capital, and especially its first chapter, without having thoroughly studied and understood the whole of Hegel's Logic.

Nor are consciousness and linguistic analysis all the instruments of the logician. .Logic has to consider the things we know, the minds by which we know them from sense, memory and experience to inference, and the sciences which systematize and extend our knowledge of things; and having considered these facts, the logician must make such a science of inference as will explain the power and the poverty of human knowledge.^ Thus logic is the science of necessary inference.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ The Liar Paradox and Beyond Paraconsistency and Theology Though such a deprecation of consistency is a novelty for logicians, it is in a sense well familiar to theologians who have generally preferred biblical fidelity to logical consistency.
  • Geometry.Net - Mathematical_Logic: Logics Admitting Inconsistency 11 October 2009 10:39 UTC www.algebraic.net [Source type: FILTERED WITH BAYES]

^ But we must also say that, not only the conclusions, but also the premisses, the presuppositions, the starting points of these sciences are subject to ethical- ultimately religious- evaluation.

.General Tendencies Of Modern Logic There are several grounds for hope in the logic of our day.^ He has high hopes for his business being successful as there's a number of large companies in the area that he can cater to....Each day he chose something different to eat, drink, and snack on.

^ Moreover, this approach is useful in itself for our understanding of logic and meaning in general.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ Naturally, logic has moved on considerably since Aristotle's day, as have mathematics and science in general.

.In the first place, it tends to take up an intermediate position between the extremes of Kant and Hegel.^ In the first place, a rationalist accepts any position that can be justified or established or supported by appeal to the rational criteria or authorities.
  • Bartley's 1964 paper on Rationality and the theory of rationality. 18 September 2009 17:23 UTC www.the-rathouse.com [Source type: Original source]

^ In the first place, the argument, if correct, implies that it is pointless from a rational point of view for men to argue rationally about their extremely different “ultimate presuppositions” or commitments.
  • Bartley's 1964 paper on Rationality and the theory of rationality. 18 September 2009 17:23 UTC www.the-rathouse.com [Source type: Original source]

^ We may begin with the problem of distinguishing between 'analytic' and 'synthetic' statements, first addressed by Kant.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

.It does not, with the former, regard logic as purely formal in the sense of abstracting thought from being, nor does it follow the latter in amalgamating metaphysics with logic by identifying being with thought.^ In this wider sense, logically necessary truths are often identified with analytic truths (see above).
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ The question rather is which formal system, in the sense of (L1), best captures the logical truths, in the sense of (L2).
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ This does not mean that ‘believes’ is a logical constant in an absolute sense.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.Secondly, it does not content itself with the mere formulae of thinking, but pushes forward to theories of method, knowledge and science; and it is a hopeful sign to find this epistemological spirit, to which England was accustomed by Mill, animating German logicians such as Lotze, Daring, Schuppe, Sigwart and Wundt.^ So, as we return to the question of the place of Scripture in the organism of revelation, we find that the importance of the Spirit's work does not lie in any limitation of the scopus of Scripture in addition to those limits noted earlier.

^ The alternative interpretation is that such probabilities are degrees of belief, but there is substantial evidence that people's thinking does not conform to probability theory (e.g.
  • Rationality and Science 18 September 2009 17:23 UTC cogsci.uwaterloo.ca [Source type: FILTERED WITH BAYES]

^ And as far as their capacity to " grasp " such 'contradictions' is concerned -- as seems plain -- dialecticians are content merely to label such ambiguous states of affairs "contradictions", and move on.

.Thirdly, there is a determination to reveal the psychological basis of logical processes, and not merely to describe them as they are in adult reasoning, but to explain also how they arise from simpler mental operations and primarily from sense.^ How to handle such phenomenawhich also arise in connection with the so-called propositional attitudes, such as beliefis another widely studied area of philosophical logic.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ And, of course, logic does not tell us how we ought to reason or infer in all particular cases.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ The technical terms in MFL are there for the same reason they are there in modern mathematics.

.This attempt is connected with the psychological turn given to recent philosophy by Wundt and others, and is dangerous only so far as psychology itself is hypothetical.^ However, some philosophers have recently attempted to revive some parts or others of Carnap's ideas.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ However, it must be emphasized that philosophical logic is not really concerned with thought insofar as thought is a psychological processthat, rather, is the province of empirical psychology and the philosophy of mindbut only insofar as thoughts have contents which are evaluable as true or false.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ However, Novack does at least try to make a weak attempt to support what he says in the following with a direct reference to Aristotle (his only one, as far as I can determine): .

Unfortunately, however, these merits are usually connected with a less admirable characteristic - contempt for tradition. .Writing his preface to his second edition in 1888, Sigwart says: " Important works have appeared by Lotze, Schuppe, Wundt and Bradley, to name only the most eminent; and all start from the conception which has guided this attempt.^ To say these things is not to say that Scripture is primarily concerned with reasoning or that the "rationality" of Scripture is its most important quality.

^ Their motivation comes from an attempt to find a simple and systematic theory of all, say, abstract entities, and they can rely on the paradigm of aiming for simplicity in the physical sciences as a guide.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ It will be important for evangelical theologians in the future to work out a concept of Scriptural authority that does justice to this variety in biblical pedagogy.

.That is, logic is grounded by them, not upon an effete tradition but upon a new investigation of thought as it actually is in its psychological foundations, in its significance for knowledge, and its actual operation in scientific methods."^ Knowledge in action : logical foundations for specifying and implementing dynamical systems .
  • http://www.cs.mu.oz.au/482/biblio/Year/2001.complete.html 18 September 2009 8:08 UTC www.cs.mu.oz.au [Source type: Academic]

^ Foundations of mathematics is the study of the most basic concepts and logical structure of mathematics, with an eye to the unity of human knowledge.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ An Investigation of the Laws of Thought on which Are Founded the Mathematical Theories of Logic and Probabilities .
  • Readings in Logic 6 January 2010 10:47 UTC orcmid.com [Source type: Academic]

How strange! .The spirit of every one of the three reforms above enumerated is an unconscious return to Aristotle's Organon. Aristotle's was a logic which steered, as Trendelenburg has shown, between Kantian formalism and Hegelian metaphysics; it was a logic which in the Analytics investigated the syllogism as a means to understanding knowledge and science: it was a logic which, starting from the psychological foundations of sense, memory and experience, built up the logical structure of induction and deduction on the profoundly Aristotelian principle that " there is no process from universals without induction, and none by induction without sense."^ On Nature's Logic, there is no odor.

^ Logic is the science of formal principles of reasoning or correct inference.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ In its definite sense it means that somewhere there is a universally offensive object.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

.Wundt's comprehensive view that logic looks backwards to psychology and forward to epistemology was hundreds of years ago one of the many discoveries of Aristotle.^ On this view, then, the true logical form of 'Mars exists' is 'There is at least one object, x , such that x is identical with Mars'.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ Thus Aristotle seems to have viewed logic not as part of philosophy but rather as a tool or instrument 1 to be used by philosophers and scientists alike.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ Admittedly, throughout its history Logic had been confused by many with an assortment of unrelated disciplines -- such as, Metaphysics, Epistemology, Ontology, Theology, Psychology (and the so-called "Laws Of Thought"), Mathematics, and Science.

I. Judgment and Conception. - .The emphasis now laid on judgment, the recovery from Hume's confusion of beliefs with ideas and the association of ideas, and the distinction of the mental act of judging from its verbal expression in a proposition, are all healthy signs in recent logic.^ Here the judgment as a mental act is assumed to operate on a mental representation that itself has syntactic structure.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Now 6 or 7 months later feeding Natures Logic Lamb kibble, the proof is in the pudding - all of our Clumbers are blooming with better coats, healthy nails, no more grass or dirt eating, and endless stamina.

^ Relevance propositional logic is relatively more recent; dating from the mid-1970s in the work of A. R. Anderson and N. D. Belnap.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

.The most fundamental question, before proceeding to the investigation of inference, is not what we say but what we think in making the judgments which, whether we express them in propositions or not, are both the premises and the conclusion of inference; and, as this question has been diligently studied of late, but has been variously answered, it will be well to give a list of the more important theories of judgment as follows: a.^ And when an inference is formally valid then the conclusion logically follows from the premises.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Of these subordinate questions, the most important has probably been: “What is the nature of the rational authority or criterion to which a rationalist appeals to justify all his opinions?“ The well-known modern theories of knowledge are usually functions of the answers philosophers have given to the question, and fall into two main categories: 1.
  • Bartley's 1964 paper on Rationality and the theory of rationality. 18 September 2009 17:23 UTC www.the-rathouse.com [Source type: Original source]

^ Making business both easy and convenient for your customers as an information technology consultant will help build a long relationship and give you a positive reputation that will bring more customers to you in the future.

.It expresses a relation between the content of two ideas, not a relation of these ideas (Lotze).^ We insist on an important grammatical or logical distinction between these two groups.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ These things and more are magnificent examples of attempts to force a person into choosing between two things that are entirely compatible.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ The relation between science and DM will examined in more detail in Essay Three Part Six, and Essay Thirteen Part Two.

b. .It is consciousness concerning the objective validity of a subjective combination of ideas, i.e. whether between the corresponding objective elements an analogous combination exists (Ueberweg).^ Applications Argumentation [ Back ] The central idea concerning the link between adaptive logics and argumentation is presented in [Bat96] .
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ The laws of logic are the reflections of the objective in the subjective consciousness of man."

c. .It is the synthesis of ideas into unity and consciousness of their objective validity, not in the sense of agreement with external reality but in the sense of the logical necessity of their synthesis (Sigwart).^ Interpretations If we identify "possible worlds" with "interpretation of a first order language", then we get a notion of logical necessity which corresponds to that of first order validity.
  • Geometry.Net - Mathematical_Logic: Logics Admitting Inconsistency 11 October 2009 10:39 UTC www.algebraic.net [Source type: FILTERED WITH BAYES]

^ We discuss some ideas about what "possible worlds" might be, partly to elucidate the character of logical necessity, and partly as an approach to metaphysics and the philosophy of science.
  • Geometry.Net - Mathematical_Logic: Logics Admitting Inconsistency 11 October 2009 10:39 UTC www.algebraic.net [Source type: FILTERED WITH BAYES]

^ In this sense, the concept of logical validity is too general and too intractable to be analyzed thoroughly.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

d. .It is the analysis of an aggregate idea (Gesammtvorstellung) into subject and predicate; based on a previous association of ideas, on relating and comparing, and on the apperceptive synthesis of an aggregate idea in consequence; but itself consisting in an apperceptive analysis of that aggregate idea; and requiring will in the form of apperception or attention (Wundt).^ If an argument's validity depends only on propositional logic relations —structure between, not within, propositions— then don't bother translating it into predicate notation.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ According to Russell's theory, a sentence of the form 'The F is G ' is not really of subject-predicate form at all, but is equivalent rather to an existentially quantified sentence of the form 'There is one and only one F and it is G '.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ The core of the argument used by skeptics and fideists to back their claim consists in a simple analysis of what is commonly regarded as the rational way to defend ideas.
  • Bartley's 1964 paper on Rationality and the theory of rationality. 18 September 2009 17:23 UTC www.the-rathouse.com [Source type: Original source]

e. .It requires an idea, because every object is conceived as well as recognized or denied; but it is itself an assertion of actual fact, every perception counts for a judgment, and every categorical is changeable into an existential judgment without change of sense (Brentano, who derives his theory from Mill except that he denies the necessity of a combination of ideas, and reduces a categorical to an existential judgment).^ Evidently, though, this kind of explanation is not available to someone who favours the so-called 'direct' theory of reference, according to which names do not possess descriptive 'senses'.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ This is because predicate expressions can only be turned into 'referring' expressions by changing them into singular terms , which is a move that destroys their original non-referential (i.e., descriptive) status.

^ So, unless we believe that the future can change the present (arguing that the fact that night is hours away allows it to 'back-cause' day to change into night!

f. .It is a decision of the validity of an idea requiring will (Bergmann, following Brentano).^ With respect to this argument schema, the only condition validity requires is the following: if, for a given interpretation, the premisses are true then the conclusion is true.

g. .Judgment (Urtheil) expresses that two ideas belong together: " by-judgment " (Beurtheilung) is the reaction of will expressing the validity or invalidity of the combination of ideas (Windelband, following Bergmann, but distinguishing the decision of validity from the judgment).^ Each syllogism corresponds to a logically valid implication where and are formulas expressing the two premises and expresses the conclusion.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

h. .Judgment is consciousness of the identity or difference and of the causal relations of the given; naming the actual combinations of the data, but also requiring a priori categories of the understanding, the notions of identity, difference and causality, as principles of thought or laws, to combine the plurality of the given into a unity (Schuppe).^ Next one studies the sophistication required by combination of the different levels.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ This doctrine requires one to distinguish sharply between existence and actuality , treating the latter as an indexical notion akin to those expressed by the words 'here' and 'now'.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ Difference and identity are, according to these two rules of formal logic, completely different, utterly disconnected, mutually exclusive characteristics of both things and thoughts.

i. .Judgment is the act which refers an ideal content recognized as such to a reality beyond the act, predicating an idea of a reality, a what of a that; so that the subject is reality and the predicate the meaning of an idea, while the judgment refers the idea to reality by an identity of content (Bradley and Bosanquet).^ We can justify our beliefs by reference to the objectivity of creation, as long as we accept God's criteria for objectivity and recognize the problematics of approaching that objective world through a fallible subjectivity.

^ But whether there really is any such characteristic is debatable, because many philosophers would now agree with Frege and Russell that '- exists' is not a first-level predicate.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ In contrast, a synthetic statement, for Kant, is one in which the concept of the predicate is not already contained in the concept of the subject, such as the statement that foxes are carnivorous.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

k. Judgment is an assertion of reality, requiring comparison and ideas which render it directly expressible in words (Hobhouse, mainly following Bradley).
.These theories are of varying value in proportion to their proximity to Aristotle's point that predication is about things, and to Mill's point that judgments and propositions are about things, not about ideas.^ [Notice once again the confused idea that the LEM is about things , and not propositions.

^ These predicates are the primitives of the theory.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ The central chapter on predicate logic is followed by chapters outlining various alternative, but essentially equivalent ways of constructing the semantics for first-order logic as well as its proof theory.
  • http://www.cs.mu.oz.au/482/biblio/Year/2001.complete.html 18 September 2009 8:08 UTC www.cs.mu.oz.au [Source type: Academic]

.The essence of judgment is belief that something is (or is not) determined, either as existing (e.g.^ For him a thing either exists or does not exist; a thing cannot at the same time be itself and something else.

" I am," " A centaur is not ") or as something in particular (e.g. " I am a man," " I am not a monkey "). .Neither Mill, however, nor any of the later logicians whose theories we have quoted, has been able quite to detach judgment from conception; they all suppose that an idea, or ideas, is a condition of all judgment.^ However, the idea of basing all of mathematics on one simple concept, sets, has exerted a powerful attraction.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ However, s is derived at stage 11 (and at all later stages).
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ However, a couple of the teams had a bumpy week...Determine the name of each team, the number of games each played this week, if they were at their home stadium or traveling all week, the number of games each team won, and the number of games each team lost.

.But judgment starts from sensation (Empfindung) and feeling (Gefiihl), and not from idea (Vorstellung). When I feel pleased or pained, or when I use my senses to perceive a pressure, a temperature, a flavour, an odour, a colour, a sound, or when I am conscious of feeling and perceiving, I cannot resist the belief that something sensible is present; and this belief that something exists is already a judgment, a judgment of existence, and, so far as it is limited to sense without inference, a true judgment.^ Strictly speaking, rules of replacement differ from inference rules, because, in a sense, when a rule of replacement is used, one is not inferring something new but merely stating what amounts to the same thing using a different combination of symbols.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ One idea to answer this is to employ the notion of a ‘constitutive aim of belief’, the idea that belief as such aims at something: the truth.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Still other limitations are said to be connected with our historical existence and with the impossibility of predicting the historical future because—among other reasons—we cannot predict the future growth of human knowledge.
  • Bartley's 1964 paper on Rationality and the theory of rationality. 18 September 2009 17:23 UTC www.the-rathouse.com [Source type: Original source]

.It is a matter of words whether or not we should call this sensory belief a judgment; but it is no matter of choice to the logician, who regards all the constituents of inference as judgments; for the fundamental constituents are sensory beliefs, which are therefore judgments in the logical sense.^ The Liar Paradox and Beyond Paraconsistency and Theology Though such a deprecation of consistency is a novelty for logicians, it is in a sense well familiar to theologians who have generally preferred biblical fidelity to logical consistency.
  • Geometry.Net - Mathematical_Logic: Logics Admitting Inconsistency 11 October 2009 10:39 UTC www.algebraic.net [Source type: FILTERED WITH BAYES]

^ And if, since the limitation is a logical one, all men share it, if no one can escape irrational commitment, then no one can be criticized rationally for having made such a commitment, no matter how idiosyncratic.
  • Bartley's 1964 paper on Rationality and the theory of rationality. 18 September 2009 17:23 UTC www.the-rathouse.com [Source type: Original source]

^ A contrary view holds that which expressions are treated as logical constants is a matter of choice, with different choices serving different purposes.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.Sense is the evidence of inference; directly of analogical and inductive, directly or indirectly of deductive, inference; and therefore, if logic refuses to include sensory beliefs among judgments, it will omit the fundamental constituents of inference, inference will no longer consist of judgments but of sensory beliefs plus judgments, and the second part of logic, the logic of judgment, the purpose of which is to investigate the constituents of inference, will be like Hamlet without the prince of Denmark.^ JOHN SAFER Logical or not, Shakespeare’s prince has a lasting appeal William Shakespeare undoubtedly achieved one of his greatest characterizations when he created the role of Hamlet, the gloomy Prince of Denmark.
  • Geometry.Net - Mathematical_Logic: Logics Admitting Inconsistency 11 October 2009 10:39 UTC www.algebraic.net [Source type: FILTERED WITH BAYES]

^ Lecture on the consistency of the continuum hypothesis (Brown University) [Gödel*1940a] In what sense is intuitionisstic logic constructive?
  • Readings in Logic 6 January 2010 10:47 UTC orcmid.com [Source type: Academic]

^ Now that he has become acclimated to Nature's Logic, he no longer vomits bile.

.If, on the other hand, all the constituents of inference are judgments, there are judgments of sense; and the evidence of the senses means that a judgment of sense is true, while a judgment of inference is true so far as it is directly or indirectly concluded from judgments of sense.^ On the true interpretation, it means 'There is one and only one number which numbers the planets and it is necessarily greater than seven'.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ But in its indefinite sense it means that everyone is offended by something or other, not necessarily by the same thing, perhaps each by a different thing.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ "Who is right? Is there more than one meaning of the word 'around?' That's a surprise! That's like discovering more than one true system of geometry. How many meanings are there and which one is right?
  • The Prodigy Review - Bio: Life of William James Sidis 18 September 2009 8:08 UTC www.quantonics.com [Source type: General]

Now a sensory judgment, e.g. that a sensible pressure is existing, is explained by none of the foregoing theories, because it requires nothing but sensation and belief. .It requires no will, but is usually involuntary, for the stimulus forces one's attention, which is not always voluntary; not all judgment then requires will, as Wundt supposes.^ Since any voluntary response to Scripture involves reasoning (good or bad), we must say that Scripture requires a rational response; the alternative is to claim that Scripture requires no voluntary response at all.

^ If we then add “The Limit Assumption”, that for each world i , there is always at least one world as good as all worlds (i.e., one i-best world), we can easily generate our earlier semantics for SDL derivatively.
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

.It requires no reference to reality beyond the sensible pressure, because it is merely a belief that this exists without inference of the external stimulus or any inference at all: not all judgment then requires the reference of subjective to objective supposed by Ueberweg, or the consciousness of logical necessity supposed by Sigwart.^ The laws of logic are the reflections of the objective in the subjective consciousness of man."

^ And if one holds that one of the crucial features of logically valid inferences is that they preserve truth then one could argue that the logical laws are norms that apply to those who have beliefs.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ No, this process will always exist and be practiced on the fringes--there will never be more than a handful of people who are qualified to use this process, requiring as it does an extensive background in art, science, mathematics, logic, and computers.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

.It requires in addition to the belief that something exists, no consideration as to whether the belief itself be true, because a man who feels pressure believes in the thing without further question about the belief: not all judgment then requires a decision of validity, as Bergmann supposes.^ Affirming the consequent : Claiming that because the result of something is true, the original statement must also be true.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ No, this process will always exist and be practiced on the fringes--there will never be more than a handful of people who are qualified to use this process, requiring as it does an extensive background in art, science, mathematics, logic, and computers.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

^ This might seem absurd at first sight, because 'a man is not white' looks as if it signifies also at the same time that no man is white; this, however, does not signify the same, nor does it necessarily hold at the same time."

.It requires nothing beyond the sensation and belief in the given existence of the given pressure: not all judgment then requires categories of understanding, or notions of identity, difference and causality, or even of existence, such as Schuppe supposes.^ Even if redemption has nothing to do with the universe, does a "focus" on such redemption exclude incidental reference to things in the universe?

^ To talk about the form of a judgment will involve a subtle different notion of ‘form’ than to talk about the form of a linguistic representation.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ "It is the recognition of this 'identity of all ( logical pairs of) opposites ,' and in the further recognition that all categories form, logically, a series from the Absolutely Universal to the Absolutely Unique -- (in each of which opposites its other is implicit) -– that the virtue of Hegel's logic consists….

.It requires no comparison in order to express it in words, for a judgment need not be expressed, and a sensory judgment of pressure is an irresistible belief that a real pressure exists, without waiting for words, or for a comparison which is wanted not to make a sensation a judgment, but to turn a judgment into language: not all judgment then requires comparison with a view to its expression, as supposed by Hobhouse.^ As with practical judgments of emotional coherence in practical decision making, we have no direct conscious access to the cognitive processes by which we judge some hypotheses to be more coherent than others.
  • Rationality and Science 18 September 2009 17:23 UTC cogsci.uwaterloo.ca [Source type: FILTERED WITH BAYES]

^ But, in order to be clear about its import, the use of the word "true" in such contexts will need clarification.

^ Any attempt to do so would demote these general terms and would thus turn these allegedly "general features of reality" into abstract particulars (as we saw in Essay Three ) --, at the same time as robbing language of its capacity to express generality (by turning predicates into singular terms).

.Lastly, all the authors of the above-quoted theories err in supposing that all judgment requires conception; for even Mill thinks a combination of ideas necessary, and Brentano, who comes still nearer to the nature of sensory judgment when he says, " Every perception counts for a judgment," yet thinks that an idea is necessary at the same time in order to understand the thing judged.^ "It is also evident that it is not possible to opine and to understand the same thing at the same time.

^ Nevertheless, the authors of DB advance certain claims (which TAR quotes approvingly; e.g., p.4) that require brief comment: .

^ At the same time the fact that I have to begin upon the process of distinguishing implies…that, apart from his special distinguishing characteristics, John is identical with all the not -Johns who comprise the rest of the human race.

.In reality, the sensation and the belief arc sufficient; when I feel a sensible pressure, I cannot help believing in its reality, and therefore judging that it is real, without any tertium quid - an idea of pressure, or of existence or of pressure existing - intervening between the sensation and the belief.^ Keypad Pascal's Wager for Believing in God For years people have contemplated the idea of a supreme being and the existence of heaven and hell.

^ Short of that , the idea that there is a link between the way we draw conclusions and fundamental aspects of reality loses all credibility.

^ But worse: are we really supposed to believe that this sub-Aristotelian syntactic jumble encapsulates ideas that lie at the very cutting edge of modern science?

.Only after sensation has ceased does an idea, or representation of what is not presented, become necessary as a substitute for a sensation and as a condition not of the first judgment that there is, but of a second judgment that there was, something sensible.^ ROp = df BA~ p NRp = df ~BA~ p NBp = df ~BAp PVp = df ~BAp & ~BA~ p The first says that it is ruled out by what our agent does that p if and only if our agent brings it about that ~ p .
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

^ Modus tollens assures us that p É q asserts that p is true only if q is true, or that q is the necessary condition of p.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ We can now clearly and distinctly express the idea that something is simply out of Jane Doe's jurisdiction.
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

.Otherwise there would be no judgment of sensible fact, for the first sensation would not give it, and the idea following the sensation would be still farther off.^ And, he argues in (Yablo 1998), since there is no fact about this distinction, ontology, in the sense of (O2), rests on a mistake and is to be rejected, as Carnap did.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Again, in the latter case, there would be nothing left to modify ; in the former, no one need bother.

^ Or, that there are any other logicians (who are not still in the "care of the community") who would accept this caricature of the LEM? No wonder they failed to provide a reference for their fictional 'version' of it.

.The sensory judgment then, which is nothing but a belief that at the moment of sense something sensible exists, is a proof that not all judgment requires conception, or synthesis or analysis of ideas, or decision about the content, or about the validity, of ideas, or reference of an ideal content to reality, as commonly, though variously, supposed in the logic of our day.^ It is, he says, impossible to give a proof “that what we regard as rational procedure really is so; that our conception of what constitutes good evidence is right.”[16] Whatever its faults, Ayer’s approach does possess the initial advantage of honesty about the unjustifiability of ultimate standards and principles.
  • Bartley's 1964 paper on Rationality and the theory of rationality. 18 September 2009 17:23 UTC www.the-rathouse.com [Source type: Original source]

^ That this set exists, perfectly defined a priori , adds to the sense that this is all "found art" that exists, and always has existed, in the immutable formalism of that predefined set.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

^ "Valid" refers to the chain of reasoning, the logic part of the argument.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

.Not, however, that all judgment is sensory: after the first judgments of sense follow judgments of memory, and memory requires ideas.^ "It is necessary to ask, first of all, whether and in what sense the fact that A necessarily relates to what is not-A permits us to insert not-A in A .

^ However, the grammar of (6) looks decidedly odd at first sight, so much so that it is debatable whether (6) really makes sense at all.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ However, the idea of basing all of mathematics on one simple concept, sets, has exerted a powerful attraction.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

Yet memory is not mere conception, as Aristotle, and Mill after him, have perceived. .To remember, we must have a present idea; but we must also have a belief that the thing, of which the idea is a representation, was (or was not) determined; and this belief is the memorial judgment.^ In that case, one is tempted to say that the idea that there is such a thing as 'commonsense' must be a "scientistic folk belief" itself , since it is not based on any clear evidence --, at least none that is not 'tainted' with the sorts of ideas many would include in 'commonsense', too.

.Originally such judgments arise from sensory judgments followed by ideas, and are judgments of memory after sense that something sensible existed, e.g. pressure existed: afterwards come judgments of memory after inference, e.g. Caesar was murdered.^ There exist examples of such artworks--the pure output of a computer program--wherein it is readily evident that something of the artist's soul has been bared.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

^ For instance, Kripke holds that if an identity statement such as 'Water is H 2O' is true, then it is necessarily truein the sense that it is true in every possible world in which water exists.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ An example of an important issue which arises under this heading is the question of how existential statements should be understoodstatements such as 'Mars exists' and 'Dogs exist'.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

Finally, most judgments are inferential. .These are conclusions which primarily are inferred from sensory and memorial judgments; and so far as inference starts from sense of something sensible in the present, and from memory after sense of something sensible in the past, and concludes similar things, inferential judgments are indirect beliefs in being and in existence beyond ideas.^ Dialectical logic moves beyond formal logic by starting not with 'things' but with processes, processes of coming into being and passing out of being.

^ To say these things is not to say that Scripture is primarily concerned with reasoning or that the "rationality" of Scripture is its most important quality.

^ But we must also say that, not only the conclusions, but also the premisses, the presuppositions, the starting points of these sciences are subject to ethical- ultimately religious- evaluation.

.When from the sensible pressures between the parts of my mouth, which I feel and remember and judge that they exist and have existed, I infer another similar pressure (e.g.^ Another is to ask for an explanation of the structural similarity between the general features of thought and the general features of reality.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Or would this recommendation reveal yet another failure to "understand" dialectics on my part?

^ "We hope that many mathematicians will pick up this book out of idle curiosity and leaf through it to get a feeling for what is going on in another part of mathematics.
  • Readings in Logic 6 January 2010 10:47 UTC orcmid.com [Source type: Academic]

of the food which presses and is pressed by my mouth in eating), the inferential judgment with which I conclude is a belief that the latter exists as well as the former (e.g. the pressure of food without as well as the sensible pressures within). .Inference, no doubt, is closely involved with conception.^ This conception of logic can, however, be closely associated with the one that takes logic to be fundamentally about certain kinds of inferences and about logical consequence.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

So far as it depends on memory, an inferential judgment presupposes memorial ideas in its data; and so far as it infers universal classes and laws, it produces general ideas. But even so the part played by conception is quite subordinate to that of belief. .In the first place, the remembered datum, from which an inference of pressure starts, is not the conceived idea, but the belief that the sensible pressure existed.^ An idea which is conceived of and which exists is better than one which is only imagined.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

.Secondly, the conclusion in which it ends is not the general idea of a class, but the belief that a class, represented by a general idea, exists, and is (or is not) otherwise determined (e.g.^ I f a writer derives a general conclusion on the basis of just a few examples that are not representative of all possible situations, cases, or scenarios, then s/he is guilty of hasty generalization .
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

that things pressing and pressed exist and move). .Two things are certain about inferential judgment: one, that when inference is based on sense and memory, inferential judgment starts from a combination of sensory and memorial judgment, both of which are beliefs that things exist; the other, that in consequence inferential judgment is a belief that smiliar things exist.^ By the same token, existentially quantified negated conjunctions are usually inaccurate translations, since they are equivalent to conditionals (one conjunct as the antecedent, the other conjunct, negated, as the consequent).
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ In this sense we associate "form" neither with the representation that is involved in the judgment, nor with the proposition which is its content, but rather with the world that is judged about.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Formal ontologies could also only have axioms that state how the things the theory is about, whatever they may be, relate to each other, but no axioms that state that certain things exist.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.There are thus three primary judgments: judgments of sense, of memory after sense, and of inference from sense.^ Thus there will be one formal language that best models what logically valid inferences there are among these natural representations.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Thus even though there are formal logical systems, in the sense of (L1) in which there are logical truths that are existential statements, this does not answer the question whether or not there are logical truths, in the sense of (L2), that are existential statements.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ For one, of course, there is an issue about what it means to say that judgments have a form, and whether they do in the relevant sense.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.All these are beliefs in being and existence, and this existential belief is first in sense, and afterwards transferred to memory and inference.^ In a very broad sense of the term 'name', names traditionally divide into two classesproper names and common names, these being species of singular and general terms respectively.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ "It is necessary to ask, first of all, whether and in what sense the fact that A necessarily relates to what is not-A permits us to insert not-A in A .

^ These are all problems in ontology in the sense that they deal with whether or not a certain thing, or more broadly entity, exists.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.Moreover, it is transferred in the same irresistible way: frequently we cannot help either feeling pressure, or remembering it, or inferring it; and as there are involuntary sensation and attention, so there are involuntary memory and inference.^ Moreover, this way of depicting things brings underlines the fact that a singular term like "The concept green" cannot express a rule, whereas "ξ is green" can.

^ This proposition states: 'A is either A or not A.' It cannot be both at the same time.

^ For him a thing either exists or does not exist; a thing cannot at the same time be itself and something else.

Again, in a primary judgment existence need not be expressed; but if expressed, it may be expressed either by the predicate, e.g. " I exist," or by the subject, e.g. " I who exist think." .There are indeed differences between primary judgments, in that the sensory is a belief in present, the memorial in past, and the inferential in present, past and future existence.^ So there is no difference between them."
  • English Composition 1: Logical Argument 6 January 2010 10:47 UTC papyr.com [Source type: FILTERED WITH BAYES]

^ If we read d atemporally as all obligations past, present, and future are met, then the only relevant worlds are those so ideal that in them there has never been a single violation of a mandatory norm.
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

^ If 'commonsense' beliefs were culturally 'relative', each generation would possess a different, or slightly different, set of 'commonsense' beliefs -- even if there were some overlap.

.But these differences in detail do not alter the main point that all these are beliefs in the existing, in the real as opposed to the ideal, in actual things which are not ideas.^ In order to overcome the problem of relativism, some advocates of the coherence theory suggest that the notion of truth is a regulative ideal, which could only be realized in a unified and completed science far in advance of the partial belief-systems of any human community that actually exists or is ever likely to.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ Other philosophers are 'actualists', maintaining that the only entities that exist at all are entities that actually exist.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ These are all problems in ontology in the sense that they deal with whether or not a certain thing, or more broadly entity, exists.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.In short, a primary judgment is a belief in something existing apart from our idea of it; and not because we have an idea of it, or by comparing an idea with, or referring an idea to, reality; but because we have a sensation of it, or a memory of it or an inference of it.^ One idea to answer this is to employ the notion of a ‘constitutive aim of belief’, the idea that belief as such aims at something: the truth.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ This is because beliefs themselves are dependent on language and thus on our capacity to articulate them accordingly.

^ The idea of dispensing with the justification of beliefs is often dismissed out of hand, on the grounds that this is the primary topic of philosophy.
  • Bartley's 1964 paper on Rationality and the theory of rationality. 18 September 2009 17:23 UTC www.the-rathouse.com [Source type: Original source]

Sensation, not conception, is the origin of judgment.
2. Dif f erent Significations of Being in dif f erent Kinds of Judgment. - .As Aristotle remarked both in the De Interpretatione and in the Sophistici Elenchi, " not-being is thinkable " does not mean " not-being exists."^ I have been unable to find the term "Monadic predicate" in Aristotle, but that does not mean he did not use monadic predicates.

^ De Interpretatione , in Aristotle (1984a), Volume One, pp.25-38.

.In the latter treatise he added that it is a fallacia a dicto secundum quid ad dictum simpliciter to argue from the former to the latter; " for," as he says, it is not the same thing to be something and to exist absolutely."^ This says that something in particular is attracted by everything, which is the same as saying that everything attracts some particular thing.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ Finally, on Novack: Aristotle says that "It is also evident that it is not possible to opine and to understand the same thing at the same time....", and with reference to Novack, at least, I think we can agree with Aristotle on that.

^ But in its indefinite sense it means that everyone is offended by something or other, not necessarily by the same thing, perhaps each by a different thing.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

.Without realizing their debt to tradition, Herbart, Mill and recently Sigwart, have repeated Aristotle's separation of the copula from the verb of existence, as if it were a modern discovery that " is " is not the same as " exists."^ At the same time, the failure of the rationalist tradition to resolve crisis of integrity enables many irrationalists, whatever their affiliations, preserve their own identities without loss of integrity.
  • Bartley's 1964 paper on Rationality and the theory of rationality. 18 September 2009 17:23 UTC www.the-rathouse.com [Source type: Original source]

.It may be added that they do not quite realize what the copula exactly signifies: it does not signify existence, but it does signify a fact, namely, that something is (or is not) determined, either absolutely in a categorical judgment, or conditionally in a conditional judgment.^ They talked about how in artificial vitamins the body does not get the whole vitamin complex and ...this may do more harm than good.

^ Due to the constraints of their cars, they listen to the books in a variety of ways...Determine the full name of each commuter, the title and genre of each book, and in what format each listens to their audio book.

^ Any premise may be added to the proof with Ø (the empty set) as its condition.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

.Now we have seen that all primary judgments signify more than this fact; they are also beliefs in the existence of the thing signified by the subject.^ They talked about how in artificial vitamins the body does not get the whole vitamin complex and ...this may do more harm than good.

^ Now Robin links to a clever study showing that this is more than just self-deception: In our...
  • EconLog: Behavioral Economics and Rationality Archives 18 September 2009 17:23 UTC econlog.econlib.org [Source type: General]

^ These are all problems in ontology in the sense that they deal with whether or not a certain thing, or more broadly entity, exists.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.But, in the first place, primary judgments signify this existence never by the copula, but sometimes by the predicate, and sometimes by the subject; and, secondly, it does not follow that all judgments whatever signify existence.^ The main point here is that, in the predicate calculus, a subject is always an individual entity, never a class of entities.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ In the first half of C5, the concept green is expressed by the use of the one-place predicable "ξ is green", which, when applied as a rule, forms the first clause of C5.

^ Sometimes an argument does not use all the structure we can express with our notation.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

.Besides inference of existence there is inference of non-existence, of things inconsistent with the objects of primary judgments.^ According to the objectual interpretation, 'There is at least one thing which is F ' is true just in case some object in the domain of discourse is F .
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ Plato seemed to insist that mathematical objects, like the Platonic forms or essences, must be perfectly abstract and have a separate, non-material kind of existence.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ But, such inferences have only ever been justified by nominalisations of this sort -- ones that conjure into existence objects at the drop of a noun.

.Hence secondary judgments, which no longer contain a belief that the thing exists, e.g. the judgment, " not-being is thinkable," cited by Aristotle; the judgment, " A square circle is impossible," cited by Herbart; the judgment, " A centaur is a fiction of the poets," cited by Mill.^ It is worth noting that the authors of DB cite no sources for their views (primary or secondary) -- and no wonder, that would have disconfirmed the picture they wished to paint.

^ Formal ontologies could also only have axioms that state how the things the theory is about, whatever they may be, relate to each other, but no axioms that state that certain things exist.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ And, of course, if day is no longer day, but is twilight, then the above "A" (day) is not in fact "A and not A", it is "C" (twilight) --, hence it is not "A and B" either.

These secondary judgments of nonexistence are partly like and partly unlike primary judgments of existence. They resemble them in that they are beliefs in being signified by the copula. .They are beliefs in things of a sort; for, after all, ideas and names are things; their objects, even though non-existent, are at all events things conceivable or nameable; and therefore we are able to make judgments that things, non-existent but conceivable or nameable, are (or are not) determined in a particular manner.^ And they all seem to make the very same sort of claims .

^ This always-anticipated event has had the student gossip buzzing all week...Determine the full name of each couple, and whether the Senior Prom is each couples first date or if theyd been dating previously.

^ Senior Prom Night Senior Prom Night was last night and the event was an enjoyable evening for all who participated.

Thus the judgment about a centaur is the belief, " A conceivable centaur is a fiction of the poets," and the judgment about a square circle is the belief, " A so-called square circle is an impossibility." .But, though beliefs that things of some sort are (or are not) determined, these secondary judgments fall short of primary judgments of existence.^ If our universe contains some things that are A's but not B's, and other things that are B's but not A's, and nothing that is neither, then the first of these expressions will be false and the second true.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ The English speaker was non-committal on the existence of things that might fall into black holes; these formulas commit themselves to the existence of something.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

.Whereas in a primary judgment there is a further belief, signified by subject or predicate, that the thing is an existing thing in the sense of being a real thing (e.g.^ And we will take the subject-predicate structure of though, and the object-property structure of reality as our example.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ But we have at least two parts to the overall philosophical project of ontology: first, say what there is, what exists, what the stuff is reality is made out off, secondly, say what the most general features and relations of these things are.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Reality being what it is, we cannot expect most truths to admit of foundation purely within logic in such a sense."
  • Readings in Logic 6 January 2010 10:47 UTC orcmid.com [Source type: Academic]

a man), different from the idea of it as well as from the name for it; in a secondary judgment there is no further belief that the thing has any existence beyond the idea (e.g. a centaur), or even beyond the name (e.g. a square circle): though the idea or name exists, there is no belief that anything represented by idea or name exists. .Starting, then, from this fundamental distinction between judgments of existence and judgments of non-existence, we may hope to steer our way between two extreme views which emanate from two important thinkers, each of whom has produced a flourishing school of psychological logic.^ The difference between the two is subtle, but important logically.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ On such a view, what practical distinction could be drawn between the word of God and my own wisdom, imagination, reasoning?

^ A formal system is a sort of game; it is a fundamental concept of mathematical, or formal logic.  [2] For our purposes we may think of a formal system as a set of given input strings, called axioms , along with a set of rules for performing transformations on, or changes to, those strings.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

.On the one hand, early in the igth century Herbart started the view that a categorical judgment is never a judgment of existence, but always hypothetical; on the other hand, in the latter part of the century Brentano started the view that all categorical judgments are existential.^ On the one hand Rosa shows up the shameful ignorance of a century of Marxism-Leninism, marshalling in the process a prodigious array of sources on logic and mathematics, and also on the sciences, information that is urgently needed by her audience in view of the ignorance she contests.

^ But if they are about a universal not taken universally it is not always the case that one is true and the other false.

^ According to Russell's theory, a sentence of the form 'The F is G ' is not really of subject-predicate form at all, but is equivalent rather to an existentially quantified sentence of the form 'There is one and only one F and it is G '.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

The truth lies between these contraries. .The view of Herbart and his school is contradicted by our primary judgments of and from sense, in which we cannot help believing existence; and it gives an inadequate account even of our secondary judgments in which we no longer indeed believe existence, but do frequently believe that a nonexistent thing is (or is not) somehow determined unconditionally.^ It is worth noting that the authors of DB cite no sources for their views (primary or secondary) -- and no wonder, that would have disconfirmed the picture they wished to paint.

^ However, as we shall see in Essay Five , DL cannot even account for the motion of domestic pets , mat or no mat; Diamat or no Diamat.

^ Laws of logic (which are necessarily ruled in) as well as contradictions (which are necessarily ruled out) are not things that are ruled out by our agent.
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

.It is true, as Herbart says, that the judgment, " A square circle is an impossibility," does not contain the belief, " A square circle is existent "; but when he goes on to argue that it means, " If a square circle is thought, the conception of impossibility must be added in thought," he falls into a non-sequitur. To be categorical, a judgment does not require a belief in existence, but only that something, existent or not, is (or is not) determined; and there are two quite different attitudes of mind even to a non-existent thing, such as a square circle, namely, unconditional and conditional belief.^ So, there must be an i -acceptable world, say j , where OB p is true, but p is false.
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

^ The two different meanings of "something": "A solution to this problem" and "A thing" are mixed and said to be the same.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ If an honest person says something, it must be true.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

.The judgment, " A non-existent but so-called square circle is an impossibility," is an unconditional, or categorical judgment of non-existence, quite different from any hypothetical judgment, which depends on the conditions " if it is thought," or " if it exists," or any other " if."^ There are several quite different topics put under the heading of ‘logic’ in contemporary philosophy, and it is controversial how they relate to each other.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Such a view of thoughts is commonly called the Language of Thought hypothesis, and if it is correct then in the language of thought there might be logical and non-logical vocabulary.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Sometimes a proposition which commits itself to the existence of something ("UFO's exist") is made the antecedent of a conditional ("If UFO's exist, then our ammonia supplies are in jeopardy").
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

.On the other hand, the view of Brentano and his school is contradicted by these very categorical judgments of non-existence; and while it applies only to categorical judgments of existence, it does so inadequately.^ The forming of judgments, conclusions and inferences is not limited to academic or theoretical activities[56].  It does not occur only when we are composing syllogisms; nor is it limited to "thinking," if by thinking we mean puzzling ourselves about some problem or other.

^ The English speaker was non-committal on the existence of things that might fall into black holes; these formulas commit themselves to the existence of something.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ Note that this notion does not apply to all things that are ruled out per se , but only to those that are specifically ruled out by our agent's exercise of her agency.
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

.To begin with the latter objection, Brentano proposed to change the four Aristotelian forms of judgment, A, E, I, 0, into the following existential forms: A. "There is not an immortal man."^ According to Russell's theory, a sentence of the form 'The F is G ' is not really of subject-predicate form at all, but is equivalent rather to an existentially quantified sentence of the form 'There is one and only one F and it is G '.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ It follows that there are two ways to be non-committal about the existence of something: (1) use a universal quantifier, or (2) use an existential quantifier in the antecedent of a conditional.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ For one, of course, there is an issue about what it means to say that judgments have a form, and whether they do in the relevant sense.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

E. "There is not a live stone." I. " There is a sick man." O. "There is an unlearned man." .This reconstruction, which merges subject and predicate in one expression, in order to combine it with the verb of existence, is repeated in similar proposals of recent English logicians.^ In doing this, he ends up in no little confusion, which is, of course, one of the reasons modern logicians have had to re-think the whole subject from the floor up.

^ In contrast, a synthetic statement, for Kant, is one in which the concept of the predicate is not already contained in the concept of the subject, such as the statement that foxes are carnivorous.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ According to Russell's theory, a sentence of the form 'The F is G ' is not really of subject-predicate form at all, but is equivalent rather to an existentially quantified sentence of the form 'There is one and only one F and it is G '.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

.Venn, in his Symbolic Logic, proposes the four forms, xy = o, xy = o, xy>o, xy> o (where y means " not-y "), but only as alternative to the ordinary forms.^ That a logic assigns the trivial consequence set to some set of premises means that, in semantic terms, the set of premises has no models or that its only model is the trivial one.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ This can only mean that this criticism itself (written in ordinary language, it seems) suffers from the same unspecified 'limitations' this critic claims to have found in the vernacular.

^ In some adaptive logics that handle such gluts all formulas of the form (2) are abnormalities, in other adaptive logics only a subset of formulas of the form (2) count as abnormalities.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

.Bradley says that " ` S-P is real' attributes S-P, directly or indirectly, to the ultimate reality," and agrees with Brentano that " ` is ' never stands for anything but ` exists ' "; while Bosanquet, who follows Bradley, goes so far as to define a categorical judgment as " that which affirms the existence of its subject, or, in other words, asserts a fact."^ In fact, Aristotle says the opposite of what Novack attributes to (him and) FL. .

^ And as far as "Byzantine jargon" is concerned, anyone who reckons they can learn something ( anything ) from Hegel's Logic , as these two do, has little room to accuse others of excessive devotion to jargon.

^ But whether there really is any such characteristic is debatable, because many philosophers would now agree with Frege and Russell that '- exists' is not a first-level predicate.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

.Now it is true that our primary judgments do contain a belief in existence; but they do not all contain it in the same way, but are beliefs sometimes that something is determined as existing, and sometimes that something existing is particularly determined.^ With reasoning like that you might as well argue that if a metre rule, say, has been made incorrectly the same must be true of all it measures!

^ (For one thing, much of the time they say "logic" when they mean "rationality"; they aren't the same thing at all.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ For him a thing either exists or does not exist; a thing cannot at the same time be itself and something else.

.Brentano's forms do not express such a judgment of existence, as " All existing men are mortal ": nor does Bradley's form, " Reality includes S-P." Metaphysically, all realities are parts of one ultimate reality; but logically, even philosophers think more often only of finite realities, existing men, dogs, horses, &c.; and children know that their parents exist long before they apprehend ultimate reality.^ This proposition forms one basis of logic.

^ All men are mortal.

^ We often form judgments, etc.

.The normal form, then, of a judgment of existence is either " S is a real P," or " A real S is P." Hence the reconstruction of all categorical judgments by merging subject and predicate, either on Brentano's or on Bradley's plan, is a misrepresentation even of normal categorical judgments of existence.^ The second form is more accurately called Irrelevant Authority, Inappropriate Authority, or Questionable Authority, and is citing someone as an expert even though they are not really an expert on the question under discussion.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ A predicate logic expression is in prenex normal form if (1) all its quantifiers are clustered at the left, (2) no quantifier is negated, (3) the scope of each quantifier extends to the right end of the expression, (4) no two quantifiers use the same variable, (5) every letter used by a quantifier is used later in the expression as a bound variable.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ For example, an individual man can be treated as a subject, but the class of all men must be treated as a predicate.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

Secondly, it is much more a misrepresentation of categorical judgments of non-existence. .No existential form suits a judgment such as " A centaur is a fiction," when we do not believe that there is a centaur, or that reality includes a centaur.^ There's no point voting for someone who can't win.Now consider how this applies to Singapore, where even second parties have no real prospect of winning.
  • EconLog: Behavioral Economics and Rationality Archives 18 September 2009 17:23 UTC econlog.econlib.org [Source type: General]

^ In fact, no one but a Dooyeweerdian would believe that there are such things as modal qualifications.

^ Thus for a believer in logical objects there can be no empty domain.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.As Mill pointed out, it cannot be implied that a centaur exists, since the very thing asserted is that the thing has no real existence.^ Indeed, that word is said to have unspecified universal inadequacies, which 'shortcomings' must of necessity feature in the very act of pointing this alleged fact out -- nullifying that criticism.

^ It is worth pointing out again that in all of this, the distinction between "not A" (predicate negation) and "not-A" (predicate-term negation) has been ignored, since Lawler and other DM-fans seem to be unaware of it.

^ There's no point voting for someone who can't win.Now consider how this applies to Singapore, where even second parties have no real prospect of winning.
  • EconLog: Behavioral Economics and Rationality Archives 18 September 2009 17:23 UTC econlog.econlib.org [Source type: General]

.In a correspondence with Mill, Brentano rejoined that the centaur exists in imagination; Bradley says, " inside our heads."^ The more we feel out of control, the more our brains imagine patterns that don't really exist.
  • EconLog: Behavioral Economics and Rationality Archives 18 September 2009 17:23 UTC econlog.econlib.org [Source type: General]

.According to one, then, the judgment becomes " There is an imaginary centaur "; according to the other " Reality includes an imaginary centaur."^ By contrast, according to the substitutional interpretation, 'There is at least one thing which is F ' is true just in case there is some true sentence of the form ' a is F ', where ' a ' is a singular term.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ According to the objectual interpretation, 'There is at least one thing which is F ' is true just in case some object in the domain of discourse is F .
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ According to Russell's theory, a sentence of the form 'The F is G ' is not really of subject-predicate form at all, but is equivalent rather to an existentially quantified sentence of the form 'There is one and only one F and it is G '.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

The rejoinder, however, though partly true, is not to the point. .The idea of the centaur does exist in our imagination, and inside our heads, and the name of it in our mouths.^ An idea which is conceived of and which exists is better than one which is only imagined.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ The more we feel out of control, the more our brains imagine patterns that don't really exist.
  • EconLog: Behavioral Economics and Rationality Archives 18 September 2009 17:23 UTC econlog.econlib.org [Source type: General]

.But the point is that the centaur conceived and named does not exist beyond the idea of it and the name for it; it is not, like a man, a real thing which is neither the idea of it nor the name for it.^ In addition, the idea that truths about fundamental aspects of reality can be uncovered by an examination of how human beings reason is highly suspect in itself; but, like most things, so much depends on what allegedly follows from that assumption.

^ An idea which is conceived of and which exists is better than one which is only imagined.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ Maybe reality does not have anything like a structure that mirrors the structure of our thoughts, at least not understood a certain way.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

No amount of subtlety will remove the difference between a categorical judgment of existence, e.g. ." An existing man is mortal," and a categorical judgment of non-existence, e.g.^ The result is that the compound proposition is non-committal on the existence of what the antecedent asserts to exist.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

." A conceivable centaur is a fiction," because in the former we believe and mean that the thing exists beyond the idea, and in the latter we do not.^ An idea which is conceived of and which exists is better than one which is only imagined.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ These hardly look like the same things (for example, the latter notion calls for an agent, the former does not).
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

.If, contrary to usage, we choose to call the latter a judgment of existence, there is no use in quarrelling about words; but we must insist that new terms must in that case be invented to express so fundamental a difference as that between judgments about real men and judgments about ideal centaurs.^ In that case, there is no "underlying reality" here for it to point to or reflect.

^ Moving The Goalposts (also called Raising The Bar) is closely related to the Sharpshooter Fallacy, but instead of you setting your goal wherever you want, you insist that your opponent must make a new argument, meeting a more restrictive set of requirements, each time he succeeds in proving his case.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ Law of Excluded Middle: No existence can be both itself and different from itself.

.So long, however, as we use words in the natural sense, and call the former judgments of existence, and the latter judgments of non-existence, then " is " will not be, as Bradley supposes, the same as " exists," for we use " is " in both judgments, but " exists " only in the first kind.^ Evidently, though, this kind of explanation is not available to someone who favours the so-called 'direct' theory of reference, according to which names do not possess descriptive 'senses'.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ The agreement to say that "p may not be both true and false in the same respect and at the same time" is a formal (and thus in an important sense meaningless) agreement unless there is agreement on the meaning of "true" and "false."

^ Now, this fatal result can only be denied by those who reject the DM-inspired version of the LOC (i.e., those who reject "A is at the same time non-A" ), and who thus do not think that the first half of B1 is false , or both false and true, "It depends...".

Bosanquet's definition of a categorical judgment contains a similar confusion. .To assert a fact and to affirm the existence of a subject are not, as he makes out, the same thing: a judgment often asserts a fact and denies existence in the same breath, e.g.^ Thus two different speakers, or the same speaker on two different occasions, may assert the same proposition by making two different statements, perhaps using sentences of two different languages.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ Ad Hominem, refers to the attempt to deny an argument by asserting that the person presenting the argument also suffers from the same flaw or has held an opposing view in the past.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ This is just another way of saying the same thing as the affirmative categorical statement , i.e., all tigers are carnivores.

"
Jupiter is nonexistent." Here, as usual in logic, tradition is better than innovation. .All categorical judgment is an unconditional belief in the fact, signified by the copula, that a thing of some sort is (or is not) determined; but some categorical judgments are also beliefs that the thing is an existing thing, signified either by the subject or by the predicate, while others are not beliefs that the thing exists at all, but are only beliefs in something conceivable, or nameable, or in something or other, without particularizing what.^ "A thing is not equal to something other than itself "?!?

^ An idea which is conceived of and which exists is better than one which is only imagined.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ It is worth pointing out again that in all of this, the distinction between "not A" (predicate negation) and "not-A" (predicate-term negation) has been ignored, since Lawler and other DM-fans seem to be unaware of it.

Judgment then always signifies being, but not always existence.
3. Particular and Universal Judgments. - .Aristotle, by distinguishing affirmative and negative, particular and universal, made the fourfold classification of judgments, A, E, I and 0, the foundation both of opposition and of inference.^ "Caesar is a man" ( W1 ) does not say the particular is the universal, and can only be made to do so by imposing on it a grammatical theory that these two comrades failed to justify.

^ If, then, it is impossible to affirm and deny truly at the same time, it is also impossible that contraries should belong to a subject at the same time, unless both belong to it in particular relations, or one in particular relation and one without qualification."

^ For dialectics, the particular and the general, the unique and the universal -- for all their logical opposition -- exist, in fact, in and by means of each other.

.With regard to inference, he remarked that a universal judgment means by " all," not every individual we know, but every individual absolutely, so that, when it becomes a major premise, we know therein every individual universally, not individually, and often do not know a given individual individually until we add a minor premise in a syllogism.^ It interprets all occurrences of a word as having the same meaning, unless and until this appears to be impossible.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ Aristotle would have denied it was a legitimate syllogism in view of the fact that it has a particular middle premiss which is not governed by a what we would now call a quantifier expression (e.g., "Some", "All", "Every", and "No"), but concerns a named individual .

^ The predicate of the conclusion is the major term; the premise in which it is contained is the major premise; the subject of the conclusion is the minor term; and the premise in which it is contained is the minor premise.

.Whereas, then, a particular judgment is a belief that some, a universal judgment is a belief that all, the individuals of a kind or total of similar individuals, are similarly determined, whether they are known or unknown individuals.^ These are all problems in ontology in the sense that they deal with whether or not a certain thing, or more broadly entity, exists.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ A glut with respect to the universal quantifier occurs when a universally quantified formula is true whereas some of its instances are false.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ As we saw in Essay Three , this is based on the idea that all words are really names, and on the belief that all concepts expressions are really singular terms (i.e., they are the names of abstract particulars -- or they 'designate' them in other ways).

.Now, as we have already seen, what is signified by the subject may be existing or not, and in either case a judgment.^ A contextually limited use may be a possible answer (either temporarily or permanently) in such cases.

^ When faced with such a challenge , one may simply treat it as a "problem" to be worked out within one's already-existing system of thought.

^ However, (as may be seen from [Bat95] or [Bat98a] ) in that case too we obtain blocks that behave exactly like the elements of the usual predicative language schema.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

remains categorical so long as it is a belief without conditions. .Thus, " Some existing men are poets," " All existing men are mortal," " Some conceivable centaurs are human in their forequarters," " All conceivable centaurs are equine in their hindquarters," are all categorical judgments, while the two first are also categorical judgments of existence.^ Another example: All humans are mortal.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ All men are mortal.

^ Let me summarize some of the important applications of Scripture to the rational enter­prise under two headings: first, the status, and, second, the practice, of human reasoning.

Nevertheless these obvious applications of Aristotelian traditions have been recently challenged, especially by Sigwart, who holds in his Logic (secs. .27, 36) that, while a particular is a categorical judgment of existence, a universal is hypothetical, on the ground that it does not refer to a definite number of individuals, or to individuals at all, but rather to general ideas, and that the appropriate form of " all M is P " is " if anything is M it is P." This view, which has influenced not only German but also English logicians, such as Venn, Bradley and Bosanquet, destroys the fabric of inference, and reduces scientific laws to mere hypotheses.^ Isn't the philosophy of mathematics of rather specialized interest, all the more so in comparison to the broad humanistic issues of philosophy proper, issues such as the good, the true, and the beautiful?
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ In such cases, not all formulas of the form (1) should be counted as abnormalities.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ "Caesar is a man" ( W1 ) does not say the particular is the universal, and can only be made to do so by imposing on it a grammatical theory that these two comrades failed to justify.

.In reality, however, particular and universal judgments are too closely connected to have such different imports.^ However, it turned out that the Army was planning no such thing as they realized that the 4077th only worked so well because of the combination of people.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ Notice, however, that exclusive disjunction is really saying that p and q have different truth-values; if one of them is true, then the other isn't, and vice versa .
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ In reality, however, all such axioms are tautologies.

.In opposition, a categorical particular is the contradictory of a universal, which is also categorical, not hypothetical, e.g., "not all M is P" is the contradictory of " all M is P," not of " if anything is M it is P." In inference, a particular is an example of a universal which in its turn may become a particular example of a higher universal.^ For example the problem how a universal relates to a particular that has it (assuming there are universals and particulars), or the problem how an event like John eating a cookie relate to the particulars John and the cookie, and the relation of eating, assuming there are events, particulars and relations.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ If all that is real is indeed rational, then the identification of rules of inference with the "rules of thought" -- and with metaphysical truths about "Being" -- becomes more all the more natural.

^ For dialectics, the particular and the general, the unique and the universal -- for all their logical opposition -- exist, in fact, in and by means of each other.

.For instance, in the history of mechanics it was first inferred from some that all terrestrial bodies gravitate, and then from these as some that all ponderable bodies, terrestrial and celestial, gravitate.^ If our universe contains some things that are A's but not B's, and other things that are B's but not A's, and nothing that is neither, then the first of these expressions will be false and the second true.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ Of all of these possibilities, the only reasonable one is the first: The product is some tangible hard copy object or print.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

.How absurd to suppose that here we pass from a particular categorical to a universal hypothetical, and then treat this very conclusion as a particular categorical to pass to a higher universal hypothetical !^ For example the problem how a universal relates to a particular that has it (assuming there are universals and particulars), or the problem how an event like John eating a cookie relate to the particulars John and the cookie, and the relation of eating, assuming there are events, particulars and relations.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ The idea here is that the only way for the universal statement to be false is if is false for some particular .
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ To appreciate why universal quantifiers usually take conditionals, try a conjunction to see how absurd it would be.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

.Sigwart, indeed, is deceived both about particulars and universals.^ "Of contradictory statements about a universal taken universally it is necessary for one or the other to be true or false; similarly if they are about particulars, e.g.

^ On the contrary, the fact that we repeat the predicate D, and quantify universally both times, guarantees that we're talking about the same group.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

.On the one hand, some particulars are not judgments of existence, e.g.^ Although I've said "something in particular, some one thing" for simplicity and clarity, the definite sense of "something" could signify a plurality of particular things.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

."
some imaginary deities are goddesses "; on the other hand, some universals are not judgments of non-existence, e.g. "every existing man is mortal."^ Prejudices against this viewpoint were responsible for the rejection of his work by some mathematicians, but others reacted favorably because the theory provided a proof of the existence of transcendental numbers.
  • Readings in Logic 6 January 2010 10:47 UTC orcmid.com [Source type: Academic]

^ On the other hand, some normative sentences do seem to follow from others, so deontic logic must be possible.
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

^ If our universe contains some things that are A's but not B's, and other things that are B's but not A's, and nothing that is neither, then the first of these expressions will be false and the second true.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

.Neither kind is always a judgment of existence, but each is sometimes the one and sometimes the other.^ But if they are about a universal not taken universally it is not always the case that one is true and the other false.

^ They will also contain (unless stated otherwise) one other principle, a thesis asserting that a logical contradiction (conventionally denoted by “⊥”) is always gratuitous: .
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

.In no case is a universal hypothetical, unless we think it under a condition; for in a universal judgment about the non-existing, e.g. about all conceivable centaurs, we do not think, " If anything is a centaur," because we do not believe that there are any; and in a universal judgment about the existent, e.g. about all existing men, we do not think, " If anything is a man," because we believe that there is a whole class of men existing at different times and places.^ I think it has made all the difference.

^ In this case, no one would be seeking to correct or revise its meaning, nor suggest that it was universally inadequate.

^ So, no wonder that that dialecticians copy Hegel and talk about concepts developing , and how FL is hamstrung because of its fixation with 'fixed' concepts.

The cause of Sigwart's error is his misconception of " all." .So far as he follows Aristotle in saying that " all " does not mean a definite number of individuals he is right; but when he says that we mean no individuals at all he deserts Aristotle and goes wrong.^ But that no more maligns MFL than it does, say, Group Theory.

^ Despite this, the proverb says " All that glitters is not gold," which is absurd; it says that no glittering things are gold, not even gold.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ If he's right, though, what does that say about the rationality of the American people?
  • EconLog: Behavioral Economics and Rationality Archives 18 September 2009 17:23 UTC econlog.econlib.org [Source type: General]

.By " all " we mean every individual whatever of a kind; and when from the experience of sense and memory we start with particular judgments of existence, and infer universal judgments of existence and scientific laws, we further mean those existing individuals which we have experienced, and every individual whatever of the kind which exists.^ Aristotle would have denied it was a legitimate syllogism in view of the fact that it has a particular middle premiss which is not governed by a what we would now call a quantifier expression (e.g., "Some", "All", "Every", and "No"), but concerns a named individual .

^ Corresponding to simple seriality for SDL (that there is always an i -acceptable world), we assume what I will call “strong seriality” for K d : for every world i , there is an i -accessible world that is among those where all normative demands are met.
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

^ This appears because, if all those occurrences had the same meaning, then the author of the text would be stating a (clearly not intended) contradiction.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

.We mean neither a definite number of individuals, nor yet an infinite number, but an incalculable number, whether experienced or inferred to exist.^ In the sentence, "All even numbers are divisible by 2, but only some are divisible by 4", the phrase "only some" means "more than none and less than all" or "neither none nor all".
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

.We do not mean existing here and now, nor yet out of time and place, but at any time and place (semper et ubique) - past, present and future being treated as simply existing, by what logicians used to call suppositio naturalis. We mean then by " all existing " every similar individual whatever, whenever, and wherever existing.^ Aristotle used ' monadic predicates' (expressions that attribute a property to an individual) a long time ago.

^ Now, if would-be critics want to revise a word in common use, all well and good; but this cannot affect the ordinary meaning of that word .

^ It is also very obscure: No one else can hope to use my programs--the meanings of the parameters are simply too obscure for another artist to practically deal with.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

.Hence Sigwart is right in saying that " All bodies are extended " means " Whatever is a body is extended," but wrong in identifying this form with " If anything is a body it is extended."^ From that unfortunate mindset, all ancient Greece's wrathful and negative unidimensional and unilogical dichotomies arise : good-evil, love-hate, right-wrong, and so on.
  • The Prodigy Review - Bio: Life of William James Sidis 18 September 2009 8:08 UTC www.quantonics.com [Source type: General]

^ Hence, as noted above: it is impossible for dialecticians to say what they mean .

^ This means that certain features of ordinary language cannot be 'reformed' without ipso facto undermining our ability to comprehend anything at all.

" Whatever " is not " if anything." .For the same reason it is erroneous to confuse " all existing" with a general idea.^ There must exist some idea which is greater than all others.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ For dialectics, the particular and the general, the unique and the universal -- for all their logical opposition -- exist, in fact, in and by means of each other.

^ With reasoning like that you might as well argue that if a metre rule, say, has been made incorrectly the same must be true of all it measures!

.Nor does the use of abstract ideas and terms make any difference.^ The term used twice is the idea of "can do anything".
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ They use the term "behavioral economics," which I think of as looking at cognitive biases in decision making.
  • EconLog: Behavioral Economics and Rationality Archives 18 September 2009 17:23 UTC econlog.econlib.org [Source type: General]

^ Reification (no, not that kind ): Sometimes related to the four terms fallacy, this is treating a abstract idea as a physical object.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

When Bosanquet says that in " Heat is a mode of motion " there is no reference to individual objects, but " a pure hypothetical form which absolutely neglects the existence of objects," he falls far short of expressing the nature of this scientific judgment, for in his Theory of Heat Clerk Maxwell describes it as " believing heat as it exists in a hot body to be in the form of kinetic energy." As Bacon would say, it is a belief that all individual bodies qua hot are individually but similarly moving in their particles. .When, again, Bradley and Bosanquet speak of the universal as if it always meant one ideal content referred to reality, they forget that in universal judgments of existence, such as " All men existing are mortal," we believe that every individually existing man dies his own death individually, though similarly to other men; and that we are thinking neither of ideas nor of reality; but of all existent individual men being individually but similarly determined.^ But if they are about a universal not taken universally it is not always the case that one is true and the other false.

^ In other words, Every man drives at least one truck.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ Similarly for other such expressions.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

.A universal is indeed one whole; but it is one whole of many similars, which are not the same with one another.^ Indeed, one excellent example (among the many) of the impact FL on technology is the development of computers.

^ Or, rather, no one is able to say whether we do or we do not share the same set , since no one is capable of listing the 'commonsense' beliefs held by everyone -- or indeed anyone -- else.

^ For example, an individual man -- one and the same -- becomes pale at one time and dark at another, and hot and cold, and bad and good .

.This is indeed the very essence of distribution, that a universal is predicable, not singly or collectively, but severally and similarly of each and every individual of a kind, or total of similar individuals.^ Indeed, that word is said to have unspecified universal inadequacies, which 'shortcomings' must of necessity feature in the very act of pointing this alleged fact out -- nullifying that criticism.

^ Similarly with predicates: if every word named something (concrete or abstract), how could we ever say anything about anything?

.So also the essence of a universal judgment is that every individual of the kind is severally but similarly determined.^ Determinism ultimately precludes free will, yet here it is used as the vehicle of expressing free will and the latitude for expression of individual judgment which free will grants.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

^ A criterion of identity for individuals of a kind K is a principle which determines, for any individuals x and y of kind K, whether or not x and y are one and the same K .
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

.Finally, a universal judgment is often existential; but whether it is so or not it remains categorical, so long as it introduces no hypothetical antecedent about the existence of the thing signified by the subject.^ Similarly, the existential quantifier does not merely say, "for at least one thing", but "for at least one thing in the universe of discourse".
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ It follows that there are two ways to be non-committal about the existence of something: (1) use a universal quantifier, or (2) use an existential quantifier in the antecedent of a conditional.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ "The law of contradiction signifies the exclusion of difference from the essence of things and of thought about things.

.It is true that even in universal judgments of existence there is often a hypothetical element; for example, " All men are mortal " contains a doubt whether every man whatever, whenever and wherever existing, must die.^ For example, an individual man can be treated as a subject, but the class of all men must be treated as a predicate.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ Proof by example works where there is 'there exists' and not 'for all'.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ All men are mortal.

.But this is only a doubt whether all the things signified by the subject are similarly determined as signified by the predicate, and not a doubt whether there are such things at all.^ Quincy Philosophy and Hegel: A Quick Overview of His Philosophy The main theme and crux of Hegel's philosophy: there are no individual or separate things, there is only one thing, and all other things are simply manifestations, reflections, and expressions of that original thing.

^ This debate thus concerns whether there is one and only one set of logical constants for a system of representations, and if so, which ones are the logical ones.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ These are all problems in ontology in the sense that they deal with whether or not a certain thing, or more broadly entity, exists.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.Hence the hypothetical element is not a hypothetical antecedent " If anything is a' man," but an uncertain conclusion that " All existing men are mortal."^ All men are mortal.

^ For example, an individual man can be treated as a subject, but the class of all men must be treated as a predicate.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ A typical formula built from these atomic formulas is which we can translate as ``for all , if is a man then there exists such that is a truck and drives ''.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

.In other words, a categorical universal is often problematic, but a problematic is not the same as a hypothetical judgment.^ If two occurrences of a word have a different meaning, then it will still be supposed that all other occurrences have the same meaning as one of the first two occurrences with a different meaning.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

4. The Judgment and the Proposition. - Judgment in general is the mental act of believing that something is (or is not) determined. .A proposition is the consequent verbal expression of such a belief, and consists in asserting that the thing as signified by the subject is (or is not) determined as signified by the predicate.^ In contrast, a synthetic statement, for Kant, is one in which the concept of the predicate is not already contained in the concept of the subject, such as the statement that foxes are carnivorous.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ One and the same speaker could, on the same occasion, assert the first sentence and yet deny the second, even while referring to the same thing by the expressions 'that person' and 'I'.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ Frege's point is that a predicate, unlike a name, is an 'unsaturated' expression (it has, as it were, one or more 'gaps' in it), and consequently it cannot function as the logical subject of a sentence.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

But the expression is not necessary. Sensation irresistibly produces a judgment of existence without needing language. .Children think long before they speak; and indeed, as mere vocal sounds are not speech, and as the apprehension that a word signifies a thing is a judgment, judgment is originally not an effect, but a cause of significant language.^ As long as readers think that they have to find 'thesis, antithesis, synthesis' in Hegel they must find him obscure -- but what is obscure is not Hegel but their coloured glasses.

^ "To understand the significance of this compare it with what is know as 'formal logic' (originally developed by Aristotle and usually thought of as the rules of sound thinking).

^ Rationality The Loss of Reasoning in America Americans think less and less these days before they act.

.At any rate, even when we have learnt to speak, we do not express all we think, as we may see not only from the fewness of words known to a child, but also from our own adult consciousness.^ After all, why should we think that only the right kind of structure of thoughts helps with survival?
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ The word "unfortunate" in the above counter-example is not being criticised because it is inadequate in all its applications, only that it is the wrong word to use here.

^ Until we know the extent of our ignorance (or where this word falls short) -- or even what the subject of this query amounts to --, all the technical/dialectical terminology in the world is of no use -- even to dialecticians!

The principle of thought is to judge enough to conclude. .The principle of language is to speak only so far as to understand and be understood.^ FL has not only contributed to the evolution of software and of computer languages, the principles of Propositional Calculus govern the operation of all standard processors (etc.

Hence speech is only a curtailed expression of thought. .Sometimes we express a whole judgment by one word, e.g.^ This doctrine requires one to distinguish sharply between existence and actuality , treating the latter as an indexical notion akin to those expressed by the words 'here' and 'now'.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

"
Fire! " or by a phrase, e.g. " What a fire! " and only usually by a proposition. .But even the normal proposition in the syllogistic form tertii adjacentis, with subject, predicate and copula, is seldom a complete expression of the judgment.^ Every predicate logic expression can be cast in prenex normal form.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ A predicate logic expression is in prenex normal form if (1) all its quantifiers are clustered at the left, (2) no quantifier is negated, (3) the scope of each quantifier extends to the right end of the expression, (4) no two quantifiers use the same variable, (5) every letter used by a quantifier is used later in the expression as a bound variable.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ This is one of the reasons why the predicative level is considered extremely important, even if, for many adaptive logics, the basic features of the dynamics are already present at the propositional level.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

.The consequence is that the proposition, being different from a judgment arising after a judgment, and remaining an imperfect copy of judgment, is only a superficial evidence of its real nature.^ This difference between the two is the very difference which prevents the concept from being directly and immediately reality and reality from being immediately its own concept.

^ Carbon Dioxide occurs in nature, and therefore, it is impossible for it to do harm , therefore, Global Warming either can't be real, or if it is real, will only help us.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ That being so, propositions can't contain only names and/or singular terms.

.Fortunately, we have more profound evidences, and at least three evidences in all: the linguistic expression of belief in the proposition; the consciousness of what we mentally believe; and the analysis of reasoning, which shows what we must believe, and have believed, as data for inference.^ Theories of truth are many and various, ranging from the robust and intuitively appealing correspondence theorywhich holds that the truth of a sentence or proposition consists in its correspondence to extra-linguistic or extra-mental factto the redundancy theory at the other extreme, according to which all talk of truth and falsehood is, at least in principle, eliminable without loss of expressive power.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ It seems that a proponent of the 'direct' theory of reference must claim that a speaker who understands the linguistic meaning of a sentence need not thereby know what proposition that sentence expresses.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ As we saw in Essay Three , this is based on the idea that all words are really names, and on the belief that all concepts expressions are really singular terms (i.e., they are the names of abstract particulars -- or they 'designate' them in other ways).

.In these ways we find that a judgment is both different from, and more than, a proposition.^ Another way to understand "form" as being concerned with what the judgment is about, rather than the judgment itself, is to think of what it is about, the world, itself as having a form.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Another way to put this is that the “can” of permissibility is much more plausibly construed as the dual of “must” than as the dual of “ought”.
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

^ Contents of judgments can be seen as propositions, and these can be understood as entities that are structured, for example Russellian propositions.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.But recent logicians, although they perceive the difference, nevertheless tend to make the proposition thej measure of the judgment.^ Nevertheless, dialecticians in general (and TAR's author in particular) take great pains to make it clear that while they do not reject FL, they regard its scope as somewhat limited.

^ The only difference is that they actually did know things that were worth knowing, like the movements of the heavenly bodies, something which cannot be said of modern logicians.

.This makes them omit sensory judgments, and count only those which require ideas, and even general ideas expressed in general terms.^ I get the feeling that much of this material only makes sense to those who wrote it (something I have to watch out for also).
  • Readings in Logic 6 January 2010 10:47 UTC orcmid.com [Source type: Academic]

^ This doctrine requires one to distinguish sharply between existence and actuality , treating the latter as an indexical notion akin to those expressed by the words 'here' and 'now'.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ Are there really "subjects" and "predicates" in nature -- features found in only one family of languages, and even then, features which only a tiny proportion of its sentences express?

.Sigwart, for example, gives as instances of our most elementary judgments, " This is Socrates," " This is snow "- beliefs in things existing beyond ourselves which require considerable inferences from many previous judgments of sense and memory.^ Logic thus understood will for example be concerned with the occurrence of subject and predicate structure that many judgments exhibit, and with other such general features of judgments.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ The premise: While guys like Lenin, Hitler, and Mao were hopelessly deluded about many things, their beliefs about how to win and hold power were probably correct.
  • EconLog: Behavioral Economics and Rationality Archives 18 September 2009 17:23 UTC econlog.econlib.org [Source type: General]

^ These are all problems in ontology in the sense that they deal with whether or not a certain thing, or more broadly entity, exists.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

Worse still, logicians seem unable to keep the judgment apart from the proposition. .Herbart says that the judgment " A is B " does not contain the usually added thought that A is, because there is no statement of A's existence; as if the statement mattered to the thought.^ Not because an athlete says he does."
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ This might seem absurd at first sight, because 'a man is not white' looks as if it signifies also at the same time that no man is white; this, however, does not signify the same, nor does it necessarily hold at the same time."

^ But that no more maligns MFL than it does, say, Group Theory.

So Sigwart, in order to reduce universals to hypotheticals, while admitting that existence is usually thought, argues that it is not stated in the universal judgment; so also Bosanquet. .But in the judgment the point is not what we state, but what we think; and so long as the existence of A is added in thought, the judgment in question must contain the thought that A exists as well as that A is B, and therefore is a judgment that something is determined both as existing and in a particular manner.^ As long as readers think that they have to find 'thesis, antithesis, synthesis' in Hegel they must find him obscure -- but what is obscure is not Hegel but their coloured glasses.

^ Post-Renaissance scientific thought therefore has been both Atomist and Organicist.

^ Sometimes a proposition which commits itself to the existence of something ("UFO's exist") is made the antecedent of a conditional ("If UFO's exist, then our ammonia supplies are in jeopardy").
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

.The statement only affects the proposition; and whenever we believe the existence of the thing, the belief in existence is part of the judgment thought, whether it is part of the proposition stated or not.^ Theories of reference are primarily concerned with the relationships between sub-propositional or sub-sentential parts of thought or speech and extra-mental or extra-linguistic entitiesfor instance, with the relationship between names and things named, and with the relationship between predicates and the properties they express or the items to which they apply.
  • Philosophical Logic 18 September 2009 8:08 UTC www.dur.ac.uk [Source type: Original source]

^ Part I : The Tribes and the States , and Part II : The Peace Paths , Sidis' 1200 page magnum opus, a revisionist history of USA. Only Part I and first page of Part II survive.
  • The Prodigy Review - Bio: Life of William James Sidis 18 September 2009 8:08 UTC www.quantonics.com [Source type: General]

^ Unless otherwise stated, we will only be interested in deontic logics that contain classical propositional calculus (PC).
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

Here Sir William Hamilton did a real service to logic in pointing out that " Logic postulates to be allowed to state explicitly in language all that is implicitly contained in the thought." Not that men should or can carry this logical postulate out in ordinary life; but it is necessary in the logical analysis of judgments, and yet logicians neglect it. This is why they confuse the categorical and the universal with the hypothetical. .Taking the carelessly expressed propositions of ordinary life, they do not perceive that similar judgments are often differently expressed, e.g.^ In fact, if ordinary folk were to talk like metaphysicians in their everyday life, they would probably find themselves regarded as psychotic, or delusional.

"
I, being a man, am mortal," and " If I am a man, I am mortal "; and conversely, that different judgments are often similarly expressed. .In ordinary life we may say, " All men are mortal," " All centaurs are figments," " All square circles are impossibilities," " All candidates arriving five minutes late are fined " (the last proposition being an example of the identification of categorical with hypothetical in Keynes's Formal Logic). But of these universal propositions the first imperfectly expresses a categorical belief in existing things, the second in thinkable things, and the third in nameable things, while the fourth is a slipshod categorical expression of the hypothetical belief, " If any candidates arrive late they are fined."^ Formal logic has said all that it has to say.

^ For all things in the universe, if they are humans, then they are mortal.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ Therefore, the first thing caused the second thing.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

.The four judgments are different, and therefore logically the propositions fully expressing them are also different.^ "You've used the 'Four Terms' fallacy, you stupid retard, therefore you're using faulty logic" is not Ad Hominem.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ Thus logically expressed, John is understood when he is most fully conceived as the 'identity' of John-in-special and not -John (i.e.

The judgment, then, is the measure of the proposition, not the proposition the measure of the judgment. .On the other hand, we may go too far in the opposite direction, as Hamilton did in proposing the universal quantification of the predicate.^ We may, on the one hand, go forward and develop further the consequences of known principles.
  • Readings in Logic 6 January 2010 10:47 UTC orcmid.com [Source type: Academic]

^ On the other hand, what is the 'internal opposite' of day that makes it change into night?

^ On the other hand, many other philosophers have maintained that such an ontological argument is possible, and they have made a variety of different proposals how it can go.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.If the quantity of the predicate were always thought, it ought logically to be always stated.^ They will also contain (unless stated otherwise) one other principle, a thesis asserting that a logical contradiction (conventionally denoted by “⊥”) is always gratuitous: .
  • Deontic Logic (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: Academic]

^ A formula of the predicate calculus is said to be logically valid if it is necessarily always true, regardless of the specific predicates and individuals involved.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

But we only sometimes think it. .Usually we leave the predicate indefinite, because, as long as the thing in question is (or is not) determined, it does not matter about other things, and it is vain for us to try to think all things at once.^ However, rather then exploring the details of these and other rival systems, in the next section, we focus on proving things about the system PC, the axiomatic system treated at length above.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ Virtually all successful politicians break their promises.When you think about it, though, politicians' penchant for promise-breaking is puzzling.
  • EconLog: Behavioral Economics and Rationality Archives 18 September 2009 17:23 UTC econlog.econlib.org [Source type: General]

^ Gary Becker's got a nice story: We're usually right to ignore such warnings:While Roubini and others who warned about weaknesses in the mortgage market and other parts...
  • EconLog: Behavioral Economics and Rationality Archives 18 September 2009 17:23 UTC econlog.econlib.org [Source type: General]

.It is remarkable that in Barbara, and therefore in many scientific deductions, to think the quantity of the predicate is not to the point either in the premises or in the conclusion; so that to quantify the propositions, as Hamilton proposes, would be to express more than a rational man thinks and judges.^ While the Propositional Calculus is simpler in one way than the natural deduction system sketched in the previous section, in many ways it is actually more complicated to use.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ Begging the question : "Proving" that something is true by taking your conclusion as one of your premises, usually done implicitly rather than explicitly (few people are fooled by having your conclusion as your only premise, such as: "Joe is mad at Jill, therefore Joe is mad at Jill."
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ [In saying this, the reader should not think that I attribute to Woods and Grant a clear logical strategy here; few of their arguments work (and many are aimed at targets that would give the phrase "straw man" a bad name, as we have seen).

.In judgments, and therefore in propositions, indefinite predicates are the rule, quantified predicates the exception.^ The rule-governed use of the template "ξ is green" allows for the formation of an indefinite number of propositions in the same way -- even though it nowhere appears in any of its instances.

^ We must add a new rule: that when an existential quantifier comes first, or applies to the subject of a sentence, it is to be understood in the definite sense, and when it does not come first, or applies to an object of the verb, then it is to be understood in the indefinite sense.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

.Consequently, A E I 0 are the normal propositions with indefinite predicates; whereas propositions with quantified predicates are only occasional forms, which we should use whenever we require to think the quantity of the predicate, e.g. (t) in conversion, when we must think that all men are some animals, in order to judge that some animals are men; (2) in syllogisms of the 3rd figure, when the predicate of the minor premise must be particularly quantified in thought in order to become the particularly quantified subject of the conclusion; (3) in identical propositions including definitions, where we must think both that i -{- i are 2 and 2 are z -}- r.^ For example, an individual man can be treated as a subject, but the class of all men must be treated as a predicate.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ The predicate of the conclusion is the major term; the premise in which it is contained is the major premise; the subject of the conclusion is the minor term; and the premise in which it is contained is the minor premise.

^ In paraphrasing, remember that we have only three quantities: all, some, and none.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

But the normal judgment, and therefore the normal proposition, do not require the quantity of the predicate. It follows also that the normal judgment is not an equation. .The symbol of equality (=) is not the same as the copula (is); it means " is equal to," where " equal to " is part of the predicate, leaving " is " as the copula.^ For example, each of the following are presuppositions of CL : that ~ A is false if A is true, that A & B is true if both A and B are true, that different occurrences of a non-logical symbol have always the same meaning, [6] etc.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ If A equals A, it cannot equal non-A. A cannot be part of two opposing classes at one and the same time.

Now, in all judgment we think " is," but in few judgments predicate " equal to." .In quantitative judgments we may think x = y, or, as Boolero oses x = v ° p p y = - ° y, or, as Jevons proposes, x = xy, or, as Venn proposes, x which is not y=o; and equational symbolic logic is useful whenever we think in this quantitative way.^ Logic’ and ‘ontology’ are big words in philosophy, and different philosophers have used them in different ways.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Propositional logic also studies way of modifying statements, such as the addition of the word “not” that is used to change an affirmative statement into a negative statement.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ Since using Natures Logic my litters of puppies have been way healthier also!!

But it is a byway of thought. .In most judgments all we believe is that x is (or is not) y, that a thing is (or is not) determined, and that the thing signified by the subject is a thing signified by the predicate, but not that it is the only thing, or equal to everything signified by the predicate.^ For example, an individual man can be treated as a subject, but the class of all men must be treated as a predicate.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ Even though not all of us have a mastery of speech equal to that of its most accomplished practitioners, no one (novice or adept alike) seems to know what 'commonsense' is.

^ Do dialecticians really think that a philosopher of Aristotle's stature and sophistication actually believed that, say, "Everything must be rat or "non-rat" --, or, "rat does not equal cat"?

.The symbolic logic, which confuses " is " with " is equal to," having introduced a particular kind of predicate into the copula, falls into the mistake of reducing all predication to the one category of the quantitative; whereas it is more often in the substantial, e.g.^ Traditional logic (the logic of one-place predicates).
  • Readings in Logic 6 January 2010 10:47 UTC orcmid.com [Source type: Academic]

^ Predicate logic with equality.
  • Readings in Logic 6 January 2010 10:47 UTC orcmid.com [Source type: Academic]

^ Some predicates require more than one argument.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

"
I am a man," not " I am equal to a man," or in the qualitative, e.g. " I am white," not " I am equal to white," or in the relative, I am born in sin," not " I am equal to born in sin." Predication, as Aristotle saw, is as various as the categories of being. .Finally, the great difficulty of the logic of judgment is to find the mental act behind the linguistic expression, to ascribe to it exactly what is thought, neither more nor less, and to apply the judgment thought to the logical proposition, without expecting to find it in ordinary propositions.^ As the only access to expression is through the formal logic of the computer program, there is no "evidence of the hand" in the final work (or if there appears to be, it is illusory).
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

^ In this sense we associate "form" neither with the representation that is involved in the judgment, nor with the proposition which is its content, but rather with the world that is judged about.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ Here the judgment as a mental act is assumed to operate on a mental representation that itself has syntactic structure.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

.Beneath Hamilton's postulate there is a deeper principle of logic - _A rational being thinks only to the point, and speaks only to understand and be understood. Inference The nature and analysis of inference have been so fully treated in the Introduction that here we may content ourselves with some points of detail.^ On Nature's Logic, there is no odor.

^ That a logic assigns the trivial consequence set to some set of premises means that, in semantic terms, the set of premises has no models or that its only model is the trivial one.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ There is an excellent account of Aristotelian Logic in Smith (2004), here .

I. False Views of Syllogism arising from False Views of Judg- ment. - The false views of judgment, which we have been examining, have led to false views of inference. .On the one hand, having reduced categorical judgments to an existential form, Brentano proposes to reform the syllogism, with the results that it must contain four terms, of which two are opposed and two appear twice; that, when it is negative, both premises are negative; and that, when it is affirmative, one premise, at least, is negative.^ Every syllogism contains three terms.
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ Each of the premises and the conclusion is of one of four types: .
  • Logic and Mathematics 6 January 2010 10:47 UTC www.math.psu.edu [Source type: FILTERED WITH BAYES]

^ Four terms fallacy : Using a standard 3-step proof-of-concept to prove your theory, but including one unconnected tenet which breaks the line of reasoning.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

.In order to infer the universal affirmative that every professor is mortal because he is a man, Brentano's existential syllogism would run as follows: There is not a not-mortal man.^ This is because it would be impossible to state the following: .

^ If FL is solely concerned with inference then there would be no reason to saddle it with metaphysical baggage of this sort, and every reason not to.

^ This is because such categories (having no fixed meanings) would sanction no inferences, for it is not possible to decide what follows from what if the meaning of the terms employed is indeterminate.

There is not a not-human professor.
. '. There is not a not-mortal professor.
.On the other hand, if on the plan of Sigwart categorical universals were reducible to hypotheticals, the same inference would be a pure hypothetical syllogism, thus: If anything is a man it is mortal.^ If, on the other hand, dialecticians were to employ non- static categories consistent with their own precepts, then that would equally undermine any conclusions they 'derived'.

^ On the other hand, one could argue that the structure of thought explains the structure of the world, which would most likely be an idealist route of sorts.
  • Logic and Ontology (Stanford Encyclopedia of Philosophy) 6 January 2010 10:47 UTC plato.stanford.edu [Source type: FILTERED WITH BAYES]

^ On the other hand, if there is a link between FL and metaphysical/scientific truths -- as legend would have it --, then that fact (if it is one) needs substantiation .

If anything is a professor it is a man.
. '. If anything is a professor it is mortal.
.But both these unnatural forms, which are certainly not analyses of any conscious process of categorical reasoning, break down at once, because they cannot explain those moods in the third figure, e.g.^ On the basis of passages like these it is not easy to contradict those who conclude that the above two comrades did not know what they were talking about.

^ So these cannot be true together, but their opposites may both be true with respect to the same thing, e.g.

^ This reasoning cannot proceed in terms of CL because the CL -consequence set of an inconsistent theory is trivial.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

.Darapti,
which reason from universal premises to a particular conclusion.^ Why should the way we knit premises and conclusions together mirror the structure of the universe?

^ An internal dynamics: a conclusion may be withdrawn in view of the better understanding of the premises provided by a continuation of the reasoning.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ For him, it was 'nothing more than an artifice' in which the conclusions were already surreptitiously introduced into the premises to give a false appearance of reasoning."

.Thus, in order to infer that some wise men are good from the example of professors, Brentano's syllogism would be the following non-sequitur: There is not a not-good professor.^ For example, each of the following are presuppositions of CL : that ~ A is false if A is true, that A & B is true if both A and B are true, that different occurrences of a non-logical symbol have always the same meaning, [6] etc.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ However, the example these two give of a syllogism is not one that Aristotle would have recognised.

^ If A is A, it follows, according to formal thinking that A cannot be non-A. Thus the second law of formal logic, the law of contradiction forms the essential supplement to the first law.

There is not a not-wise professor.
.There is a wise good (non-sequitur). So Sigwart's syllogism would be the following non-sequitur:- If anything is a professor, it is good.^ It follows that there are two ways to be non-committal about the existence of something: (1) use a universal quantifier, or (2) use an existential quantifier in the antecedent of a conditional.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ Even worse still, if every "A" is also "non-A", then these would surely follow from B3: .

If anything is a professor, it is wise.
.Something wise is good (non-sequitur). But as by the admission of both logicians these reconstructions of Darapti are illogical, it follows that their respective reductions of categorical universals to existentials and hypotheticals are false, because they do not explain an actual inference.^ Because this was the scent they were originally trained to follow, dragging a bundle containing red herring across a real scent trail could draw an adult pack off on a false trail.
  • You Fail Logic Forever - Television Tropes & Idioms 6 January 2010 10:47 UTC tvtropes.org [Source type: FILTERED WITH BAYES]

^ Hence, these premisses are not actually about anything until they have been interpreted ; before that they are neither true nor false .

^ Because a statement of the form α → β is false for any truth-value assignment making α true and β false, it would then follow that some truth-value assignment makes α → β false, which is impossible if it too is a tautology.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

.Sigwart does not indeed shrink from this and greater absurdities; he reduces the first figure to the modus ponens and the second to the modus tollens of the hypothetical syllogism, and then, finding no place for the third figure, denies that it can infer necessity; whereas it really infers the necessary consequence of particular conclusions.^ Modus ponens” is Latin for affirming mode, and “modus tollens” is Latin for denying mode .
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ For under modus tollens , from p É q and ~q we can validly infer ~p.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

^ Modus tollens assures us that p É q asserts that p is true only if q is true, or that q is the necessary condition of p.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

.But the crowning absurdity is that, if all universals were hypothetical, Barbara in the first figure would become a purely hypothetical syllogism - a consequence which seems innocent enough until we remember that all universal affirmative conclusions in all sciences would with their premises dissolve into mere hypothesis.^ We can continue this line of reasoning until all the premises are removed.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ Nevertheless, the adaptive logics interprets the premises as normally as possible, and delivers all CL -consequences if the premises have CL -models (that is: are normal with respect to CL ).
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ The above syllogism is valid, and would remain valid even if all motion ceased .

No logic can be sound which leads to the following analysis: If anything is a body it is extended. If anything is a planet it is a body.
. If anything is a planet it is extended.
Sigwart, indeed, has missed the essential difference between the categorical and the hypothetical construction of syllogisms. .In a categorical syllogism of the first figure, the major premise, " Every M whatever is P," is a universal, which we believe on account of previous evidence without any condition about the thing signified by the subject M, which we simply believe sometimes to be existent (e.g.^ Every thing about them said healthy; their coats, alertness and level of energy.

^ By metatheoretic result 2, we can remove from each of these sets of premises either p n or ¬p n , depending on which it contains, and make it an antecedent of a conditional in which α is consequent, and the result will be provable without using p n or ¬p n as a premise.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ It follows that there are two ways to be non-committal about the existence of something: (1) use a universal quantifier, or (2) use an existential quantifier in the antecedent of a conditional.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

." Every man existent "), and sometimes not (e.g., " Every centaur conceivable "); and the minor premise, " S is M," establishes no part of the major, but adds the evidence of a particular not thought of in the major at all.^ Consequently large parts of analysis, which for centuries have been thought well established, are rendered doubtful."
  • Readings in Logic 6 January 2010 10:47 UTC orcmid.com [Source type: Academic]

^ It is not correct to argue that induction only involves the number from 0 to n [when establishing that θ ( n ) implies θ ( n +1)]; the property of n being established may be a formula with bound variables that are thought of as ranging over all numbers.
  • Readings in Logic 6 January 2010 10:47 UTC orcmid.com [Source type: Academic]

^ 'Caesar is a man,' 'Fido is a dog,' 'the tree is green,' all state that the particular is the universal.

.But in a hypothetical syllogism of the ordinary mixed type, the first or hypothetical premise is a conditional belief, e.g.^ "Another type of syllogism is conditional in form (if...then), for example, 'If an animal is a tiger, it is a carnivore.'

."
If anything is M it is P," containing a hypothetical antecedent, " If anything is NI," which is sometimes a hypothesis of existence (e.g.^ Sometimes a proposition which commits itself to the existence of something ("UFO's exist") is made the antecedent of a conditional ("If UFO's exist, then our ammonia supplies are in jeopardy").
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

" If anything is an angel), and sometimes a hypothesis of fact (e.g. ." If an existing man is wise "); and the second premise or assumption, " Something is NI," establishes part of the first, namely, the hypothetical antecedent, whether as regards existence (e.g.^ In artistic terms, these two parts correspond to process and medium : the first concerns itself with the machinations of artistic creation while the second is about producing a physical manifestation.
  • FLnSE_text.html1 22 September 2009 20:020 UTC www.wizardnet.com [Source type: FILTERED WITH BAYES]

^ The recognition that the above argument is valid requires one to recognize that the subject in the first premise is the same as the subject in the second premise.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

^ While the above compound sentence is itself a statement, because it is true, the two parts, “Ganymede is a moon of Jupiter” and “Ganymede is a moon of Saturn”, are themselves statements, because the first is true and the second is false.
  • Propositional Logic [The Internet Encyclopedia of Philosophy] 6 January 2010 10:47 UTC www.iep.utm.edu [Source type: Academic]

" Something is an angel "), or as regards fact (e.g. " This existing man is wise "). .These very different relations of premises are obliterated by Sigwart's false reduction of categorical universals to hypotheticals.^ A different form of dynamics is related to the fact that humans are unable to see at once all the consequences of a set of premises.
  • Adaptive Logics 11 October 2009 10:39 UTC logica.ugent.be [Source type: FILTERED WITH BAYES]

^ If our universe contains some things that are A's but not B's, and other things that are B's but not A's, and nothing that is neither, then the first of these expressions will be false and the second true.
  • Peter Suber, "Translation Tips" 6 January 2010 10:47 UTC www.earlham.edu [Source type: Original source]

.But even Sigwart's errors are outdone by Lotze, who not only reduces " Every NI is P " so " If S is M, S is P," but proceeds to reduce this hypothetical to the disjunctive, " If S is NI, S is P L or P 2 or 1 33 ," and finds fault with the Aristotelian syllogism because it contents itself with inferring " S is P " without showing what P. Now there are occasions when we want to reason in this disjunctive manner, to consider whether S is I n or P 2 or P 3, and to conclude that " S is a particular P "; but ordinarily all we want to know is that " S is P ";
e.g.^ This is an error: the belief that something won't work is not automatically a reason for not trying it, for even if failures is certain the manner of it might be instructive."
  • Readings in Logic 6 January 2010 10:47 UTC orcmid.com [Source type: Academic]

^ The web site for the conference says that full video will be available, but for now there are only short clips.
  • EconLog: Behavioral Economics and Rationality Archives 18 September 2009 17:23 UTC econlog.econlib.org [Source type: General]

^ There's no point voting for someone who can't win.Now consider how this applies to Singapore, where even second parties have no real prospect of winning.
  • EconLog: Behavioral Economics and Rationality Archives 18 September 2009 17:23 UTC econlog.econlib.org [Source type: General]

.in arithmetic, that 2+ 2 are 4, not any particular 4, and in life that all our contemporaries must die, without enumerating all their particular sorts of deaths.^ This means that certain features of ordinary language cannot be 'reformed' without ipso facto undermining our ability to comprehend anything at all.

^ It could be replied that if language is part of the world, it must have coded into it all sorts of things that are part of reality too.

^ In Moliere's comedy, Le Bourgeois Gentilhomme, M. Jourdain was surprised to be told that he had been talking prose all his life, without realising it.

.Lotze's mistake is the same as that of Hamilton about the quantification of the predicate, and that of those symbolists who held that reasoning ought always to exhaust all alternatives by equations.^ On the basis of passages like these it is not easy to contradict those who conclude that the above two comrades did not know what they were talking about.
  • Formal Logic 22 September 2009 20:020 UTC