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For other article subjects named induction, see
Induction.
.^ Inductive logic — the logic of what is operative — reasons from the specific to the general.- What is Design Thinking Anyway? : Observatory: Design Observer 21 January 2010 11:49 UTC observatory.designobserver.com [Source type: FILTERED WITH BAYES]
^ Inductive reasoning, and the third myth of neutrality Bacon proposed that we examine facts and use inductive reasoning (reasoning from specifics to generalities) to draw conclusions.- What went wrong? The bad seeds sowed from Bacon to Kant 21 January 2010 11:49 UTC www.renewamerica.com [Source type: Original source]
^ Inductive reasoning is useful, deductive reasoning is indispensable.
The premises of an inductive
logical argument indicate some degree of support (inductive probability) for the conclusion but do not
entail it; i.e. they do not ensure its truth. Induction is used to ascribe
properties or relations to
types based on
an observation instance (i.e., on a number of observations or experiences); or to formulate
laws based on limited observations of recurring
phenomenal patterns. Induction is employed, for example, in using specific propositions such as:
- This ice is cold. (Or: All ice I have ever touched has been cold.)
- This billiard ball moves when struck with a cue. (Or: Of one hundred billiard balls struck with a cue, all of them moved.)
...to infer general propositions such as:
- All ice is cold.
- All billiard balls move when struck with a cue.
Another example would be:
- 3+5=8 and eight is an even number. Therefore, an odd number added to another odd number will result in an even number.
.^ Inductive reasoning is not the same as mathematical induction.- First Draft: Inductive and deductive reasoning 21 January 2010 11:49 UTC mblog.lib.umich.edu [Source type: FILTERED WITH BAYES]
^ It should also be remarked that Hume's argument applies just to enumerative induction, and primarily to singular predictive inference, but, again, its generalization to other forms of inductive reasoning is straightforward.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ The force of induction, the force that drives the inference, is thus not an objective feature of the world, but a subjective power; the mind's capacity to form inductive habits.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
.^ Case-based reasoning flowchart.- Intelligent Learning Systems 21 January 2010 11:49 UTC rilw.itim-cj.ro [Source type: Reference]
^ Note that Deductive Reasoning questions may not be an in argument form.- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
^ This form of Reasoning is inferior to deductive reasoning .- On Argument. 21 January 2010 11:49 UTC www.blupete.com [Source type: Original source]
.^ "Church Growth" uses inductive reasoning.- authorityresearch.com Deductive-Inductive Reasoning Part I 21 January 2010 11:49 UTC authorityresearch.com [Source type: Original source]
^ You often use d Deductive reasoning is often used in the legal field, as well as in philosophical and mathematical proofs.- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
^ The predictor variables were gender, prior cognitive status (stable or decline on inductive reasoning ability), training group (reasoning, spatial orientation), and chronic disease status.- Effects of Cognitive Training on Change in Accuracy in Inductive Reasoning Ability -- Boron et al. 62 (3): P179 -- Journals of Gerontology Series B: Psychological Sciences and Social Sciences 21 January 2010 11:49 UTC psychsoc.gerontologyjournals.org [Source type: Academic]
.^ Use inductive reasoning to "defend" your faith and you will destroy your faith.- authorityresearch.com Deductive-Inductive Reasoning Part I 21 January 2010 11:49 UTC authorityresearch.com [Source type: Original source]
^ "Church Growth" uses inductive reasoning.- authorityresearch.com Deductive-Inductive Reasoning Part I 21 January 2010 11:49 UTC authorityresearch.com [Source type: Original source]
^ Although this device is useful, such probability functions should be considered mere abbreviations of proper, logically explicit, non-enthymematic, inductive support functions.- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
Strong and weak induction
Strong induction
- All observed crows are black.
- Therefore:
- All crows are black.
.^ This does exemplify the nature of induction: inducing the universal from the particular.- Philosophical Reflections 25: Inductive Reasoning 21 January 2010 11:49 UTC www.thoughtware.com.au [Source type: Original source]
^ Inductive Method, Induction In logic, the process of reasoning from the parts to the whole, from the particular to the general, or from the individual to the universal; contrasted with the deductive method, which reasons from the whole to the parts, from the general to the particular from the universal to the individual.
^ This is not to denigrate the leading authority on English vocabulary—until the middle of the previous century induction was understood to be what we now know as enumerative induction or universal inference ; inference from particular instances: .- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
However, the conclusion is not certain.
.^ And if we must entertain the possibility that the objective chances may change unpredictably, it is far less obvious how inductive conclusions can be derived.- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
^ Even the best inductive methods applied to all available evidence may get it wrong; good inductions may lead from true premises to false conclusions.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ This is not to say that induction applies only in the actual world: The premises of a good induction confirm its conclusion whether those premises are true or false in the actual world.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
.^ Specifically, we examined whether training enhancement on fluid ability could be attributed to an increase in accuracy, or whether training effects were primarily associated with an increased number of reasoning items attempted.- Effects of Cognitive Training on Change in Accuracy in Inductive Reasoning Ability -- Boron et al. 62 (3): P179 -- Journals of Gerontology Series B: Psychological Sciences and Social Sciences 21 January 2010 11:49 UTC psychsoc.gerontologyjournals.org [Source type: Academic]
^ You just have to tell me what experiment I could do if I wanted to (and if I had the resources to) that would have different results depending on whether or not your god exists.- Keith Devens .com - Weblog: The inductive principle - July 04, 2005 21 January 2010 11:49 UTC keithdevens.com [Source type: Original source]
^ Marzipan and cyanide are examples of two substances that bear similar scents, but are so different in molecular structure that one is a food and the other is a poison.- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
In doing so, we could discover that
albinism is possible, resulting in light-coloured crows.
.^ What I am submitting to you is that without a Sovreign and Holy God you would not even understand the experiment.- Keith Devens .com - Weblog: The inductive principle - July 04, 2005 21 January 2010 11:49 UTC keithdevens.com [Source type: Original source]
^ You should always consider the possibility of confounding factors when presented with a correlative relationship in GMAT questions.- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
^ The best way to tackle these questions is to gradually eliminate the possible answers until you have one or two and then choose the last one by scope.- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
.^ "In a deductive argument, the truth of the premises is supposed to guarantee the truth of the conclusion; in an inductive argument, the truth of the premises merely makes it probable that the conclusion is true."- authorityresearch.com Deductive-Inductive Reasoning Part I 21 January 2010 11:49 UTC authorityresearch.com [Source type: Original source]
^ Inductive skeptics are naturally read as claiming that the conclusion of an inductive argument is not rendered more probable by its premises.- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
^ For, the whole idea of inductive logic is to provide a measure of the extent to which contingent premise sentences indicate the likely truth-values of contingent conclusion sentences.- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
Weak induction
- I always hang pictures on nails.
- Therefore:
- All pictures hang from nails.
.^ Inductive thinking, of course, does not always lead to true conclusions.- Math - Induction 21 January 2010 11:49 UTC math.editme.com [Source type: FILTERED WITH BAYES]
^ Inductive reasoning moves from specific premises to a general conclusion.
^ Clearly, the conclusion of an inductive argument is not certain to be true given that the premises are.- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
.^ We have just shown that there is no way to prove that it is reasonable to accept inductive inferences.
^ For there is no respect of persons with God.- authorityresearch.com Deductive-Inductive Reasoning Part I 21 January 2010 11:49 UTC authorityresearch.com [Source type: Original source]
^ In the end, there was no other way to escape the evil Demon.- Keith Devens .com - Weblog: The inductive principle - July 04, 2005 21 January 2010 11:49 UTC keithdevens.com [Source type: Original source]
Indeed, not all pictures are hung from nails; moreover, not all pictures are hung.
.^ In the case of a strong inductive argument it is unlikely or improbable that the conclusion would turn out to be false and all the premises be true, but it is logically possible that it might.- Legal Studies Reasoning Profile Scales 21 January 2010 11:49 UTC www.insightassessment.com [Source type: FILTERED WITH BAYES]
- Scales of the Test of Everyday Reasoning 21 January 2010 11:49 UTC www.insightassessment.com [Source type: FILTERED WITH BAYES]
^ There are at least three main differences between an inductively strong argument and a valid argument : As already noted, in a valid argument, the conclusion follows logically from the premises, but this is not the case in an inductively strong argument.- [A05] Inductive Reasoning 21 January 2010 11:49 UTC philosophy.hku.hk [Source type: Original source]
^ Induction or inductive reasoning, sometimes called inductive logic, is the process of reasoning in which the premises of an argument are believed to support the conclusion but do not ensure it.- What is the difference between inductive reasoning and deductive resoning? - Yahoo! Answers 21 January 2010 11:49 UTC answers.yahoo.com [Source type: General]
.^ Here is a simple example of the use of induction.- Handout - Induction 29 September 2009 17:17 UTC www.cs.cornell.edu [Source type: FILTERED WITH BAYES]
^ This allows us to consider what is required of the human mind if we are to accurately use a probability calculus to guide our reasoning with uncertain knowledge.- Standard Probability Axioms 21 January 2010 11:49 UTC www.rci.rutgers.edu [Source type: FILTERED WITH BAYES]
^ In the case of a strong inductive argument it is unlikely or improbable that the conclusion would turn out to be false and all the premises be true, but it is logically possible that it might.- Legal Studies Reasoning Profile Scales 21 January 2010 11:49 UTC www.insightassessment.com [Source type: FILTERED WITH BAYES]
- Scales of the Test of Everyday Reasoning 21 January 2010 11:49 UTC www.insightassessment.com [Source type: FILTERED WITH BAYES]
Conclusions drawn in this manner are usually overgeneralisations.
- Many speeding tickets are given to teenagers.
- Therefore:
- All teenagers drive fast.
.^ One cannot use deduction, the usual process of moving logically from premise to conclusion, because there is simply no syllogism that will allow such a move.- Induction 21 January 2010 11:49 UTC www.jahsonic.com [Source type: FILTERED WITH BAYES]
^ For example, it is well established that people have difficulty reaching valid conclusions with negative premises.- TIP: Concepts 21 January 2010 11:49 UTC home.sprynet.com [Source type: Academic]
^ However, if this argument were ever seriously advanced, we must assume that the author would believe that the truth of the premises guarantees the truth of the conclusion.- Deductive and Inductive Arguments [The Internet Encyclopedia of Philosophy] 21 January 2010 11:49 UTC www.iep.utm.edu [Source type: Academic]
- Deductive and Inductive Arguments [Internet Encyclopedia of Philosophy] 21 January 2010 11:49 UTC www.utm.edu [Source type: Original source]
- Deductive and Inductive Arguments [The Internet Encyclopedia of Philosophy] 21 January 2010 11:49 UTC www.iep.utm.edu [Source type: Academic]
Not every teenager observed has been given a speeding ticket.
.^ The sun rising is a sign of the morning.
^ Arguing that the sun will rise tomorrow because it has risen for the last several years every morning is also a generalization about the future based on past events.
^ For example, in inferring that the next grape sampled will taste sweet, I have implicitly concluded that all grapes in the bunch are sweet because there have no information about the next grape apart from its being from that bunch.
Therefore the conclusion drawn is false.
.^ For, the whole idea of inductive logic is to provide a measure of the extent to which contingent premise sentences indicate the likely truth-values of contingent conclusion sentences.- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ At any rate, an inference, whatever it maybe, comes about in Logic , and is "the forming of a conclusion from data or premisses, either by inductive or deductive methods ..."- On Argument. 21 January 2010 11:49 UTC www.blupete.com [Source type: Original source]
^ What does Equation ( 13 ) tell us about the effects of inductive evidence?- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
.^ Inductive reasoning is not the same as mathematical induction.- First Draft: Inductive and deductive reasoning 21 January 2010 11:49 UTC mblog.lib.umich.edu [Source type: FILTERED WITH BAYES]
^ Both of these are valid forms and the conclusions logically can be deduced if the premises are true.- ALWD | JALWD | Archives | Fall 2006 | Mary Massaron Ross 21 January 2010 11:49 UTC www.alwd.org [Source type: FILTERED WITH BAYES]
^ Inductive reasoning moves from specific premises to a general conclusion.
Validity
.^ Most people use deductive reason by Enthymeme rather than by deductive syllogisms.- Lecture on Logos for English 399 21 January 2010 11:49 UTC webpages.shepherd.edu [Source type: Original source]
^ Deductive reasoning should be distinguished from the related concept of natural deduction, an approach to proof theory that attempts to provide a formal model of logical reasoning as it "naturally" occurs.- What is the difference between inductive reasoning and deductive resoning? - Yahoo! Answers 21 January 2010 11:49 UTC answers.yahoo.com [Source type: General]
^ These will be accomplished through an analysis of logical fallacies, the logical syntax of statements, hypotheses, deductive and inductive arguments and reasoning.
.^ If you give up logic, the very possibility of rational argument or discussion goes away, so we really can't even discuss whether you should have a coherent worldview without first assuming that you must have a coherent worldview.- Keith Devens .com - Weblog: The inductive principle - July 04, 2005 21 January 2010 11:49 UTC keithdevens.com [Source type: Original source]
.^ Inductive reasoning is not the same as mathematical induction.- First Draft: Inductive and deductive reasoning 21 January 2010 11:49 UTC mblog.lib.umich.edu [Source type: FILTERED WITH BAYES]
^ First Draft: Inductive and deductive reasoning First Draft .- First Draft: Inductive and deductive reasoning 21 January 2010 11:49 UTC mblog.lib.umich.edu [Source type: FILTERED WITH BAYES]
^ While deductive reasoning carries with it certainty , nothing is certain as a result of inductive reasoning .- authorityresearch.com Deductive-Inductive Reasoning Part I 21 January 2010 11:49 UTC authorityresearch.com [Source type: Original source]
.^ A hypothesis may not be a true representation of the events or things to be perceived; but any self-respecting hypothesist would only put forth a hypothesis which is consistent with all known facts.- On Argument. 21 January 2010 11:49 UTC www.blupete.com [Source type: Original source]
^ This cross induction will reveal the unreliability of the inference even in the absence of counterinstances (black swans found in Australia).- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ If h is any statistical hypothesis a test of h can go wrong in either of two ways: h may be rejected though true—this is known as a type I error ; or it may be accepted though false—this is a type II error.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
.^ And when he presents his inductively persuasive arguments to others and they don't respond as he expects, he contemptuously dismisses them as deluded fools.- USS Clueless - Inductive logic 21 January 2010 11:49 UTC denbeste.nu [Source type: Original source]
^ Reasons may include deductive arguments, inductive arguments, perceptions, etc.
^ Paul Tournier They may forget what you said, but they will never forget how you made them feel.- down the avenue: Improve Your Inductive Reasoning Through Mind360 21 January 2010 11:49 UTC www.downtheavenue.com [Source type: General]
.^ We will refer to these as Inductive and Deductive Reasoning.
^ What is the difference between deductive and inductive reasoning?- Frequently asked questions about how science works 21 January 2010 11:49 UTC undsci.berkeley.edu [Source type: FILTERED WITH BAYES]
^ What is Inductive /deductive reasoning ?- Inductive Reasoning - Ask.com 21 January 2010 11:49 UTC www.ask.com [Source type: General]
.^ Clearly, the conclusion of an inductive argument is not certain to be true given that the premises are.- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
^ Inductive skeptics are naturally read as claiming that the conclusion of an inductive argument is not rendered more probable by its premises.- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
^ For, the whole idea of inductive logic is to provide a measure of the extent to which contingent premise sentences indicate the likely truth-values of contingent conclusion sentences.- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
)
.^ The deductive method reasons from certain premises to a necessary conclusion.- Trivium Pursuit: Inductive and Deductive Bible Studies 21 January 2010 11:49 UTC www.triviumpursuit.com [Source type: Original source]
^ Q 1 : Is "for that reason" a conclusion indicator or a premise indicator?
^ One cannot use deduction, the usual process of moving logically from premise to conclusion, because there is simply no syllogism that will allow such a move.- Induction 21 January 2010 11:49 UTC www.jahsonic.com [Source type: FILTERED WITH BAYES]
Inductions are open; deductions are closed.
.^ A conclusion you reach using inductive reasoning.
^ Using inductive reasoning, you hypothesize that the bulb has burned out.- What is Deducation? 21 January 2010 11:49 UTC sahs.utmb.edu [Source type: FILTERED WITH BAYES]
^ With deductive reasoning, you can begin with a few true statements, and then deduce more statements that you know are also true.
.^ Clearly, the conclusion of an inductive argument is not certain to be true given that the premises are.- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
^ If the initial premise is true, the conclusion must be true.- The HeadScratcher Post - Deductive and Inductive Thinking 21 January 2010 11:49 UTC headscratchers.com [Source type: General]
^ Inductive arguments are the only sort that can tell you that a conclusion is true.- Suppose we define Inductive reasoning as that reasoning whose conclusionis justified not by there being any necessity of its 21 January 2010 11:49 UTC www.american-philosophy.org [Source type: Original source]
.^ With inductive reasoning, you reach a conclusion that is believed to be true but not guaranteed .- The Inductive Oracle, The Deductive Merovingian 21 January 2010 11:49 UTC hunternuttall.com [Source type: Original source]
^ In other words, you can't have one without the other.- What is Design Thinking Anyway? : Observatory: Design Observer 21 January 2010 11:49 UTC observatory.designobserver.com [Source type: FILTERED WITH BAYES]
^ Share your findings with others in your organization.
.^ In other words, you can't have one without the other.- What is Design Thinking Anyway? : Observatory: Design Observer 21 January 2010 11:49 UTC observatory.designobserver.com [Source type: FILTERED WITH BAYES]
^ You cannot meaningfully say one way or the other.- August « 2004 « Skimmed Cream 21 January 2010 11:49 UTC skimmed.cream.org [Source type: Original source]
^ The only way you can know is to correlate each word with empirical observations that you have had in the past.- Keith Devens .com - Weblog: The inductive principle - July 04, 2005 21 January 2010 11:49 UTC keithdevens.com [Source type: Original source]
.^ Inductive arguments are the only sort that can tell you that a conclusion is true.- Suppose we define Inductive reasoning as that reasoning whose conclusionis justified not by there being any necessity of its 21 January 2010 11:49 UTC www.american-philosophy.org [Source type: Original source]
^ If it were not for inductive reasoning, you would not be reading this.
^ Since, unlike in the case of gravity, experience is not a good predictor of the way grades are determined, it is unlikely that this claim would be argued inductively.- Mission: Critical (Induction vs. Deduction) 21 January 2010 11:49 UTC www.sjsu.edu [Source type: FILTERED WITH BAYES]
.^ The comprehensive interactive help takes you through the process of building and using a case-based application.- Inductive Solutions, Inc. - INDUCE-IT Case Based Reasoning 21 January 2010 11:49 UTC www.inductive.com [Source type: Reference]
^ If your partial beliefs don't conform to them then there is a set of bets all of which you will accept and on which your gain is negative in every possible world.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ Induce-It also provides an interactive 30 minute tutorial that takes you through the process of building and using a case-based spreadsheet.- Inductive Solutions, Inc. - INDUCE-IT Case Based Reasoning 21 January 2010 11:49 UTC www.inductive.com [Source type: Reference]
.^ But it’s still not as strong as a deductive arguments where the conclusion is proven with certainty.- Inductive Logic 21 January 2010 11:49 UTC neo-philosophy.com [Source type: Original source]
^ Which of the conclusions above could only be reached via deductive reasoning?- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
^ Correct inductive arguments sometimes have false conclusions because the reasoning is only probable.- Lee Archie - Inductive Arguments and True Conclusions 21 January 2010 11:49 UTC my.opera.com [Source type: FILTERED WITH BAYES]
.^ But scientific reasoning is ultimately inductive.
^ Thus, training on the strategies employed in the SLS contributes to improved accuracy on inductive reasoning ability.- Effects of Cognitive Training on Change in Accuracy in Inductive Reasoning Ability -- Boron et al. 62 (3): P179 -- Journals of Gerontology Series B: Psychological Sciences and Social Sciences 21 January 2010 11:49 UTC psychsoc.gerontologyjournals.org [Source type: Academic]
^ Thus, there is no way to show that it is reasonable to accept inductive inferences.
.^ Hume, induction and justification .- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ Perhaps the best argument that can be made for this view is to appeal to the Problem of Induction, first formulated by the Scottish philosopher David Hume (1711-1776).
^ Hume's argument is often credited with raising the problem of induction in its modern form.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
.^ Examples : Argument 1 is deductively valid, while argument 2 is not.
^ Argument 1 is deductively valid, while argument 2 is not.
^ We also use Inductive reasoning more often in our everyday lives than we use Deductive.- Reasoning 21 January 2010 11:49 UTC spot.pcc.edu [Source type: FILTERED WITH BAYES]
.^ Most of us would probably not bet our lives on it, because there is always the chance that the last apple is not rotten.- Inductive Logic 21 January 2010 11:49 UTC neo-philosophy.com [Source type: Original source]
^ In the examples above, the unsupported inferences are: that the Congressman is irresponsible and leaves us defenseless; and that you must believe that pollution and other adverse effectsare of no concern.- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
^ But we saw in the last example that just because something is true for ten or a thousand or a million cases, that doesn’t guarantee that it’s true for all cases.- The Inductive Oracle, The Deductive Merovingian 21 January 2010 11:49 UTC hunternuttall.com [Source type: Original source]
.^ Now we are all inclined to believe that someone who has seen lots of cold snow and no snow of any other sort would be crazy not to expect that the snow he has not seen is also cold.- The Problem of Induction 29 September 2009 17:17 UTC www.princeton.edu [Source type: Original source]
^ (Hume THN, 89) And were this premise to be established by reasoning, that reasoning would be either deductive or probabilistic (i.e.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
.^ Psychology, epistemology, and skepticism in Hume's argument about induction,” Synthese , 152: 321–338.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ Reaching the appropriate parameter settings is not practical or even possible via common-sense human reasoning alone.- The Learning Hearing Aid: Common-Sense Reasoning in Hearing Aid Circuits | October 2007 | The Hearing Review | Hearing Review Products 21 January 2010 11:49 UTC www.hearingreview.com [Source type: FILTERED WITH BAYES]
^ The problem of induction is the problem of explaining why it often makes sense to accept conclusions that are supported only by inductive arguments.- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
.^ By accepting conclusions derived from inductive reasoning as true (in a practical sense), good managers can build on these conclusions and move forward effectively and successfully.- Inductive reasoning is the development of a theory or a conclusion afterconsideration of several empirical observations. Inductive reasoning is based on, orcharacterized by induction; using a method of induction. 21 January 2010 11:49 UTC sociologyindex.com [Source type: Academic]
^ Arguing that the sun will rise tomorrow because it has risen for the last several years every morning is also a generalization about the future based on past events.
^ Sometimes people can come to conclusions reliably without being able to know or explain how the conclusion was reached.
.^ This is not to denigrate the leading authority on English vocabulary—until the middle of the previous century induction was understood to be what we now know as enumerative induction or universal inference ; inference from particular instances: .- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
.^ A faulty analogy occurs when the conclusion drawn about one thing due to its connection with the other thing isnt valid ( x is not also C).This can happen if: .- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
^ Reasoning: Which conclusion can be drawn about clean burning coal power plants?- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
^ That is, Victor’s alarmist rhetoric may derive from his anxiety that the creature will become an endless series, rather than a singular instance.- Érudit | Romanticism on the Net v n44 2006 : Morgan | Frankenstein’s Singular Events: Inductive Reasoning, Narrative Technique, and Generic Classification 21 January 2010 11:49 UTC www.erudit.org [Source type: FILTERED WITH BAYES]
.^ One of the classic twentieth century accounts of the problem of induction, that of Nelson Goodman (Goodman 1955), focuses on enumerative inductions that support causal laws.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ Twentieth Century Philosophy (3) Principal developments in philosophy after 1900.- California State University, Fresno - Catalog 21 January 2010 11:49 UTC www.csufresno.edu [Source type: Academic]
.^ Likewise, I assume that observing the present and making predictions about the future is worthwhile.- Keith Devens .com - Weblog: The inductive principle - July 04, 2005 21 January 2010 11:49 UTC keithdevens.com [Source type: Original source]
^ They make observations about the system under study and then try to fit a model to the observed data.- Abstract: Continuous System Modeling 21 January 2010 11:49 UTC www.ece.arizona.edu [Source type: Academic]
^ In fact, the inductive method--whether guided in classrooms or occurring in non-academic settings--is one of the most common and natural forms of making logical assumptions about what we observe.- Inductive methods - WikEd 21 January 2010 11:49 UTC wik.ed.uiuc.edu [Source type: Academic]
.^ It should also be remarked that Hume's argument applies just to enumerative induction, and primarily to singular predictive inference, but, again, its generalization to other forms of inductive reasoning is straightforward.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ The problem is raised in a pointed way by Nelson Goodman's famous grue paradox (Goodman 1955, 73–75).- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ One of the classic twentieth century accounts of the problem of induction, that of Nelson Goodman (Goodman 1955), focuses on enumerative inductions that support causal laws.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
Criticism of inductive reasoning
.^ We use inductive reasoning all of the time.
^ Inductive reasoning has been attacked several times.- What is the difference between inductive reasoning and deductive resoning? - Yahoo! Answers 21 January 2010 11:49 UTC answers.yahoo.com [Source type: General]
^ Inductive reasoning: (1) Conclusion based on several past observations (2) Conclusion is probably true, but not necessarily true .
.^ Historically, David Hume denied its logical admissibility.- What is the difference between inductive reasoning and deductive resoning? - Yahoo! Answers 21 January 2010 11:49 UTC answers.yahoo.com [Source type: General]
.^ After the completion of the eight questions, the subjects, with the examination paper in hand and any written notes made during the examination, were asked to explain how they arrived at each diagnosis.- BioMed Central | Full text | The impact of two multiple-choice question formats on the problem-solving strategies used by novices and experts 21 January 2010 11:49 UTC www.biomedcentral.com [Source type: Academic]
^ In this section we will first examine each of these two kinds of factors in some detail, and then see precisely how the values of posterior probabilities depend on them.- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ These are some of the elementary questions that come to one who inquires into the nature and ultimate significance of the universe.- An Essay On Philosophy by blupete. 21 January 2010 11:49 UTC www.blupete.com [Source type: Original source]
Examining all the particulars is difficult as they are infinite in number.
^{[2]} .^ These considerations suggest deemphasizing the question of justification—show that inductive arguments lead from truths to truths—in favor of exploring methods to assess the reliability of specific inferences.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ The question was asked of Marshall who I have no reason to believe is not you, if you are two people then you parrot the exact same contradicting Kantian nonsense.- Does inductive reasoning lead to knowledge? - sci.logic | Google Groups 21 January 2010 11:49 UTC groups.google.com [Source type: FILTERED WITH BAYES]
^ Conversely, if, as I believe, inductive skepticism is unjustified, then a Humean account of causation and laws is unjustified.- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
.^ However, there is good reason for caution about viewing inductive support functions as Bayesian belief-strength functions, as we will see a bit later.- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ The Romantic rebellion against Reason was unleashed during that period which started the long toboggan ride of reason down to the depths of twentieth century Existentialism, Postmodernism, and narcissistic nihilism.- What went wrong? The bad seeds sowed from Bacon to Kant 21 January 2010 11:49 UTC www.renewamerica.com [Source type: Original source]
^ Subjectivist Bayesians usually take inductive probability to just be this notion of probabilistic belief-strength .- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^{[3]} .^ Inductive logic — the logic of what is operative — reasons from the specific to the general.- What is Design Thinking Anyway? : Observatory: Design Observer 21 January 2010 11:49 UTC observatory.designobserver.com [Source type: FILTERED WITH BAYES]
^ It should also be remarked that Hume's argument applies just to enumerative induction, and primarily to singular predictive inference, but, again, its generalization to other forms of inductive reasoning is straightforward.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ The nature of the connections between the six criteria for analogical reasoning, which are not aimed at general or universal propositions, and Mills five canons of inductive logic are not discussed in this article.- Inductive, analogical and communicative generalization 21 January 2010 11:49 UTC www.ualberta.ca [Source type: Academic]
.^ And as the posterior probabilities of false competitors fall, the posterior probability of the true hypothesis heads towards 1.- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ If h is any statistical hypothesis a test of h can go wrong in either of two ways: h may be rejected though true—this is known as a type I error ; or it may be accepted though false—this is a type II error.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ Some theories have been so thoroughly tested over years that they have become accepted facts of nature.- An Essay On Philosophy by blupete. 21 January 2010 11:49 UTC www.blupete.com [Source type: Original source]
.^ Does inductive reasoning lead to knowledge?- Does inductive reasoning lead to knowledge? - sci.logic | Google Groups 21 January 2010 11:49 UTC groups.google.com [Source type: FILTERED WITH BAYES]
^ Date: Thu, 7 Jan 2010 08:11:55 -0800 (PST) Local: Thurs, Jan 7 2010 11:11 am Subject: Re: Does inductive reasoning lead to knowledge?- Does inductive reasoning lead to knowledge? - sci.logic | Google Groups 21 January 2010 11:49 UTC groups.google.com [Source type: FILTERED WITH BAYES]
^ You appear to be looking for a reason why the universe should be consistent.- Keith Devens .com - Weblog: The inductive principle - July 04, 2005 21 January 2010 11:49 UTC keithdevens.com [Source type: Original source]
.^ You often use d Deductive reasoning is often used in the legal field, as well as in philosophical and mathematical proofs.- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
^ These types of questions often ask you to analyze a passage using deductive reasoning.- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
^ Try to fully understand what the passage's point is and the exact reasoning used in the argument so that if the question asks you to extend that reasoning, you will be are able to accurately do so.- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
Types of inductive reasoning
Generalization
.^ Inductive skeptics are naturally read as claiming that the conclusion of an inductive argument is not rendered more probable by its premises.- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
^ For, the whole idea of inductive logic is to provide a measure of the extent to which contingent premise sentences indicate the likely truth-values of contingent conclusion sentences.- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ At any rate, an inference, whatever it maybe, comes about in Logic , and is "the forming of a conclusion from data or premisses, either by inductive or deductive methods ..."- On Argument. 21 January 2010 11:49 UTC www.blupete.com [Source type: Original source]
- The proportion Q of the sample has attribute A.
- Therefore:
- The proportion Q of the population has attribute A.
- Example
.^ In the Scriptures the contrast is either blessing or cursing, right or wrong, black or white, light or dark, sheep or goat, saved or lost, heaven or hell, etc.- authorityresearch.com Deductive-Inductive Reasoning Part I 21 January 2010 11:49 UTC authorityresearch.com [Source type: Original source]
^ The argument above assumes, like every either/or fallacy, that there are only two possible alternatives open to us: either/or, one or the other, black or white.- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
^ This conflict looks to require that we must either reject enumerative induction or agree that the observation of a white shoe confirms “all ravens are black”.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
.^ H 0 : zero reds, three blacks H 1 : one red, two blacks H 2 : two reds, one black H 3 : three reds zero blacks Let the probabilities of these hypotheses be h 0 , h 1 , h 2 , h 3 , respectively.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ Suppose, for example, from an urn containing balls each of which is red or black, we are to draw (with replacement) three balls.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ Suppose, however, that unbeknownst to you each time a red ball is drawn and replaced a black ball is withdrawn and replaced with a red ball.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
.^ However, there is good reason for caution about viewing inductive support functions as Bayesian belief-strength functions, as we will see a bit later.- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ (Williams 1947, 15) Williams and Stove, for their part, maintain that, though there may be no demonstrative proof of the principle of the uniformity of nature, there are good demonstrative or deductive proofs that certain inductive methods yield their conclusions with high probability.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ If we did not know that many non-ravens are not black, the observation of a white shoe would increase our knowledge.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
.^ The ‘individuals’ of the hyperpopulation are k -samples of individuals from the population X .- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ Premise: In random sample S consisting of n members of population B , the proportion of members that have attribute A is r .- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ How do you identify premises and conclusions?- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
.^ The Fallacy of the Biased Sample is committed whenever the data for a statistical inference is drawn from a sample that is not representative of the population under consideration.- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
^ Here is an argument that commits the fallacy of the biased sample: .- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
^ Whereas in a Biased Sample, people are pulled from a non-representative group, in an Insufficient Sample fallacy, not enough people are polled to make anything statistically significant .- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
Statistical syllogism
.^ A sample must be representative of the overall population to make a general conclusion about the population in question (in this case, Oregon residents).- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
- A proportion Q of population P has attribute A.
- An individual I is a member of P.
- Therefore:
- There is a probability which corresponds to Q that I has A.
.^ It would be better to consider it something like Wittgenstein would - Bedrock to a stream.- Keith Devens .com - Weblog: The inductive principle - July 04, 2005 21 January 2010 11:49 UTC keithdevens.com [Source type: Original source]
^ A histogram would look something like this.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ Some argument would have to be presented to show that it was in fact God, and not something else (e.g., some other supernatural being, one's upbringing, or one's own emotional needs, etc.
Two
dicto simpliciter fallacies can occur in statistical syllogisms: "
accident" and "
converse accident".
Simple induction
.^ Thus good inductions from the same set of premises may lead to conclusions that are conjunctively inconsistent.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ When they began to gather more information about the disease, researchers were able to understand that the disease is a virus passed from one individual to another via bodily fluids.- Materials for Students: Writing the Academic Paper: Logic and Argument 21 January 2010 11:49 UTC www.dartmouth.edu [Source type: General]
^ The Humean problem of induction challenges all arguments that use observed cases as premises to draw conclusions about unobserved cases.- Suppose we define Inductive reasoning as that reasoning whose conclusionis justified not by there being any necessity of its 21 January 2010 11:49 UTC www.american-philosophy.org [Source type: Original source]
- Proportion Q of the known instances of population P has attribute A.
- Individual I is another member of P.
- Therefore:
- There is a probability corresponding to Q that I has A.
.^ If the General Premise is correct, and the Secondary Premise is correct and linked correctly to the General Premise, then the Conclusion must be true.- Reasoning 21 January 2010 11:49 UTC spot.pcc.edu [Source type: FILTERED WITH BAYES]
^ It's very clear that in the first syllogism, the major premise is not true.- Materials for Students: Writing the Academic Paper: Logic and Argument 21 January 2010 11:49 UTC www.dartmouth.edu [Source type: General]
^ It gathers together particular observations in the form of premises, then it reasons from these particular premises to a general conclusion.
Argument from analogy
Main article:
False analogy
.^ Whether or not analogical reasoning is seen as a sort of inductive argumentation, analogical reasoning nevertheless has its own character.- Inductive, analogical and communicative generalization 21 January 2010 11:49 UTC www.ualberta.ca [Source type: Academic]
^ For a detailed discussion of these arguments, see Jaynes 4 and the articles on "deductive reasoning" and "inductive reasoning" on Wikipedia.- The Learning Hearing Aid: Common-Sense Reasoning in Hearing Aid Circuits | October 2007 | The Hearing Review | Hearing Review Products 21 January 2010 11:49 UTC www.hearingreview.com [Source type: FILTERED WITH BAYES]
^ Analogical reasoning can be seen as a special sort of inductive argumentation, as Copi (1982) does, or as a separate form of argumentation which must be distinguished from inductive argumentation, as does, for example, Walton (1989).- Inductive, analogical and communicative generalization 21 January 2010 11:49 UTC www.ualberta.ca [Source type: Academic]
An argument from analogy has the following form:
- I has attributes A, B, and C
- J has attributes A and B
- So, J has attribute C
.^ It works like this: first, two things are shown to be similar in some way, or to share some similar attributes (example: x is A and B; and z is A, B, and C).- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
.^ How can the fallacy of false analogy be avoided?- Inductive, analogical and communicative generalization 21 January 2010 11:49 UTC www.ualberta.ca [Source type: Academic]
^ For, the whole idea of inductive logic is to provide a measure of the extent to which contingent premise sentences indicate the likely truth-values of contingent conclusion sentences.- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ Similarly, in a good inductive argument the premises should provide some degree of support for the conclusion, where such support means that the truth of the premises indicates with some degree of strength that the conclusion is true.- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
.^ Hence, if the premises were truths, so would be the conclusions.- An Essay On Philosophy by blupete. 21 January 2010 11:49 UTC www.blupete.com [Source type: Original source]
^ "In a deductive argument, the truth of the premises is supposed to guarantee the truth of the conclusion; in an inductive argument, the truth of the premises merely makes it probable that the conclusion is true."- authorityresearch.com Deductive-Inductive Reasoning Part I 21 January 2010 11:49 UTC authorityresearch.com [Source type: Original source]
^ The liberal misrepresents deductive reasoning by linking it to an inductive-deductive cycle, "where the truth of its premises make it likely or probable that its conclusion is also true."- authorityresearch.com Deductive-Inductive Reasoning Part I 21 January 2010 11:49 UTC authorityresearch.com [Source type: Original source]
.^ The fitting of a hearing aid with many tunable parameters is often too complex for common sense reasoning, but computers can carry out the calculations and assist the dispenser.- The Learning Hearing Aid: Common-Sense Reasoning in Hearing Aid Circuits | October 2007 | The Hearing Review | Hearing Review Products 21 January 2010 11:49 UTC www.hearingreview.com [Source type: FILTERED WITH BAYES]
^ Man can induct only what he sees or senses (human experience .- authorityresearch.com Deductive-Inductive Reasoning Part I 21 January 2010 11:49 UTC authorityresearch.com [Source type: Original source]
^ A dispenser can no longer use only common sense and expert knowledge to cope with all the complexities and draw the optimal conclusions about parameter settings.- The Learning Hearing Aid: Common-Sense Reasoning in Hearing Aid Circuits | October 2007 | The Hearing Review | Hearing Review Products 21 January 2010 11:49 UTC www.hearingreview.com [Source type: FILTERED WITH BAYES]
.^ Dont choose answers based on sentimental appeal in the critical reasoning section (in Reading Comprehension this is sometimes not the case, however).- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
^ Generalization based on good analogical reasoning is sometimes more suitable, especially when research results obtained from one case are to be generalized to another case.- Inductive, analogical and communicative generalization 21 January 2010 11:49 UTC www.ualberta.ca [Source type: Academic]
^ The six criteria may help to evaluate and criticize case-to-case generalizations based on other forms of (inductive) reasoning.- Inductive, analogical and communicative generalization 21 January 2010 11:49 UTC www.ualberta.ca [Source type: Academic]
.^ One significant advantage of this development is that the cost of gathering more information, of adding to the evidence for an inductive inference, can be factored into the decision.- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
Causal inference
.^ An Inference is a conclusion based on what is already known.- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
^ The Humean problem of induction challenges all arguments that use observed cases as premises to draw conclusions about unobserved cases.- Suppose we define Inductive reasoning as that reasoning whose conclusionis justified not by there being any necessity of its 21 January 2010 11:49 UTC www.american-philosophy.org [Source type: Original source]
^ A faulty analogy occurs when the conclusion drawn about one thing due to its connection with the other thing isnt valid ( x is not also C).This can happen if: .- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
.^ Either way, the relationship is established between two different phenomenon.- reasoning 21 January 2010 11:49 UTC www.comm.pitt.edu [Source type: FILTERED WITH BAYES]
^ A correlation is a statistical linking between two things that seem to be parallel.- GMAT: Critical Reasoning Chapter 3 21 January 2010 11:49 UTC www.800score.com [Source type: FILTERED WITH BAYES]
^ Either way, the relationship is established between two different phenomena.
Prediction
.^ Arguing that the sun will rise tomorrow because it has risen for the last several years every morning is also a generalization about the future based on past events.
^ The Humean problem of induction challenges all arguments that use observed cases as premises to draw conclusions about unobserved cases.- Suppose we define Inductive reasoning as that reasoning whose conclusionis justified not by there being any necessity of its 21 January 2010 11:49 UTC www.american-philosophy.org [Source type: Original source]
^ These conclusions seem unjustified unless backed up with a general assumption that the world is uniform: that the unobserved (say, the future) will be like the observed (say, the past).- Suppose we define Inductive reasoning as that reasoning whose conclusionis justified not by there being any necessity of its 21 January 2010 11:49 UTC www.american-philosophy.org [Source type: Original source]
- Proportion Q of observed members of group G have had attribute A.
- Therefore:
- There is a probability corresponding to Q that other members of group G will have attribute A when next observed.
Bayesian inference
.^ One of the most important applications of a formal inductive logic is to the confirmation or refutation of scientific hypotheses.- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ Most systems of logic have been, since the 19th century, largely supplanted as a field of study by symbolic logic, which replaces ordinary language with mathematical symbols.- An Essay On Philosophy by blupete. 21 January 2010 11:49 UTC www.blupete.com [Source type: Original source]
^ Bayesian Confirmation Theory: Inductive Logic, or Mere Inductive Framework?” Synthese 141, 365-379.- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
.^ Currently more an art than a science, it is likely that probability theory will play a large role in future generations of fitting software used by dispensing professionals.- The Learning Hearing Aid: Common-Sense Reasoning in Hearing Aid Circuits | October 2007 | The Hearing Review | Hearing Review Products 21 January 2010 11:49 UTC www.hearingreview.com [Source type: FILTERED WITH BAYES]
^ We will show that probability theory is consistent with common-sense reasoning, a feature that is not shared by alternative mathematical frameworks for intelligent reasoning.- The Learning Hearing Aid: Common-Sense Reasoning in Hearing Aid Circuits | October 2007 | The Hearing Review | Hearing Review Products 21 January 2010 11:49 UTC www.hearingreview.com [Source type: FILTERED WITH BAYES]
^ Teaching Theory of Knowledge: Probability and Induction , organization of topics and bibliography by Brad Armendt (Arizona State University) and Martin Curd (Purdue).- The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
.^ Now, Bayes Theorem tells us, for any hypothesis h and evidence e : .- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
^ Evaluate the strength of the reasons (how accurate?- �Reasoning� in Argument 21 January 2010 11:49 UTC oregonstate.edu [Source type: FILTERED WITH BAYES]
^ The subjective expectedness of the evidence may be circumvented by considering a ratio form of Bayes' Theorem, a form that compares hypotheses one pair at a time: .- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
.^ We will see that there are good reasons to distinguish inductive probabilities from both Bayesian degree-of-belief probabilities and from purely logical probabilities.- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
.^ If a hypothesis together with auxiliaries and observation conditions deductively entails an evidence claim, the axioms of probability make the corresponding likelihood objective in the sense that every support function must agree on its values: i.e., P [ e .- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ That is one possible value of the objective chance, out of a continuous infinity of possibilities, so the prior probability of the objective chance taking on exactly that value is zero.- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
^ Equation ( 13 ) gives the probability of the inductive prediction A i +1 as a function of the number, i , of consecutive positive instances observed and the initial probability, s , assigned to the hypothesis of stable objective chances.- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
.^ For Bayesians, the Likelihood Ratio Convergence Theorem further implies the likely convergence to agreement (near 0) of the posterior probabilities of false competitors of a true hypothesis.- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ It is sometimes claimed that Bayesian convergence results only work when an agent locks in values for the prior probabilities of hypotheses once and for all, and updates posterior probabilities from there only by conditioning on evidence via Bayes Theorem.- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ But suppose that the prior probabilities of the various competing hypotheses can be represented (at least very nearly) by a probability density function p α [ F [ A , B ] = r .- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
.^ But as a measure of the power of evidence to distinguish among hypotheses, likelihood ratios themselves provide a rather lopsided scale, a scale that ranges from 0 to infinity with the midpoint, where e n doesn't distinguish at all between h i and h j , at 1.- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ In short, the existence of "evil" requires objective moral standards which are only provided on the Christian worldview.- Keith Devens .com - Weblog: The inductive principle - July 04, 2005 21 January 2010 11:49 UTC keithdevens.com [Source type: Original source]
.^ On the other hand, to a materialist, justification is always found in natural-rational actions of mankind (human praxis ) and is not found in belief, unless that belief happens to be in the theory of evolution .- authorityresearch.com Deductive-Inductive Reasoning Part I 21 January 2010 11:49 UTC authorityresearch.com [Source type: Original source]
^ Although the catch-all hypothesis may lack objective likelihoods, the influence of the catch-all term in Bayes' theorem diminishes as additional positive hypotheses are articulated.- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ Moreover, it can be shown that any function P β that satisfies these axioms is a possible rational belief function for some ideally rational agent β.- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
.^ In other words, a given diagnostician will use a given strategy, such as scheme-inductive, on all questions which ask for a problem-solving task (i.e.- BioMed Central | Full text | The impact of two multiple-choice question formats on the problem-solving strategies used by novices and experts 21 January 2010 11:49 UTC www.biomedcentral.com [Source type: Academic]
^ Where faith involves being guided by good reasons, such that the beliefs one has faith in are also supported by adequate evidence, then there is obviously no conflict between faith and reason.
^ And by using the inductive system, if any interpretation we hold conflicts with the facts of scripture, it cannot have been inducted 'from' scripture.
.^ Only insofar as that simplicity bears on either the prior probability of the hypothesis, P( h ), or the likelihood P( e .- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
^ The evaluation of the impact of objective likelihoods on agents' posterior probabilities depends on each agent's individual subjective prior probability, which represents plausibility considerations that have nothing to do with the evidence.- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ The version of the Likelihood Ratio Convergence Theorem we will examine depends only on the Independent Evidence Conditions and on the axioms of probability theory.- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
.^ Using a generalization of the Principle of Indifference, we assign a flat probability density over the range of possible durations of the trip, from 1 hour to 2 hours.- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
^ We would thus want to begin by assigning probabilities to those alternatives in a suitably neutral manner.- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
^ Again using a generalization of the Principle of Indifference, we assign a flat probability density over the range of possible average velocities with which Sue may have traveled.- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
.^ Using a generalization of the Principle of Indifference, we assign a flat probability density over the range of possible durations of the trip, from 1 hour to 2 hours.- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
^ Again using a generalization of the Principle of Indifference, we assign a flat probability density over the range of possible average velocities with which Sue may have traveled.- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
^ These two answers are inconsistent, yet both seem to be arrived at by equally natural applications of the Principle of Indifference.- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
.^ Thus, given the Explanatory Priority Proviso, the three theories would call for different probability distributions over the set of possible mental states of a given subject.- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
^ A great deal of additional work needs to be done, both in attempting to apply this principle to problem cases, and in seeking additional principles governing a priori probabilities.- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
^ If we are to wield the Principle of Indifference against inductive skepticism, then, we must supply a rationale for preferring an inductivist prior probability distribution, such as Laplace's distribution, over the inductive skeptic's distribution.- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
.^ Studies in Inductive Logic and Probability, vol.- Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]
^ Thus, given the Explanatory Priority Proviso, the three theories would call for different probability distributions over the set of possible mental states of a given subject.- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
^ Intuitive motivation for the Principle of Indifference Objective Bayesians recognize constraints on initial probability distributions that go beyond the Kolmogorov axioms.- Explanationist Aid for the Theory of Inductive Logic -- Huemer 60 (2): 345 -- The British Journal for the Philosophy of Science 21 January 2010 11:49 UTC bjps.oxfordjournals.org [Source type: Academic]
See also
- ^ "Induction definition". Yourdictionary.com. 2005. http://www.yourdictionary.com/induction. Retrieved 2009-08-20.
- ^ Sextus Empiricus, Outlines Of Pyrrhonism. Trans. R.G. Bury, Harvard University Press, Cambridge, Massachusetts, 1933, p. 283.
- ^ Karl R. Popper, David W. Miller: A proof of the impossibility of inductive probability. Nature 302 (1983), 687–688.
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