# Encyclopedia

.Inductive reasoning, also known as induction or inductive logic, is a type of reasoning that involves moving from a set of specific facts to a general conclusion.It uses premises from objects that have been examined to establish a conclusion about an object that has not been examined[1] It can also be seen as a form of theory-building, in which specific facts are used to create a theory that explains relationships between the facts and allows prediction of future knowledge.^ 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.
.Note that mathematical induction is not a form of inductive reasoning.^ 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]

.While mathematical induction may be inspired by the non-base cases, the formulation of a base case firmly establishes it as a form of deductive reasoning.^ 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]

.Many philosophers believe that the ability to use inductive reasoning is essential for understanding and that it accumulates from observation and ideas which are the fabric of insight.^ "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]

.Many philosophical topics such as morality and faith are explained using inductive reasoning.^ 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 exemplifies the nature of induction: inducing the universal from the particular.^ 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. .Unless we can systematically falsify the possibility of crows of another colour, the statement (conclusion) may actually be false.^ 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]

.For example, one could examine the bird's genome and learn whether it is capable of producing a differently coloured bird.^ 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. .Even if you change the definition of "crow" to require blackness, the original question of the colour possibilities for a bird of that species would stand, only semantically hidden.^ 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]

.A strong induction is thus an argument in which the truth of the premises would make the conclusion probable, but not necessitate it as being factual.^ "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.
.Assuming the first statement to be true, this example is built on the certainty that "I always hang pictures on nails" leading to the generalization that "All pictures hang from nails". However, the link between the premise and the inductive conclusion is weak.^ 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]

.No reason exists to believe that just because one person hangs pictures on nails that there are no other ways for pictures to be hung, or that other people cannot do other things with pictures.^ 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. .The conclusion cannot be strongly inductively made from the premise.^ 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]

.Using other knowledge we can easily see that this example of induction would lead us to a clearly false conclusion.^ 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.
.In this example, the premise is built upon a certainty; however, it is not one that leads to the conclusion.^ 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. .In other words, unlike "The sun rises every morning", there are already plenty of examples of teenagers not being given speeding tickets.^ 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. .Moreover, when the link is weak, the inductive logic does not give us a strong conclusion.^ 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]

.In both of these examples of weak induction, the logical means of connecting the premise and conclusion (with the word "therefore") are faulty, and do not give us a strong inductively reasoned statement.^ 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

.Formal logic, as most people learn it, is deductive rather than inductive.^ 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.

.It is controversial whether a logic of induction is even possible.^ 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]

.In contrast to deductive reasoning, conclusions arrived at by inductive reasoning do not have the same degree of certainty as the initial premises.^ 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]

.For example, a conclusion that all swans are white is false, but may have been thought true in Europe until the settlement of Australia or New Zealand, when Black Swans were discovered.^ 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]

.Inductive arguments are never binding but they may be cogent.^ 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]

.Inductive reasoning is deductively invalid.^ 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]

.(An argument in formal logic is valid if and only if it is not possible for the premises of the argument to be true while the conclusion is false.^ 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]

) .In induction there are always many conclusions that can reasonably be related to certain premises.^ 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. .It is however possible to derive a true statement using inductive reasoning if you know the conclusion.^ A conclusion you reach using inductive reasoning.
• Inductive Reasoning 21 January 2010 11:49 UTC www.slideshare.net [Source type: Reference]

^ 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.

.The only way to have an efficient argument by induction is for the known conclusion to be able to be true only if an unstated external conclusion is true, from which the initial conclusion was built and has certain criteria to be met in order to be true (separate from the stated 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]

^ 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]

.By substitution of one conclusion for the other, you can inductively find out what evidence you need in order for your induction to be true.^ 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]

.For example, you have a window that opens only one way, but not the other.^ 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]

.Assuming that you know that the only way for that to happen is that the hinges are faulty, inductively you can postulate that the only way for that window to be fixed would be to apply oil (whatever will fix the unstated conclusion).^ 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]

.From there on you can successfully build your case.^ 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]

.However, if your unstated conclusion is false, which can only be proven by deductive reasoning, then your whole argument by induction collapses.^ 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]

.Thus ultimately, inductive reasoning is not reliable.^ 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.

.The classic philosophical treatment of the problem of induction, meaning the search for a justification for inductive reasoning, was by the Scottish philosopher David Hume.^ 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]

.Hume highlighted the fact that our everyday reasoning depends on patterns of repeated experience rather than deductively valid arguments.^ 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]

.For example, we believe that bread will nourish us because it has done so in the past, but this is not a guarantee that it will always do so.^ 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]

.As Hume said, someone who insisted on sound deductive justifications for everything would starve to death.^ 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]

.Instead of approaching everything with severe skepticism, Hume advocated a practical skepticism based on common sense, where the inevitability of induction is accepted.^ 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]

.Induction is sometimes framed as reasoning about the future from the past, but in its broadest sense it involves reaching conclusions about unobserved things on the basis of what has been observed.^ 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.

.Inferences about the past from present evidence – for instance, as in archaeology, count as induction.^ 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]

.Induction could also be across space rather than time, for instance as in physical cosmology where conclusions about the whole universe are drawn from the limited perspective we are able to observe (see cosmic variance); or in economics, where national economic policy is derived from local economic performance.^ 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]

.Twentieth-century philosophy has approached induction very differently.^ 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]

.Rather than a choice about what predictions to make about the future, induction can be seen as a choice of what concepts to fit to observations or of how to graph or represent a set of observed data.^ 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]

.Nelson Goodman posed a "new riddle of induction" by inventing the property "grue" to which induction as a prediction about the future does not apply.^ 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

.Inductive reasoning has been attacked several times.^ 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.^ 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]

.Sextus Empiricus questioned how the truth of the Universals can be established by examining some of the particulars.^ 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] .Empiricus believed that inductive reasoning assumed truths which disagreed with his position as a believer of universal skepticism, the assumed truths which inductive reasoning purposes, according to Empiricus, can never be fully understood and must always be questioned.^ 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]

.During the twentieth century, thinkers such as Karl Popper and David Miller have disputed the existence, necessity and validity of any inductive reasoning, including probabilistic (Bayesian) reasoning.^ 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] .Karl Popper assessed that inductive reasoning leaves too much room for assumptions and generalizations.^ 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 Mills 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]

.According to Popper, nothing can be accurately confirmed or assumed, the only way to acquire true understanding is to test whether a theory is false, if it can be tested and is shown to be not false it becomes probable but newer confirmed.^ 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]

.This is why inductive reasoning, according to Popper, should not be used and does not have to be used.^ 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]

.Popper beleived that it is more accurate to use deductive reasoning to observe the falsifiability of a theory.^ 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

.A generalization (more accurately, an inductive generalization) proceeds from a premise about a sample to a conclusion about the population.^ 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
.There are 20 balls in an urn, either black or white.^ 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]

.To estimate their respective numbers you draw a sample of 4 balls and find that 3 are black, one is white.^ 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]

.A good inductive generalisation would be: there are 15 black and 5 white balls in the urn.^ 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]

.How great the support is which the premises provide for the conclusion is dependent on (a) the number of individuals in the sample group compared to the number in the population; and (b) the degree to which the sample is representative of the population (which may be achieved by taking a random sample).^ 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 hasty generalisation and biased sample are fallacies related to generalisation.^ 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 statistical syllogism proceeds from a generalization to a conclusion about an individual.^ 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.
.The proportion in the first premise would be something like "3/5ths of", "all", "few", etc.^ 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

.Simple induction proceeds from a premise about a sample group to a conclusion about another individual.^ 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.
.This is a combination of a generalization and a statistical syllogism, where the conclusion of the generalization is also the first premise of the statistical syllogism.^ 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

.Some philosophers believe that an argument from analogy is a kind of inductive reasoning.^ 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
.An analogy relies on the inference that the attributes known to be shared (the similarities) imply that C is also a shared property.^ 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]

.The support which the premises provide for the conclusion is dependent upon the relevance and number of the similarities between I and J. The fallacy related to this process is false analogy.^ 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]

.As with other forms of inductive argument, even the best reasoning in an argument from analogy can only make the conclusion probable given the truth of the premises, not certain.^ 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]

.Analogical reasoning is very frequent in common sense, science, philosophy and the humanities, but sometimes it is accepted only as an auxiliary method.^ 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]

.A refined approach is case-based reasoning.^ 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]

.For more information on inferences by analogy, see Juthe, 2005.^ 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

.A causal inference draws a conclusion about a causal connection based on the conditions of the occurrence of an effect.^ 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]

.Premises about the correlation of two things can indicate a causal relationship between them, but additional factors must be confirmed to establish the exact form of the causal relationship.^ 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

.A prediction draws a conclusion about a future individual from a past sample.^ 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

.Of the candidate systems for an inductive logic, the most influential is Bayesianism.^ 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]

.This uses probability theory as the framework for induction.^ 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]

.Given new evidence, Bayes' theorem is used to evaluate how much the strength of a belief in a hypothesis should change.^ 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]

.There is debate around what informs the original degree of belief.^ 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]

.Objective Bayesians seek an objective value for the degree of probability of a hypothesis being correct and so do not avoid the philosophical criticisms of objectivism.^ 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]

.Subjective Bayesians hold that prior probabilities represent subjective degrees of belief, but that the repeated application of Bayes' theorem leads to a high degree of agreement on the posterior probability.^ 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]

.They therefore fail to provide an objective standard for choosing between conflicting hypotheses.^ 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]

.The theorem can be used to produce a rational justification for a belief in some hypothesis, but at the expense of rejecting objectivism.^ 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]

.Such a scheme cannot be used, for instance, to decide objectively between conflicting scientific paradigms.^ 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.

.Edwin Jaynes, an outspoken physicist and Bayesian, argued that "subjective" elements are present in all inference, for instance in choosing axioms for deductive inference; in choosing initial degrees of belief or prior probabilities; or in choosing likelihoods.^ 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]

.He thus sought principles for assigning probabilities from qualitative knowledge.^ 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]

.Maximum entropy – a generalization of the principle of indifference – and transformation groups are the two tools he produced.^ 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]

.Both attempt to alleviate the subjectivity of probability assignment in specific situations by converting knowledge of features such as a situation's symmetry into unambiguous choices for probability distributions.^ 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]

.Cox's theorem, which derives probability from a set of logical constraints on a system of inductive reasoning, prompts Bayesians to call their system an inductive logic.^ 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]

## Footnotes

1. ^ "Induction definition". Yourdictionary.com. 2005. Retrieved 2009-08-20.
2. ^ Sextus Empiricus, Outlines Of Pyrrhonism. Trans. R.G. Bury, Harvard University Press, Cambridge, Massachusetts, 1933, p. 283.
3. ^ Karl R. Popper, David W. Miller: A proof of the impossibility of inductive probability. Nature 302 (1983), 687–688.

## References

.
• Herms, D. "Logical Basis of Hypothesis Testing in Scientific Research" (pdf).^ We will examine the extent to which this kind of logic may pass muster as an adequate logic of evidential support, especially in regard to the testing of scientific hypotheses.
• Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]

http://www.dartmouth.edu/~bio125/logic.Giere.pdf
.
• Kemerling, G (2001-10-27). "Causal Reasoning"
• First Draft: Inductive and deductive reasoning 21 January 2010 11:49 UTC mblog.lib.umich.edu [Source type: FILTERED WITH BAYES]

• down the avenue: Improve Your Inductive Reasoning Through Mind360 21 January 2010 11:49 UTC www.downtheavenue.com [Source type: General]

• First Draft: Inductive and deductive reasoning 21 January 2010 11:49 UTC mblog.lib.umich.edu [Source type: FILTERED WITH BAYES]

.Induction: Processes of Inference, Learning, and Discovery.^ Because the creature must learn the causes of phenomena the reader takes for granted, his story defamiliarizes both the reader’s world and the process of induction itself.
• 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]

.Cambridge, MA, USA: MIT Press.^ Fact, Fiction, & Forecast , Cambridge, MA: Harvard University Press.
• The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]

^ The Enterprise of Knowledge , Cambridge, Mass.: MIT Press.
• Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]

^ A Critical Examination of Bayesian Confirmation Theory , Cambridge, MA: MIT Press.
• Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]

ISBN 0262580969.
• Holyoak, K; Morrison R (2005). The Cambridge Handbook of Thinking and Reasoning. .New York: Cambridge University Press.^ Fact, Fiction, & Forecast , Cambridge, MA: Harvard University Press.
• The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]

^ Betting on Theories , Cambridge: Cambridge University Press.
• Inductive Logic (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]

^ Symmetry and Its Discontents , Cambridge: Cambridge University Press.
• The Problem of Induction (Stanford Encyclopedia of Philosophy) 21 January 2010 11:49 UTC plato.stanford.edu [Source type: Academic]

ISBN 978-0521824170.

# Simple English

Induction is one of the two main forms of logical reasoning. The other is deduction. In induction, we find a general rule by using a large number of particular cases. For example, watching water in many different situations, we can conclude that water always flows downhill.

Induction is the method of science. A scientist makes a large number of observations, and then suggests a general rule that all of these observations follow. He then publishes his ideas, and they are checked in many other cases by other scientists. The general rule becomes a scientific theory only if it passes all of these tests. If it fails even one test, then the theory must be either changed or thrown out. The major scientific theories of today have been tested many thousands of times and have passed every test.

The method of induction must be used carefully, because even one failure disproves the theory. For example, people noticed that when the letters "i" and "e" appear together in a word, the "i" usually comes first, as in "sieve", "bier", and "die". So, should we use induction to make a rule "Always put 'i' before 'e'?" No, because there are exceptions: "ceiling", "deceive", and "receive". Then do we want a rule, "i before e except after c"? But there is another set of exceptions, "neighbor" and "weigh". So someone proposed the rule, "i before e except after c, or when sounded like 'a' as in 'neighbor' and 'weigh'." Even that rule is not always true. Consider the word "weird".

You can see how hard it is to come up with a rule that is always true.

When a person uses induction carelessly, and believes a rule that is not always true, we say that they "jump to a conclusion".

# Citable sentences

Up to date as of December 24, 2010

Here are sentences from other pages on Inductive reasoning, which are similar to those in the above article.