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| + | =Induction= |
| − | {{dablink|Inductive reasoning is the complement of [[deductive]] reasoning. For other article subjects named induction, see [[Induction]].}}
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| − | writer: Quay.—[[User:Keisuke Noda|Keisuke Noda]] 14:06, 13 May 2006 (UTC)
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| − | __TOC__
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| − | '''Induction''' or '''inductive reasoning''', sometimes called '''inductive logic''', is the process of [[reasoning]] in which the premises of an argument support the conclusion but do not ensure it. It is used to ascribe [[Category of being|properties or relations]] to [[Type (metaphysics)|types]] based on tokens (i.e., on one or a small number of observations or experiences); or to formulate [[law]]s based on limited observations of recurring [[phenomena]]l patterns. Induction is used, for example, in using specific propositions such as:
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| − | : This ice is cold.
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| − | : A billiard ball moves when struck with a cue.
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| − | ...to infer general propositions such as:
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| − | : All ice is cold.
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| − | : There is no ice in the Sun.
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| − | : For every action, there is an equal and opposite reaction.
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| − | : Anything struck with a cue moves.
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| − | == Strong and weak induction ==
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| − | ===Strong induction===
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| − | : All observed crows are black.
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| − | : therefore
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| − | : All crows are black.''
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| − | This exemplifies the nature of induction: inducing the universal from the particular. However, the conclusion is not certain. Unless we are certain that we have seen every'' crow – something that is impossible – there may be one of a different colour. (Being black may be added to the definition of a crow; but if two crow-like birds were to be identical except for their colour, one would become an instance of a black crow and the other a (rare) instance of, say, a blue crow – but both would still be regarded as crows.)
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| − | ===Weak induction===
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| − | : I always hang pictures on nails.
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| − | : therefore
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| − | : All pictures hang from nails.
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| − | Assuming the first statement to be true, this example is built on the certainty that "I always hang pictures on nails" leading to the generalisation that "All pictures hang from nails". However, not all pictures are hung from nails; indeed, not all pictures are hung. Conclusions drawn in this manner are usually overgeneralisations.
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| − | : Teenagers are given many speeding tickets.
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| − | : therefore
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| − | : All teenagers speed.
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| − | In this example, the premise is not built upon a certainty: not every teenager observed has been given a speeding ticket. Therefore the conclusion drawn cannot be the certainty it claims to be.
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| − | == Validity ==
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| − | Formal logic as most people learn it is deductive rather than inductive. Some philosophers claim to have created systems of inductive logic, but it is controversial whether a logic of induction is even possible. In contrast to [[deductive reasoning]], conclusions arrived at by inductive reasoning do not necessarily have the same degree of certainty as the initial premises. For example, a conclusion that all swans are white is false, but may have been thought true in [[Europe]] until the settlement of [[Australia]]. Inductive arguments are never [[validity|binding]] but they may be [[cogency|cogent]]. Inductive reasoning is deductively invalid. (An argument in formal logic is valid if and only if it is not possible for the premises of the argument to be true whilst the conclusion is false.) In induction there are always many conclusions that can reasonably be related to certain premises. Inductions are open; deductions are closed.
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| − | The classic philosophical treatment of the [[problem of induction]], meaning the search for a justification for inductive reasoning, was by the [[Scottish people|Scottish]] philosopher [[David Hume]]. Hume highlighted the fact that our everyday reasoning depends on patterns of repeated experience rather than deductively valid arguments. 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. As Hume said, someone who insisted on sound deductive justifications for everything would starve to death.
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| − | Instead of unproductive [[Philosophical skepticism|radical skepticism]] about everything, Hume advocated a [[Scientific skepticism|practical skepticism]] based on [[common sense]], where the inevitability of induction is accepted.
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| − | 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. Inferences about the past from present evidence – for instance, as in [[archaeology]], count as induction. Induction could also be across space rather than time, for instance as in [[cosmology]] where conclusions about the whole universe are drawn from what we are able to observe from within our own galaxy; or in [[economics]], where national economic policy is derived from local economic performance. | |
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| − | Twentieth-century philosophy has approached induction very differently. 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. [[Nelson Goodman]] posed a "new riddle of induction" by inventing the property "grue" to which induction does not apply (see [[Grue (color)|Grue]]).
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| − | ==Types of inductive reasoning==
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| − | ''Sources for the examples that follow are:'' [http://ethics.acusd.edu/Courses/logic/answers/Exercise1_3.html (1)], [http://www.dartmouth.edu/~bio125/logic.Giere.pdf (2)], [http://www.philosophypages.com/lg/e14.htm (3)].
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| − | ===Generalization===
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| − | A generalization (more accurately, an ''inductive generalization'') proceeds from a premise about a [[statistical sample|sample]] to a conclusion about the [[statistical population|population]]:
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| − | : The proportion Q of the sample has attribute A.
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| − | : therefore
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| − | : The proportion Q of the population has attribute A.
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| − | How great the support 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 randomness of the sample. The [[hasty generalization]] and [[biased sample]] are fallacies related to generalization.
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| − | ===Statistical syllogism===
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| − | A statistical syllogism proceeds from a generalization to a conclusion about an individual:
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| − | : A proportion Q of population P has attribute A.
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| − | : An individual I is a member of P.
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| − | : therefore
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| − | : There is a probability which corresponds to Q that I has A.
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| − | The proportion in the first premise would be something like "3/5ths of", "all", "few", etc. Two [[dicto simpliciter]] fallacies can occur in statistical syllogisms: "[[accident (fallacy)|accident]]" and "[[converse accident]]".
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| − | ===Simple induction===
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| − | Simple induction proceeds from a premise about a sample group to a conclusion about another individual.
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| − | : Proportion Q of the known instances of population P has attribute A.
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| − | : Individual I is another member of P.
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| − | : therefore
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| − | : There is a probability corresponding to Q that I has A.
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| − | 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.
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| − | ===Argument from analogy===
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| − | An (inductive) [[analogy]] proceeds from known similarities between two things to a conclusion about an additional attribute common to both things:
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| − | : P is similar to Q.
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| − | : P has attribute A.
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| − | : therefore
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| − | : Q has attribute A.
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| − | An analogy relies on the inference that the properties known to be shared (the similarities) imply that A is also a shared property. The support which the premises provide for the conclusion is dependent upon the relevance and number of the similarities between P and Q.
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| − | ===Causal inference===
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| − | An inference draws a conclusion about a causal connection based on the conditions of the occurrence of an effect. 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.
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| − | : A prediction draws a conclusion about a future individual from a past sample.
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| − | : Proportion Q of observed members of group G have had attribute A.
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| − | : therefore
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| − | : There is a probability corresponding to Q that the next observed .
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| − | ===Argument from authority===
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| − | An argument from authority draws a conclusion about the truth of a statement based on the proportion of true propositions provided by a source. It has the same form as a prediction.
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| − | : Proportion Q of the claims of authority A have been true.
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| − | : therefore
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| − | : There is a probability corresponding to Q that this claim of A is true.
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| − | For instance:
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| − | : All observed claims from websites about logic are true.
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| − | : Information X came from a website about logic.
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| − | : therefore
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| − | : Information X is likely to be true.
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| − | == Bayesian inference ==
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| − | Of the candidate systems for an inductive logic, the most influential is [[Bayesianism]]. This uses [[probability]] theory as the framework for induction. Given new evidence, [[Bayes' theorem]] is used to evaluate how much the strength of a belief in a hypothesis should change.
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| − | There is debate around what informs the original degree of belief. 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 (metaphysics)|objectivism]]. 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. They therefore fail to provide an objective standard for choosing between conflicting hypotheses. The theorem can be used to produce a rational justification for a belief in some hypothesis, but at the expense of rejecting objectivism. Such a scheme cannot be used, for instance, to decide objectively between conflicting scientific paradigms.
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| − | [[Edwin Thompson Jaynes|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 [[priors|prior probabilities]]; or in choosing [[likelihood|likelihoods]]. He thus sought principles for assigning probabilities from qualitative knowledge. [[Maximum entropy]] – a generalization of the [[principle of indifference]] – and [[transformation groups]] are the two tools he produced. 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.
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| − | [[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''.
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| − | == Footnotes ==
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| − | <div style=font-size:90%><references /></div>
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| − | == External links ==
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| − | * [http://www.uncg.edu/phi/phi115/induc4.htm ''Four Varieties of Inductive Argument''] from the Department of Philosophy, [[University of North Carolina at Greensboro]].
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| − | * [http://plato.stanford.edu/entries/logic-inductive/ ''Inductive Logic''] from the [[Stanford Encyclopedia of Philosophy]].
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| − | * {{PDFlink}} [http://faculty.ucmerced.edu/eheit/heit2000.pdf ''Properties of Inductive Reasoning''], a psychological review by Evan Heit of the [[University of California, Merced]].
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| − | == See also ==
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| − | {{col-begin}}
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| − | {{col-break}}
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| − | * [[Abductive reasoning]]
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| − | * [[Deductive reasoning]]
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| − | * [[Explanation]]
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| − | * [[Falsifiability]]
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| − | * [[Inductive reasoning aptitude]]
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| − | {{col-break}}
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| − | * [[Inferential statistics]]
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| − | * [[Inquiry]]
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| − | * [[Logic]]
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| − | * [[Mathematical induction]]
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| − | * [[Retroductive reasoning]]
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| − | {{col-end}}
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| − | {{Philosophy navigation}}
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| | + | <b>Induction</b>, sometimes called <b>inductive logic</b>, is the process of reasoning in which the premises of an argument support a conclusion, but do not ensure it. Induction contrasts with [[deduction]], or <b>deductive logic</b>, which is the process of reasoning in which the premises ''guarantee'' a conclusion. |
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