Contents 1 Description 2 Inductive vs. deductive reasoning 3 Criticism 3.1 Biases 4 Types 4.1 Generalization 4.2 Statistical syllogism 4.3 Simple induction 4.4 Argument from analogy 4.5 Causal inference 4.6 Prediction 5 Bayesian inference 6 Inductive inference 7 See also 8 References 9 Further reading 10 External links Description[edit]
All biological life forms that we know of depend on liquid water to exist. Therefore, if we discover a new biological life form it will probably depend on liquid water to exist. This argument could have been made every time a new biological life form was found, and would have been correct every time; however, it is still possible that in the future a biological life form not requiring liquid water could be discovered. As a result, the argument may be stated less formally as: All biological life forms that we know of depend on liquid water to exist. All biological life probably depends on liquid water to exist. Inductive vs. deductive reasoning[edit] Argument terminology Unlike deductive arguments, inductive reasoning allows for the possibility that the conclusion is false, even if all of the premises are true.[4] Instead of being valid or invalid, inductive arguments are either strong or weak, which describes how probable it is that the conclusion is true.[5] Another crucial difference is that deductive certainty is impossible in non-axiomatic systems, such as reality, leaving inductive reasoning as the primary route to (probabilistic) knowledge of such systems.[6] Given that "if A is true then that would cause B, C, and D to be true", an example of deduction would be "A is true therefore we can deduce that B, C, and D are true". An example of induction would be "B, C, and D are observed to be true therefore A might be true". A is a reasonable explanation for B, C, and D being true. For example: A large enough asteroid impact would create a very large crater and cause a severe impact winter that could drive the non-avian dinosaurs to extinction. We observe that there is a very large crater in the Gulf of Mexico dating to very near the time of the extinction of the non-avian dinosaurs Therefore it is possible that this impact could explain why the non-avian dinosaurs became extinct. Note however that this is not necessarily the case. Other events also
coincide with the extinction of the non-avian dinosaurs. For example,
the
All of the swans we have seen are white. Therefore, all swans are white. (Or more precisely, "We expect that all swans are white") The definition of inductive reasoning described in this article
excludes mathematical induction, which is a form of deductive
reasoning that is used to strictly prove properties of recursively
defined sets.[7] The deductive nature of mathematical induction is
based on the non-finite number of cases involved when using
mathematical induction, in contrast with the finite number of cases
involved in an enumerative induction procedure with a finite number of
cases like proof by exhaustion. Both mathematical induction and proof
by exhaustion are examples of complete induction. Complete induction
is a type of masked deductive reasoning.
Criticism[edit]
Main article: Problem of induction
The proportion Q of the sample has attribute A. Therefore: The proportion Q of the population has attribute A. Example There are 20 balls—either black or white—in an urn. To estimate their respective numbers, you draw a sample of four balls and find that three are black and one is white. A good inductive generalization would be that there are 15 black and five white balls in the urn. How much the premises support the conclusion depends upon (a) the number in the sample group, (b) the number in the population, and (c) the degree to which the sample represents the population (which may be achieved by taking a random sample). The hasty generalization and the biased sample are generalization fallacies. Statistical syllogism[edit] Main article: Statistical syllogism A statistical syllogism proceeds from a generalization to a conclusion about an individual. A proportion Q of population P has attribute A. An individual X is a member of P. Therefore: There is a probability which corresponds to Q that X has A. 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" and "converse accident". Simple induction[edit] Simple induction proceeds from a premise about a sample group to a conclusion about another individual. 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. Argument from analogy[edit] Main article: Argument from analogy The process of analogical inference involves noting the shared properties of two or more things, and from this basis inferring that they also share some further property:[15] P and Q are similar in respect to properties a, b, and c. Object P has been observed to have further property x. Therefore, Q probably has property x also. Analogical reasoning is very frequent in common sense, science, philosophy and the humanities, but sometimes it is accepted only as an auxiliary method. A refined approach is case-based reasoning.[16] Causal inference[edit] A causal 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. Prediction[edit] A prediction draws a conclusion about a future individual from a past sample. 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[edit]
As a logic of induction rather than a theory of belief, Bayesian
inference does not determine which beliefs are a priori rational, but
rather determines how we should rationally change the beliefs we have
when presented with evidence. We begin by committing to a prior
probability for a hypothesis based on logic or previous experience,
and when faced with evidence, we adjust the strength of our belief in
that hypothesis in a precise manner using Bayesian logic.
Inductive inference[edit]
Around 1960,
Thinking portal
Abductive reasoning
Algorithmic probability
Analogy
Bayesian probability
Counterinduction
Deductive reasoning
Explanation
Failure mode and effects analysis
Falsifiability
Grammar induction
Inductive inference
Inductive logic programming
Inductive probability
Inductive programming
References[edit] ^ Copi, I. M.; Cohen, C.; Flage, D. E. (2007). Essentials of Logic
(Second ed.). Upper Saddle River, NJ: Pearson Education.
ISBN 978-0-13-238034-8.
^ "Deductive and Inductive Arguments", Internet Encyclopedia of
Philosophy, Some dictionaries define "deduction" as reasoning from the
general to specific and "induction" as reasoning from the specific to
the general. While this usage is still sometimes found even in
philosophical and mathematical contexts, for the most part, it is
outdated.
^ Kosko, Bart (1990). "Fuzziness vs. Probability". International
Journal of General Systems. 17 (1): 211–240.
doi:10.1080/03081079008935108.
^ John Vickers. The Problem of Induction. The Stanford Encyclopedia of
Philosophy.
^ Herms, D. "Logical Basis of Hypothesis Testing in Scientific
Research" (pdf).
^ "Stanford Encyclopedia of Philosophy : Kant's account of
reason".
^ Chowdhry, K.R. (January 2, 2015). Fundamentals of Discrete
Mathematical Structures (3rd ed.). PHI
Further reading[edit] Cushan, Anna-Marie (1983/2014). Investigation into Facts and Values: Groundwork for a theory of moral conflict resolution. [Thesis, Melbourne University], Ondwelle Publications (online): Melbourne. [1] Herms, D. "Logical Basis of Hypothesis Testing in Scientific Research" (PDF). Kemerling, G. (27 October 2001). "Causal Reasoning". Holland, J. H.; Holyoak, K. J.; Nisbett, R. E.; Thagard, P. R. (1989). Induction: Processes of Inference, Learning, and Discovery. Cambridge, MA: MIT Press. ISBN 0-262-58096-9. Holyoak, K.; Morrison, R. (2005). The Cambridge Handbook of Thinking and Reasoning. New York: Cambridge University Press. ISBN 978-0-521-82417-0. External links[edit] Wikiquote has quotations related to: Inductive reasoning Look up inductive reasoning in Wiktionary, the free dictionary.
"Confirmation and Induction". Internet Encyclopedia of
Philosophy.
Zalta, Edward N. (ed.). "Inductive Logic". Stanford Encyclopedia of
Philosophy.
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