Inductive reasoning

==Problem of induction==
{{Main|The problem of induction}}

Although philosophers at least as far back as the [[Pyrrhonism|Pyrrhonist]] philosopher [[Sextus Empiricus]] have pointed out the unsoundness of inductive reasoning,<ref>Sextus Empiricus, ''Outlines of Pyrrhonism''. Trans. [[Robert Gregg Bury|R.G. Bury]], Harvard University Press, Cambridge, Massachusetts, 1933, p. 283.</ref> the classic philosophical critique of the [[problem of induction]] was given by the Scottish philosopher [[David Hume]].<ref>{{cite book|url=http://18th.eserver.org/hume-enquiry.html#4|title=An Enquiry concerning Human Understanding|author=David Hume|author-link=David Hume|publisher=P.F. Collier & Son|year=1910|isbn=978-0-19-825060-9|access-date=27 December 2007|orig-year=1748|archive-url=https://web.archive.org/web/20071231182807/http://18th.eserver.org/hume-enquiry.html#4|archive-date=31 December 2007|url-status=dead|df=dmy-all}}</ref> Although the use of inductive reasoning demonstrates considerable success, the justification for its application has been questionable. Recognizing this, Hume highlighted the fact that our mind often draws conclusions from relatively limited experiences that appear correct but which are actually far from certain. In deduction, the truth value of the conclusion is based on the truth of the premise. In induction, however, the dependence of the conclusion on the premise is always uncertain. For example, let us assume that all ravens are black. The fact that there are numerous black ravens supports the assumption. Our assumption, however, becomes invalid once it is discovered that there are white ravens. Therefore, the general rule "all ravens are black" is not the kind of statement that can ever be certain. Hume further argued that it is impossible to justify inductive reasoning: this is because it cannot be justified deductively, so our only option is to justify it inductively. Since this argument is circular, with the help of [[Hume's fork]] he concluded that our use of induction is not logically justifiable .<ref>Vickers, John. [http://plato.stanford.edu/entries/induction-problem/#2HumIndJus "The Problem of Induction"] {{Webarchive|url=https://web.archive.org/web/20140407014814/http://plato.stanford.edu/entries/induction-problem/#2HumIndJus |date=7 April 2014 }} (Section 2). ''Stanford Encyclopedia of Philosophy''. 21 June 2010</ref>

Hume nevertheless stated that even if induction were proved unreliable, we would still have to rely on it. So instead of a position of [[Philosophical skepticism|severe skepticism]], Hume advocated a [[Scientific skepticism|practical skepticism]] based on [[common sense]], where the inevitability of induction is accepted.<ref>Vickers, John. [http://plato.stanford.edu/entries/induction-problem/#IndJus "The Problem of Induction"] {{Webarchive|url=https://web.archive.org/web/20140407014814/http://plato.stanford.edu/entries/induction-problem/#IndJus |date=7 April 2014 }} (Section 2.1). ''Stanford Encyclopedia of Philosophy''. 21 June 2010.</ref> [[Bertrand Russell]] illustrated Hume's skepticism in a story about a chicken who, fed every morning without fail and following the laws of induction, concluded that this feeding would always continue, until his throat was eventually cut by the farmer.<ref>{{Cite book|last=Russel|first=Bertrand|title=The Problems of Philosophy|publisher=Oxford University Press|year=1997|isbn=978-0195115529|location=Oxford|pages=66}}</ref>

In 1963, [[Karl Popper]] wrote, "Induction, ''i.e.'' inference based on many observations, is a myth.  It is neither a psychological fact, nor a fact of ordinary life, nor one of scientific procedure."<ref>{{cite journal|last1=Popper|first1=Karl R.|last2=Miller|first2=David W.|year=1983|title=A proof of the impossibility of inductive probability|journal=[[Nature (journal)|Nature]]|volume=302|issue=5910|pages=687–88|bibcode=1983Natur.302..687P|doi=10.1038/302687a0|s2cid=4317588}}</ref><ref name="Gillies">Donald Gillies, "Problem-solving and the problem of induction", in ''Rethinking Popper'' (Dordrecht: [[Springer (publisher)|Springer]], 2009), Zuzana Parusniková & Robert S Cohen, eds, [https://books.google.com/books?id=R3aywtFIKKsC&pg=PA103#v=twopage pp. 103–05].</ref>  Popper's 1972 book ''Objective Knowledge''—whose first chapter is devoted to the problem of induction—opens, "I think I have solved a major philosophical problem: the [[problem of induction]]".<ref name="Gillies" /> In Popper's schema, enumerative induction is "a kind of optical illusion" cast by the steps of conjecture and refutation during a ''problem shift''.<ref name="Gillies" />  An imaginative leap, the ''tentative solution'' is improvised, lacking inductive rules to guide it.<ref name="Gillies" />  The resulting, unrestricted generalization is deductive, an entailed consequence of all explanatory considerations.<ref name="Gillies" />  Controversy continued, however, with Popper's putative solution not generally accepted.<ref>Ch 5 "The controversy around inductive logic" in [[Richard Mattessich]], ed, ''Instrumental Reasoning and Systems Methodology: An Epistemology of the Applied and Social Sciences'' (Dordrecht: [[D. Reidel|D. Reidel Publishing]], 1978), [https://books.google.com/books?id=i8kmptHdx3MC&pg=PA141#v=twopage pp. 141–43] {{Webarchive|url=https://web.archive.org/web/20220509192130/https://books.google.com/books?id=i8kmptHdx3MC&pg=PA141#v=twopage |date=9 May 2022 }}.</ref>

[[Donald A. Gillies]] argues that [[Rule of inference|rules of inferences]] related to inductive reasoning are overwhelmingly absent from science, and describes most scientific inferences as "involv[ing] conjectures thought up by human ingenuity and creativity, and by no means inferred in any mechanical fashion, or according to precisely specified rules."<ref name="Gillies-p111" /> Gillies also provides a rare counterexample "in the machine learning programs of [[Artificial Intelligence|AI]]."<ref name="Gillies-p111">Donald Gillies, "Problem-solving and the problem of induction", in ''Rethinking Popper'' (Dordrecht: [[Springer (publisher)|Springer]], 2009), Zuzana Parusniková & Robert S Cohen, eds, [https://books.google.com/books?id=R3aywtFIKKsC&pg=PA111 p. 111] {{Webarchive|url=https://web.archive.org/web/20220509192129/https://books.google.com/books?id=R3aywtFIKKsC&pg=PA111 |date=9 May 2022 }}: "I argued earlier that there are some exceptions to Popper's claim that rules of inductive inference do not exist. However, these exceptions are relatively rare.  They occur, for example, in the machine learning programs of [[Artificial Intelligence|AI]]. For the vast bulk of human science both past and present, rules of inductive inference do not exist.  For such science, Popper's model of conjectures which are freely invented and then tested out seems to be more accurate than any model based on inductive inferences. Admittedly, there is talk nowadays in the context of science carried out by humans of 'inference to the best explanation' or 'abductive inference', but such so-called inferences are not at all inferences based on precisely formulated rules like the deductive rules of inference. Those who talk of 'inference to the best explanation' or 'abductive inference', for example, never formulate any precise rules according to which these so-called inferences take place. In reality, the 'inferences' which they describe in their examples involve conjectures thought up by human ingenuity and creativity, and by no means inferred in any mechanical fashion, or according to precisely specified rules".</ref>

===Biases===
Inductive reasoning is also known as hypothesis construction because any conclusions made are based on current knowledge and predictions.{{Citation needed|date=March 2012}} As with deductive arguments, biases can distort the proper application of inductive argument, thereby preventing the reasoner from forming the most [[Logical consequence|logical conclusion]] based on the clues. Examples of these biases include the [[availability heuristic]], [[confirmation bias]], and the  [[Gambler's fallacy|predictable-world bias]].

The availability heuristic is regarded as causing the reasoner to depend primarily upon information that is readily available. People have a tendency to rely on information that is easily accessible in the world around them. For example, in surveys, when people are asked to estimate the percentage of people who died from various causes, most respondents choose the causes that have been most prevalent in the media such as terrorism, murders, and airplane accidents, rather than causes such as disease and traffic accidents, which have been technically "less accessible" to the individual since they are not emphasized as heavily in the world around them.

Confirmation bias is based on the natural tendency to confirm rather than deny a hypothesis. Research has demonstrated that people are inclined to seek solutions to problems that are more consistent with known hypotheses rather than attempt to refute those hypotheses. Often, in experiments, subjects will ask questions that seek answers that fit established hypotheses, thus confirming these hypotheses. For example, if it is hypothesized that Sally is a sociable individual, subjects will naturally seek to confirm the premise by asking questions that would produce answers confirming that Sally is, in fact, a sociable individual.

The predictable-world bias revolves around the inclination to perceive order where it has not been proved to exist, either at all or at a particular level of abstraction. Gambling, for example, is one of the most popular examples of predictable-world bias. Gamblers often begin to think that they see simple and obvious patterns in the outcomes and therefore believe that they are able to predict outcomes based on what they have witnessed. In reality, however, the outcomes of these games are difficult to predict and highly complex in nature. In general, people tend to seek some type of simplistic order to explain or justify their beliefs and experiences, and it is often difficult for them to realise that their perceptions of order may be entirely different from the truth.<ref>{{cite book|title=Psychology|last=Gray|first=Peter|publisher=Worth|year=2011|isbn=978-1-4292-1947-1|edition=Sixth|location=New York}}</ref>