Editing Abductive reasoning (section)

== Deduction, induction, and abduction==
{{Main|Logical reasoning}}

=== Deduction ===
{{Main|Deductive reasoning}}
Deductive reasoning allows deriving <math>b</math> from <math>a</math> only where <math>b</math> is a formal [[logical consequence]] of <math>a</math>. In other words, deduction derives the consequences of the assumed. Given the truth of the assumptions, a valid deduction guarantees the truth of the conclusion. For example, given that "Wikis can be edited by anyone" (<math>a_1</math>) and "Wikipedia is a wiki" (<math>a_2</math>), it follows that "Wikipedia can be edited by anyone" (<math>b</math>).

=== Induction ===
{{Main|Inductive reasoning}}
Inductive reasoning is the process of inferring some ''general'' principle <math>b</math> from a body of knowledge <math>a</math>, where <math>b</math> does not necessarily follow from <math>a</math>. <math>a</math> might give us very good reason to accept <math>b</math> but does not ensure <math>b</math>. For example, if it is given that 95% percent of the elephants are gray, and Louise is an elephant, one can ''induce'' that Louise is gray. Still, this is not necessarily the case: 5 percent of the time this conclusion will be wrong.<ref name=":0">{{Citation |last=Douven |first=Igor |title=Abduction |date=2021 |encyclopedia=The Stanford Encyclopedia of Philosophy |editor-last=Zalta |editor-first=Edward N. |url=https://plato.stanford.edu/archives/sum2021/entries/abduction/ |access-date=2024-04-17 |edition=Summer 2021 |publisher=Metaphysics Research Lab, Stanford University}}</ref>

However, an inference being derived from statistical data is not sufficient to classify it as inductive. For example, if all swans that a person has observed so far are white, they may instead ''abduce'' the possibility that all swans are white. They have good reason to believe the conclusion from the premise because it is the ''best explanation'' for their observations, and the truth of the conclusion is still not guaranteed. (Indeed, it turns out that [[Black swan|some swans are black]].)<ref name=":0" />

=== Abduction ===
Abductive reasoning allows inferring <math>a</math> as an explanation of <math>b</math>. As a result of this inference, abduction allows the precondition <math>a</math> to be abducted from the consequence <math>b</math>. [[Deductive reasoning]] and abductive reasoning thus differ in which end, left or right, of the proposition "<math>a</math> [[entailment|entail]]s <math>b</math>" serves as conclusion. For example, in a billiard game, after glancing and seeing the eight ball moving towards us, we may abduce that the cue ball struck the eight ball. The strike of the cue ball would account for the movement of the eight ball. It serves as a hypothesis that ''best explains'' our observation. Given the many possible explanations for the movement of the eight ball, our abduction does not leave us certain that the cue ball in fact struck the eight ball, but our abduction, still useful, can serve to orient us in our surroundings. Despite many possible explanations for any physical process that we observe, we tend to abduce a single explanation (or a few explanations) for this process in the expectation that we can better orient ourselves in our surroundings and disregard some possibilities. Properly used, abductive reasoning can be a useful source of [[prior probability|priors]] in [[Bayesian statistics]].

One can understand abductive reasoning as inference to the best explanation,<ref>{{cite book |last=Sober |first=Elliott |author-link=Elliott Sober |date=2013 |title=Core Questions in Philosophy: A Text with Readings |edition=6th |location=Boston |publisher=Pearson Education |isbn=9780205206698 |oclc=799024771 |page=28 |quote=I now move to abduction—inference to the best explanation.}}</ref> although not all usages of the terms ''abduction'' and ''inference to the best explanation'' are equivalent.<ref>{{cite journal |last=Campos |first=Daniel G. |date=June 2011 |title=On the distinction between Peirce's abduction and Lipton's inference to the best explanation |journal=[[Synthese]] |volume=180 |issue=3 |pages=419–442 |doi=10.1007/s11229-009-9709-3 |s2cid=791688 |quote=I argue against the tendency in the philosophy of science literature to link abduction to the inference to the best explanation (IBE), and in particular, to claim that Peircean abduction is a conceptual predecessor to IBE. [...] In particular, I claim that Peircean abduction is an in-depth account of the process of generating explanatory hypotheses, while IBE, at least in [[Peter Lipton]]'s thorough treatment, is a more encompassing account of the processes both of generating and of evaluating scientific hypotheses. There is then a two-fold problem with the claim that abduction is IBE. On the one hand, it conflates abduction and induction, which are two distinct forms of logical inference, with two distinct aims, as shown by Charles S. Peirce; on the other hand it lacks a clear sense of the full scope of IBE as an account of scientific inference.}}</ref><ref>{{cite journal |last=Walton |first=Douglas |author-link=Douglas N. Walton |date=2001 |title=Abductive, presumptive and plausible arguments |journal=[[Informal Logic (journal)|Informal Logic]] |volume=21 |issue=2 |pages=141–169 |doi=10.22329/il.v21i2.2241 |quote=Abductive inference has often been equated with inference to the best explanation. [...] The account of abductive inference and inference to the best explanation presented above has emphasized the common elements found in the analyses given by Peirce, Harman and the Josephsons. It is necessary to add that this brief account may be misleading in some respects, and that a closer and more detailed explication of the finer points of the three analyses could reveal important underlying philosophical differences. Inferences to the best explanation, as expounded by Harman and the Josephsons, can involve deductive and inductive processes of a kind that would be apparently be excluded by Peirce's account of abduction.|citeseerx=10.1.1.127.1593 }}</ref>