Monday, October 26, 2020

What Is "Abductive Reasoning"?

Abductive reasoning (also called abduction, abductive inference, or retroduction) is a form of logical inference formulated and advanced by American philosopher Charles Sanders Peirce beginning in the last third of the 19th century. It starts with an observation or set of observations and then seeks to find the simplest and most likely conclusion from the observations. This process, unlike deductive reasoning, yields a plausible conclusion but does not positively verify it. Abductive conclusions are thus qualified as having a remnant of uncertainty or doubt, which is expressed in retreat terms such as "best available" or "most likely". One can understand abductive reasoning as inference to the best explanation, although not all usages of the terms abduction and inference to the best explanation are exactly equivalent.

In the 1990s, as computing power grew, the fields of law, computer science, and artificial intelligence research spurred renewed interest in the subject of abduction. Diagnostic expert systems frequently employ abduction.

Deduction, Induction and Abduction

Deduction

Deductive reasoning allows deriving b from a only where b is a formal logical consequence of a.  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" (a1) and "Wikipedia is a wiki" (a2), it follows that "Wikipedia can be edited by anyone."

Induction

Inductive reasoning allows inferring b from a, where b does not follow necessarily from a. might give us very good reason to accept b, but it does not ensure b.  For example, if all swans that we have observed so far are white, we may induce that the possibility that all swans are white is reasonable. We have good reason to believe the conclusion from the premise, but the truth of the conclusion is not guaranteed. (Indeed, it turns out that some swans are black.)

Abduction

Abductive reasoning allows inferring a as an explanation of b. As a result of this inference, abduction allows the precondition a to be abduced from the consequence b. Deductive reasoning and abductive reasoning thus differ in the direction in which a rule like "a entails b” is used for inference.

As such, abduction is formally equivalent to the logical fallacy of affirming the consequent (or post hoc ergo propter hoc) because of multiple possible explanations for b.  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 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 priors in Bayesian statistics.

Introduction and Development of Abduction by Peirce

The American philosopher Charles Sanders Peirce introduced abduction into modern logic. Over the years he called such inference hypothesis, abduction, presumption, and retroduction. He considered it a topic in logic as a normative field in philosophy, not in purely formal or mathematical logic, and eventually as a topic also in economics of research.

As two stages of the development, extension, etc., of a hypothesis in scientific inquiry, abduction and also induction are often collapsed into one overarching concept — the hypothesis. That is why, in the scientific method known from Galileo and Bacon, the abductive stage of hypothesis formation is conceptualized simply as induction. Thus, in the twentieth century this collapse was reinforced by Karl Popper's explication of the hypothetico-deductive model, where the hypothesis is considered to be just "a guess" (in the spirit of Peirce). However, when the formation of a hypothesis is considered the result of a process it becomes clear that this "guess" has already been tried and made more robust in thought as a necessary stage of its acquiring the status of hypothesis. Indeed, many abductions are rejected or heavily modified by subsequent abductions before they ever reach this stage.

Before 1900, Peirce treated abduction as the use of a known rule to explain an observation. For instance: it is a known rule that, if it rains, grass gets wet; so, to explain the fact that the grass on this lawn is wet, one abduces that it has rained. Abduction can lead to false conclusions if other rules that might explain the observation are not taken into account—e.g. the grass could be wet from dew. This remains the common use of the term "abduction" in the social sciences and in artificial intelligence.

Peirce consistently characterized it as the kind of inference that originates a hypothesis by concluding in an explanation, though an unassured one, for some very curious or surprising (anomalous) observation stated in a premise. As early as 1865 he wrote that all conceptions of cause and force are reached through hypothetical inference; in the 1900s he wrote that all explanatory content of theories is reached through abduction. In other respects Peirce revised his view of abduction over the years.

In later years his view came to be:

  • Abduction is guessing. It is "very little hampered" by rules of logic. Even a well-prepared mind's individual guesses are more frequently wrong than right. But the success of our guesses far exceeds that of random luck and seems born of attunement to nature by instinct (some speak of intuition in such contexts).
  • Abduction guesses a new or outside idea so as to account in a plausible, instinctive, economical way for a surprising or very complicated phenomenon. That is its proximate aim.
  • Its longer aim is to economize inquiry itself. Its rationale is inductive: it works often enough, is the only source of new ideas, and has no substitute in expediting the discovery of new truths. Its rationale especially involves its role in coordination with other modes of inference in inquiry. It is inference to explanatory hypotheses for selection of those best worth trying.
  • Pragmatism is the logic of abduction. Upon the generation of an explanation (which he came to regard as instinctively guided), the pragmatic maxim gives the necessary and sufficient logical rule to abduction in general. The hypothesis, being insecure, needs to have conceivable implications for informed practice, so as to be testable and, through its trials, to expedite and economize inquiry. The economy of research is what calls for abduction and governs its art.

Writing in 1910, Peirce admits that "in almost everything I printed before the beginning of this century I more or less mixed up hypothesis and induction" and he traces the confusion of these two types of reasoning to logicians' too "narrow and formalistic a conception of inference, as necessarily having formulated judgments from its premises."

He started out in the 1860s treating hypothetical inference in a number of ways which he eventually peeled away as inessential or, in some cases, mistaken:

  • as inferring the occurrence of a character (a characteristic) from the observed combined occurrence of multiple characters which its occurrence would necessarily involve; for example, if any occurrence of A is known to necessitate occurrence of B, C, D, E, then the observation of B, C, D, E suggests by way of explanation the occurrence of A. (But by 1878 he no longer regarded such multiplicity as common to all hypothetical inference. Wikisource)
  • as aiming for a more or less probable hypothesis (in 1867 and 1883 but not in 1878; anyway by 1900 the justification is not probability but the lack of alternatives to guessing and the fact that guessing is fruitful; by 1903 he speaks of the "likely" in the sense of nearing the truth in an "indefinite sense"; by 1908 he discusses plausibility as instinctive appeal.) In a paper dated by editors as circa 1901, he discusses "instinct" and "naturalness", along with the kind of considerations (low cost of testing, logical caution, breadth, and incomplexity) that he later calls methodeutical.
  • as induction from characters (but as early as 1900 he characterized abduction as guessing)
  • as citing a known rule in a premise rather than hypothesizing a rule in the conclusion (but by 1903 he allowed either approach)
  • as basically a transformation of a deductive categorical syllogism (but in 1903 he offered a variation on modus ponens instead, and by 1911 he was unconvinced that any one form covers all hypothetical inference).

Applications

Abduction can be utilized in artificial intelligence, medicine, automated planning, intelligence analysis, belief revision, philosophy of science, historical linguistics, applied linguistics, anthropology, and computer programming.

Related Concepts and Persons

                                         https://en.wikipedia.org/wiki/Abductive_reasoning

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Footnote by the Blog Author

It appears that abduction is a critical element in important areas of decision making such as games of incomplete information (such as poker, contract bridge and Bayesian games), as well as  asymmetric warfare, troubleshooting, and forecasting.

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