Abductive reasoning

[11] The methods are sound and complete and work for full first-order logic, without requiring any preliminary reduction of formulae into normal forms.

Abductive validation is common practice in hypothesis formation in science; moreover, Peirce claims that it is a ubiquitous aspect of thought: Looking out my window this lovely spring morning, I see an azalea in full bloom.

"[14] After obtaining possible hypotheses that may explain the facts, abductive validation is a method for identifying the most likely hypothesis that should be adopted.

It is thus possible to perform abductive analysis in the presence of uncertain arguments, which naturally results in degrees of uncertainty in the output conclusions.

To this point, George Pólya, in his treatise on problem-solving, makes reference to the following Latin truism: simplex sigillum veri (simplicity is the seal of truth).

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"[17] (in the spirit of Peirce).

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.

[18] In later years his view came to be: 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.

S is probably M. In 1878, in "Deduction, Induction, and Hypothesis",[31] there is no longer a need for multiple characters or predicates in order for an inference to be hypothetical, although it is still helpful.

[37] Like "Deduction, Induction, and Hypothesis" in 1878, it was widely read (see the historical books on statistics by Stephen Stigler), unlike his later amendments of his conception of abduction.

Today abduction remains most commonly understood as induction from characters and extension of a known rule to cover unexplained circumstances.

[38][39][40] In 1902 Peirce wrote that he now regarded the syllogistical forms and the doctrine of extension and comprehension (i.e., objects and characters as referenced by terms), as being less fundamental than he had earlier thought.

Peirce held that that is precisely tailored to abduction's purpose in inquiry, the forming of an idea that could conceivably shape informed conduct.

He regarded economics as a normative science whose analytic portion might be part of logical methodeutic (that is, theory of inquiry).

[26][27] To increase the assurance of a hypothetical conclusion, one needs to deduce implications about evidence to be found, predictions which induction can test through observation so as to evaluate the hypothesis.

In 1902, Peirce wrote that, in abduction: "It is recognized that the phenomena are like, i.e. constitute an Icon of, a replica of a general conception, or Symbol.

"[46] At the critical level Peirce examined the forms of abductive arguments (as discussed above), and came to hold that the hypothesis should economize explanation for plausibility in terms of the feasible and natural.

Still, for Peirce, any justification of an abductive inference as "good" is not completed upon its formation as an argument (unlike with induction and deduction) and instead depends also on its methodological role and promise (such as its testability) in advancing inquiry.

[26][27][48] At the methodeutical level Peirce held that a hypothesis is judged and selected[26] for testing because it offers, via its trial, to expedite and economize the inquiry process itself toward new truths, first of all by being testable and also by further economies,[28] in terms of cost, value, and relationships among guesses (hypotheses).

For examples: Peirce[50] indicated that abductive reasoning is driven by the need for "economy in research"—the expected fact-based productivity of hypotheses, prior to deductive and inductive processes of verification.

Omphalos is the classic example of an utterly untestable notion, for the world will look exactly the same in all its intricate detail whether fossils and strata are prochronic [signs of a fictitious past] or products of an extended history.

The process of updating the web of beliefs can be done by the use of abduction: once an explanation for the observation has been found, integrating it does not generate inconsistency.

It is defined as "The use of an unclear premise based on observations, pursuing theories to try to explain it" (Rose et al., 2020, p. 258)[61][62] In anthropology, Alfred Gell in his influential book Art and Agency defined abduction (after Eco[63]) as "a case of synthetic inference 'where we find some very curious circumstances, which would be explained by the supposition that it was a case of some general rule, and thereupon adopt that supposition'".

That is, abduction can explain how works of art inspire a sensus communis: the commonly held views shared by members that characterize a given society.

He answers by saying that "No reasonable person could suppose that art-like relations between people and things do not involve at least some form of semiosis.

"[64] However, he rejects any intimation that semiosis can be thought of as a language because then he would have to admit to some pre-established existence of the sensus communis that he wants to claim only emerges afterwards out of art.

Therefore, through abduction, Gell claims that art can have the kind of agency that plants the seeds that grow into cultural myths.

This is approximately the doctrine of pragmatism.Consequently, to discover is simply to expedite an event that would occur sooner or later, if we had not troubled ourselves to make the discovery.

The mind seeks to bring the facts, as modified by the new discovery, into order; that is, to form a general conception embracing them.

The secret of the business lies in the caution which breaks a hypothesis up into its smallest logical components, and only risks one of them at a time.