Editing Abductive reasoning (section)

====Three levels of logic about abduction====
Peirce came over the years to [[Classification of the sciences (Peirce)#Sciences|divide (philosophical) logic]] into three departments: 
# Stechiology, or speculative grammar, on the conditions for meaningfulness. Classification of signs (semblances, symptoms, symbols, etc.) and their combinations (as well as their objects and [[interpretant]]s).
# Logical critic, or logic proper, on validity or justifiability of inference, the conditions for true representation. Critique of arguments in their various modes (deduction, induction, abduction).
# Methodeutic, or speculative rhetoric, on the conditions for determination of interpretations. Methodology of inquiry in its interplay of modes.
Peirce had, from the start, seen the modes of inference as being coordinated together in scientific inquiry and, by the 1900s, held that hypothetical inference in particular is inadequately treated at the level of critique of arguments.<ref name="L75" /><ref name="prag" /> 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. That is [[Charles Sanders Peirce#Scientific method|Peirce's outline of the scientific method]] of inquiry, as covered in his inquiry methodology, which includes [[pragmatism]] or, as he later called it, [[pragmaticism]], the clarification of ideas in terms of their conceivable implications regarding informed practice.

=====Classification of signs=====
As early as 1866,<ref>Peirce, C. S., the 1866 Lowell Lectures on the Logic of Science, ''[[Charles Sanders Peirce bibliography#W|Writings of Charles S. Peirce]]'' v. 1, p. 485. See under "[http://www.helsinki.fi/science/commens/terms/hypothesis.html Hypothesis]" at ''Commens Dictionary of Peirce's Terms''.</ref> Peirce held that:

1. Hypothesis (abductive inference) is inference through an ''icon'' (also called a ''likeness''). <br />
2. Induction is inference through an ''index'' (a sign by factual connection); a sample is an index of the totality from which it is drawn. <br />
3. Deduction is inference through a ''symbol'' (a sign by interpretive habit irrespective of resemblance or connection to its object).

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."<ref>Peirce, C. S., "A Syllabus of Certain Topics of Logic", written 1903. See ''[[Charles Sanders Peirce bibliography#EP|The Essential Peirce]]'' v. 2, p. 287. Quote viewable under "[http://www.helsinki.fi/science/commens/terms/abduction.html Abduction]" at ''Commens Dictionary of Peirce's Terms''.</ref>

=====Critique of arguments=====
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. In 1908 Peirce described this plausibility in some detail.<ref name="NA" /> It involves not likeliness based on observations (which is instead the inductive evaluation of a hypothesis), but instead optimal simplicity in the sense of the "facile and natural", as by Galileo's natural light of reason and as distinct from "logical simplicity" (Peirce does not dismiss logical simplicity entirely but sees it in a subordinate role; taken to its logical extreme it would favor adding no explanation to the observation at all). Even a well-prepared mind guesses oftener wrong than right, but our guesses succeed better than random luck at reaching the truth or at least advancing the inquiry, and that indicates to Peirce that they are based in instinctive attunement to nature, an affinity between the mind's processes and the processes of the real, which would account for why appealingly "natural" guesses are the ones that oftenest (or least seldom) succeed; to which Peirce added the argument that such guesses are to be preferred since, without "a natural bent like nature's", people would have no hope of understanding nature. In 1910 Peirce made a three-way distinction between probability, verisimilitude, and plausibility, and defined plausibility with a normative "ought": "By plausibility, I mean the degree to which a theory ought to recommend itself to our belief independently of any kind of evidence other than our instinct urging us to regard it favorably."<ref>Peirce, A Letter to Paul Carus 1910, ''Collected Papers'' v. 8, see paragraph 223.</ref> For Peirce, plausibility does not depend on observed frequencies or probabilities, or on verisimilitude, or even on testability, which is not a question of the critique of the hypothetical inference ''as'' an inference, but rather a question of the hypothesis's relation to the inquiry process.

The phrase "inference to the best explanation" (not used by Peirce but often applied to hypothetical inference) is not always understood as referring to the most simple and natural hypotheses (such as those with the [[Occam's razor|fewest assumptions]]). However, in other senses of "best", such as "standing up best to tests", it is hard to know which is the best explanation to form, since one has not tested it yet. 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.<ref name="L75" /><ref name="prag" /><ref>Peirce, C. S. (1902), Application to the Carnegie Institution, Memoir 27, [http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-08.htm#m27 Eprint] {{Webarchive|url=https://web.archive.org/web/20110524021101/http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-08.htm#m27 |date=2011-05-24 }}: "Of the different classes of arguments, abductions are the only ones in which after they have been admitted to be just, it still remains to inquire whether they are advantageous."</ref>

=====Methodology of inquiry=====
At the methodeutical level Peirce held that a hypothesis is judged and selected<ref name="L75" /> 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,<ref name="econ" /> in terms of cost, value, and relationships among guesses (hypotheses). Here, considerations such as probability, absent from the treatment of abduction at the critical level, come into play. For examples:
* Cost: A simple but low-odds guess, if low in cost to test for falsity, may belong first in line for testing, to get it out of the way. If surprisingly it stands up to tests, that is worth knowing early in the inquiry, which otherwise might have stayed long on a wrong though seemingly likelier track.
* Value: A guess is intrinsically worth testing if it has instinctual plausibility or reasoned objective probability, while [[Subjective probability|subjective likelihood]], though reasoned, can be treacherous.
* Interrelationships: Guesses can be chosen for trial strategically for their
** ''caution'', for which Peirce gave as an example the game of [[Twenty Questions]],
** ''breadth'' of applicability to explain various phenomena, and
** ''incomplexity'', that of a hypothesis that seems too simple but whose trial "may give a good 'leave', as the billiard-players say", and be instructive for the pursuit of various and conflicting hypotheses that are less simple.<ref name="econ2">Peirce, "On the Logic of Drawing Ancient History from Documents", ''Essential Peirce'' v. 2, see pp. 107–9 and 113. On Twenty Questions, p. 109, Peirce has pointed out that if each question eliminates half the possibilities, twenty questions can choose from among 2<sup>20</sup> or 1,048,576 objects, and goes on to say: {{blockquote|Thus, twenty skillful hypotheses will ascertain what 200,000 stupid ones might fail to do. 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.}}</ref>