Editing Abductive reasoning (section)

===Introduction and development by Peirce===
====Overview====
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 [[inductive reasoning|induction]] are often collapsed into one overarching concept—the hypothesis. That is why, in the [[scientific method]] known from [[Galileo Galilei|Galileo]] and [[Francis Bacon|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"<ref>{{cite book|last=Popper|first=Karl|title=Conjectures and Refutations: The Growth of Scientific Knowledge|location=London|publisher=Routledge|edition=2|date=2002|page=536}}</ref> (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{{mdash}}e.g. the grass could be wet from [[dew]]. This remains the common use of the term "abduction" in the [[social science]]s 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.<ref>See Santaella, Lucia (1997) "The Development of Peirce's Three Types of Reasoning: Abduction, Deduction, and Induction", 6th Congress of the [[IASS]]. [http://www.pucsp.br/~lbraga/epap_peir1.htm Eprint].</ref>

In later years his view came to be:
* Abduction is guessing.<ref name="guess">Peirce, C. S. 
* "On the Logic of drawing History from Ancient Documents especially from Testimonies" (1901), ''Collected Papers'' v. 7, paragraph 219.
* "PAP" ["Prolegomena to an Apology for Pragmatism"], MS 293 c. 1906, ''New Elements of Mathematics'' v. 4, pp. 319–320.
* A Letter to F. A. Woods (1913), ''Collected Papers'' v. 8, paragraphs 385–388.
(See under "[http://www.helsinki.fi/science/commens/terms/abduction.html Abduction]" and "[http://www.helsinki.fi/science/commens/terms/retroduction.html Retroduction]" at ''Commens Dictionary of Peirce's Terms''.)</ref> It is "very little hampered" by rules of logic.<ref name="HL">Peirce, C. S. (1903), Harvard lectures on pragmatism, ''Collected Papers'' v. 5, [http://www.textlog.de/7664-2.html paragraphs 188–189].</ref> Even a well-prepared mind's individual guesses are more frequently wrong than right.<ref>Peirce, C. S. (1908), "[[s:A Neglected Argument for the Reality of God|A Neglected Argument for the Reality of God]]", ''Hibbert Journal'' v. 7, pp. 90–112, see §4. In ''Collected Papers'' v. 6, see paragraph 476. In ''The Essential Peirce'' v. 2, see p. 444.</ref> But the success of our guesses far exceeds that of random luck and seems born of attunement to nature by instinct<ref name="NA">Peirce, C. S. (1908), "[[s:A Neglected Argument for the Reality of God|A Neglected Argument for the Reality of God]]", ''Hibbert Journal'' v. 7, pp. 90–112. See both part III and part IV. Reprinted, including originally unpublished portion, in ''Collected Papers'' v. 6, paragraphs 452–85, ''Essential Peirce'' v. 2, pp. 434–50, and elsewhere.</ref> (some speak of [[logical intuition|intuition]] in such contexts<ref>Peirce used the term "intuition" not in the sense of an instinctive or anyway half-conscious inference as people often do currently. Instead he used "intuition" usually in the sense of a cognition devoid of logical determination by [[a priori and a posteriori|previous cognitions]]. He said, "We have no power of Intuition" in that sense. See his "Some Consequences of Four Incapacities" (1868), [http://www.peirce.org/writings/p27.html Eprint] {{Webarchive|url=https://web.archive.org/web/20110514094121/http://www.peirce.org/writings/p27.html |date=2011-05-14 }}.</ref>).
* 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.<ref name="NA" />
* 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.<ref>For a relevant discussion of Peirce and the aims of abductive inference, see McKaughan, Daniel J. (2008), "[https://muse.jhu.edu/article/252833/summary From Ugly Duckling to Swan: C. S. Peirce, Abduction, and the Pursuit of Scientific Theories]", ''Transactions of the Charles S. Peirce Society'', v. 44, no. 3 (summer), 446–468.</ref> 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<ref>Peirce means "conceivable" very broadly. See ''Collected Papers'' v. 5, paragraph 196, or ''Essential Peirce'' v. 2, p. 235, "Pragmatism as the Logic of Abduction" (Lecture VII of the 1903 Harvard lectures on pragmatism): {{blockquote|It allows any flight of imagination, provided this imagination ultimately alights upon a possible practical effect; and thus many hypotheses may seem at first glance to be excluded by the pragmatical maxim that are not really so excluded.}}</ref> implications for informed practice, so as to be testable<ref name="L75">Peirce, C. S., Carnegie Application (L75, 1902, ''New Elements of Mathematics'' v. 4, pp. 37–38. See under "[http://www.helsinki.fi/science/commens/terms/abduction.html Abduction]" at the ''Commens Dictionary of Peirce's Terms'': {{blockquote|Methodeutic has a special interest in Abduction, or the inference which starts a scientific hypothesis. For it is not sufficient that a hypothesis should be a justifiable one. Any hypothesis which explains the facts is justified critically. But among justifiable hypotheses we have to select that one which is suitable for being tested by experiment.}}</ref><ref name="prag">Peirce, "Pragmatism as the Logic of Abduction" (Lecture VII of the 1903 Harvard lectures on pragmatism), see parts III and IV. Published in part in ''Collected Papers'' v. 5, paragraphs 180–212 (see 196–200, [http://www.textlog.de/7663.html Eprint] and in full in ''Essential Peirce'' v. 2, pp. 226–241 (see sections III and IV). {{blockquote|.... What is good abduction? What should an explanatory hypothesis be to be worthy to rank as a hypothesis? Of course, it must explain the facts. But what other conditions ought it to fulfill to be good? .... Any hypothesis, therefore, may be admissible, in the absence of any special reasons to the contrary, provided it be capable of experimental verification, and only insofar as it is capable of such verification. This is approximately the doctrine of pragmatism.}}</ref> and, through its trials, to expedite and economize inquiry. The economy of research is what calls for abduction and governs its art.<ref name="econ">Peirce, C.S. (1902), application to the Carnegie Institution, see MS L75.329-330, from [http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-08.htm#m27 Draft D] {{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 Memoir 27:
{{blockquote|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. Consequently, the art of discovery is purely a question of economics. The economics of research is, so far as logic is concerned, the leading doctrine with reference to the art of discovery. Consequently, the conduct of abduction, which is chiefly a question of [[heuristic]] and is the first question of heuristic, is to be governed by economical considerations.}}</ref>

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."<ref>Peirce, A Letter to [[Paul Carus]] circa 1910, ''Collected Papers'' v. 8, paragraphs 227–228. See under "[http://www.helsinki.fi/science/commens/terms/hypothesis.html Hypothesis]" at the ''Commens Dictionary of Peirce's Terms''.</ref>

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;<ref name="NCA">(1867), "On the Natural Classification of Arguments", ''Proceedings of the American Academy of Arts and Sciences'' v. 7, pp. 261–287. Presented April 9, 1867. See especially starting at [{{google books |plainurl=y |id=nG8UAAAAYAAJ|page=284}} p. 284] in Part III §1. Reprinted in ''Collected Papers v. 2, paragraphs 461–516 and ''Writings'' v. 2, pp. 23–49.''</ref> 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.<ref name="DIH">Peirce, C. S. (1878), "Deduction, Induction, and Hypothesis", ''Popular Science Monthly'', v. 13, pp. 470–82, see [{{google books |plainurl=y |id=u8sWAQAAIAAJ|page=472}} 472]. ''Collected Papers'' 2.619–44, see 623.</ref>[https://en.wikisource.org/wiki/Popular_Science_Monthly/Volume_13/August_1878/Illustrations_of_the_Logic_of_Science_VI 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;<ref name="L2L">A letter to Langley, 1900, published in ''Historical Perspectives on Peirce's Logic of Science''. See excerpts under "[http://www.helsinki.fi/science/commens/terms/abduction.html Abduction]" at the ''Commens Dictionary of Peirce's Terms''.</ref> by 1903 he speaks of the "likely" in the sense of nearing the truth in an "indefinite sense";<ref>"A Syllabus of Certain Topics of Logic'" (1903 manuscript), ''Essential Peirce'' v. 2, see p. 287. See under "[http://www.helsinki.fi/science/commens/terms/abduction.html Abduction]" at the ''Commens Dictionary of Peirce's Terms''.</ref> by 1908 he discusses ''plausibility'' as instinctive appeal.<ref name="NA" />) 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.<ref>Peirce, C. S., "On the Logic of Drawing History from Ancient Documents", dated as ''circa'' 1901 both by the editors of ''Collected Papers'' (see CP v. 7, bk 2, ch. 3, footnote 1) and by those of the ''Essential Peirce'' (EP) ([http://www.iupui.edu/~peirce/ep/ep2/headers/ep2headx.htm#8 Eprint] {{Webarchive|url=https://web.archive.org/web/20120905022758/http://www.iupui.edu/~peirce/ep/ep2/headers/ep2headx.htm#8 |date=2012-09-05 }}. The article's discussion of abduction is in CP v. 7, paragraphs 218–31 and in EP v. 2, pp. 107–14.</ref>
* as induction from characters (but as early as 1900 he characterized abduction as guessing<ref name="L2L" />)
* as citing a known rule in a premise rather than hypothesizing a rule in the conclusion (but by 1903 he allowed either approach<ref name="HL" /><ref name="newidea">Peirce, C. S., "A Syllabus of Certain Topics of Logic" (1903), ''Essential Peirce'' v. 2, p. 287:
{{blockquote| The mind seeks to bring the facts, as modified by the new discovery, into order; that is, to form a general conception embracing them. In some cases, it does this by an act of ''generalization''. In other cases, no new law is suggested, but only a peculiar state of facts that will "explain" the surprising phenomenon; and a law already known is recognized as applicable to the suggested hypothesis, so that the phenomenon, under that assumption, would not be surprising, but quite likely, or even would be a necessary result. This synthesis suggesting a new conception or hypothesis, is the Abduction.}}</ref>)
* as basically a transformation of a deductive categorical syllogism<ref name="DIH" /> (but in 1903 he offered a variation on ''modus ponens'' instead,<ref name="HL" /> and by 1911 he was unconvinced that any one form covers all hypothetical inference<ref name="kehler">A Letter to J. H. Kehler (1911), ''New Elements of Mathematics'' v. 3, pp. 203–4, see under "[http://www.helsinki.fi/science/commens/terms/retroduction.html Retroduction]" at ''Commens Dictionary of Peirce's Terms''.</ref>).

====''The Natural Classification of Arguments'' (1867)====
In 1867, Peirce's "On the Natural Classification of Arguments",<ref name="NCA" /> hypothetical inference always deals with a cluster of characters (call them ''P′, P′′, P′′′,'' etc.) known to occur at least whenever a certain character (''M'') occurs. Note that categorical syllogisms have elements traditionally called middles, predicates, and subjects. For example: All ''men'' [middle] are ''mortal'' [predicate]; ''Socrates'' [subject] is a ''man'' [middle]; ergo ''Socrates'' [subject] is ''mortal'' [predicate]". Below, 'M' stands for a middle; 'P' for a predicate; 'S' for a subject. Peirce held that all deduction can be put into the form of the categorical [[syllogism]] [[Syllogism#Barbara (AAA-1)|Barbara (AAA-1)]].

<blockquote>
{| cellspacing=1 cellpadding=7 style="background-color:#999"
|- style="vertical-align:top;background-color:#fff"
|[Deduction].

[Any] M is P <br />
[Any] S is M <br />
<math>\therefore</math> [Any] S is P. 
| Induction.

''S′, S′′, S′′′'', &c. are taken at random as ''M'''s; <br />
''S′, S′′, S′′′'', &c. are ''P'': <br />
<math>\therefore</math> Any ''M'' is probably ''P''.
|Hypothesis.

Any ''M'' is, for instance, ''P′, P′′, P′′′,'' &c.; <br />
''S'' is ''P′, P′′, P′′′,'' &c.: <br />
<math>\therefore</math> ''S'' is probably ''M''.
|}
</blockquote>

====''Deduction, Induction, and Hypothesis'' (1878)====
In 1878, in "Deduction, Induction, and Hypothesis",<ref name="DIH" /> there is no longer a need for multiple characters or predicates in order for an inference to be hypothetical, although it is still helpful. Moreover, Peirce no longer poses hypothetical inference as concluding in a ''probable'' hypothesis. In the forms themselves, it is understood but not explicit that induction involves random selection and that hypothetical inference involves response to a "very curious circumstance". The forms instead emphasize the modes of inference as rearrangements of one another's propositions (without the bracketed hints shown below).

{| cellspacing=1 cellpadding=3 style="background-color:#999"
|- vAlign=top style="background-color:#fff"
|Deduction.

''Rule:'' All the beans from this bag are white. <br />''Case:'' These beans are from this bag. <br /><math>\therefore</math> ''Result:'' These beans are white.
| Induction.

''Case:'' These beans are [randomly selected] from this bag. <br />''Result:'' These beans are white. <br /><math>\therefore</math> ''Rule:'' All the beans from this bag are white.
|Hypothesis.

''Rule:'' All the beans from this bag are white. <br />''Result:'' These beans [oddly] are white. <br /><math>\therefore</math> ''Case:'' These beans are from this bag.
|}

====''A Theory of Probable Inference'' (1883)====
Peirce long treated abduction in terms of induction from characters or traits (weighed, not counted like objects), explicitly so in his influential 1883 "A theory of probable inference", in which he returns to involving probability in the hypothetical conclusion.<ref name="Pierce-1883">{{cite book |author-last=Peirce |author-first=Charles S. |title=Studies in Logic by Members of the Johns Hopkins University |title-link=Charles Sanders Peirce bibliography#SIL |date=1883 |publisher=Little, Brown, and Company |editor-last=Peirce |editor-first=Charles S. |location=Boston, MA |chapter=A theory of probable inference |access-date=March 7, 2019 |chapter-url=http://www.commens.org/bibliography/collection_article/peirce-charles-s-1883-theory-probable-inference-studies-logic |archive-url=https://web.archive.org/web/20190308080846/http://www.commens.org/bibliography/collection_article/peirce-charles-s-1883-theory-probable-inference-studies-logic |archive-date=March 8, 2019 |url-status=dead}}</ref> 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.

[[Sherlock Holmes]] used this method of reasoning in the stories of [[Arthur Conan Doyle]], although Holmes refers to it as "[[deductive reasoning]]".<ref>{{cite journal |last1=Sebeok |first1=Thomas A. |author-link1=Thomas Sebeok |last2=Umiker-Sebeok |first2=Jean |date=1979 |title='You know my method': A juxtaposition of Charles S. Peirce and Sherlock Holmes |journal=[[Semiotica]] |volume=26 |issue=3–4 |pages=203–250 |doi=10.1515/semi.1979.26.3-4.203 |s2cid=170683439 |quote=[[Marcello Truzzi]], in a searching article on Holmes's method (1973:93–126), anticipated our present work by pointing to the similarities between the detective's so-called deductions, or inductions, and Peirce's abductions, or conjectures. According to Peirce's system of logic, furthermore, Holmes's observations are themselves a form of abduction, and abduction is as legitimate a type of logical inference as either induction or deduction (Peirce 8.228).}}</ref><ref>{{cite journal |last=Niiniluoto |first=Ilkka |author-link=Ilkka Niiniluoto |date=September 1999 |title=Defending abduction |journal=[[Philosophy of Science (journal)|Philosophy of Science]] |volume=66 |issue=Supplement&nbsp;1 |pages=S436–S451 (S440–S441) |doi=10.1086/392744 |s2cid=224841752 |quote=A historically interesting application of abduction as a heuristic method can be found in classical detective stories, as shown by the semiotical and logical essays collected in Eco and Sebeok 1983. [[C. Auguste Dupin]], the hero of [[Edgar Allan Poe]]'s novels in the 1840s, employed a method of 'ratiocination' or 'analysis' which has the structure of retroduction. Similarly, the logic of the 'deductions' of Sherlock Holmes is typically abductive.}}</ref><ref>{{cite journal |last=Carson |first=David |date=June 2009 |title=The abduction of Sherlock Holmes |journal=International Journal of Police Science & Management |volume=11 |issue=2 |pages=193–202 |doi=10.1350/ijps.2009.11.2.123 |s2cid=145337828 |quote=Sherlock Holmes, although a fictional character, remains renowned as a great detective. However, his methodology, which was ''abduction'' rather than deduction, and which is innocently used by many real detectives, is rarely described, discussed, or researched. This paper compares and contrasts the three forms of inferential reasoning, and makes a case for articulating and developing the role of abduction in the work, and training, of police officers. |url=https://researchportal.port.ac.uk/ws/files/84295/ijps.2009.11.2.pdf }}</ref>

====''Minute Logic'' (1902) and after====
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.<ref>In Peirce, C. S., 'Minute Logic' circa 1902, ''Collected Papers'' v. 2, paragraph 102. See under "[http://www.helsinki.fi/science/commens/terms/abduction.html Abduction]" at ''Commens Dictionary of Peirce's Terms''.</ref> In 1903 he offered the following form for abduction:<ref name="HL" /> 
{{blockquote|The surprising fact, C, is observed; 
:But if A were true, C would be a matter of course,
:Hence, there is reason to suspect that A is true.}}
The hypothesis is framed, but not asserted, in a premise, then asserted as rationally suspectable in the conclusion. Thus, as in the earlier categorical syllogistic form, the conclusion is formulated from some premise(s). But all the same the hypothesis consists more clearly than ever in a new or outside idea beyond what is known or observed. Induction in a sense goes beyond observations already reported in the premises, but it merely amplifies ideas already known to represent occurrences, or tests an idea supplied by hypothesis; either way it requires previous abductions in order to get such ideas in the first place. Induction seeks facts to test a hypothesis; abduction seeks a hypothesis to account for facts.

Note that the hypothesis ("A") could be of a rule. It need not even be a rule strictly necessitating the surprising observation ("C"), which needs to follow only as a "matter of course"; or the "course" itself could amount to some known rule, merely alluded to, and also not necessarily a rule of strict necessity. In the same year, Peirce wrote that reaching a hypothesis may involve placing a surprising observation under either a newly hypothesized rule or a hypothesized combination of a known rule with a peculiar state of facts, so that the phenomenon would be not surprising but instead either necessarily implied or at least likely.<ref name="newidea" />

Peirce did not remain quite convinced about any such form as the categorical syllogistic form or the 1903 form. In 1911, he wrote, "I do not, at present, feel quite convinced that any logical form can be assigned that will cover all 'Retroductions'. For what I mean by a Retroduction is simply a conjecture which arises in the mind."<ref name="kehler" />

====Pragmatism====
In 1901 Peirce wrote, "There would be no logic in imposing rules, and saying that they ought to be followed, until it is made out that the purpose of hypothesis requires them."<ref>Peirce, "On the Logic of drawing History from Ancient Documents", 1901 manuscript, ''Collected Papers'' v. 7, paragraphs 164–231, see 202, reprinted in ''Essential Peirce'' v. 2, pp. 75–114, see 95. See under "[http://www.helsinki.fi/science/commens/terms/abduction.html Abduction]" at ''Commens Dictionary of Peirce's Terms''.</ref> In 1903 Peirce called [[pragmatism]] "the logic of abduction" and said that the [[pragmatic maxim]] gives the necessary and sufficient logical rule to abduction in general.<ref name="prag" /> The pragmatic maxim is:

{{blockquote|Consider what effects, that might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these effects is the whole of our conception of the object.}}

It is a method for fruitful clarification of conceptions by equating the meaning of a conception with the conceivable practical implications of its object's conceived effects. Peirce held that that is precisely tailored to abduction's purpose in inquiry, the forming of an idea that could conceivably shape informed conduct. In various writings in the 1900s<ref name="econ" /><ref>Peirce, "On the Logic of Drawing Ancient History from Documents", ''Essential Peirce'' v. 2, see pp. 107–9.</ref> he said that the conduct of abduction (or retroduction) is governed by considerations of economy, belonging in particular to the economics of research. He regarded economics as a normative science whose analytic portion might be part of logical methodeutic (that is, theory of inquiry).<ref>Peirce, Carnegie application, L75 (1902), Memoir 28: "On the Economics of Research", scroll down to Draft E. [http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-08.htm#m28 Eprint] {{Webarchive|url=https://web.archive.org/web/20110524021101/http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-08.htm#m28 |date=2011-05-24 }}.</ref>

====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>

====Uberty====
Peirce<ref>{{Cite web|title=An Essay toward Improving Our Reasoning in Security and in Uberty|url=http://www.commens.org/|access-date=2022-02-05|website=www.commens.org|language=en|archive-date=August 26, 2014|archive-url=https://web.archive.org/web/20140826222027/http://www.commens.org/|url-status=dead}}</ref> 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. A key concept proposed by him in this regard is "[[wiktionary:uberty|uberty]]"<ref>{{Cite web|title=Peirce's last philosophic will and testament: Uberty in the logic of|url=https://paperzz.com/doc/7856381/peirce-s-last-philosophic-will-and-testament--uberty-in-t...|access-date=2022-02-05|website=paperzz.com}}</ref>—the expected fertility and pragmatic value of reasoning. This concept seems to be gaining support via association to the [[Free energy principle|Free Energy Principle]].<ref>{{Cite journal|last1=Beni|first1=Majid D.|last2=Pietarinen|first2=Ahti-Veikko|date=2021-09-10|title=Aligning the free-energy principle with Peirce's logic of science and economy of research|url=https://doi.org/10.1007/s13194-021-00408-y|journal=European Journal for Philosophy of Science|language=en|volume=11|issue=3|pages=94|doi=10.1007/s13194-021-00408-y|s2cid=237475038 |issn=1879-4920}}</ref>