Editing Charles Sanders Peirce (section)

== Modes of inference ==
{{Main|Inquiry}}

Borrowing a brace of concepts from [[Aristotle]], Peirce examined three basic modes of [[inference]]—''[[abductive reasoning|abduction]]'', ''[[deductive reasoning|deduction]]'', and ''[[Inductive reasoning|induction]]''—in his "critique of arguments" or "logic proper". Peirce also called abduction "retroduction", "presumption", and, earliest of all, "hypothesis". He characterized it as guessing and as inference to an explanatory hypothesis. He sometimes expounded the modes of inference by transformations of the categorical [[Syllogism#Barbara (AAA-1)|syllogism Barbara (AAA)]], for example in "Deduction, Induction, and Hypothesis" (1878).<ref>''Popular Science Monthly'', v. 13, pp. 470–482, see [https://books.google.com/books?id=u8sWAQAAIAAJ&pg=PA472 472] or [[s:Popular Science Monthly/Volume 13/August 1878/Illustrations of the Logic of Science VI|the book at Wikisource]]. ''Collected Papers of Charles Sanders Peirce'', 2.619–644 [623]</ref> He does this by rearranging the ''rule'' (Barbara's major premise), the ''case'' (Barbara's minor premise), and the ''result'' (Barbara's conclusion):

{{col-begin}}
{{col-break}}
Deduction.

''Rule:'' All the beans from this bag are white. <br>
''Case:'' These beans are beans from this bag. <br>
<math>\therefore</math> ''Result:'' These beans are white.
{{col-break|gap=1%}}
Induction.

''Case:'' These beans are &#91;randomly selected&#93; from this bag.<br>
''Result:'' These beans are white.<br>
<math>\therefore</math> ''Rule:'' All the beans from this bag are white.
{{col-break|gap=1%}}
Hypothesis (Abduction).

''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.
{{col-end}}

In 1883, in "A Theory of Probable Inference" (''[[#SIL|Studies in Logic]]''), Peirce equated hypothetical inference with the induction of characters of objects (as he had done in effect before<ref name="SCFI"/>). Eventually dissatisfied, by 1900 he distinguished them once and for all and also wrote that he now took the syllogistic forms and the doctrine of logical extension and comprehension as being less basic than he had thought. In 1903 he presented the following logical form for abductive inference:<ref>See, under "[http://www.helsinki.fi/science/commens/terms/abduction.html Abduction]" at ''Commens Digital Companion to C.S. Peirce'', the following quotes:
* On correction of "A Theory of Probable Inference", see quotes from "Minute Logic", ''Collected Papers of Charles Sanders Peirce'', 2.102, c. 1902, and from the Carnegie Application (L75), 1902, ''Historical Perspectives on Peirce's Logic of Science'' v. 2, pp. 1031–1032.
* On new logical form for abduction, see quote from Harvard Lectures on Pragmatism, 1903, ''Collected Papers of Charles Sanders Peirce'', 5.188–189.
See also 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>

{{quote|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 logical form does not also cover induction, since induction neither depends on surprise nor proposes a new idea for its conclusion. Induction seeks facts to test a hypothesis; abduction seeks a hypothesis to account for facts. "Deduction proves that something ''must'' be; Induction shows that something ''actually is'' operative; Abduction merely suggests that something ''may be''."<ref>"Lectures on Pragmatism", 1903, ''Collected Papers of Charles Sanders Peirce'', 5.171.</ref> Peirce did not remain quite convinced that one logical form covers all abduction.<ref>A Letter to J. H. Kehler (dated 1911), ''[[#NEM|The New Elements of Mathematics]]'' v. 3, pp. 203–204, see in "[http://www.helsinki.fi/science/commens/terms/retroduction.html Retroduction]" at ''Commens Digital Companion to C.S. Peirce''.</ref> In his [[methodeutic]] or theory of inquiry (see below), he portrayed abduction as an economic initiative to further inference and study, and portrayed all three modes as clarified by their coordination in essential roles in inquiry: hypothetical explanation, deductive prediction, inductive testing