I am reading some random bits from Peirce's collected works and they give me the impression that Peirce tried to integrate every(or nearly every) major scientific and mathematical concept which he was aware of(or some conceptual negation that he derived from it) in his philosophy. Were there any descriptions of a close enough concept to abductive reasoning in the works of any previous mathematician?
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2$\begingroup$ Hanson in Is there a logic of scientific discovery? names Aristotle (e.g. his guessing of a middle term for syllogisms) as Peirce's direct predecessor. But Peirce separated abduction from what logicians used to call induction (generically, as not deduction), and e.g. Mill catalogued a list of methods for that. $\endgroup$– ConifoldNov 23, 2020 at 8:40
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3$\begingroup$ Maybe useful: A Burks, Peirce's Theory of Abduction (1946) $\endgroup$– Mauro ALLEGRANZANov 23, 2020 at 15:39
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Poincare mentions that inductive reasoning, in his Geometry and the Imagination, that is, generalising from the special to the general case as being the essence of mathematics, and that of science.
I don't know if Pierce was familiar with this work, but I assume it is likely that he was ...
(It's worth adding that this is not special to science, it's a general feature of the rational faculty of the human mind and seen very much in evidence in everyday life).
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$\begingroup$ This doesn't answer the question. $\endgroup$– user466Nov 26, 2020 at 23:23
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$\begingroup$ To begin with, “Geometry and Imagination” was by Hilbert and Cohn-Vossen, not Poincare. Secondly, much of Peirce’s work in logic was done before Poincare wrote his first papers. And Hilbert was even later. $\endgroup$ Dec 26, 2020 at 20:56