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?
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).