Theorematic Reasoning and Purity of Proofs

EDUARDO N. GIOVANNINI; JAVIER LEGRIS

Revisiting History and Philosophy of Logic and Mathematics

COLLEGE PUBLICATIONS

Lugar: LONDRES; Año: 2023;

Certain parallelism between Peirce´s distinction between corollarial andtheorematic reasoning in mathematics and Hilbert’s classification of mathematicalproofs between pure and impure proofs has been observed. In this paper, we showthat the comparison between them can be useful, inasmuch we are lead to aclarification of both distinctions. However, we argue that they arose in quitedifferent contexts of problems, so they cannot be subsumed or combined in a singleapproach. Hilbert´s distinction concerns specific kinds of proofs in geometry, andit is directly related to the methodological program he devised in his Foundationsof Geometry in 1899. On the contrary, Peirce’s insights into two essential forms ofmathematical reasoning are embedded into his pragmatic philosophy and includelogical, methodological, and cognitive aspects. Hence, it has a more generalsignificance for the epistemology of mathematics.