Introducing Heuristic Philosophy of Mathematics
Abstract
Mainstream philosophy of mathematics, namely the philosophy of mathematics that has prevailed for the past century, holds that mathematics is theorem proving by the axiomatic method. But this is incompatible with Gödel's incompleteness theorems, and cannot account for many features of mathematics. This article proposes an alternative approach, heuristic philosophy of mathematics, according to which mathematics is problem-solving by the analytic method. The article argues that this is compatible with Gödel's incompleteness theorems, and can account for the features of mathematics not accounted for by mainstream philosophy of mathematics, such as the nature of mathematical objects and mathematical definitions.
Keywords
heuristic philosophy of mathematics
mathematics as problem-solving
philosophy of mathematical practice
mathematical objects
mathematical definitions
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Cite this article
Cellucci, C. (2023). Introducing Heuristic Philosophy of Mathematics. M×Φ — Annals of Mathematics and Philosophy, 1(1), 25–46.
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