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.
Cellucci, C. (2023). Introducing Heuristic Philosophy of Mathematics. Annals of Mathematics and Philosophy, 1(1), 25–46. https://doi.org/10.67678/nxrm63z6
Cellucci, Carlo. “Introducing Heuristic Philosophy of Mathematics.” Annals of Mathematics and Philosophy 1, no. 1 (2023): 25–46. https://doi.org/10.67678/nxrm63z6.
Cellucci, Carlo. “Introducing Heuristic Philosophy of Mathematics.” Annals of Mathematics and Philosophy, vol. 1, no. 1, 2023, pp. 25–46. https://doi.org/10.67678/nxrm63z6.
@article{Cellucci2023,
title = {{Introducing Heuristic Philosophy of Mathematics}},
author = {Carlo Cellucci},
journal = {Annals of Mathematics and Philosophy},
volume = {1},
number = {1},
pages = {25--46},
year = {2023},
issn = {3038-6381},
doi = {10.67678/nxrm63z6},
language = {en},
keywords = {heuristic philosophy of mathematics, mathematics as problem-solving, philosophy of mathematical practice, mathematical objects, mathematical definitions},
url = {https://www.mxphi.com/all-issues/volume-i-number-1-2023/introducing-heuristic-philosophy/},
note = {License: CC BY-ND 4.0},
}
TY - JOUR
AU - Carlo Cellucci
TI - Introducing Heuristic Philosophy of Mathematics
JO - Annals of Mathematics and Philosophy
JF - Annals of Mathematics and Philosophy
VL - 1
IS - 1
SP - 25
EP - 46
PY - 2023
SN - 3038-6381
DO - 10.67678/nxrm63z6
LA - en
KW - heuristic philosophy of mathematics
KW - mathematics as problem-solving
KW - philosophy of mathematical practice
KW - mathematical objects
KW - mathematical definitions
UR - https://www.mxphi.com/all-issues/volume-i-number-1-2023/introducing-heuristic-philosophy/
N1 - License: CC BY-ND 4.0
ER -