A definition of what counts as an explanation of a mathematical statement, and when one explanation is better than another, is given. Since all mathematical facts must be true in all causal models, and hence known by an agent, mathematical facts cannot be part of an explanation (under the standard notion of explanation). This problem is solved using impossible possible worlds.
Halpern, J. (2025). Explanations of Mathematical Statements. M×Φ — Annals of Mathematics and Philosophy, 3(1), 23–42.
Halpern, Joseph Y.. “Explanations of Mathematical Statements.” M×Φ — Annals of Mathematics and Philosophy 3, no. 1 (2025): 23–42.
Halpern, Joseph Y.. “Explanations of Mathematical Statements.” M×Φ — Annals of Mathematics and Philosophy, vol. 3, no. 1, 2025, pp. 23–42.
@article{Halpern2025,
title = {{Explanations of Mathematical Statements}},
author = {Joseph Y. Halpern},
journal = {M×Φ — Annals of Mathematics and Philosophy},
volume = {3},
number = {1},
pages = {23--42},
year = {2025},
issn = {3038-6381},
language = {en},
keywords = {mathematical explanation, partial explanation, causality, impossible possible worlds},
url = {https://www.mxphi.com/all-issues/volume-iii-number-1-2025/explanations-mathematical-statements/},
note = {License: CC BY-ND 4.0},
}
TY - JOUR
AU - Joseph Y. Halpern
TI - Explanations of Mathematical Statements
JO - M×Φ — Annals of Mathematics and Philosophy
JF - M×Φ — Annals of Mathematics and Philosophy
VL - 3
IS - 1
SP - 23
EP - 42
PY - 2025
SN - 3038-6381
LA - en
KW - mathematical explanation
KW - partial explanation
KW - causality
KW - impossible possible worlds
UR - https://www.mxphi.com/all-issues/volume-iii-number-1-2025/explanations-mathematical-statements/
N1 - License: CC BY-ND 4.0
ER -