Abstract
The implicit commitment thesis is the claim that believing in a mathematical theory
S carries an implicit commitment to further sentences not deductively entailed by
the theory, such as the consistency sentence Con(S). I provide a new argument for
this thesis based on the notion of mathematical certainty. I also reply to a recent
argument by Walter Dean against the implicit commitment thesis, showing that my
formulation of the thesis avoids the difficulties he raises.
S carries an implicit commitment to further sentences not deductively entailed by
the theory, such as the consistency sentence Con(S). I provide a new argument for
this thesis based on the notion of mathematical certainty. I also reply to a recent
argument by Walter Dean against the implicit commitment thesis, showing that my
formulation of the thesis avoids the difficulties he raises.
| Original language | English |
|---|---|
| Article number | 51 |
| Pages (from-to) | 1410-1432 |
| Journal | Ergo: An Open Access Journal of Philosophy |
| Volume | 9 |
| Early online date | 18 Jul 2023 |
| DOIs | |
| Publication status | E-pub ahead of print - 18 Jul 2023 |
Bibliographical note
Precursors of this paper go back several years, and I am grateful to the various people who have discussed these issues with me, including Steve Dalglish, Chris Pincock, Stewart Shapiro, Neil Tennant, and Dan Waxman. Thanks are also dueto several referees for both Ergo and other journals, whose comments led to an
improved paper.