Ásgeir, Berg (2023) Was Wittgenstein a radical conventionalist? [Preprint]
|
Text
radical_conventionlism.pdf - Accepted Version Download (184kB) | Preview |
Abstract
This paper defends a reading of Wittgenstein’s philosophy of mathematics in the Lectures on the Foundation of Mathematics as a radical conventionalist one, whereby our agreement about the particular case is constitutive of our mathematical practice and ‘the logical necessity of any statement is a direct expression of a convention’ (Dummett 1959, p. 329).
On this view, mathematical truths are conceptual truths and our practices determine directly for each mathematical proposition individually whether it is true or false. Mathematical truths are thus not consequences of a prior adoption of a convention or rules as orthodox conventionalism has it.
The goal of the paper is not merely exegetical, however, and argues that radical conventionalism can withstand some of the most difficult objections that have been brought forward against it, including those of Dummett himself, and thus that radical conventionalism has been prematurely excluded from consideration by philosophers of mathematics.
| Export/Citation: | EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL |
| Social Networking: |
| Item Type: | Preprint | ||||||
|---|---|---|---|---|---|---|---|
| Creators: |
|
||||||
| Keywords: | Wittgenstein; radical conventionalism, | ||||||
| Subjects: | Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > History of Philosophy Specific Sciences > Mathematics |
||||||
| Depositing User: | Dr Ásgeir Berg Matthíason | ||||||
| Date Deposited: | 12 Dec 2023 21:57 | ||||||
| Last Modified: | 12 Dec 2023 21:57 | ||||||
| Item ID: | 22836 | ||||||
| Subjects: | Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > History of Philosophy Specific Sciences > Mathematics |
||||||
| Date: | 10 December 2023 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/22836 |
Monthly Views for the past 3 years
Monthly Downloads for the past 3 years
Plum Analytics
Actions (login required)
 |
View Item |
![[feed]](http://philsci-archive.pitt.edu/style/images/feed-icon-32x32.png){kind=icon}