PhilSci Archive

Wittgenstein, Peirce, and paradoxes of mathematical proof

Koshkin, Sergiy (2020) Wittgenstein, Peirce, and paradoxes of mathematical proof. Analytic Philosophy. ISSN 2153-960X

[img]
Preview
Text
WittParadox.pdf

Download (185kB) | Preview

Abstract

Wittgenstein's paradoxical theses that unproved propositions are meaningless, proofs form new concepts and rules, and contradictions are of limited concern, led to a variety of interpretations, most of them centered on rule-following skepticism. We argue, with the help of C. S. Peirce's distinction between corollarial and theorematic proofs, that his intuitions are better explained by resistance to what we call conceptual omniscience, treating meaning as fixed content specified in advance. We interpret the distinction in the context of modern epistemic logic and semantic information theory, and show how removing conceptual omniscience helps resolve Wittgenstein's paradoxes and explain the puzzle of deduction, its ability to generate new knowledge and meaning.


Export/Citation: EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
Social Networking:
Share |

Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Koshkin, Sergiy0000-0001-8264-3701
Keywords: Wittgenstein; Peirce; Scandal of deduction; logical omniscience; corollarial theorematic distinction; semantic information; conservative extension; epistemic logic
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > History of Philosophy
Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics > Proof
Specific Sciences > Mathematics
Depositing User: Dr. Sergiy Koshkin
Date Deposited: 18 Feb 2020 15:38
Last Modified: 18 Feb 2020 15:38
Item ID: 16924
Journal or Publication Title: Analytic Philosophy
Publisher: Wiley
Official URL: https://onlinelibrary.wiley.com/doi/full/10.1111/p...
DOI or Unique Handle: https://doi.org/10.1111/phib.12177
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > History of Philosophy
Specific Sciences > Mathematics > Practice
Specific Sciences > Mathematics > Proof
Specific Sciences > Mathematics
Date: 13 February 2020
ISSN: 2153-960X
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/16924

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Altmetric.com

Actions (login required)

View Item View Item