The Library
Arithmetical reflection and the provability of soundness
Tools
Tools
Tools
Dean, Walter (2015) Arithmetical reflection and the provability of soundness. Philosophia Mathematica, 23 (1). pp. 31-64. doi:10.1093/philmat/nku026
Research output not available from this repository, contact author.
Official URL: https://doi.org/10.1093/philmat/nku026
Abstract
Proof-theoretic reflection principles are schemas which attempt to express the soundness of arithmetical theories within their own language, e.g., ProvPA(┌φ┐)→φ can be understood to assert that any statement provable in Peano arithmetic is true. It has been repeatedly suggested that justification for such principles follows directly from acceptance of an arithmetical theory T or indirectly in virtue of their derivability in certain truth-theoretic extensions thereof. This paper challenges this consensus by exploring relationships between reflection principles and principles of mathematical and transfinite induction as well as the status of the latter with respect to various foundational characterizations of number theory.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Social Sciences > Philosophy | ||||
| Journal or Publication Title: | Philosophia Mathematica | ||||
| Publisher: | Oxford University Press | ||||
| ISSN: | 0031-8019 | ||||
| Official Date: | 24 December 2015 | ||||
| Dates: |
|
||||
| Volume: | 23 | ||||
| Number: | 1 | ||||
| Page Range: | pp. 31-64 | ||||
| DOI: | 10.1093/philmat/nku026 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
