Dean, Walter (2015) Arithmetical reflection and the provability of soundness. Philosophia Mathematica, 23 (1). pp. 31-64. doi:10.1093/philmat/nku026 ISSN 0031-8019.

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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:	Date Event 24 December 2015 Published
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

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