Arithmetical Reflection and the Provability of Soundness

Philosophia Mathematica 23 (1):31-64 (2015)
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Proof-theoretic reflection principles are schemas which attempt to express the soundness of arithmetical theories within their own language, e.g., ${\mathtt{{Prov}_{\mathsf {PA}} \rightarrow \varphi }}$ 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 $\mathsf {T}$ 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



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Walter Dean
University of Warwick

Citations of this work

Truth is Simple.Leon Horsten & Graham E. Leigh - 2017 - Mind 126 (501):195-232.
On Reflection.Leon Horsten - 2021 - Philosophical Quarterly 71 (4):pqaa083.

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