Philosophia Mathematica 23 (1):31-64 (2015)

Authors
Walter Dean
University of Warwick
Abstract
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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DOI 10.1093/philmat/nku026
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References found in this work BETA

Truth.Paul Horwich - 1999 - In Meaning. Oxford University Press. pp. 261-272.
Axiomatic Theories of Truth.Volker Halbach - 2010 - Cambridge, England: Cambridge University Press.
Proof Theory.Gaisi Takeuti - 1975 - Elsevier.
Systems of Logic Based on Ordinals.Alan Mathison Turing - 1939 - London: Printed by C.F. Hodgson & Son.
Finitism.W. W. Tait - 1981 - Journal of Philosophy 78 (9):524-546.

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Truth is Simple.Leon Horsten & Graham E. Leigh - 2017 - Mind 126 (501):195-232.
Incompleteness Via Paradox and Completeness.Walter Dean - 2020 - Review of Symbolic Logic 13 (3):541-592.

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