Varieties of Self-Reference in Metamathematics

Journal of Philosophical Logic 52 (4):1005-1052 (2023)
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Abstract

This paper investigates the conditions under which diagonal sentences can be taken to constitute paradigmatic cases of self-reference. We put forward well-motivated constraints on the diagonal operator and the coding apparatus which separate paradigmatic self-referential sentences, for instance obtained via Gödel’s diagonalization method, from accidental diagonal sentences. In particular, we show that these constraints successfully exclude refutable Henkin sentences, as constructed by Kreisel.

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Volker Halbach
Oxford University

Citations of this work

A Step Towards Absolute Versions of Metamathematical Results.Balthasar Grabmayr - 2024 - Journal of Philosophical Logic 53 (1):247-291.

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References found in this work

Logic, semantics, metamathematics.Alfred Tarski - 1956 - Oxford,: Clarendon Press. Edited by John Corcoran & J. H. Woodger.
Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Recursion-theoretic hierarchies.Peter G. Hinman - 1978 - New York: Springer Verlag.
Classical recursion theory: the theory of functions and sets of natural numbers.Piergiorgio Odifreddi - 1989 - New York, N.Y., USA: Sole distributors for the USA and Canada, Elsevier Science Pub. Co..

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