Philosophia Mathematica 15 (1):1-29 (2007)

Authors
Richard Kimberly Heck
Brown University
Abstract
I here investigate the sense in which diagonalization allows one to construct sentences that are self-referential. Truly self-referential sentences cannot be constructed in the standard language of arithmetic: There is a simple theory of truth that is intuitively inconsistent but is consistent with Peano arithmetic, as standardly formulated. True self-reference is possible only if we expand the language to include function-symbols for all primitive recursive functions. This language is therefore the natural setting for investigations of self-reference.
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DOI 10.1093/philmat/nkl028
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References found in this work BETA

Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
The Logic of Provability.George S. Boolos - 1993 - Cambridge University Press.
An Axiomatic Approach to Self-Referential Truth.Harvey Friedman & Michael Sheard - 1987 - Annals of Pure and Applied Logic 33 (1):1--21.
Toward Useful Type-Free Theories. I.Solomon Feferman - 1984 - Journal of Symbolic Logic 49 (1):75-111.
Arithmetization of Metamathematics in a General Setting.S. Feferman - 1966 - Journal of Symbolic Logic 31 (2):269-270.

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Citations of this work BETA

Faithfulness for Naive Validity.Ulf Hlobil - 2019 - Synthese 196 (11):4759-4774.
Self-Reference in Arithmetic I.Volker Halbach & Albert Visser - 2014 - Review of Symbolic Logic 7 (4):671-691.
A Liar Paradox.Richard Heck - 2012 - Thought: A Journal of Philosophy 1 (1):36-40.
Reference in Arithmetic.Lavinia Picollo - 2018 - Review of Symbolic Logic 11 (3):573-603.

View all 12 citations / Add more citations

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