Self-reference and the languages of arithmetic

Philosophia Mathematica 15 (1):1-29 (2007)
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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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Richard Kimberly Heck
Brown University

Citations of this work

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.
Gödel’s theorem and direct self-reference.Saul A. Kripke - forthcoming - Review of Symbolic Logic:1-5.
Non-reflexivity and Revenge.Julien Murzi & Lorenzo Rossi - 2022 - Journal of Philosophical Logic 51 (1):201-218.

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References found in this work

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The Logic of Provability.George Boolos - 1993 - Cambridge and New York: Cambridge University Press.
Computability and Logic.George S. Boolos, John P. Burgess & Richard C. Jeffrey - 2003 - Bulletin of Symbolic Logic 9 (4):520-521.
Toward useful type-free theories. I.Solomon Feferman - 1984 - Journal of Symbolic Logic 49 (1):75-111.
Computability and Logic.G. S. Boolos & R. C. Jeffrey - 1977 - British Journal for the Philosophy of Science 28 (1):95-95.

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