Self-reference and the languages of arithmetic

Philosophia Mathematica 15 (1):1-29 (2007)
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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Richard Heck (2012). A Liar Paradox. Thought: A Journal of Philosophy 1 (1):36-40.
Julien Murzi (2012). On Heck's New Liar. Thought: A Journal of Philosophy 1 (2):258-269.
Richard Heck (2012). More on 'A Liar Paradox'. Thought: A Journal of Philosophy 1 (4):270-280.
David Ripley (2013). Response to Heck. Thought: A Journal of Philosophy 4 (3):n/a-n/a.

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