Heterologicality and Incompleteness

Mathematical Logic Quarterly 48 (1):105-110 (2002)
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Abstract

We present a semantic proof of Gödel's second incompleteness theorem, employing Grelling's antinomy of heterological expressions. For a theory T containing ZF, we define the sentence HETT which says intuitively that the predicate “heterological” is itself heterological. We show that this sentence doesn't follow from T and is equivalent to the consistency of T. Finally we show how to construct a similar incompleteness proof for Peano Arithmetic.

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Cezary Cieslinski
University of Warsaw

Citations of this work

Incompleteness Via Paradox and Completeness.Walter Dean - 2020 - Review of Symbolic Logic 13 (3):541-592.
Gödelizing the Yablo Sequence.Cezary Cieśliński & Rafal Urbaniak - 2013 - Journal of Philosophical Logic 42 (5):679-695.
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References found in this work

A Note on Boolos' Proof of the Incompleteness Theorem.Makoto Kikuchi - 1994 - Mathematical Logic Quarterly 40 (4):528-532.
On the incompleteness theorems.Henryk Kotlarski - 1994 - Journal of Symbolic Logic 59 (4):1414-1419.

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