A constructive proof of Tarski's undefinability theorem and Gödel's incompleteness theorems

The paper presents a fundamentally new constructive proof of Tarski's theorem on the undefinability of truth and Gödel's incompleteness theorems, based on the inexpressibility, by purely formal means, of the existential content of a theory (the "ostension deficit"), without which formalism loses its meaning. It is shown why the classical Gödel theorem arises from the same reason.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-18
DOI
https://doi.org/10.5281/zenodo.20275008
Primary Topic
Philosophy and Theoretical Science
Type
article
Field-Weighted Citation Impact
0.00
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article

A constructive proof of Tarski's undefinability theorem and Gödel's incompleteness theorems

Alexey Torgashin
Zenodo (CERN European Organization for Nuclear Research)
Philosophy and Theoretical Science
article

A constructive proof of Tarski's undefinability theorem and Gödel's incompleteness theorems

Alexey Torgashin
article en

Abstract

The paper presents a fundamentally new constructive proof of Tarski's theorem on the undefinability of truth and Gödel's incompleteness theorems, based on the inexpressibility, by purely formal means, of the existential content of a theory (the "ostension deficit"), without which formalism loses its meaning. It is shown why the classical Gödel theorem arises from the same reason.

Zenodo (CERN European Organization for Nuclear Research)
Systems Analytics (United States) (US), EP Analytics (United States) (US)
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Openalex Percentile: Top 4%
Philosophy and Theoretical Science
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