, Volume 26, Issue 1, pp 45-56

On a Paradox of Hilbert and Bernays

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Abstract

The paper is a discussion of a result of Hilbert and Bernays in their Grundlagen der Mathematik. Their interpretation of the result is similar to the standard intepretation of Tarski’s Theorem. This and other interpretations are discussed and shown to be inadequate. Instead, it is argued, the result refutes certain versions of Meinongianism. In addition, it poses new problems for classical logic that are solved by dialetheism.