Defining Gödel Incompleteness Away

Abstract

We can simply define Gödel 1931 Incompleteness away by redefining the meaning of the standard definition of Incompleteness: A theory T is incomplete if and only if there is some sentence φ such that (T ⊬ φ) and (T ⊬ ¬φ). This definition construes the existence of self-contradictory expressions in a formal system as proof that this formal system is incomplete because self-contradictory expressions are neither provable nor disprovable in this formal system. Since self-contradictory expressions are neither provable nor disprovable only because they are self-contradictory we could define them as unsound instead of defining the formal system as incomplete.

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References found in this work

Remarks on the foundations of mathematics.Ludwig Wittgenstein - 1956 - Oxford [Eng.]: Blackwell. Edited by G. E. M. Anscombe, Rush Rhees & G. H. von Wright.
Remarks on the Foundations of Mathematics.Ludwig Wittgenstein - 1956 - Oxford: Macmillan. Edited by G. E. M. Anscombe, Rush Rhees & G. H. von Wright.

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