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On the Invariance of Goedel's Second Theorem with Regard to Numberings
The prevalent interpretation of Gödel’s Second Theorem states that a sufficiently adequate and consistent theory does not prove its consistency. It is however not entirely clear how to justify this informal reading, as the ...
Wittgenstein's Elimination of Identity for Quantifier-free logic
One of the central logical ideas in Wittgenstein’s Tractatus logico-philosophicus is the elimination of the identity sign in favor of the so-called “exclusive interpretation” of names and quantifiers requiring different ...
Self-reference upfront: a study of self-referential Godel numberings
In this paper we examine various requirements on the formalisation choices under which self-reference can be adequately formalised in arithmetic. In particular, we study self-referential numberings, which immediately provide ...