THE REFLEXIVITY OF A LANGUAGE (SOME COMMENTS ON GÖDEL AND WITTGENSTEIN).

In its special forms of self-reference or diagonalization, the reflexivity of language leads to the paradoxes. How do we manage these paradoxical constructions? In order to answer the question I take two paradigmatic cases: Gödel and Wittgenstein. Even if in both cases the starting point is the same, the Russell's Paradox, as section 2 of this paper shows, the managements of these constructions are very different. In the first case we speak about fundamental results of mathematical logic with substantial philosophical applications: the limitative theorems. Section 1 exemplifies how to construct a Gödel-type sentence using the Diagonal Lemma, and proves its undecidability in Peano Arithmetic. Section 3 argues how the diagonalization leads, via Kleene's Theorem, to the Turing form of Gödel's Theorem, the core of Lucas/Penrose Argument. In the second case, instead, as section 4 shows, the same procedure of diagonalization suppresses the reflexivity of a language in Wittgenstein's Tractatus, leading finally to the self-suppressing of the philosophical discourse. [ABSTRACT FROM AUTHOR]