Gödel Mathematics Versus Hilbert Mathematics. II Logicism and Hilbert Mathematics, the Identification of Logic and Set Theory, and Gödel’s 'Completeness Paper' (1930)

Logic, mathematics, physics: from a loose thread to the close link: Or what gravity is for both logic and mathematics rather than only for physics

“…However, one can stare at the Cartesian "abyss" between Descartes's "body" and "mind", being in turn one of the most fundamental problems of philosophy in Modernity, seeing that the problem shares the same formal structure as that already resolved by quantum mechanics by introducing the separable complex Hilbert space and thus it can be mathematically interpreted to be the same, that is, isomorphic. This implies, that solution invented by huge efforts of many great minds for quantum mechanics in the beginning of the 20 th century is to fit to that main philosophical problem as long the two problems are granted to be isomorphic mathematically, which in turn suggests a new kind of Pythagoreanism, called quantum neo-Pythagoreanism in other papers (e.g., Penchev 2021 August 14).…”