On philosophical meaning of metamathematical limitation theorems (Q2894610)

The paper is devoted to the philosophical meaning of limitation theorems: Löwenhein-Skolem-Tarski theorem, Gödel's completeness theorem, Gödel's first and second incompleteness theorems, Tarski's theorem on the undefinability of truth, and Church's theorem on undecidability. The author distinguishes their meaning for the philosophy of mathematics and their role for general philosophy. He concentrates on the latter -- though the former is also considered. The main thesis of the paper says that metamathematical limitation theorems do not lead directly to univocal philosophical consequences. They have a philosophical sense only when interpreted in a certain way. The thesis is illustrated by some examples.