In the paper we introduce a wide range of Anderson-like variants of Gödel's theory and prove for each of them strong completeness theorem wrt. corresponding class of modal structures.These theories — all formulated in the 2nd order modal language with a 2nd order unary predicate of positiveness — differ among themselves with respect of: properties of the necessity operator and of the predicate of positiveness, axioms characterizing identity between 1st sort terms, definitions of identity between 2nd sort terms, the treatment (...) of Godlikeness as a term of the 2nd order, the treatment of necessary existence as a term of the 2nd order if there exists the necessity of its presence, the treatment of Ix (Ix(y) is read: terms x, y are identical), for every 1st sort term x, as a term of the 2nd order if there exists the necessity of its presence.Concerning to semantical commitments, the following are essential: (i) 1st order terms order receive only rigid extensions in the constant objectual 1st order domain; (ii) 2nd order terms receive non-rigid extensions in the constant objectual domain of 2nd order and rigid intensions in the constant conceptual 2nd order domain; (iii) The behavior of the identity between 1st sort terms shifts from possible worlds to possible worlds. (shrink)

ON SPINOZA’S PROOFS OF (SPINOZIAN) GOD’S EXISTENCE AND THE PROOF OF THE UNIQUENESS OF THE SPINOZIAN SUBSTANCE In this paper I analyze Spinozian ontological arguments for God’s existence from Ethica ordine geometrico demonstrata. I argue that the first proof suffers from circulus vitiosus, whereas the others have at least one non-obvious premise. I also consider P. Gut’s modification of the first proof, reported to me during the conference “The Philosophy of the 17th Century—Its Origins and Continuations” (Gdańsk, 16.06.2011). Meanwhile, I (...) address D. Chlastawa’s remark that theorem 7 and 14 from Ethica… makes Spinoza’s theory inconsistent. Keywords: SPINOZA, GOD’S EXISTENCE, PROOF, UNIQUENESS, SUBSTANCE Discipline: PHILOSOPHY. (shrink)