Semantics, general semantics, semiotic. New acceptations of old terms. Synthese (Bussum), vol. 7 (1948–1949), pp. 229–232.

G. F . C. G R I S S . Logique des mathematiques intuitionistes sans negation. Comptes rendus hebdomadaires des seances de I'Academie des Sciences (Paris) , vol. 227 (1948), pp. 946-948 In the author 's negationless intuitionistic mathematics , only realizable assumptions are allowed, i.e., a property is acceptable only if there is an element which possesses it in the fundamental set considered. So there is no empty set. Such a negationless intuitionistic mathematics would seem to involve some rather difficult logical problems, not expressly pointed out by the author . In this note, we find brief indications regarding the propositional calculus in M. Griss's conception. He gives the conjunction " o r " a significance only in a class calculus, and states t h a t his propositional calculus contains only implication and conjunction. The author t rea ts Heyting 's propositional calculus as a class calculus or set calculus, and shows tha t many of the intuitionistic logical formulae remain available when this interpretat ion is made. This note must be considered as a summary sketch, since many points of consequence for logicians are not t reated. Compare X I 24(1); X I I 62(3); X I I I 163(1,2), 174(1). P . DESTOUCHES-FEVRIER