Non-Fregean Semantics for Sentences

Abstract

In this paper I intend to present the general and formal principles of non-Fregean semantics for sentences and to derive the simplest consequences of these principles. The semantic principles constitue foundation of non-Fregean sentential calculus and its formal semantics and the philosophical interpretations of it. Non-Fregean sentential calculus is the basic part of non-Fregean logic. Non-Fregean logic is a generalization of classical logic. It was conceived by Roman Suszko under the influence of Wittgensteinian’s Tractatus Logico-Philosophicus. The term “non-Fregean” indicates that the set of semantic correlate of sentences need not contain of just two elements, as it assumed by Frege in [1]. Frege accepted the following semantic principle:

(A.F.) all true sentences have the same common referent, and similarly all false sentences also have the one common referent.