x1. In this paper we are concerned with some special theories of non-Fregean logic which determine correspondingly spe- cial elementary, i.e. axiomatic, strengthenings of that logic. The construc- tions presented here extend what has been done in [1] and [2] within the SCI-language. They also apply to the non-Fregean logic in comprehensive languages of kind W involving quantiers binding sentential variables and nominal variables, as well, . However, for the sake of sim- plicity, the underlying language considered here is the (...) SCI-language with quantiers 8 and 9. The reader may inspect the case when the numerical quantiers also occur in the language. (shrink)

The fundamental features of the non-fregean logic (formulated both in structural and in invariant version) are discussed. The difference between two notions introduced by Suszko in his article Reification of Situations is analyzed : semantic homomorphism (projection of the set of sentences of a given language into the universe of situations) and of reification of situations (projection of the universe of situations into the universe of events).

We try to define the essential features of the Fregean paradigm. Then we demonstrate that Suszko's non-fregean logic, Wolniewicz's ontology of situation and Barwise-Perry's situational semantics go meaningfully beyond the fregean paradigm: what is presupposed in all of these theories is that as semantic correlates of sentences serve certain objects which are not logical values of these sentences.