Abstract

I am going to describe several variant formulations of semantic concepts against the background of the standard formulations. The fact that the notion of semantic entailment can be varied in suitable ways, while proof-theoretic devices stay supposedly fixed, get due attention. A methodological interpretation of the newly introduced semantic concepts forms the backbone of my tentative, at most programmatic approach to the methodology of science via logical techniques. First, a familiar feature of first order formal languages will be discussed, which has shown itself relevant to the working out of the nonstandard semantic concepts. Namely, that while closed quantificational formulas take as their values propositions, i.e. they express statements, open quantifi- cational formulas are systematically ambiguous between propositions and predicates. The ambiguity generated by the two-sidedness of the notion of individual variable. Individual variables have two disparate uses on the one hand, they function like names designating certain objects, on the other – they serve the purpose of larking the argument places and function more or less like pronouns