Remarks on Value Assignment and Truth

This article focuses attention on the specification of language expressions in order to express statements having a truth value. Each specified expression (= value expression) introduced can be derived by adding a specification to an expression of the natural language (“Mario Rossi”—“Mario Rossi born in … on …”) or it can be associated with it without sharing any part of it (“water”—“H2O”). We can imagine different languages and different translation procedures from natural language; each procedure imposes a choice among different value expressions. There are two “windows” that the syntax of the specified expressions “opens up to the world”, so to speak; these are the following formulas: The value of /x/ = x', where “x”, “x'” are names, /x/ is true iffx', where “x”, “x'” are sentences. In the second formula categorical reductions and compositions of the specified expressions must have been performed. In cases where these passages are not available, we would remain with a syntactic expression of the type of sentences, but not, such as to exemplify the traditional definition of truth.