The standard truth-conditional semantics for substitutional quantification, due to Saul Kripke, does not specify what proposition is expressed by sentences containing the particular substitutional quantifier. In this paper, I propose an alternative semantics for substitutional quantification that does. The key to this semantics is identifying an appropriate propositional function to serve as the content of a bound occurrence of a formula containing a free substitutional variable. I apply this semantics to traditional philosophical reasons for interest in substitutional quantification, namely, theories (...) of truth and ontological commitment. (shrink)

When Russell argued for his ontological convictions, for instance that there are negative facts or that there are universals, he expressed himself in English. But Wittgenstein must have noticed that from the point of view of Russell's ideal language these ontological statements appear to be pseudo-propositions. He believed therefore that what these statements pretend to say, could not really be said but only shown. Carnap discovered a way out of this mutism: what in the material mode of speech of the (...) object language looks like a pseudo-proposition can be translated into a perfectly meaningful proposition in the formal mode of speech (in the metalinguistic mode of speech of the logical syntax of language). But is this ascent into the metalanguage necessary? Taking advantage of Lésniewski's logical system there exists another way outwe can expand the number of categories of our ideal language. But Leniewski's formulas raise another profound problem, the problem of semantical muteness (cf. W. G. Lycan Semantic Competence and Funny Functors Monist 64 (1979), 209–222). (shrink)