A Russell-Gödel Theory of Propositional Functions


According to Russell, the theory of types is based on two assumptions: (i) that every propositional function (concept, predicate) has a range of significance and (ii) that these ranges of significance are mutually exclusive. (i) and (ii) are logically independent of one another, and, according to Gödel, an attractive solution to the logical paradoxes (i.e. Russell’s paradox, as applied to propositional functions, concepts etc.) would be to adopt (i) but reject (ii). In this talk, a theory of propositional functions loosely based on these ideas of Russell and Gödel, RG, is presented, and a strategy to get a translation of Simple Type Theory into the theory RG is provided.

February 8, 2020
The logical function of property talk