Logic Seminar: Session 1

The most widely used version of predicate logic, due to Tarski and promulgated in formal semantics by his student Montague, countenances well-formed expressions that contain "free" occurrences of variables which may become "bound" by quantifier expressions. This talk will show, by developing in some detail an alternative Wehmeier calls Fregean predicate logic, that the distinction between free and bound occurrences of variables, and concomitantly the phenomenon of variable binding, is an artifact of Tarski's particular formulation of predicate logic. Moreover, Fregean predicate logic has certain theoretical advantages over its Tarskian rival, in that it admits of a non-representational compositional semantics for which Fine's so-called antinomy of the variable does not arise. In Fregean predicate logic, variables are not meaning-bearing items, but rather marks of punctuation akin to the parentheses. Given that the issues that plague Tarskian predicate logic all seem to arise from its treatment of variables as meaningful, Wehmeier suggests that we should take the Fregean system to reveal the true nature of the variable.

Chair for Session: Sean Walsh