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