When Freedom Becomes a Liability -- Reflections on the Variable

Kai Wehmeier (University of California, Irvine)

Kai Wehmeier (Irvine) will present "When Freedom Becomes a Liability -- Reflections on the Variable" at 11 in Arts West 561 North Wing on 8 June.

Abstract: Michael Dummett, in his magisterial exposition of Frege's theory of quantification (Dummett 1973: chapter 2), makes a somewhat surprising claim about the role of free variables in the now standard, Tarskian account of predicate logic: "'Free variables' are merely a convenient notational device which simplifies the statement of the formation rules: they correspond to no type of expression for which there is any need in a language actually in functional use (...)" (p. 18). This might seem surprising because mainstream linguistic semantics typically assumes that deictic or referential pronouns in English---certainly "a language actually in functional use"---are free variables in Tarski's sense. And if Dummett is wrong about free variables, it seems that Tarski's account of the logical form of quantification is indeed superior to Frege's, which has no place for free variables. I will argue not only that Dummett is in fact right, but also that Tarski's trick of allowing free occurrences of variables in order to simplify predicate-logical syntax has led us down the garden path in the semantics of formal and natural languages, with adverse consequences in the philosophy of language.