The antinomy of the variable: A Tarskian resolution

Bryan Pickel, Brian Rabern

Research output: Contribution to journalArticlepeer-review

Abstract

Kit Fine has reawakened a puzzle about variables with a long history in analytic philosophy, labeling it “the antinomy of the variable”. Fine suggests that the antinomy demands a reconceptualization of the role of variables in mathematics, natural language semantics, and first-order logic. The difficulty arises because: (i) the variables ‘x’ and ‘y’ cannot be synonymous, since they make different contributions when they jointly occur within a sentence, but (ii) there is a strong temptation to say that distinct variables ‘x’ and ‘y’ are synonymous, since sentences differing by the total, proper substitution of ‘x’ for ‘y’ always agree in meaning. We offer a precise interpretation of the challenge posed by (i) and (ii). We then develop some neglected passages of Tarski to show that his semantics for variables has the resources to resolve the antinomy without abandoning standard compositional semantics.
Original languageEnglish
Pages (from-to)137-170
JournalJournal of Philosophy
Volume113
Issue number3
Early online date1 Mar 2016
DOIs
Publication statusPublished - Mar 2016

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