The antinomy of the variable: a Tarskian resolution

Pickel, B. and Rabern, B. (2016) The antinomy of the variable: a Tarskian resolution. Journal of Philosophy, 113(3), pp. 137-170. (doi: 10.5840/jphil201611338)

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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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Pickel, Dr Bryan
Authors: Pickel, B., and Rabern, B.
College/School:College of Arts & Humanities > School of Humanities > Philosophy
Journal Name:Journal of Philosophy
Publisher:Journal of Philosophy
ISSN:0022-362X
ISSN (Online):1939-8549

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