The Antinomy of the Variable: A Tarskian Resolution

Journal of Philosophy 113 (3):137-170 (2016)
Authors
Brian Rabern
University of Edinburgh
Bryan Pickel
University of Edinburgh
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.
Keywords variables  quantification  structured propositions  Tarski  antinomy of the variable
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DOI 10.5840/jphil201611338
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References found in this work BETA

Does Semantic Relationism Solve Frege’s Puzzle?Bryan Pickel & Brian Rabern - 2017 - Journal of Philosophical Logic 46 (1):97-118.

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Citations of this work BETA

Relational Approaches to Frege's Puzzle.Aidan Gray - 2017 - Philosophy Compass 12 (10):e12429.
Does Semantic Relationism Solve Frege’s Puzzle?Bryan Pickel & Brian Rabern - 2017 - Journal of Philosophical Logic 46 (1):97-118.
The Proper Treatment of Variables in Predicate Logic.Kai F. Wehmeier - 2018 - Linguistics and Philosophy 41 (2):209-249.

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