Journal of Philosophy 113 (3):137-170 (2016)

Bryan Pickel
University of Glasgow
Brian Rabern
University of Edinburgh
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

Word and Object.Willard Van Orman Quine - 1960 - Cambridge, MA, USA: MIT Press.
Meaning and Necessity: A Study in Semantics and Modal Logic.Rudolf Carnap - 1947 - Chicago, IL, USA: University of Chicago Press.

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Citations of this work BETA

The Myth of Occurrence-Based Semantics.Bryan Pickel & Brian Rabern - 2021 - Linguistics and Philosophy 44:813-837.
Relational Approaches to Frege's Puzzle.Aidan Gray - 2017 - Philosophy Compass 12 (10):e12429.
The Proper Treatment of Variables in Predicate Logic.Kai Wehmeier - 2018 - Linguistics and Philosophy 41 (2):209-249.

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