Descriptivism about the Reference of Set-Theoretic Expressions: Revisiting Putnam’s Model-Theoretic Arguments

The Monist 103 (4):442-454 (2020)
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Putnam’s model-theoretic arguments for the indeterminacy of reference have been taken to pose a special problem for mathematical languages. In this paper, I argue that if one accepts that there are theory-external constraints on the reference of at least some expressions of ordinary language, then Putnam’s model-theoretic arguments for mathematical languages don’t go through. In particular, I argue for a kind of descriptivism about mathematical expressions according to which their reference is “anchored” in the reference of expressions of ordinary language. These anchors add enough to the content of mathematical expressions to forestall the radical kind of indeterminacy that model-theoretic arguments are purported to show, while still leaving room for a plausible, moderate kind of indeterminacy.



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Zeynep Soysal
University of Rochester

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References found in this work

How to define theoretical terms.David Lewis - 1970 - Journal of Philosophy 67 (13):427-446.
Putnam’s paradox.David Lewis - 1984 - Australasian Journal of Philosophy 62 (3):221 – 236.
From Metaphysics to Ethics: A Defence of Conceptual Analysis.Frank Jackson - 1999 - Philosophical Quarterly 49 (197):539-542.
Realism, Mathematics, and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.
Models and reality.Hilary Putnam - 1980 - Journal of Symbolic Logic 45 (3):464-482.

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