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Quantifier Variance Dissolved

Published online by Cambridge University Press:  03 July 2018

Suki Finn  and
Otávio Bueno
Suki Finn*
Affiliation:
University of Southampton
Otávio Bueno*
Affiliation:
University of Miami
*
[email protected]
[email protected]
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Abstract

Quantifier variance faces a number of difficulties. In this paper we first formulate the view as holding that the meanings of the quantifiers may vary, and that languages using different quantifiers may be charitably translated into each other. We then object to the view on the basis of four claims: (i) quantifiers cannot vary their meaning extensionally by changing the domain of quantification; (ii) quantifiers cannot vary their meaning intensionally without collapsing into logical pluralism; (iii) quantifier variance is not an ontological doctrine; (iv) quantifier variance is not compatible with charitable translation and as such is internally inconsistent. In light of these troubles, we recommend the dissolution of quantifier variance and suggest that the view be laid to rest.

Type
Papers
Information
Royal Institute of Philosophy Supplements , Volume 82: Metaphysics , July 2018 , pp. 289 - 307
Copyright
Copyright © The Royal Institute of Philosophy and the contributors 2018 

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References

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15 See da Costa, Krause, and Bueno, ‘Paraconsistent Logics and Paraconsistency’, for a discussion of this.

16 The ‘at least’ here is italicized in an attempt to distance ourselves from committing to one side of the debate over whether the meanings of logical constants are fully determined by logical rules of inference. Those who think the meanings are completely specified in this way can be called ‘inferentialists’ (see, for instance, Rumfitt, Ian, ‘The Categoricity Problem and Truth-Value Gaps’, Analysis 57 (1997), 223–36CrossRefGoogle Scholar). Such a proposal can be objected to on the basis of Carnapian considerations, for example, in Raatikainen, Panu, ‘On Rules of Inference and the Meanings of Logical Constants’, Analysis 68 (2008), 282–87CrossRefGoogle Scholar. For a critical discussion of this line of objection, see Murzi, Julien and Hjortland, Ole, ‘Inferentialism and the Categoricity Problem: Reply to Raatikainen’, Analysis 69/3 (2009), 480–488CrossRefGoogle Scholar. We take it that a difference in the introduction and elimination rules is necessary (rather than sufficient) for a difference in a logical constant. After all, two logical constants are interchangeable if they have the same operational rules (this is the so-called ‘collapse’ argument, examined in Harris, John H., ‘What's So Logical About the Logical Axioms?’, Studia Logica 41 (1982), 159–171CrossRefGoogle Scholar; for how this relates to the quantifier variance view, see Warren, Jared, ‘Quantifier Variance and the Collapse Argument’, The Philosophical Quarterly 65.259 (2015), 241–253CrossRefGoogle Scholar).

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33 Our thanks go to Matti Eklund for extremely helpful comments on an earlier version of this paper, and to the audience of the ‘Deflationary Metaphysics Workshop’ at the University of Leeds where this paper was presented and received fruitful discussion.