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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
*
suki.finn@soton.ac.uk
otaviobueno@me.com
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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

1 Hirsch, E., Quantifier Variance and Realism: Essays on Metaontology (Oxford: Oxford University Press, 2011)CrossRefGoogle Scholar.

2 Hirsch, Eli, ‘Quantifier Variance and Realism’, Philosophical Issues 12 (2002), 51CrossRefGoogle Scholar.

3 Putnam, Hilary, ‘Truth and Convention: On Davidson's Refutation of Conceptual Relativism’, Dialectica 41 (1987), 71CrossRefGoogle Scholar.

4 Hirsch, ‘Quantifier Variance and Realism’, 59.

5 A similar point was made by Rossberg, in Marcus Rossberg, ‘The Logic of Quantifier Variance’, accessed online (08/2017) at http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.405.5953. Rossberg notes that domain variation (both in terms of restriction and shifting) leads to ‘maximalism’, which is not in the spirit of the quantifier variant view that aims for a sparser ontology than maximalism. Rossberg further states that Hirsch insists on varying the meanings rather than ranges of the quantifiers. For more on maximalism, see Eklund, Matti, ‘Neo-Fregean Ontology’, Philosophical Perspectives 20 (2006), 95–121CrossRefGoogle Scholar.

6 Priest, G., In Contradiction, 2nd Edition, (Oxford: Clarendon Press, 2006)CrossRefGoogle Scholar.

7 Hale, Compare B., Abstract Objects, (Oxford: Blackwell, 1987)Google Scholar, with Field, H., Science without Numbers, (Princeton, NJ: Princeton University Press, 1980)Google Scholar.

8 Compare Armstrong, D. M., Universals and Scientific Realism, volumes I and II (Cambridge: Cambridge University Press, 1978)Google Scholar, with Rodriguez-Pereyra, G., Resemblance Nominalism: A Solution to the Problem of Universals (Oxford: Clarendon Press, 2002)CrossRefGoogle Scholar.

9 Compare Lewis, D., On the Plurality of Worlds (Oxford: Blackwell, 1986)Google Scholar, with Rosen, Gideon, ‘Modal Fictionalism’, Mind 99 (1990), 327–354CrossRefGoogle Scholar.

10 Compare Redhead, M., Incompleteness, Non-Locality, and Realism: A Prolegomenon to the Philosophy of Quantum Mechanics (Oxford: Oxford University Press, 1987)Google Scholar, with van Fraassen, B. C., Quantum Mechanics: An Empiricist View (Oxford: Clarendon Press, 1991)CrossRefGoogle Scholar.

11 Compare Thomasson, A., Ordinary Objects (New York: Oxford University Press, 2007)CrossRefGoogle Scholar, with Merricks, T., Objects and Persons (Oxford: Clarendon Press, 2001)CrossRefGoogle Scholar.

12 da Costa, Newton C.A., Krause, Décio, and Bueno, Otávio, ‘Paraconsistent Logics and Paraconsistency’, in Jacquette, D. (ed.), Philosophy of Logic (Amsterdam: North-Holland, 2007), 791–911CrossRefGoogle Scholar.

13 Hellman, G., Mathematics without Numbers: Towards a Modal-Structural Interpretation (Oxford: Clarendon Press, 1989)Google Scholar.

14 See Priest, In Contradiction, and da Costa, Krause and Bueno, ‘Paraconsistent Logics and Paraconsistency’.

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).

17 This is related to Eklund's multitude view in Eklund, Matti, ‘The Multitude View of Logic’, in Restall, G., and Russell, G. (eds), New Waves in Philosophical Logic (Basingstoke: Palgrave Macmillan, 2012), 217–240CrossRefGoogle Scholar.

18 This is the way that Beall and Restall articulate the view, in Beall, Jc., Restall, and G., Logical Pluralism (Oxford: Oxford University Press, 2006)Google Scholar.

19 For a survey of some of these logics, see Akama, Seiki and da Costa, Newton C.A., ‘Why Paraconsistent Logics?’ in Akama, S. (ed.), Towards Paraconsistent Engineering (Dordrecht: Springer, 2016), 7–24CrossRefGoogle Scholar.

20 This is the version favoured in Bueno, Otávio and Shalkowski, Scott, ‘Modalism and Logical Pluralism’, Mind 118 (2009), 295–321CrossRefGoogle Scholar.

21 Hirsch, ‘Quantifier Variance and Realism’, 53.

22 Berto, F. and Plebani, M., Ontology and Metaontology: A Contemporary Guide (Bloomsbury Academic, 2015)Google Scholar.

23 Eklund, Matti, ‘Metaontology’, Philosophy Compass 1/3 (2006), 317–334CrossRefGoogle Scholar.

24 See Willard V.O. Quine, ‘On What There Is’, reprinted from the Review of Metaphysics 2/5 (1948) in the Proceedings of the Aristotelian Society 25 (1951), 217–234.

25 Parsons, T., Nonexistent Objects (New Haven: Yale University Press, 1980)Google Scholar.

26 Azzouni, J., Deflating Existential Consequence: A Case for Nominalism (New York: Oxford University Press, 2004)CrossRefGoogle Scholar.

27 Sainsbury, R.M., Reference without Referents (Oxford: Oxford University Press, 2005)CrossRefGoogle Scholar.

28 This is argued in Finn, Suki, ‘The Role of Existential Quantification in Scientific Realism’, Philosophy 92/361 (2017), 351–367CrossRefGoogle Scholar. See also Azzouni, Deflating Existential Consequence: A Case for Nominalism, for a different way of making this point.

29 Strawson, Peter, ‘Is Existence Never a Predicate?’, Critica 1 (1967), 5–15Google Scholar.

30 See Azzouni, Deflating Existential Consequence: A Case for Nominalism, and Bueno, Otávio, ‘Dirac and the Dispensability of Mathematics’, Studies in History and Philosophy of Modern Physics 36 (2005), 465–490CrossRefGoogle Scholar.

31 See Azzouni, Deflating Existential Consequence: A Case for Nominalism.

32 Evans-Pritchard, E., Witchcraft, Oracles, and Magic Among the Azande (Oxford: Clarendon Press, 1937)Google Scholar. For discussion, see da Costa, Newton C.A., Bueno, Otávio, and French, Steven, ‘Is there a Zande Logic?’, History and Philosophy of Logic 19 (1998), 41–54CrossRefGoogle Scholar.

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.