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ABSTRACT
Generality relativism is the view that any domain of quantification can always be expanded. The view promises to resolve a broad range of paradoxes, but, without an explanation of how domains expand, it sounds very mysterious. Proponents of linguistic versions of generality relativism try to demystify the view by likening domain expansions to semantic change. They think that domains expand when we re-interpret certain terms so that, upon re-interpretation, the quantifiers range over more things. This article makes trouble for linguistic approaches. According to the so-called charge of ineffability, generality relativism cannot be asserted in a coherent manner—given that asserting the view requires generalising over absolutely all domains of quantification. Generality relativists typically try to answer the charge with the help of modal operators; but linguistic approaches interpret these operators in semantically and syntactically idiosyncratic ways. I argue that, because of these commitments, linguistic approaches ultimately do not have a good response to the charge of ineffability.
Notes
1 That is, I do not presuppose the so-called all-in-one principle [Cartwright Citation1994], according to which the use of a quantifier presupposes that the objects over which it ranges make up a unified whole.
2 The earliest proponents of generality relativism include Russell [Citation1907] and Dummett [Citation1973: 317]. In the more recent literature, generality relativism has been defended by Glanzberg [Citation2004], Fine [Citation2005, Citation2006], Linnebo [Citation2013], Warren [Citation2017], Studd [Citation2019], and others.
3 Lewis [Citation1991: 68] raises this objection as follows: ‘Maybe [the generality relativist says] that some mystical censor stops us from quantifying over absolutely everything without restriction. Lo, he violates his own stricture in the very act of proclaiming it.’ This objection has two parts. Lewis’s reference to a ‘mystical censor’ suggests that the mechanism that supposedly explains indefinite extensibility is opaque and implausible. The rest of the argument amounts to saying that generality relativism is self-undermining.
4 Fine [Citation2005] and Studd [Citation2019] distinguish between ‘restrictionist’ and ‘expansionist’ versions of generality relativism. Restrictionists think that domains expand when a restriction on the domain of quantification is lifted; expansionists think that domains may expand without the lifting of a restriction. Restrictionist views always belong in the linguistic camp; expansionist views may be either linguistic or metaphysical. My objection to linguistic versions of generality relativism applies equally to restrictionist and expansionist accounts. See Studd [Citation2019: ch. 4] for a critical discussion of restrictionist views.
5 Studd [Citation2019: sec. 1.5] argues for this point, using the example of ‘hoover’.
6 Many philosophers regard the charge of ineffability as a decisive problem. See Lewis [Citation1991: 68], McGee [Citation2000: 55], and Williamson [Citation2003: 433].
7 See Fine [Citation2006] and Studd [Citation2019] for alternative implementations of a modal strategy.
8 Proponents of schematic approaches include Glanzberg [Citation2004], Lavine [Citation2006], and Parsons [Citation2006: 217–18]. Glanzberg and Parsons use the term ‘typical ambiguity’ when addressing the use of schemata. See Studd [Citation2019: ch. 5] for a critical discussion of schematic approaches.
9 Warren [Citation2017] explicitly defends a close connection between generality relativism and Hirsch’s [Citation2011] so-called quantifier variance view.
10 The images for and were created by Pippin Schupbach.
11 Here is how Studd [Citation2019: 105] puts this point:
universe expansion is a matter of liberalizing the interpretation of the lexicon. Suppose that under our initial interpretation (and context) the nominal ‘thing’ and the quantifier ‘everything’ is unrestricted. In this case, the universe of discourse expands if we come to attach new, more inclusive meanings to the nominal and the quantifier’.
12 See Fine [Citation2006] for a non-plural implementation.
13 I will not argue for (GR). For an argument, see Studd [Citation2019: ch. 7].
14 Studd [Citation2019; sec. 6.5] explicitly endorses this view.
15 This is a necessary, not sufficient, condition for a metaphysical approach. Modal operators that shift a parameter of the index may express a deontic or epistemic modality.
16 See, for instance, Williamson [Citation2003: 433].
17 In the above quotation, Kaplan blurs over the distinction between context-shifting and character-shifting operators. He is typically understood to be ruling out context-shifting operators. In section 5, I discuss a framework that allows for character-shifting operators.
18 See Schlenker [Citation2003] and Anand and Nevins [Citation2004].
19 See Rabern [Citation2012], Yli-Vakkuri [Citation2013], and Santorio [Citation2019].
20 Rabern and Ball [Citation2019] helpfully distinguish between formal monsters and content monsters. Formal monsters shift a context parameter. They are impossible within both a Kaplanian and a Lewisian semantic framework. Content monsters, however, shift a content-determining parameter. Content monsters are impossible within a Kaplanian, but possible within a Lewisian, framework.
21 It is commonly thought that semantic values must determine assertoric contents, since otherwise speakers would not be able to understand what a sentence is used to say on a given occasion of use, while knowing only its semantic value.
22 As mentioned before, metaphysical approaches can alternatively introduce a non-standard index parameter that fixes the domain of evaluation.
23 Ur-elements are non-sets and have no elements.
24 In more detail, Studd introduces two modal operators. □< is ‘backward-looking’ and generalises over previous interpretations, while □> is forward-looking and generalises over subsequent interpretations. However, the two operators can be used to define an undirected modal operator, and the bimodal aspect of Studd’s view does not make a difference with respect to the problem that I raise for his view.
25 The example is due to Hawthorne and Magidor [Citation2009].
26 On this view, the i-parameter is like a variable assignment that’s determined by the context of use.
27 Modalism can be traced back to Prior and Fine [Citation1977].
28 Thanks to an anonymous referee for making this point.
29 This is established by the so-called Kripke Normal Form Theorem [Studd Citation2019: sec. 6.5].
30 Williamson [Citation2003: sec. IV] presents a related argument, according to which no quantifier ever includes all interpretations in its domain. See also Studd [Citation2019: ch. 7].
31 Studd [Citation2019: ch. 7] presents a related argument, according to which generality relativism—and not just linguistic approaches—leads to thoroughgoing relativism. But Studd also suggests a way in which the argument can be resisted: the argument rests on a distinction between two modal operators, □ and ▪. The intended interpretation is that □ generalises over the stages of the initial set-theoretic hierarchy, while ▪ generalises over the stages of a (perhaps vacuously) extended hierarchy. I here argue that proponents of linguistic approaches should accept the possible existence of various interpretational modalities. This leaves it open that the proponents of metaphysical approaches might resist Studd’s argument by adopting a view on which □ = ▪.
32 Alternatively, one might also try to argue that R is not interpretationally possible. My response to this idea is essentially the same: this move calls into question whether the immediately relevant sense of ‘possible’ really is interpretational possibility.
33 Studd [Citation2019: sec. 4.4] criticises Fine’s view along similar lines:
Fine’s additional parameter view is intriguing; but I’m not sure what to make of it. It seems that we have a robust grasp on what it is to change the circumstances, or to shift the context of utterance, or to reinterpret our lexicon. Even if we do not always know what the mechanisms behind such shifts are, it is clear that they happen. This is not the case for Fine’s supposed ontology parameter.
34 I would like to thank the members of my dissertation committee—David Chalmers, Cian Dorr, Gary Ebbs, and Anja Jauernig—for their advice on the dissertation and helpful comments on the dissertation chapter of which this article is a development. I would also like to thank Chris Barker, David Builes, Kit Fine, Peter Fritz, Harvey Lederman, Jon Litland, Agustín Rayo, Sam Roberts, Chris Scambler, James Studd, Gabriel Uzquiano, Øystein Linnebo, and Yale Weiss for helpful comment and discussions. Parts or early versions of this work were presented at the ABD seminar at NYU in Fall 2017, the 11th Cambridge Graduate Conference on the Philosophy of Mathematics and Logic in 01/2018, the CUNY Workshop on Logic and Metaphysics in 03/2018, the ConceptLab Core Seminar (University of Oslo) in 06/2018, the ConceptLab/NYU conference on The Foundations of Conceptual Engineering at NYU in 09/2018, the metaphysics reading group at Princeton in 03/2019, and at the higher-order metaphysics workshop in Birmingham in 05/19. Thanks to the audiences on these occasions for helpful and engaging discussions. Further thanks to two anonymous referees and an editor for the Australasian Journal of Philosophy for extremely helpful comments and suggestions.