Quality and Quantifiers

ABSTRACT

I examine three ‘anti-object’ metaphysical views: nihilism (there are no objects at all), generalism (reality is ultimately qualitative), and anti-quantificationalism (quantification over objects does not perspicuously represent the world). After setting aside nihilism, I argue that generalists should be anti-quantificationalists. Along the way, I attempt to articulate what a ‘metaphysically perspicuous’ language might even be.

KEYWORDS:

• metaphysics
• ontology
• quantifiers
• generalism
• nihilism

Notes

¹ See, for instance, Adams [1979], O'Leary-Hawthorne and Cover [1996], Fine [2005], Ladyman and Ross [2007], Dasgupta [2009], Kment [2012: 578ff], Russell [2013], Dasgupta [2014, 2016], and Turner [2016]. Of course, these terms are also sometimes used with other meanings.

² See Magidor [2013], especially chapter 4; thanks to Ross Cameron for discussion of this point. Note that I am using ‘true’ and ‘false’ in thin senses: by it's true that I just mean , and by it's false that I just mean not-. This is to be contrasted with being determinately true or determinately false.

³ It may be helpful to note the parallels with supervaluationist treatments of vagueness (see Fine [1975] and Keefe [2000]). Unfortunately, some confusion arises from the fact that some supervaluationists use the word ‘true’ (or ‘True’) for determinate truth, rather than for ordinary ‘thin’ truth.

⁴ I discuss the prospects for Ground Generalism in Russell [2016].

⁵ It's worth noting that it isn't obvious that Bertrand Russell is any more committed than Sider to an ontology of facts, since according to Russell ‘you cannot properly name a fact’ or put one ‘in the position of a logical subject’ [Russell 1918: 13–14]. This is connected to his theory of types: in modern terminology, we might say that facts are not eligible values of first-order variables; rather, commitment to facts involves quantification of type . By a common Quinean standard, then, facts are not included in Russell's ‘ontology’ proper.

⁶ Rayo's ‘moderate metaphysicalism’ is maybe a bit closer in spirit: ‘the constraint that there be a correspondence between logical form and metaphysical structure applies only to assertions made by philosophers in the “ontology room”’ [2013: 11]. But—like Russell and Sider, I think—I am not thinking of perspicuity as a condition on speaking truly on any occasions, even special philosophical ones. Similarly, unlike metaphysicalism, Anti-Quantificationalism does not bar one from accepting certain ‘just is’ sentences to which Rayo is friendly—such as ‘for the number of dinosaurs to be zero just is for there to be no dinosaurs’ [ibid.: 3, 7]. Even if ‘there are no dinosaurs’ is more perspicuous than ‘the number of dinosaurs is zero,’ this difference between the two expressions does not require any difference in what they express.

⁷ Turner [2016] uses this label for a slightly different view in the same spirit, which is framed in terms of ‘fundamental facts’ rather than perspicuous language.

⁸ Thanks to two anonymous referees for pressing this.

⁹ An alternative argument for (3) turns on the possibility of qualitative indiscernibles, although there is no space here to spell it out in detail. In brief, Black [1952] argued that there could be two qualitatively indiscernible spheres; and Adams [1979] argued that either one of these spheres could have been spontaneously destroyed. If that much is right, then, if is the surviving sphere, it is not a qualitative matter that survives: for all of the qualitative facts would have been the same if the other sphere survived instead. (If Goodman [manuscript] is right, then this claim must be qualified—but not in a way that I think matters for the argument.) One may well wonder whether the generalist should accept these possibilities. Some bundle theorists, for example, reject Black's case as misdescribed (e.g. O'Leary-Hawthorne [1995]). But, as it happens, many generalists do accept the relevant possibilities of qualitative symmetry and symmetry-breaking. (See O'Leary-Hawthorne and Cover [1996: 11–12], Saunders [2003: sec. 2], Pooley [2006: 17–18], Dasgupta [2009: sec. 2], Pooley [manuscript: secs 2.2–2.3], and Dasgupta [2014: 23].) For further discussion, see Russell [2016].

¹⁰ Thanks to an anonymous referee for pressing this.

¹¹ Turner [2011: sec. 3.2] argues that languages that add lambda-abstraction ‘are just as ontologically guilty as first-order ones’. Whether we regiment existential claims in the form or instead as , they are equally unacceptable to the nihilist. This is plausibly so, but there still may be a difference regarding which expression is part of a perspicuous language that is acceptable to the generalist.

¹² Thanks to Ross Cameron, Shamik Dasgupta, Cian Dorr, Jeremy Goodman, John Hawthorne, Michaela McSweeney, Thomas Møller-Nielsen, Louis de Rossett, Jason Turner, Dean Zimmerman, several anonymous referees, and audiences at Columbia, Notre Dame, Stanford, and Leeds for helpful comments and discussion. Thanks to Jesse Wilson for editorial assistance.