Temporal quantifier relativism

ABSTRACT

In this paper, I introduce a quantifier-pluralist theory of time, temporal quantifier relativism. Temporal quantifier relativism includes a restricted quantifier for every instantaneous moment of time. Though it flies in the face of orthodoxy, it compares favorably to rival theories of time. To demonstrate this, I first develop the basic syntax and semantics of temporal quantifier relativism. I then compare the theory to its rivals on three issues: the passage of time, the analysis of change, and temporal ontology.

KEYWORDS:

• Quantifier pluralism
• passage of time
• temporary intrinsics
• ontology
• eternalism

Acknowledgements

This paper’s ancestry can be traced as far back as 2012. Consequently, I owe my thanks to many over the years, including Andrew Brenner, Rebecca Chan, Robin Dembroff, David Dick, Michael Longenecker, Brannon McDaniel, Callie K. Phillips, Michael Rea, Amy Seymour, Ted Sider, Joshua Spencer, Jason Turner, the audience of my 2015 Central APA conference presentation, and the audience of my 2013 Western Michigan University graduate student conference presentation. Thanks, also, to the anonymous reviewers and editors of Inquiry for their patience and support. Special thanks belong to Meghan Sullivan, who many years ago encouraged me to keep working on my seminar paper. It took me longer than expected, but I kept working!

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 For some representative discussion, see van Inwagen (1998); Sider (2001).

2 Cf. Sider (2011): 223–224; Turner (Forthcoming)

3 See van Inwagen (1998): 234–235

4 Cf. McDaniel (2017): 8–11

5 See, for example, Sider (2011): 285–290, Sullivan (2012a): 150–153.

6 See, for example, Prior and Fine (1997); Zimmerman (2005).

7 Cf. Javier-Castellanos (2019)

8 See Merricks (2019); Builes (2019); Rettler (2020).

9 I am alluding to the so-called ‘There Can Only Be One’ argument. See Turner (2012): 430–431.

10 Cf. Turner (2012): 430, 431.

11 There are other strategies. Most notably, some philosophers abandon the original intuition that what exists varies from one world to another. See, for instance, Williamson (2013).

12 See, for instance, Prior (1957); Müller (2011).

13 The temporal ordering relation may be skipped if there is no ‘arrow of time’; see 3.3 for when this issue becomes relevant.

14 See Sider (2001): 42–52 for a standard presentation of this argument.

15 See, for instance, Builes and Impagnatiello (Forthcoming). Rea (1998): 226–236 discusses how, even if the argument succeeds against presentism, it has little impact on other theories in the philosophy of time.

16 For more on the A-theorist camp, see: Zimmerman (2005); Sullivan (2016).

17 For more on the B-theorist camp, see: Mellor (1998); Sider (2001).

18 For a more systematic discussion of ‘the’ argument from experience, see Skow (2011).

19 For more, see McDaniel (2017): 78–109.

20 Cf. Sider (2001); Turner (2020)

21 Cf. Sider (2001): 218

22 In fact, despite Lewis’s endorsement of theoretical conservativism, he himself endorses four-dimensionalism!

23 See, inter alia, Horgan and Potrč (2008); Lewis (1986).

24 See Bourne (2006): 68–69; Miller (2009); Tallant (2013). Sider (2001): 75–76 discusses a version of four-dimensionalism, inspired by Bertrand Russell, according to which persisting objects are excluded. Such a view may be on a par with presentism with respect to ontological parsimony, but it suffers from other disadvantages.

25 Sider (2011); Sullivan (2016). Cf. Zimmerman (2005)

26 See McDaniel (2017): 6–7.

27 For more on the differences between quantitative parsimony and qualitative parsimony, as well as reasons to prefer one or the other, see: Lewis (1973); Nolan (1997). In Finocchiaro (Forthcoming), I raise a puzzle about how we regard these differences. Thankfully, that puzzle does not impact what I want to say here in this paper.

28 See Turner (2016) for an attempt to make sense of a quantifier-free fundamental metaphysics. For more careful discussions of ideological parsimony and ideological kinds, see Cowling (2013); Finocchiaro (2019). For an alternative approach, see Rubio (2022). Interestingly, on Rubio’s approach, presentism is expressively weaker than four-dimensionalism and is therefore not less ideologically parsimonious.

29 As is, the analysis provided doesn’t obviously solve the problem of temporary intrinsics. What is needed is a more developed treatment of the tense operators. In particular, they must deny the validity of ‘P(∃xFx) → ∃xFx’ and ‘∃xP(Fx) → ∃xFx’. Tense operators must be ‘prophylactic’. For more, see Sullivan (2012b).

30 I am summarizing a fairly large literature here. For more on the truth-maker objection to presentism and its connection to change, see Sider (2001): 35–42, Merricks (2007): 119–145.

31 Nominals were first introduced in Prior (1967), but see Areces and Balder ten (2006) for a more comprehensive treatment of nominals and hybrid logic more generally.

32 Nominals are typically used to construct a satisfaction operator that shifts the evaluation of an arbitrary statement to the moment in question. But this function is already provided by TQR’s temporally relativized quantifiers.

33 See, e.g., Sider (2001): 93–97.

34 See, inter alia, Sider (2013); Lewis (1986).

35 Though see Langendoen and Postal (1991) for an argument that natural languages are, in some sense, really big.

36 Lakoff and Johnson (2003)

37 See Turner (2015) for an analogous defence of second-order logic.