The Moodless Theory of Modality: An Introduction and Defence

ABSTRACT

This paper proposes a new reductive theory of modality, called the moodless theory of modality. This theory, and not modal realism, is the closest modal analogue of the tenseless theory of time. So, if the tenseless theory is true, and the temporality–modality analogy is good, it is the moodless theory that follows. I also argue that the moodless theory, considered on its own, is better than modal realism: arguments often thought to be decisive against modal realism are weak against it.

KEYWORDS:

• modality
• possible worlds
• time
• reductionism

Disclosure Statement

No potential conflict of interest was reported by the author.

Notes

1 This is a theme of Dyke’s [1998] and Markosian’s [2001].

2 Defences of the tenseless theory include Russell [1915], Smart [1963], Mellor [1998], Sider [2001], and Skow [2015]. Defences of presentism include Markosian [2004], Bourne [2006], and Zimmerman [2008]. The analogy thesis has its yin and yang in A.N. Prior and David Lewis. Both accepted it; with Prior defending anti-reductionism about time and modality, and Lewis defending reductionism [Prior and Fine 1977, Lewis 1986]. Rini and Cresswell [2012] is a book-length defence of the analogy thesis, and two recent papers defending it are by Emery [2019, 2020]. Arguments against the analogy thesis include Forbes [1983], Lowe [1986], and Dyke [1998]. Since I am pro-analogy, I will note that Dyke claims that the arguments by Forbes and Lowe fail, and that Markosian [2001] claims that Dyke’s own argument against the analogy fails.

3 Elsewhere [2019], I explore some other aspects of the moodless theory, including what it says about advanced modalizing.

4 Although Sider’s book is from 2011, this approach had been common for many years by then, if sometimes implicit and sometimes articulated in somewhat different terms (such as in talk of truthmaking). In the theory of time, the ‘old’ tenseless theory required synonymy; largely in response to Prior [1959], the ‘new’ one requires only truth-conditions (see the papers in Oaklander and Smith [1994]). Dyke claims that this distinction is under-appreciated in debates about modality, and suggests that ‘one could offer any of the possible worlds analyses of modality’ and assert that ‘the content of the proposed reduction would play the role, not of analysis [that is, providing synonyms], but of stating the truthmakers for modal truths’ [2007: 285]. The theory that I shall propose is an instance of this approach.

5 To be qualitative, a sentence must also be free of phrases whose analyses contain names, demonstratives, or free variables. If ‘mammal’ is analysed as ‘organism descended from these organisms’, then ‘There are mammals’ is not qualitative. For simplicity, I will assume that ‘mammal’, ‘donkey’, and so on are qualitative.

6 Technically, these quotation marks should be corner quotes. I ask the reader’s forgiveness for ignoring this distinction. Also, some authors distinguish between truth in a world and truth at a world (e.g. Adams [1981]); that distinction won’t matter here.

7 Technically, the last clause needs to be ‘anything, all the parts of which are spatio-temporally related to any of its parts, is already one of its parts’ (see Lewis [1986: 70]). I will ignore this complication. Note that Lewis intends his theory to entail that, if anything is spatio-temporally related to anything, there is at least one possible world. This requires the assumption that is spatio-temporally related to is an equivalence relation.

8 Bricker [2001] also argues for the possibility of island universes using recombination, or recombination-adjacent, principles. For an argument based on quite different principles, see Bigelow and Pargetter [1987]. A referee worries that the recombination principle that I use might generate problematic results for certain unusual ‘F’ and ‘G’. For example, let ‘F’ be ‘thing which is such that everything is red (all over)’, and ‘G’ be ‘thing which is such that everything is green (all over)’; then the principle seems to entail that it is possible that something be both red and green all over. I would argue that these and other problematic cases run afoul of the restriction: as I am using ‘analytic’ (roughly following Dorr [2005]), ‘something is red and green’ is analytically false. Also, on these definitions, whether something is an F or a G depends on the intrinsic natures of things wholly distinct from it; I am tempted to restrict the principle to exclude such definitions.

9 See Bricker [2001: 34]:

If the notion of island universe were obscure, or very complex … we might not know what possibility we had in mind. But since the notion of island universe, once disambiguated, is simple and clear, Lewis’s substitutes are plainly beside the point.

10 By ‘R is pervasive’, Lewis means, more or less, that R is transitive, or maybe transitive and symmetric. Bricker [1993] argues that in relativistic worlds the basic relations tying spacetime together are not pervasive.

11 Possible worlds, that is, are fusions of equivalence classes of material things under the worldmate relation. It is part of the theory that this relation is, in fact, an equivalence relation.

12 The moodless theory’s analysis doesn’t look quite like this. Its truth-condition is moodless, rather than indicative. I will explain the difference in section 4.

13 The theory does require that if two things are spatio-temporally related, they are parts of the same possible world.

14 You might object that the moodless theory cannot say that ‘Everything is a worldmate of everything else’ is analytic, since it asserts its denial. Does it not say that there are many worlds, and isn’t it true that no world is a worldmate of another? Actually there is no problem here, but I will not be able to explain why so until section 6. As a preview, the response will resemble the tenseless theory’s claim that ‘Everything is present’ has both an analytically true reading and a false reading. Section 6 also defends the thesis that ‘Everything is a worldmate of everything else’ has an analytic reading.

15 By ‘simple’, I mean that P is in the present tense; for embedded tenses, a recursion clause is needed. The statement of the truth-condition assumes that a tensed sentence like ‘X was F’ has been re-written to put the tense in a sentential operator, as ‘It was the case that X is F.’ As Prior [1968] pointed out, this is convenient when doing the formal logic of tense but does some violence to English grammar, which requires ‘X was F’ to become ‘It was the case that X was F.’ For reasons that will appear below, P* also differs from P in that present-tensed verbs have been replaced by tenseless ones.

16 I described another version of the moodless theory, which has ‘is a worldmate of’ but not ‘possible world’ in its fundamental language. There is a version of the tenseless theory that does the parallel thing. It puts ‘is simultaneous with’ in its fundamental language, and defines ‘x is a time’ as ‘every part of x is simultaneous with every other part of x, and everything simultaneous with a part of x is a part of x’: a time is a thing maximally related by the simultaneity relation. (Sometimes the domain here is restricted to parts of spacetime. A different definition would be needed to deal with relativistic spacetimes.)

17 Modal realism has a simpler ideology (in the Quinean sense) than the moodless theory, since ‘possible world’ is not in its fundamental language. And many metaphysicians think that the theory with the simpler ideology is better, other things being equal. Quine was the original source [1948]; David Lewis agreed [1986: 4]. Might modal realism’s advantage in simplicity be so great that it is better overall than the moodless theory? I think that the answer is ‘no’. But a full defence of this would require delving more deeply into the epistemology of metaphysics than I have space for.

18 The tenseless theory’s fundamental language contains, not just a word for instants, but also phrases for temporal relations between times, like ‘earlier than’. The moodless theory does not—so far—have in its fundamental language any phrases for modal relations between worlds. But a fully developed version of the moodless theory might: it might, for example, have ‘w* is the nearest world to w in which A is true’ (where this phrase would not be defined in terms of non-modal similarities between worlds), and use this phrase when giving truth-conditions for counterfactuals. Exploring this idea is beyond the scope of this paper.

19 This objection is sometimes called ‘the irrelevance objection’. Others who press it include Jubien [1988] and Chihara [1998: 95]. Maybe the most famous objection to modal realism is the ‘Humphrey Objection’ [Kripke 1980]. It targets modal realism’s analyses of de re modal claims, analyses like this: ‘Humphrey could have won the election’ is true iff Humphrey has a winning counterpart. I will not discuss this objection directly, but I think that the ‘changing the subject’ objection is, as it were, its de dicto counterpart.

20 The locus classicus is Quine [1951]. An argument against Quine’s epistemological holism, focusing on scientific theories, is in Glymour [1980].

21 A precise description of Leibnizian spacetime may be found in Earman [1989]. Other spacetime structures also permit the definition of ‘instant’ that I will give, but many, including Newtonian, Galilean, and Relativistic spacetimes, do not. The theory of time that I’m describing is thus falsified by known physics. But I am using it to make a philosophical point, not proposing it as true.

22 This is a non-temporal analysis only if x is spatially related to y is a non-temporal relation. I think that it is, but I acknowledge that there is room for disagreement and uncertainty about this. More generally, there is also room for disagreement and uncertainty about what it takes for an analysis to be non-modal or non-temporal. Regarding whether ‘is spatially related to’ (or more specific things like ‘is ten metres from’) names a non-temporal relation, in favour of this one might note that this is in some sense the relation’s canonical name (it provides the best guide to the relation’s nature), and that the name contains no words having anything to do with time or temporality. Alternatively, one might note that ‘is spatially related to’ relates spacetime points, that its job is to help knit spacetime points together into a spatio-temporal structure, and that it relates only simultaneous points. (Thanks here to a referee.)

23 This theory will also want analyses of past and future tense operators. That will require a non-temporal definition of ‘earlier than’. To avoid a detour through what such a definition might look like, I focus on a sentence with ‘sometimes’. For an attempt to define ‘earlier than’ in non-temporal terms, see Barbour [2001].

24 Many have argued that modal realism fails to reduce the modal to the non-modal: see Cameron [2012] for discussion. The basis for my argument is, as far as I know, new.

25 Iatridou [2000] discusses in more detail modal interpretations of the past tense in counterfactuals.

26 Smart [1963: 134], the first I know of to pick a convention, uses italics.

27 Tichy [1980] attacks ‘the myth of atemporal predication’, which includes the thesis that ‘is’ can have a tenseless meaning. That ‘is, was, or will be’ is the only available meaning for ‘IS’ is a premise of some versions of the argument that presentism and eternalism are compatible: see Sider [2001: 15], Crisp [2004], and Sider [2006] for discussion.

28 Grammar books tell me that verbs in English lack future tensed forms. Instead, English talks about the future using the modal auxiliary ‘will’, together with the plain form of the verb. But we non-linguists call ‘Jones will be hungry’ a future-tensed sentence.

29 Note that, while I boldface verbs, it is clauses as a whole that are indicative, subjunctive, or moodless. (Of course, a clause of one mood can embed a clause of another, as in ‘Anyone who would have jumped into the lake is a fool.’)

30 Lycan and Lewis talk about quantifiers, but I read their dispute as about the meaning of an entire clause. This isn’t a misreading, because the properties of being indicative, and being subjunctive, and being moodless are properties of clauses that influence the interpretation of quantifiers that the clauses contain.

31 Van Inwagen [2001b: 222] argues against modal realism in this way—he talks of million-carat diamonds rather than of talking donkeys—but does not use the distinction between indicative and moodless clauses that I think is needed to bolster the argument.

32 All examples so far have been of existential quantification expressed by using ‘There is/are’, but the claim is general. For example, the moodless truth-condition of ‘Some donkeys talk (indicative)’ is that some donkeys that are part of this world talk. The claims that I make in the text about the influence of the present and the indicative on quantifiers are over-simplified. Closer to the truth is that these are their default interpretations. For discussion of the use of the present for other times, and of the indicative for other worlds, see Mackay [2013]. These other uses are fully compatible with the tenseless and the moodless theories.

33 Similarly, the moodless theory validates the common (among metaphysicians) belief that ‘Everything is (indicative) actual’ is analytic, even though it agrees with Lewis that ‘actual’ applies to all and only things that are part of the possible world of utterance. What is false, in the moodless theory, is ‘Everything is actual.’ Modal realism, by contrast, entails that ‘Everything is (indicative) actual’ is false, and so Lewis tries to show that this sentence is not analytic [1986: 97]. I don’t think that he succeeds.

34 Deasy [2019] argues, on the contrary, that tenseless theorists should say that quantifiers in present-tensed clauses can be completely unrestricted. One of his premises is that tenseless theorists assert the present-tensed ‘There are many instants of time.’ I think that this premise is false; they assert only the tenseless ‘There ARE many instants of time’. Elsewhere [2019], I say more about my disagreement with Deasy’s view.

35 The principle of recombination in section 2 was modal. One might wonder whether a moodless principle of recombination entails this possibility. Well, the moodless analogue of the principle from section 2 says that if there is an F in some possible world and there is a G in some possible world then some possible world contains an F and a G. This principle is subject to the moodless version of the original restriction: ‘Some possible world contains an F and something else that is a G’ must not be analytically false. This principle does not yield a world containing things that aren’t worldmates. (The moodless theory might be incompatible with other moodless principles of recombination; whether to amend the theory or reject the principle would depend on the details. Thanks here to a referee.)

36 I have focused on modality de dicto. Modality de re (involving claims about what is possible or necessary for a particular thing) raises a whole host of other well-known problems. The moodless theory could adapt modal realism’s strategy of using counterparts. Modal realism needs a non-modal definition of ‘counterpart’, but it is in the spirit of the moodless theory to use a modal definition, or no definition. I believe that this change will be to the moodless theory’s advantage; but defending this is the project for another paper.

37 If the distinction between the past and the future is not metaphysically fundamental, then it is T is temporally between S and V that is an unanalysable temporal relation, not later than.

38 For helpful comments and probing criticisms that made this paper far better than it might have been, thanks to Jack Spencer and two anonymous referees.