¹ See Rynasiewicz, Robert, ‘Absolute Versus Relational Space-Time: An Outmoded Debate?’, Journal of Philosophy, 93 (1996), 279–306 CrossRefGoogle Scholar.

² Cf. Earman, John, ‘Who's Afraid of Absolute Space?’, Australasian Journal of Philosophy, 48 (1970), 287–319 CrossRefGoogle Scholar.

³ For a clear introductory exposition, see Callender, Craig, ‘Is Time an Illusion?’, Scientific American (June 1, 2010)CrossRefGoogle ScholarPubMed.

⁴ For an ambitious attempt to build a coherent relational physics, see Julian Barbour Barbour, The End of Time. The Next Revolution in Our Understanding of the Universe, Weidenfeld and Nicholson, London (1999). For defenses of the reality of time based on quantum gravity, cf. Smolin, Lee, ‘Temporal Naturalism’, Studies in History and Philosophy of Modern Physics, 52 (2015), 86–102 CrossRefGoogle Scholar, and Matteo Morganti, ‘Relational Time’, in Tomasz Bigaj and Christian Wüthrich (eds): Metaphysics in Contemporary Physics, special issue of the Poznan Studies in the Philosophy of the Sciences and the Humanities, (Leiden, Rodopi, 2015), 215–236 Google Scholar.

⁵ See Shoemaker, Sidney, ‘Time without Change’, Journal of Philosophy, 66 (1969), 363–381 CrossRefGoogle Scholar.

⁶ See, e.g., LePoidevin, Robin, ‘Time without Change (in Three Steps)’, American Philosophical Quarterly, 47 (2010), 171–180 Google Scholar.

⁷ Op. cit. See also LePoidevin, Robin, Change, Cause and Contradiction, (MacMillan, London, 1991), 94–98 Google Scholar.

⁸ Freezes rule out every interaction with the outside, including interaction with observation ‘tools’ of any type.

⁹ And the way in which these (may) suddenly appear to change in radically discontinuous fashion.

¹⁰ As pointed out by some authors ( Corish, Denis, ‘Could Time Be Change?’, Philosophy, 84 (2009), 219–232 CrossRefGoogle Scholar, Ken Warmbrõd, ‘Time, Change, and Time without Change’, Synthese (forthcoming)), Shoemaker's argument assumes that the way in which time passes is not relative to particular observers/regions, while that time in a (supposedly) frozen region can be measured by clocks in a different one is, as a matter of fact, by no means obvious – in particular, in view of the theory of relativity. We will set this issue aside here, if only in consideration of the fact that Warmbrõd himself suggests a way out – i.e., the use of what he calls the ‘Clock-Law’ as a way of accounting for differences among different clocks. According to Warmbrõd, a general law can be defined that provides shared measures of the degree of fit of particular clocks with empirical data and natural laws, and ways of comparing different temporal measures.

¹¹ Based on a careful examination of Physics IV, Corish (‘Could Time Be Change?’, op. cit.) concludes that time in Aristotle should rather be understood as ‘change in abstraction’ – much like geometrical space is the result of a process of abstraction from certain features of actual bodies. Although we will get back to the interpretation of what Aristotle had to say about time in a later section, we do not need to be too worried about exegesis here, and can continue to attribute to Aristotle a form of ‘canonical’ relationism.

¹² If one believes that events must be ‘point-like’ in time (where the concept of a point is intended broadly to refer to the minimum of temporal extension, whatever it may be), this needs to be translated into talk of a series of point-like events constituting x. This makes no difference for present purposes, but we will, at any rate, come back to this later on.

¹³ Leibniz, Gottfried Wilhelm, New Essays on Human Understanding, translated and edited by Remnant, Peter and Bennett, Jonathan, Cambridge University Press, Cambridge (1981, original 1705)Google Scholar, II, 14. As rightly pointed out by an anonymous referee, what Leibniz seems to have in mind here is that we are dealing with eternal truths, which equally concern the possible and the actual, not that mere possibles ought to be admitted into time.

¹⁴ See Newton-Smith, William Herbert, The Structure of Time, Routledge and Kegan Paul, London (1980)Google Scholar, Butterfield, Jeremy, ‘Relationism and Possible Worlds’, British Journal for the Philosophy of Science, 35 (1984), 101–113 CrossRefGoogle Scholar, and Forbes, Graeme, ‘Time, Events, and Modality’, in LePoidevin, Robin and MacBeath, Murray (eds), The Philosophy of Time (Oxford University Press, Oxford, 1993), 80–95 Google Scholar.

¹⁵ For considerations along these lines, see Warmbrõd, Ken, ‘Temporal Vacua’, Philosophical Quarterly, 54, 266–286 CrossRefGoogle Scholar.

¹⁶ It is not necessary here to determine specifically which temporal units should used, and to what extent these are conventionally defined.

¹⁷ See his ‘Temporal Vacua’, op. cit.

¹⁸ See also Lepoidevin, ‘Time without Change (in Three Steps)', op. cit., 172. To anticipate a later theme, this reminds of Adams' ( Adams, Robert Merrihew, ‘Primitive Thisness and Primitive Identity’, Journal of Philosophy, 76 (1979), 5–26 CrossRefGoogle Scholar) arguments against the Identity of the Indiscernibles based on *almost* indiscernible worlds. Teichmann ( Teichmann, Roger, ‘Time and Change’, Philosophical Quarterly, 43 (1993), 158–177 CrossRefGoogle Scholar) also maintains that Shoemaker's inductive-evidence-based arguments are insufficient, and suggests that they should be integrated with Wittgensteinian criteria of meaningfulness to be applied to claims about changeless periods of time. Scott ( Scott, Michael, ‘Time and Change’, Philosophical Quarterly, 45 (1995), 213–218 CrossRefGoogle Scholar) disagrees.

¹⁹ See ‘Temporal Vacua’, op. cit., 279 and 282.

²⁰ This does not contradict the earlier claim that substantivalism may be said to provide a better explanation of temporal vacua than modal relationism. That claim was based on the irrelevance of certain trans-world considerations for hypotheses concerning what is the case in a world, and on the preferability of sufficiently explanatory hypotheses not requiring such considerations.

²¹ See Shoemaker, ‘Temporal Vacua’, op. cit., 373.

²² Nor do we need here to enter the debate concerning the opportunity to avoid primitive identities (and brute facts more generally) whenever possible. The explanatory advantage of primitive numerical distinctness is assumed to be manifest in the present case.

²³ Leibniz, for instance, writes that ‘we observe also novelty or change, that is, contradictory attributes of the same thing [and] the only difference […] that brings it about that there is no contradiction of any kind [is the difference of time]’ (in Leibniz, Gottfried Wilhelm, The Labyrinth of the Continuum: Writings on the Continuum Problem, 1672–1686, edited by Arthur, Richard T.W. (Yale University Press, New Haven and London, 2001), 267Google Scholar).

²⁴ Quotation from Leibniz, Gottfried Wilhelm, The Leibniz-Clarke Correspondence, edited by Alexander, H.G. (Manchester University Press, Manchester, 1956, original 1704)Google Scholar, third paper, Section 6, emphasis added.

²⁵ The gap appears thereby filled between the quotation from Leibniz just given and the earlier ones from the New Essays and the Leibnizian writings on the continuum, where he explicitly refers to qualitative change and its possibility, rather than to mere succession.

²⁶ As for Aristotle, as we have seen above he makes an explicit reference to (qualitative/positional) change in his definition of time. But it is plausible to think that this is because his views of the issue intimately connect ontological considerations and epistemological/psychological considerations. Indeed, it is by no means a coincidence that a popular (perhaps the most popular) interpretation of Aristotle's views on time is a psychologistic interpretation according to which – roughly! – time depends on the conscious activity of human beings, and would not exist if there were no agents counting or, more generally, becoming aware of changes in the surrounding environment. This subject-based view naturally requires more than mere numerical difference for the passing of time: for, it takes more than just two, or more, (merely) numerically distinct events for a conscious subject to become aware that something ‘has happened’. However, this particular view of time is not only separable from relationism. It is arguably incompatible with it, at least on a strongly realistic conception of time. Be this as it may, for present purposes it is sufficient to point out that talk of distinct relata and talk of qualitative/positional change can be decoupled even within the context of Aristotle's views, provided that one sets aside the psychologistic elements of Aristotle's conception of time just mentioned. One obvious, yet important, consequence of all this is that the idea (developed, for instance, by Corish, Denis, ‘Could Time Be Change?’, op. cit., ‘Time as Relative’, Philosophy, 90 (2015), 369–391 CrossRefGoogle Scholar) that time coincides with the exemplification of contradictory qualities by the same individual (also endorsed, as we have seen in an earlier footnote 23, by Leibniz) should not be regarded as essential to relationism.

²⁷ Leibniz, as mentioned, did regard (possible) qualitative difference as essential. Leibniz* doesn't.

²⁸ To be absolutely clear and avoid misunderstandings with respect to Leibnizian exegesis, the argument being put forward is that a) Leibniz endorses relationism about time and the Identity of the Indiscernibles, hence would not be prepared to allow for (actual) purely numerical distinctness; b) relationism and commitment to the Identity of the Indiscernibles are however conceptually independent; c) there are reasons for endorsing primitive thisness for events, so rejecting the Identity of the Indiscernibles (see below); hence d) it is possible (indeed, advisable) for relationists to retain only part of the Leibnizian view, allowing for violations of the Identity of the Indiscernibles. Something along the lines of b) and d) above can be found in LePoidevin, ‘Time without Change (in Three Steps)', op. cit., 176–178. LePoidevin, however, besides speaking of states of affairs rather than events, does not provide an extensive discussion. (In connection to this, while it is fair to acknowledge an overlap between the ideas put forward here and LePoidevin's defence of relationism, it must also be pointed out that the present author came across LePoidevin's article only after completing this paper).

²⁹ Cf. Diekemper, Joseph, ‘Thisness and Events’, Journal of Philosophy, 106 (2009), 255–276 CrossRefGoogle Scholar.

³⁰ See Black, Max, ‘The Identity of Indiscernibles’, Mind, 61 (1952), 153–164 CrossRefGoogle Scholar, and Hacking, Ian, ‘The Identity of Indiscernibles’, Journal of Philosophy, 72 (1975), 249–256 CrossRefGoogle Scholar.

³¹ Cf. Ayer, Alfred Jules, ‘The Identity of Indiscernibles’, in Philosophical Essays (New York, MacMillan, 1954), 26–35 Google Scholar.

³² The former family of views affirming and the latter denying, respectively, the idea that there is an objective ontological distinction between the present and the future.

³³ It is probably worth it at this point to make it explicit (following, for instance, Adams, ‘Primitive Thisness’, op. cit.), that the attribution of primitive identities is not tantamount to postulating mysterious metaphysical properties additional to the ‘normal’ properties of things. Following the Ockhamian tradition whereby ‘[w]hatever is singular is singular through nothing added to it, but by itself’ (Ockham, Ordinatio I.2.6), individuality can instead be taken as a brute, fundamental fact of numerical difference without postulating some ‘haecceitas’ as a cause for it.

³⁴ It is interesting to note that the distinction between static and dynamic processes has also been individuated (see Schlesinger, George, ‘Change and Time’, Journal of Philosophy, 67 (1970), 294–300 CrossRefGoogle Scholar) as a possible basis for the definition of potential empirical tests of the presupposition, allegedly key to Shoemaker's reasoning in favour of temporal vacua, that the freezing (or slowing down) of worlds involves events, but not time.

³⁵ Adjustments and additional qualifications may be required once one considers certain possibilities that appear to undermine the correspondence between the identities of events and those of putatively more fundamental ontological items – or, at any rate, to add complexity to the identities of the relevant entities. Think, for example, of extended simples, or of enduring objects, identical across several instants. However, there does not seem to be any insurmountable difficulty here. Notice, in particular, that (reasons of space only permit some very brief remarks): the point-likeness of events is not required for relationism to work, as events that qualify as ‘extended simples’ can perfectly do their job of temporally separating; all temporal measures can and should be, at least indirectly, be based on the shortest events (‘extended and simple’ events thereby qualifying as composite events for the purposes of determining temporal relations); if at all needed, merely possible events may be employed to define these latter shortest events, the Leibnizian* view in any case remaining preferable over modal relationism in terms of amount of work done by merely possible events; lastly, it can plausibly be contended that endurantism does not need to presuppose the numerical distinctness of instants, and can instead make the latter dependent on the diachronic (self-)identity of things. (The above holds, mutatis mutandis, if the relata of temporal relations are entities different from events).

³⁶ Cf. Benovsky, Jiri, ‘The Relationist and Substantivalist Theories of Time: Foes or Friends?’, European Journal of Philosophy, 19 (2011), 491–506 CrossRefGoogle Scholar.

³⁷ For related criticism of Benovsky's views on relationism and temporal vacua, and more generally of his views on the significance of the substantivalism/relationism dispute, see Mazzola, Claudio, ‘Still Foes: Benovsky on Relationism and Substantivalism’, European Journal for Philosophy of Science, 6 (2016), 247–260 CrossRefGoogle Scholar.

³⁸ To repeat, it is this fact about actuality, the Leibnizian* relationist contends, that makes it the case that the world might have been qualitatively different in the interval between the occurrence of a and that of b.

³⁹ Of course, the proposed relationist view of time requires further development. For instance, as acknowledged earlier, one may ask for a precise account of duration and temporal distance, i.e., of the way in which time as a quantity emerges from the mere relational facts of succession that ground the earlier-later distinction. For some suggestions concerning this, see, e.g., Corish, ‘Time as Relative’, op. cit. Here, however, we do not need to pretend that a fully developed account is already available, and will instead stay content with having put forward, defended, and motivated the basic idea underlying Leibnizian* relationism.

⁴⁰ I wish to thank Mauro Dorato and Andrea Roselli for discussing with me issues surrounding time, and a couple of anonymous referees for their useful remarks. I also gratefully acknowledge the financial support received from the Italian Ministry of University and Research in the form of grant FIRB F81J12000430001.