Abstract
Presentists argue that only the present is real. In this paper, I ask what duration the present has on a presentist’s account. While several answers are available, each of them requires the adoption of a measure and, with that adoption, additional work must be done to define the present. Whether presentists conclude (1) that a reductionist account of duration is acceptable, (2) that duration is not an applicable concept for their notion of the present, (3) that the present has a duration of zero, or that (4) that the present has a duration, a more robust account of the present is required. I suggest that some of the most difficult questions about duration can be avoided at the cost of no longer viewing presentism as a theory about time, but rather as a theory about existence. In the conclusion, I suggest an interpretation of presentism that allows it to endorse the view that time is nothing more than the measure of change.
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Notes
Where a standard interpretation of relativity theory is that it denies the existence of a privileged foliation (where a privileged foliation is the division of a 4-dimensional space–time into a series of 3-dimensional spatial slices, each one a state of our spatially 3-dimensional world at an instant). Some presentists take this standard interpretation as challenging their versions of presentism.
On the one hand, our mathematics is in some respects well suited to accomplish this sort of work. On the other hand, our mathematics is a tool that we must choose how to use, apply, and explain in any given context—it cannot circumvent the need for theorists to do the work of contextualizing it. For example, calculus is about the business of allowing us to integrate over intervals, but it is not about the business of defining those intervals—that business must be the work of those wanting to use it in particular contexts.
We might call this other sort of time a super-time which seems to operate as the “real time” to which we appeal and refer, despite protestations that this constructed measure is merely how we measure “invisible, real time”. While there are many ontological questions we might, and perhaps should, ask about such a super-time, I bracket them for this paper.
For this paper, I choose standard, intuitive, and desirable requirements for a measure (e.g. (i), (ii), (iii), the Lebesgue measure, and so on) and I largely bracket both discussions about alternative, less traditional choices we might make as well as a careful discussion of what makes the standard choices intuitive and desirable. I limit myself to traditional requirements not only because most of us will want a traditional measure, but also because it is the simpler case—non-traditional measures not only retain the same issues I raise here, but, quite likely, increase the issues that want addressing (as, in fact, the one non-traditional, reductionist answer I offer demonstrates).
Subsets of continuous sets, such as real numbers, prove challenging to measure because the set itself is uncountable. Consequently, since our measure does not always result in a defined size, when we try to measure these sorts of sets, we have to spend more time defining what will count as a sufficient measure. Defining our measure more carefully requires that we develop a list of properties that we want a measure to satisfy, but which properties should make it on the list is not obvious. We will have to include definitions for what counts as equal and equivalent sets, such as a one-to-one correspondence, as well as long lists of other properties about which we may care for a variety of reasons (Partee et al. 1993, pp. 8 and 55–70).
By a ‘finite interval’ I mean a set of real numbers of the form: {x| x > a and x < b}. We write a finite interval as (a,b). The less-than and greater-than signs can also be less-than-or-equal-to (and similarly for greater than), in which case we would write one of the following: [a,b), (a,b], or [a,b]. (‘[‘and ‘]’ indicate “or equal to”).
Notice as well that this process of defining intervals so that we can integrate over them is the work that mathematics such as calculus does. But that such mathematical fields do this work does not remove the impetus on metaphysicians to acknowledge and account for the adoption of such mathematics or consider the further metaphysical implications of such adoptions.
Adopting this measure brings with it its own set of additional complications. For example: as soon as we include the properties of the Lebesque measure, we find that for any single point, r, on the real line, m({r}) = 0. Moreover, by countable additivity, for any collection of countable points, r1, r2, r3,…., m(r1, r2, r3, ….) = 0. But because countable additivity does not apply to uncountable sets of points, it can be the case that all countable sets of points have measure zero while all uncountable sets have a finite measure (Tao 2011, p. 23). See Terence Tao’s (2011) for a closer look at defining the Lebesgue measure, both inner and outer measures (Sect. 1.2) and Lebesgue integrals (Sect. 1.3).
Thanks to Alexander Pruss for suggesting this potential presentist response.
Thanks to Michael Dickson for offering this concern.
It is worth noting that some presentists might not affirm that only the present moment is real (such as Zimmerman (2013), who is a substantivalist but thinks that only the present moment is occupied).
Some presentists worry that a duration of zero seems to create a sharp divide between what exists and what does not exist and, therefore, raises further worries about how to account for things with partial being—such as things coming into being (Ford 1974, p. 101).
We might anticipate that this answer will be popular among presentists, in part because it seems a more obvious thing to mean when a person claims that the present does not have duration. However, since most presentists do not specifically address the question of duration or do so with slightly different aims (see the earlier discussion from Markosian 1993 on duration and Tallant 2010b; Philips 2009; Olson 2009), whether they will endorse it, remains to be seen.
It is worth noticing that an analog to this account of the process of measuring duration exists for the process of measuring distance. Our measures of distance require similar details and defining. We must specify our measures to define intervals of distance, just as we had to do for intervals of duration, and to define the context in which the measure is accurate and applicable. Spelling out the details of this parallel account of space and its metaphysical implications warrants its own paper.
We might wonder why the question of duration cannot be answered by science through something like the adoption of the Planck length. However, even if we think that the Planck unit has some special priority—someone must do the work of defining it, which just is the sort of measurement work that I have outlined in this section. While nothing prohibits such adoptions, we must recognize them as just that—assuming a measure. And there will still be questions about the adopted.
Some have already suggested similar ideas (Craig 2017; Tallant 2010b; Hestevold 2008). Craig’s account still prioritizes the time-model as special among models—whereas what I suggest here does not prioritize it, though perhaps what I suggest could be made more compatible with his account. Tallant likewise develops an account of presentism that affirms rates of change and denies the reality of time, so it seems likely that he would be sympathetic to at least some aspects of this account. However, just as we might wonder whether Zimmerman’s substantivalism (2013) makes him no longer a presentist, so we might wonder if Tallant’s denial of the reality of time in favor of talking about rates of change makes presentism a theory no longer about time but about something else such as metaphysics of change or about “what exists”—a conclusion I fully endorse, and similar to a point that Deasy (2017) has made. Given Tallant’s (2019) response to Deasy, it seems less likely that he will want to recast presentism as a theory about what exists. But if Tallant did, the account I offer is convenient because it provides a companion account to his account of presentism—a companion account of time to his account of existence. And a similar sort of response could be given to Hestevold.
Accounts as old as Aristotle’s account of change (1995) consider this possibility (Coope 2001, 2014). I recommend that time, understood as nothing more than a measure of change, be developed in light of recent literature in epistemology of measurement. Moreover, while I take it as a virtue of this account of time that various accounts of change might work in it, accounts such as Aristotle’s have the virtue of defining change without reference to time, thereby helping us avoid worries about circularity (see Coope 2009; Anagnostopoulos 2011 for interpretations of Aristotle on change) and allow us to locate “temporal ordering” not in an account of time but in an account of change.
van Fraassen (2012) argues that we must do careful work in defining and articulating the parameters of our measurement.
The concerns and debates about using tools to confirm the very theories that produced said tools do not undermine this more general point about the constructed nature of tools and so belong to a different discussion (see Bas van Fraassen 2012; Cartwright 2002, 1994; Chang 1995; Kuhn 1961; Tal 2017; Latour 1992; Duhem 1998).
It is worth noting, and a virtue of this idea, that there is room for people who might want to affirm the idea that time is a measure of change but maintain its ontological status and deny that it is nothing more than a constructed measure (Aristotelian scholars often do so when interpreting Aristotle’s account of time, Coope 2001, 2005). While I provide an interpretation of time as a measure of change that does not accommodate being a realist about time, that interpretation is not required.
See Eran Tal’s discussion of atomic clocks and making time (2011 and 2016) for an example of a non-traditional account between realist and constructivist positions.
For example, Daniel Deasy (2017) suggests that presentism is properly about questions of existence. See also Jonathan Tallant (2018) for a response to Deasy.
In some cases presentists seem to have already switched to using ‘the present’ as a metric and in such cases, ‘the present’ does just as much work as it ever did, (for example, Tallant 2010a, b, 2018) seems already to use “present” as a metric, i.e. the measure ‘past’, ‘present’, and ‘future’). Also see Baron 2015 and Crisp 2005.
References
Anagnostopoulos, A. (2011). Change in Aristotle’s physics III. Oxford Studies in Ancient Philosophy, 39, 33–79.
Aristotle. (1995). Physics III. Jonathan Barnes (ed and translator) of The complete works of Aristotle. Vol. One. Chichester, West Sussex: Princeton University Press.
Audoin, C., & Bernard, G. (2001). The measurement of time: Time, frequency and the atomic clock. Cambridge: Cambridge University Press.
Auletta, G. (2000). Foundation of quantum mechanics: in light of a critical-historical analysis of the problems and of a synthesis of the results. Singapore: World Scientific Publishing Company Inc.
Barbour, J. (2001). The end of time: The next revolution in physics. Oxford: Oxford University Press.
Baron, S. (2015). The priority of the now. Pacific Philosophical Quarterly, 96(3), 325–348.
Boesch, B. (2017). There a special problem of scientific representation. Philosophy of Science, 84(5), 970–981. https://doi.org/10.1007/978-94-010-1727-5_54.
Bokulich, A. (2011). How scientific models can explain. Synthese, 180(1), 33–45.
Cartwright, N. (1994). Fundamentalism vs. the patchwork of laws. Proceedings of the Aristotelian Society, 94, 279–292.
Cartwright, N. (2002). How the laws of physics lie. Oxford: Oxford University Press.
Chang, H. (1995). Circularity and reliability in measurement. Perspectives on Science, 3(2), 153–172.
Coope, U. (2001). Why does aristotle say that there is no time without change? Proceedings of the Aristotelian Society, 101, 359–367.
Coope, U. (2005). Time for Aristotle: Physics IV, 10–14. Oxford: Oxford University Press.
Coope, U. (2009). Change and its relations to actuality and potentiality. In G. Anagnostopoulos (Ed.), A companion to Aristotle (pp. 277–291). West Sussex: Wiley-Blackwell.
Crisp, T. (2003). “Presentism.” In Michael J. (ed) Loux and Dean (ed) Zimmerman The oxford handbook of metaphysics (pp. 211–45). Oxford: Oxford University Press.
Crisp, T. (2005). Presentism and ‘cross-time’ relations. American Philosophical Quarterly, 42(1), 5–17.
Deasy, D. (2017). What is presentism? Noûs, 51(2), 378–397.
Duhem, P. (1998). Physical theory and experiment. In Philosophy of science (pp. 257–79). London: W.W. Norton and Company, Inc.
Ford, L. S. (1974). The duration of the present. Philosophy and Phenomenological Research, 35(1), 100.
Hagar, A. (2015). Discrete or continuous? The quest for fundamental lengths in modern physics. Cambridge: Cambridge University Press.
Hestevold, H. Scott. (2008). Presentism: Through thick and thin. Pacific Philosophical Quarterly, 89, 325–347.
Hinchcliff, M. (2000). A Defense of Presentism in a Relativistic Setting. Philosophy of Science, 67, S575–S586.
Hughes, Richard I. G. (1997). Models and representation. Philosophy of Science, 64, S325–S336.
Knuuttila, T. (2011). Modelling and representing: An artefactual approach to model-based representation. Studies in History and Philosophy of Science Part A, 42(2), 262–271.
Knuuttila, T., & Loettgers, A. (2017). Modelling as indirect representation? The Lotka-Volterra model revisited. The British Journal for the Philosophy of Science, 68(4), 1007–1036.
Kuhn, T. S. (1961). The function of measurement in modern physical science. Isis, 52(2), 161–193.
Latour, B. (1992). One more turn after the social turn: Easing science studies into the non-modern world. The Social Dimensions of Science, 1, 292.
Le Poidevin, R. (1990). Relationism and temporal topology: Physics or metaphysics? The Philosophical Quarterly, 40(161), 419.
Markosian, N. (1993). How FAST DOES TIME PASS? Philosophy and Phenomenological Research, 53(4), 829.
Olson, E. (2009). The rate of time’s passage. Analysis, 69, 3–9.
Partee, B., Ter Meulen, A., & Wall, R. (1993). Mathematical methods in linguistics. Dordrecht: Kluwer Academic Publishers.
Pauli, W. (1990). Die Allgemeinen Prinzipien Der Wellenmechanik. Berlin: Springer.
Phillips, I. (2009). Rate abuse: A reply to olson. Analysis, 69, 503–505.
Poincaré, H. (1905). Science and hypothesis. New York: The Science Press.
Poincaré, H. (1976). The measure of time. In M. Čapek (Ed.), The concept of space and time. Boston studies in the philosophy of science (Vol. 22, pp. 317–327). Dordrecht: Springer.
Prior, A. (2008). The notion of the present. In M. J. Loux (Ed.), Metaphysics: Contemporary readings (2nd ed., pp. 379–383). New York: Routledge.
Savitt, S. (2000). There’s no time like the present (in Minkowski Spacetime). Philosophy of Science, 67, S563–S574.
Skow, B. (2011). On the meaning of the question ‘how fast does time pass?’. Philosophical Studies, 155(3), 325–344.
Suárez, M. (2010). Scientific representation. Philosophy Compass, 5(1), 91–101.
Tal, E. (2011). How accurate is the standard second? Philosophy of Science, 78(5), 1082–1096.
Tal, E. (2016). Making time: A study in the epistemology of measurement. The British Journal for the Philosophy of Science, 67(1), 297–335.
Tallant, J. (2010a). Time for presence? Philosophia, 38, 271–280.
Tallant, J. (2010b). A sketch of a presentist theory of passage. Erkenntnis, 73(1), 133–140.
Tallant, J. (2019). Presentism remains. Erkenntnis, 84, 409–435.
Tao, T. (2011). An introduction to measure theory. Graduate Studies in Mathematics, 126, 206.
Van Bendegem, J. P. (2013). The possibility of discrete time. In C. Callender (Ed.), The oxford handbook of philosophy of time (pp. 145–162). Oxford University Press.
van Fraassen, B. (1988). The pragmatic theory of explanation. Theories of Explanation, 8, 135–155.
van Fraassen, B. (2008). Scientific representation: Paradoxes of perspective. Oxford: Oxford University Press.
van Fraassen, B. (2012). Modeling and measurement: The criterion of empirical grounding. Philosophy of Science, 79(5), 773–784.
Zimmerman, D. (2013). Presentism and the space-time manifold. In C. Callender (Ed.), The oxford handbook of philosophy of time (pp. 163–246). Oxford: Oxford University Press.
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Many thanks to Michael Dickson for extensive comments on this paper. I am also grateful to Alexander Pruss, David Albert, Dean Zimmerman, Sam Baron, and Jonathan Tallant for helpful suggestions and critiques, and to the audience at the International Association for the Philosophy of Time 6th Annual Conference at Colorado University. Finally, this publication was made possible through the support of a grant from the John Templeton Foundation. The opinions expressed in this publication are those of the author and do not necessarily reflect the views of the John Templeton Foundation.
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Gentry, B.A. Measuring the present: What is the duration of ‘now’?. Synthese 198, 9357–9371 (2021). https://doi.org/10.1007/s11229-020-02644-w
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DOI: https://doi.org/10.1007/s11229-020-02644-w