Abstract
There are two no-change objections that can be raised against the B-theory of time. One (McTaggart’s objection) stems from the observation that in a B-theoretic scenario changes of determinations can only be represented by propositions which have eternal truth values. The other (James’ objection) derives from the principle that nothing can vary over a period of time if it doesn’t instantiate a state of change at all the instants of time which compose it. Here I argue that both objections apply to all comparative conceptions of change, regardless of whether they take tense seriously or not. It follows that, contrary to what is widely believed, A-theoretic accounts of time are not immune to no-change objections, just in virtue of being realist about tense. A-theorists must either (1) accept the conclusion that time, according to their account, does not flow, or (2) put forward an account of flow that is not comparative. A number of difficulties with both of these options are discussed.
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Notes
We may add that, at least, the object must have been moving at a number of time instants that constitute a set whose (Lebesgue) measure is not zero. This clarification, however, is not going to have any consequence for our discussion. In what follows, the expressions “at least for some time” and “for enough time” will mean the same as: “at a number of time instants that constitute a set whose Lebesgue measure is not zero”.
Notice that at each time during the motion of the ship its current, past and future positions can be used to form a mathematical (abstract) vector that consists of the time-derivative of the trajectory at that time. However, if dual-fact accounts of motion are correct such vectors should be taken to further represent real intrinsic properties possessed by the ship at the respective times, rather than merely reflecting global properties of the trajectory itself.
Note that what the foes of the B-package deny is not that changes of determinations are necessarily followed by variations of these determinations. What they deny is the identity thesis: that changes in things are (identical to) variations in these things.
Cf. Crisp (2005).
Prior (1970, pp. 246–247).
Christensen (1993, p. 168); cf. p. 226.
“My present”, says Broad (1923), “is just the last thin slice that has joined up to my life-history. When it ceases to be present and becomes past this does not mean that it has changed its relations to anything to which it was related when it was present. It will simply mean that other slices have been tacked on to my life history” (p. 84).
Thanks to an anonymous referee for pointing this out to me.
As noted by Sanson (2011) (p. 6): “taken by itself, Presentism is consistent with the view that reality is static: it does not entail that reality is temporary or that there is any real change”.
Cf. Crisp (2007, p. 99).
Here I disregard all the complexities related to the fact that Caesar was not a well-defined simple entity. All the arguments put forward in this paper should be understood as applying to simple entities and states of affairs.
Ibid., p. 236. Underlined verbs must be understood as tenseless.
Maudlin, a self-professed defender of the block universe, conceives of temporal passage as an intrinsic tenseless feature of the four-dimensional manifold (Maudlin 2007, 109); confront this feature of Crisp’s Presentism also with Fine’s contention that “the fact that time flows is a tenseless fact about time; it is not one that holds at one time rather than another” (Fine 2005, 287).
Not, at least, in any sense that is compatible with the explanatory role of the notion of “becoming past” with respect to the notion of “being past”.
Physics: 231b28–232a1.
Kit Fine (2005) seems to have noticed this when he asked: “how can the passage of time be seen to rest on the fact that a given time is present and that various other times are either earlier or later than that time?” (p. 287).
“That a thing which is previously at rest should be afterwards in motion”, observes Parmenides in Plato’s famous dialogue, “or previously in motion and afterwards at rest, without experiencing change, is impossible […]. [A thing] cannot change without changing”. Parmenides (in the dialogue) uses Plato‘s Principle to argue that change is impossible. “Surely”, he says, “there cannot be a time in which a thing can be at once neither in motion nor at rest […] But neither can it change without changing […] When then does it change? For it cannot change either when at rest, or when in motion […]”. Here, however, we shall not be concerned with the alleged contradictions involved in the endorsement of Plato‘s Principle, but only with the reasons one may have to endorse it in the first place.
Notice that the relevant notion of explanation here is not causal explanation: we are not in the business of revealing the causes of Caesar’s death. We are in the business of explicating the metaphysical grounds of Caesar’s disappearance from reality, grounds which, in turn, ought to provide us with a sufficient reason for the current non-existence of Caesar (given his former existence).
Nedd Hall (2004) made a powerful case for distinguishing two concepts of causation: dependence (mere counterfactual dependence) and production, a stronger notion of cause that accounts for the production of later states from previous ones. I think that this distinction can (and should) be generalized to include all metaphysical explanations. We can rephrase the complaint raised here by saying that the facts which make comparative truths true fail to provide us with a productive (metaphysical) explanation of these truths. The facts which make it true that time passes, by contrast, should provide such a productive explanation. This suggests that the fact(s) of passage cannot be the same which make it true that A-determinations vary.
Commenting the use of the “new infinite” in solving Zeno’s paradoxes, James expressed an analogous worry: “that being should be identified with the consummation of an endless chain of units (such as 'points'), no one of which contains any amount whatever of the being (such as 'space') expected to result, this is something which our intellect not only fails to understand, but which it finds absurd”. The arguments presented here can be thought of as an application of this line of argument to the case of temporal durations.
Braddon-Mitchell (2004) used this fact to argue that, in a Growing Block world, it would be impossible to know if the current time is really the present or not.
While this paper is mainly concerned with explicating the ontological grounds for truths of kind a, hence with explanations of the kind offered by truthmakers, it is worth noting again that the relevant kind of explanation which features in desideratum (2) is the one that is captured by the notion of sufficient reason.
See for example Tallant (2010, p. 18): As a presentist, I don’t believe in the existence of a thing called “time”, or “temporal passage”.
As Fine (2005, p. 287) aptly put it, “even if presentness is allowed to shed its light upon the world, there is nothing in [a Tense Realist’s] metaphysics to prevent that light being ‘frozen’ on a particular moment of time”.
Many authors, for example, argue that dispositions must be based on categorical properties (cf. Armstrong 1997, p. 97).
Analogously, we have seen, the ship must possess a dispositional kinematic property that (1) is not dependent on its future and past positions, but that nevertheless (2) is capable of fully explaining the subsequent displacements of the ship.
A related difficulty stems from the observation that an instant of time can become present only after each previous instant ceased being present in its due turn. It follows that, if times form a class of the growing variety, like Dynamicists should think, then the passage of time involves the performance of a hypertask (an uncountably infinite number of operations that occur sequentially within a finite interval of time); something which many find impossible (cf. Clark and Read 1984).
Passage, under these dialetheist accounts, would consist in a single time being both present and not present (see for example Priest 1987).
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Acknowledgements
Predecessors of parts of this paper were presented at a conference at the Universities of Geneva and Barcelona. I’m grateful to the respective audiences for their useful comments. I would also like to thank the anonymous reviewers of this essay. Finally, I would like to acknowledge a special debt to Dr. Federico Perelda for helpful discussions.
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Boccardi, E. If It Ain’t Moving It Shall Not be Moved. Topoi 34, 171–185 (2015). https://doi.org/10.1007/s11245-013-9230-7
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DOI: https://doi.org/10.1007/s11245-013-9230-7