Problemas tecnológicos

Objection 1: The temporal parts theorists need only account for physically possible change. While it may be metaphysically possible for an object in a discrete-time world to exist in a world in which time is more fine-grained than that (i.e. dense or continuous), it is not physically possible. Sider said that anything potentially divisible must actually have parts; but by ‘potentially divisible’ he meant divisible within the bounds of the physical laws of the world in which the desk actually exists.22 For an object to instantiate change more fine- grained than actual time it would have to exist in a world with different laws of nature, but what might happen to objects in such metaphysically (but not physically) possible worlds is not something that a temporal parts theory is required to account for.

Reply: As with any such attempt to scale back P1, this last claim would need to be

substantiated.23 What is the difference between metaphysically possible change, on the one hand, and physically possible change, on the other, such that the metaphysics of persistence is required to account for the latter but not the former? I will not say that there is no such

22 _{Cf. Markosian (1998), Section IV: Simples as Indivisibles.}

23 _{Another way of scaling back P1 is to say that, for any world w, parts in w are only required to account for}

possible inhomogeneity/change in worlds where the structure of space/time is not more fine-grained than it is at w (thanks to an anonymous referee for Thought for this suggestion). This is to propose an interesting

asymmetry: it means that, for instance, if the actual world is one of continuous time, actual parts are needed to explain possible change in worlds of discrete time; yet, if the actual world is one of discrete time, actual parts are not needed to explain possible change in worlds in which time is continuous. To this suggestion, we should ask, why is there such an asymmetry in the demand for explanation? To avoid being ad hoc, something more would need to be said here – particularly since the original demand for an explanation of possible change came from the indiscernibility of identicals, and said nothing of possible space/time topologies. That said, I will consider a further proposal to scale back P1 below, in section 5.

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difference to be found, but I cannot think of a good one. Moreover, it is unlikely that Sider intended to make such a distinction. He claimed that since the desk could be divided every which way, we should say it has parts, both spatial and temporal, as fine-grained as space and time. But is it really physically possible that the desk be divided arbitrarily? Perhaps not; rather, I suggest, Sider’s modal claim about possible desk division is only plausible enough to support the argument if it is a claim about what is metaphysically possible.

Objection 2: Discrete time is metaphysically impossible (for proof, see Zeno’s stadium paradox). Hence P3* is necessarily false, in the strongest sense.

Reply: The argument for C* would work just as well if we replace the instances of ‘discrete’

with ‘merely dense’. 24 _{For even if time is actually merely dense, I would urge, it could have}

been continuous. Yet Zeno’s stadium paradox does not apply to dense orderings. Moreover, as Hawley notes, it has been argued by Newton-Smith that the success of our best physical theories does not decide between the competing hypotheses that space and time are merely dense, on the one hand, and that they are continuous, on the other (Hawley 2001, 51; Newton-Smith 1980, Section VI.3).

Objection 3: Newton-Smith was wrong. As Penrose has observed, in all successful

dynamical theories, “on the small end of the scale, it is the entire range of real numbers that is in principle being made use of. The ideas of calculus underlie other physical notions, such as velocity, momentum, and energy. Consequently, the real-number system enters our

24 _{Since continuous orderings are also dense, I use “merely dense” to refer to orderings which are dense but not}

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successful physical theories in a fundamental way for our descriptions of these quantities also” (Penrose 2004, 61; quoted in Dainton 2010, 271).

Reply: Be that as it may, current physics hardly warrants closing the book on the structure of space and time (Dainton 2010, Section 22.7), and it would surely be a mistake to be moved to thinking otherwise simply to maintain a version of temporal parts theory that can claim to account for possible change. But more to the point, let’s suppose that we do somehow have certain knowledge that time is continuous: even so, does the temporal parts theorist only want to claim that worlds like the actual world – worlds of continuous time – are populated by temporal parts? That would certainly be an option, but it would represent a significant concession on the part of certain temporal parts theorists;25 moreover, it would be an

interesting concession at that, effectively being an admission that facts about composition and persistence are contingent. We will return to this potential upshot in the next section.

Objection 4: The physical laws are metaphysically necessary, as according to the

dispositional essentialism of Bird (2007), so it is not really possible for any object of this world to exist in a world where the micro-structure of time is any different. While

dispositional essentialism allows that there are possible worlds in which the laws of nature are different from our own, it says that objects in these alien worlds do not represent genuine possibilities for objects in the actual world. The intuition that it is metaphysically possible for

25 _{For Sider’s part, this can be seen in his discussion of the homogeneous rotating disc argument, an argument}

supposed to show that temporal parts theorists cannot account for motion in certain possible worlds containing homogeneous substances. Sider says: “Someone who defended four-dimensionalism’s truth in the actual world might claim that three-dimensionalism must be true at the disk-worlds. But this would involve granting the possibility of endurance, and thus giving up on the possibility of purely conceptual arguments in favor of perdurance… A four‐dimensional solution must be sought.” (2001, 226).

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an object in a discrete-time world to instantiate change more fine-grained than discrete-time is merely epistemic.

Reply: This would certainly block my argument, as it is effectively a denial of P2*. Nevertheless, adopting dispositional essentialism is a substantive commitment. Of course, one may find that theory independently plausible. But Sider and Hawley no doubt intended their formulations of temporal parts theory – positing temporal parts as fine-grained as possible change and therefore as fine-grained as time – to be plausible without having to invoke this contentious account of natural laws.

***

Admittedly, the options that we have just considered are not exhaustive. But they are perhaps enough to indicate that the temporal parts theorist – who would argue from modal premises to claims about actual parthood – has more explaining to do. As we saw in Objection 3 above, one option is to insist – or rather, gamble – on the claim that space and time are continuous. However, it would be implausible to suggest this as a metaphysically necessary truth – at least not without extensive argument. As such, the temporal parts advocate, according to whom temporal parts are as fine-grained as time, may have to concede that it is not necessarily the case that temporal parts can account for possible change.