#nathanoaklander

McTaggart’s argument for the unreality of time has has occupied the attention of many philosophers of time since its publication in 1908. While few today accept the soundness of the argument in its entirety, his categorization of the serial conceptions of time into what he called, rather blandly, A-Series and B-Series, have been almost universally adopted. An A-Series is a tensed, dynamic series of time, in which the positions run from the past, to the present, and to the future. The B-Series, on the other hand, is a tenseless, static time series, in which positions run from “earlier to later” (McTaggart 1908). Broadly, McTaggart’s argument has two basic parts; firstly, he shows that the A-Series is the only true time series, and then, secondly, he proceeds to show the A-Series to be incoherent, leading to his famous conclusion that time does not exist. We will here briefly outline both of these parts, and then assess a popular criticism of the argument.

McTaggart begins his proof by outlining two basic intuitions about the nature of time; (1) that time involves change, and (2) that time has a direction. The B-Series certainly accommodates the latter of these intuitions, but it is not clear whether it can account for real change. Perhaps change occurs in the B-Series when one event stops, and another starts - but the B-Series involves an eternally ordered set; events can not simply ‘pop in’ or ‘pop out’ of the series! Perhaps then, the change occurs when two events overlap in time. The same problem, however, reoccurs here; while two events can have a common element, they can not be the same event, for this would preclude the possibility of change. If some event M changes into some other event N, M has ceased to be M and N has become to be N - but as we have already seen, no event can begin or cease to be in the B series. Hence, the B-Series cannot account for change.

The A-Series, on the other hand, involves both direction and change; events in the A-Series change from being future, to being present, and then become past - therefore making it a true time series. However, according to McTaggart, on closer inspection the A-Series appears to be incoherent. If we take the A-properties of “being past” or “being present” or “being future” in the A-Series as being non-relational, then every event simultaneously has all three of these contradictory properties, as every event will be past, present or future at some point in the series. Of course, we know that an event cannot be past, present and future all at once; events travel from ‘being future’ to ‘being present’, then to ‘being past’ - but this is a vicious circle, as it assumes the existence of time in order to make sense. Perhaps then, our A-properties are relational to something - the present. But by what virtue do we take a certain event to be present? Perhaps it is that a present event will have the A-property of being present - but if this is the case, all events would have this property, as all events are/will present at some point. It would seem that the relational point needs to exist outside the A-Series. With this in mind, we could posit another A* Series that gives a special property to present events. But again, all events would have this property, so another A** Series would be needed, and so on ad infinitum. So, McTaggart concludes, as the A-Series is the only true theory of time (because it accommodates both of our intuitions about time, while the B-Series cannot), and the A-Series is incoherent, and these exhaust the options, therefore time does not exist.

Most attempts to refute McTaggart’s argument have either involved accepting his first premise (that the A-Series is the only true time series) while denying the second (that the A- Series is incoherent - also known as McTaggart’s paradox), or denying the first while maintaining the second. One instance of the former has been posited by William Lane Craig and Robin DePoidevin, who point out that McTaggart may not be attacking the A-Theory at all in the second part of his argument, but rather a hybrid A-B Theory, which “combines tenseless ontology with temporal intrinsic properties of tense” (Craig 2001). Although this seems to be an odd objection (McTaggart defined our terms, after all), McTaggart does seem to implicitly maintain that any series of time must always include some kind of B-Theoretic event ontology; an eternally indexed, tenseless series of events. An A-Theory of this kind certainly exists; the moving spotlight A-Theory combines the B-Ontology of eternalism with a privileged present and thus tense, and hence falls easily for McTaggart’s paradox. However, as the paradox relies on “an event ontology of tenselessly existing events” (DePoidevin 1991), an A-Theory that has no such B-Ontology - such as presentism - would never see it arise. On presentism, the relational point of the present is easily defined, as present events are the only events that exist. This eliminates the need for a relational point outside of the A-Series, thus avoiding the infinite regress of A* Series’ that follow in the paradox.

Nathan Oaklander has disputed this point, however, pointing out that Craig appeals to tensed possible successive worlds¹ which “did, do or will obtain” to justify his talk about events having existed in the past (Oaklander, 1999, emphasis mine) - that is to say, that the past and the future exist in some sense, but only obtain as they become present. This, however, obviously begs the B-theoretical concept of succession; past and future events still exist both tenselessly and in an eternal relation on this view, even if they are abstract objects. With this in mind, Craig’s view of presentism seems to be little more than a hybrid A-B Theory - a group which he himself claims are ‘in deep trouble’ with regard to the paradox (Craig 1998).

This is not to say that every presentist is committed to a B-ontology in this way. Oaklander points out that Prior, Levison and Christensen - presentists, of whom Craig counts himself alongside - all reject B-ontology in favor of a ‘pure A-Theory’ of presentism. According to Oaklander, their presentism differs from Craig’s, in that they “... reject an ontology that includes events, they reject the property of presentness that events acquire and shed, and most importantly, they reject the notion that there is a genuine change that an event, or anything else, undergoes as it becomes present and recedes into the past” (Oaklander 1999). Prior explicates this in his (1968), claiming that “... what looks like talk about events is really at bottom talk about things, and that what looks like talk about changes in events is really just slightly more complicated talk about changes in things.” (Prior 1968:10). The flow of time, he thus claims, is “merely metaphorical, not only because what is meant by it isn’t a genuine movement, but further because what is meant by it isn’t a genuine change” (Prior 1968:11).

By denying that temporal becoming involves change, this form of presentism adriotly avoids McTaggart’s paradox, as it denies the existence of the A-properties ‘past’, ‘present’ and ‘future’ that events gain and shed. It does not, however, avoid the first premise of his argument, as it flatly denies McTaggart’s first intuition about time; that time involves change. This is because, as Oaklander points out, on a pure A-Theory of presentism, “... there are only individual things and the present tensed facts that such individuals or substances enter into” (Oaklander 1999). By McTaggart’s lights, this “pure A-theory” would not be a true time series at all, for exactly the same reason that initially disqualified the B-Series.

By way of summary, we have assessed two unsuccessful strategies that presentists have deployed to avoid McTaggart’s argument for the unreality of time; to either reject B-ontology completely in favour of a ‘pure A-theory’ that denies temporal becoming as a species of change, and thus disqualify itself in the first premise of McTaggart’s argument, or, in an effort to make sense of talk about past and future events, accept a hybrid A-B theory that rests (in some capacity) on B- ontology, and in doing so become subject to McTaggart’s paradox in his second premise. Of course, this does not prove presentism or the A-series as a whole to be necessarily inconsistent; one could certainly reject McTaggart’s intuitions about time, or attack his argument in other ways than which we have discussed, but, as we have seen, either disposition of presentism cannot completely avoid McTaggart’s argument, as it has been claimed.

  Notes

¹ Meant in the serious actualist sense. Oaklander: '... states of affairs which exist as abstract objects but which are not instantiated' (Oaklander, 1999)

        References

Craig, W. L. 1998. McTaggart’s Paradox and the problem of temporary intrinsics. Analysis 58: 122–27.

–––––. 2001. McTaggart's Paradox and Temporal Solipsism. Australasian Journal of Philosophy 79, Iss. 1

LePoidevin, Robin. 1991. Change, Cause and Contradiction: A Defense of the Tenseless Theory of Time. London: Macmillan.

McTaggart, John Ellis. 1908. The Unreality of Time. Mind: A Quarterly Review of Psychology and Philosophy 17: 456-73.

Oaklander, L. N. 1996. McTaggart’s Paradox and Smith’s tensed theory of time. Synthese 107: 205–21

–––––. 1999. Craig on McTaggart’s Paradox and the problem of temporary intrinsics. Analysis 59: 314.