McTaggart's Paradox

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Analysis 58.2, April 1998, pp. 122–127. © William Lane Craig

McTaggart’s paradox and the problem of temporaryintrinsics

William Lane Craig

McTaggart’s Paradox is so well-ploughed a field that one might doubtwhether anything fresh can be said about it. But sometimes new light canbe shed on a problem by stepping back and seeing it within a conceptualframework which has hitherto gone unnoticed. For example, DavidLewis (1979: 235–40) sought to illuminate the Prisoners’ Dilemma by hisinsight that the puzzle is actually an instance of Newcomb’s Paradox. Inthe same way, I believe that McTaggart’s Paradox is actually a special case

of what Lewis has called the Problem of Temporary Intrinsics – aconceptual contextualization of the paradox which, to my knowledge,has gone unnoticed in the philosophical literature. A realization of theproper conceptual context of the paradox will serve to advance our anal-ysis of it.

The Problem of Temporary Intrinsics is the problem of identity andintrinsic change. The question is, how can an object be self-identical at twodifferent times if it possesses different intrinsic properties at those times?As Lewis says,

Persisting things change their intrinsic properties. For instance, shape:when I sit, I have a bent shape, when I stand, I have a straightenedshape. Both shapes are temporary intrinsic properties; I have themonly some of the time. How is such change possible? (1986: 203–4)

As Trenton Merricks’s formulation of the problem makes clear (1994:165–84), the difficulty arises from the application of the principle of theIndiscernibility of Identicals to diachronic identity:

(1) O at t is identical with O at t*. [assume for reductio](2) O at t is bent. [premiss](3) O at t* is not bent. [premiss](4) If O at t is identical with O at t*, then O at t is F iff O at t* is F.

[Indiscernibility of Identicals](5) Therefore, O at t is bent and is not bent.

The Problem of Temporary Intrinsics thus purports to show that no objectcan exist at two times at which it differs in its intrinsic properties.

Lewis believes that there are only three ostensible solutions to thisproblem:



123 william lane craig

First solution: contrary to what we might think, shapes are not genu-ine intrinsic properties. They are disguised relations, which an endur-ing thing may bear to times. One and the same enduring thing maybear the bent-shape relation to some times, and the straight-shape

relation to others. In itself, considered apart from its relations to otherthings, it has no shape at all. And likewise for all other seemingtemporary intrinsics; all of them must be reinterpreted as relationsthat something with an absolutely unchanging intrinsic nature bearsto different times ….

Second solution: the only intrinsic properties of a thing are those it hasat the present moment. Other times are like false stories; they areabstract representations, composed out of the materials of the present,

which represent or misrepresent the way things are. When somethinghas different intrinsic properties according to one of these ersatz othertimes, that does not mean that it, or anything else, just has them--nomore so than when a man is crooked according to the Times or honestaccording to the News ….

Third solution: the different shapes, and the different temporaryintrinsics generally, belong to different things. Endurance is to berejected in favor of perdurance. We perdure; we are made up of

temporal parts, and our temporary intrinsics are properties of theseparts, wherein they differ one from another. There is no problem at allabout how different things can differ in their intrinsic properties(1986: 204).

Lewis’s own preferred solution is the third, which presupposes, in McTag-gart’s terminology, a pure B-theory of time, which denies the objectivereality of tensed facts and temporal becoming, in contrast to the secondsolution, which presupposes a pure A-theory of time, according to which

the only temporal entitites which exist are present ones.Now McTaggart’s Paradox – with which I assume the reader is familiar– is a peculiar case of the Problem of Temporary Intrinsics. A-determina-tions are taken to be intrinsic properties which are exemplified by temporalitems. But some event E cannot have both the properties of presentness andpastness, for example, since these are different properties. It does no goodto say that E possesses presentness and pastness at different times, for thisis precisely the problem of temporary intrinsics: how can E be self-identicalwhen it possesses different intrinsic properties at different times? If E was

present and is past, then E has undergone a change in its intrinsic tensedeterminations – but then how can E be self-identical if it has differentintrinsic properties at different times? We cannot be talking about twodifferent events, for then it will not be true that E itself was present and is



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past. A-determinations must therefore be illusory.1

It is particularly interesting to see how Lewis’s three available solutionswork out with respect to McTaggart’s Paradox. The first solution wouldhold that A-determinations are not intrinsic properties, but disguised rela-

tions to times. E, for example, may be present in relation to some time andfuture in relation to others. In itself, considered apart from its relations totimes, E has no intrinsic A-determination at all. Now if, as this solutionsuggests, A-determinations are really relations to items in the time series,then they must be construed as relations to items in either the A-series orthe B-series.2 With respect to the A- series, E is, for example, future relativeto some moment ten years ago (an A-series position). With respect to theB-series, E is, for example, past relative to 1 October, 1997 (a B-series posi-tion). Now if we relativize events to moments in the B-series, then A-determinations are effectively converted into B-relations: to say, for exam-ple, that E is past relative to 1 October, 1997, is to say that E is earlier than1 October, 1997. Thus, A-determinations are reducible to tenseless B-rela-tions, so that tensed facts have no place in one’s ontology. Thus, this optioncannot solve the challenge posed by the Problem of Temporary Intrinsicsto changing A-determinations. But if we construe A-determinations asrelations to moments in the A-series, we solve nothing because tense deter-minations are on this option relative to the present, which must itself, as a

relational tense determination, be present relative to the present relative tothe present, and so on, which is, as McTaggart complains, either a viciouscircle or infinite regress. The only way to halt this regress would be to saythat there is a non-relational present – but then the present must be fixedand unchanging if the Problem of Temporary Intrinsics is to be avoided,which is absurd. Thus, the first solution is unavailing in saving the objec-tivity of tense determinations from the Problem of Temporary Intrinsics--which is perhaps why no A-theorist since McTaggart (with the possible

exception of Schlesinger) has construed A-determinations as relations.Skip, then, to the third solution, preferred by Lewis with regard to theProblem of Temporary Intrinsics. What makes McTaggart’s Paradox sopeculiar an instance of this problem is that Lewis’s solution will not workin McTaggart’s case. The perdurantist solution, with its appeal to anentity’s different temporal parts’ being located at different times, is inap-plicable to McTaggart’s Paradox because E need not persist over time at

1 More recent attempts to cast McTaggart’s Paradox, not in terms of events and their

properties, but, for example, in terms of propositions and their changing truth valuesare also instances of the Problem of Temporary Intrinsics, since the properties of having the truth value T and having the truth value F are temporary intrinsic proper-ties of the postulated entities.

2 As explained by Buller and Foster (1992: 358–59).




all, but could exist only at an instant t . Thus we are not concerned, as innormal cases of the Problem of Temporary Intrinsics, with some entitywhich persists from t to t * but has different intrinsic properties at thoserespective locations and yet remains self-identical. Rather E may exist only

at t and yet is self-identical at that moment despite its being the case thatE-at-t has both presentness and pastness. Because E does not persistthrough time, there is no place for a solution postulating temporal parts of E each having different intrinsic properties (for example, presentness andpastness).3 McTaggart’s Paradox involves a strange case of E’s synchronicidentity being diachronically preserved. To prevent E’s self-identity frombeing destroyed over time, one must, it seems, deny that there are objectiveA-determinations.

What, then, of the second solution, a metaphysic of presentism?4 Thegerm of the presentist solution is the insistence that the having of a prop-erty simpliciter is a tensed having. On a presentist ontology, the Problemof Temporary Intrinsics cannot even arise because there are (present tense)no times which overlap in sharing an object O. For O exists (present tense)only at one time, the present time, and so does not have (present tense)incompatible properties, as it would if it existed tenselessly in the B-serieswith different properties at different times. All the properties O has are theones it presently has, and so no contradiction can arise. For even if O

undergoes intrinsic change between t and t*, it nonetheless does not have(present tense) incompatible properties: O has only the properties it haspresently and these are mutually compatible. Hence, the presentist willconstrue Merricks’s (1) to (4) as:

(1′) O existed at t and exists at t*.(2′) O was bent at t.(3′) O is not bent at t*.(4′) If O existed at t and exists at t*, O which existed at t is F iff O

which exists at t* is F.By tensing all the verbs in (1′) to (4′) the presentist avoids contradiction.

Applying this solution to the case of McTaggart’s Paradox, we realizethat the A-theorist cannot understand grammatical ascriptions of pastnessand futurity to events in terms of the literal inherence of properties of past-ness and futurity in events. For on a presentist ontology, such items do not

3 Even if E is an extended event lasting, say, throughout 1989, the perdurantist

solution does not make sense. For E’s change from being present to being past cannotbe accounted for on the basis of E’s having different temporal parts possessing differ-ent A-properties, since all of E’s parts exist in 1989, where they are all alike eitherpresent or past. In 1990, when E becomes past, there are no temporal parts of E atall.



mctaggart’s paradox and temporary intrinsics 126

exist and so possess no properties. Such ascriptions must be parsed asasserting that the item in question was or will be F . 5 Only ascriptions of presentness may be taken literally as the possession of an A-determinationby some temporal item. The presentist thus adroitly avoids McTaggart’s

Paradox because the only intrinsic tensed properties there are are present-tensed and therefore compatible.

What all this implies is that McTaggart’s Paradox only defeats the tense-theorist who holds, like McTaggart, to a hybrid A-B Theory of time, whichcouples a B-theoretical ontology with objective, non-relational A-determi-nations. Such a theorist runs afoul of the Problem of Temporary Intrinsics,in that he cannot explain how E-at-t could at t have had the intrinsic prop-erty of presentness and now at t* have the intrinsic property of pastnessand yet remain the same event in the transition from t to t*. This conclu-sion is highly significant, since most proponents of McTaggart’s Paradox,like Smart, Williams, Mellor, Oaklander, and so on, have presented it as arefutation of the A-Theory tout simple, whereas it is in fact ineffectualagainst pure A-theorists like Broad, Prior, Christensen, Levinson, andothers. On the other hand, hybrid A-B theorists, like McCall, Schlesinger,and Smith are, it seems, in deep trouble.

4 Lewis’s own characterization of the second solution is deliciously tendentious. In

saying that non-present times are like false stories, abstract representationscomposed out of the materials of the present, he is thinking of non-present times onthe analogy of the serious actualist’s conception of possible worlds as states of affairswhich exist as abstract objects but which are not instantiated. As a counterparttheorist Lewis rejects these ersatz worlds with the same disdain he evinces towardnon-present, ersatz times. Borrowing Lewis’s analogy, we can characterize presentismby allowing tensed states of affairs to be constituents of possible worlds. A tensedpossible world is then a maximal possible state of affairs at some time t . Tensed possi-ble worlds which did, do, or will obtain are tensed actual worlds. The tensed actualworld at t will be the tensed actual world which obtains when t’s being present

obtains, or when t is present. The tensed history of any possible world W will be allthe tensed possible worlds constituted by the states of affairs entailed by W and eachsuccessive t ’s being present in W . To say that a temporal entity x exists in a tensedpossible world W t is to say that if W t were actual, then x would exist (present tense).To say that x exists in a tensed actual world α

t is to say that when α t becomes actual,

then x exists (present-tense). Each tensed possible world exists in each such world.The tensed actual world ν is the maximal state of affairs that obtains (present-tense).Were some other tensed possible world actual, then ν would not obtain, but it wouldstill exist as a tensed possible state of affairs. When some other tensed actual worldobtains (present-tense), then ν either does not yet or no longer obtains, but νnonethe-

less exists as a tensed state of affairs which was or will be actualized. Since ν alone is(present-tense) actual, none of the other tensed actual worlds (not to speak of tensedmerely possible worlds) is (present-tense) actual though they either were or will beactual. Thus, ν is uniquely distinguished as the tensed actual world, the one tensedpossible world which obtains (present-tense).




If the analysis presented here is correct, then the debate over McTag-gart’s Paradox needs to be re-focused on the tenability of the metaphysicof presentism. For as Le Poidevin, one of the most ardent contemporarydefenders of McTaggart’s Paradox recognizes, presentism “represents the

only means to block McTaggart’s proof of the unreality of time consist-ently with the assumption of a non-relational past, present, and future”(1991: 36).6 The discussion of McTaggart’s Paradox can break fertileground by a fresh consideration of the arguments for and againstpresentism.7

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References

Buller, D. and T. Foster. 1992. The new paradox of temporal transience. Philosophical Quarterly 42: 357–66.

Le Poidevin, R. 1991. Change, Cause, and Contradiction. London: Macmillan.Lewis, D. 1979. Prisoners’ dilemma is a Newcomb problem. Philosophy and Public

Affairs 8: 235–40.Lewis, D. 1986. On the Plurality of Worlds. Oxford: Basil Blackwell.Lowe, E. J. 1987. The indexical fallacy in McTaggart’s proof of the unreality of time.

Mind 96: 62–70.Merricks, T. 1994. Endurance and indiscernibility. Journal of Philosophy 91: 165-84.

5 As emphasized by Lowe (1987: 64 – 66), who seems, however, unduly diffident abouttensed ascriptions of presentness to events.

6 Le Poidevin appropriately provides a sustained attack on presentism.

7 Lewis’s own objections to the second solution are almost playful rather than serious.He says that the presentist denies persistence, even though the presentist’s account of endurance fulfils Lewis’s own definition that “something persists, iff, somehow orother, it exists at various times.” He alleges that on a presentist ontology, we must

say that we have no past or future, which no one believes. But surely on presentismI have a past in the sense that I existed at and lived through times which once werepresent, and I have a future in that I shall exist and live through times which will bepresent. We need more substantive reasons than these to reject the presentist solutionto the Problem of Temporary Intrinsics, y compris McTaggart’s Paradox.

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