Time by J. M. E. McTaggart Chapter 33 of The Nature of Existence McTaggart s Destructive Argument Thesis: Time is unreal. Outline (P1) There is no time without change. (P2) There is no change without an A-series. (P3) The existence of an A-series is selfcontradictory. Consider (P3). Let us use Pe to abbreviate e is past, Ne for e is present (or e is Now ), and Fe for e is future. Since these properties express properties that are distinct determinate degrees of a given determinable, no event can have more than one of them. That is: (1) Pe ~Ne Ne ~Pe Fe ~Pe Pe ~Fe Ne ~Fe Fe ~Ne On the other hand, all events (except possibly a first of last event, if there are such) occupy all A-
series positions (or tenses). So the A-theory of time must also imply that for every event e: (2) Pe & Ne & Fe. Clearly, (1) and (2) are inconsistent. There is an obvious RESPONSE, of course. One might argue that (2) as it stands is not true and that the A-theory of time need not endorse it. Suppose, for example, that Ne that e is present. Then surely it is not true, one might claim, that e is past. Rather, one would claim that e will be past. That is, one would claim that FPe. And similarly, one would claim that PFe. So all that the A- theorist of time is committed to is (2') FPe & Ne & PFe, which does not yield a contradiction when added to (1). Similar claims can be made for Pe and Fe. McTaggart s Reply. But of you wish to iterate or compound tenses, you surely must admit that (a) Pe NPe Ne NNe Fe NFe. In addition, whatever is past once was present and also was future. So we have (b) Pe PNe Pe PFe. 2
Similarly, whatever is future will be present and also will be past. That is (c) Fe FNe Fe FPe. Finally, suppose that e happened two days ago. That is, suppose that Pe. But yesterday, e was still past. That is PPe. So we have that (d) Pe PPe Fe FFe. So there are nine possible compound (or level- 2) A-characteristics and McTaggart s argument applies to them (as well as to the three first-level characteristics) That is (1*) All nine level-2 A-characteristics (or tenses) are incompatible. Yet (2*) The A-theory of time is committed to the view that every event has all these nine compound A-characteristics. An attempt to deny (2*) by denying that e need have all nine level - tenses simultaneously will only lead to the introduction of 27 level-3 tenses and the contradiction will break out again. The A-theorist faces either contradiction or infinite regress. 1 1 This version of McTaggart s argument is based on chapter 6 of Hugh Mellor s Real Time. Mellor thinks the argument is sound. 3
Objections to C. D. Broad s growing block view (in Broad s Scientific Thought) 336. Broad s view entails that statements about the future are neither true nor false. McT points out how implausible this is. England will be a republic in 1920 was, he says, false in 1919. Note: One motivation for a claim like Broad s is that statements about the future lack current truthmakers there are no current facts that make them true (or false). But why should statements about the future require current, rather than future, truthmakers? Cf. statements about the past. What happened back then makes our statements about the past true (or false). So, one might think, what will happen then equally makes our statements about the future true (or false). It is possible to develop a coherent logic of coming true, however. Note: Another motivation for a view like Broad s (though not one he expresses) is the fear that the current truth of statements about the future entails some kind of logical fatalism. Claim: Arguments for 4
fatalism fail even if full bivalence (or the Law of Excluded Middle) is taken as a premise. 337-340. Broad s theory is inconsistent with determinism, according to McTaggart. It may be that determinism is false, but assuming a theory of time that entails that it is false is too quick or too cheap a way to deal with a complex issue. What s the argument for the inconsistency? If (future, Laplacean) determinism is true, then any physically possible world agreeing with ours now will agree with ours for all future time t. That is, given the state of the world now, all its future states are fixed (by the physical laws). So should not the truthvalues of statements describing these future states, or any parts of them, also be fixed? Objection: Can t this be handled in terms of coming true? It may be set now whether a given statement will become true or become false, but that need not imply that they are true (or false) now. Reply: There are some statements that look as if they would resist this sort of treatment. Consider the statement No human being will set foot on Mars. If this statement is false, it is easy to see when it would become false. But if it is not false, when would it become true? When the last human dies (and no one has ever reached Mars)? That seems arbitrary. Second Version. One could put McTaggart s objection another way. If any scientific theory can 5
make true predictions about the future evolution of a system in any respect), then some statement of the form If Φ, then Θ is true, where Θ is later than Φ. But if Φ is now true and also If Φ, then Θ is true, then by modus ponens we must conclude Θ. Since modus ponens is a truth-preserving form of inference, we can also conclude that Θ is true, where Θ is a statement about the future. It is not appealing to try to block this conclusion by supposing that no statement of the form If Φ, then Θ is ever true, when Θ is a statement about the future. Third Version. Consider the following law of falling bodies: if an object is released at distance s meters above the surface of the Earth at time t, then (neglecting air resistance) it will strike the surface of the Earth at time t = t + 2s g where t' is evidently later than t. For instance, if s = 4.9 meters, then t is one second later than t. If this law is true, says McTaggart, then it is always true. So either (a) at any time t, if an object can be dropped at t, then there a statement true at some later time t or (b) no proposition about any time can entail a proposition about any other time, since there is nothing special about our law beyond the fact that it relates events at different times. 6
341. Broad must admit that all moments (except perhaps the very last moment, if there is one) are both present and past, but these properties are incompatible. This claim is the core of McTaggart s argument for the unreality of time. Note: This argument rests on the claim, at first sight not compelling, that every moment which is past is also present. (27) But McTaggart claims that any attempt to evade this claim will cause one to begin an infinite vicious regress. This claim has generated considerable controversy. 7