V. Alan White
"Did Somebody Say ‘McTaggart’?"®
The following note is a response to a paper by Professor Steven Savitt (and both) presented to the Philosophy of Time Society at the May 2000 Central Division meetings of the APA. Savitt's paper ("A Limited Defense of Passage") declared that a famous attempt by J. M. E. McTaggart—and lately updated and reasserted by D. H. Mellor in his book Real Time II—showing that a presentist A-theory of time is inconsistent, actually does not at all establish such inconsistency. My comments below finally ended up agreeing with Savitt, though with the indicated reservations.
P
rofessor Savitt’s lucid and careful criticism of what he has elsewhere compactly and delightfully referred to as "the McMellor argument" [apparently due to Jeremy Butterfield, according to Savitt] is dead-on in so many respects that I could easily exhaust my time extolling its virtues over its vices. Regrettably, commentators are usually relegated to being single-minded vice cops. In that role, I’ll certainly attempt to trump up charges against Savitt’s argument—but, believe me, don’t expect a conviction!Savitt claims quite rightly, of course, that the McMellor argument essentially rests on two claims attributed to any A-theory that accepts a temporal-property expression of that view. In terms of such properties interpreted monadically, the first claim is that any actual event (as opposed to merely possible ones) has (in some sense) the properties of being-future (F), -present (N), and -past (P). Symbolically this is:
(6*) eF&eN&eP
though please note that this departs syntactically from the MellSavittorian (sorry!)
(6) eP&eN&eF
by what is apparently an application of commutation on the reversal of the first and last terms. But as I shall later argue, the difference between (6) and (6*) may be much more significant than that.
The second claim amounts to an A-theory concession that these temporal properties are incompatible as they apply in some sense simultaneously to events—
(5*) (eP
É~eN)&(eN É~P)&(eF É~P). . .for all six possible combinations of such entailments. Note that my expression of what is labeled as (5) in Savitt’s paper is here explicitly a conjunction, although Mellor and Savitt’s use of a semicolon where I use "&" suffices to connote that truth-functional operation as well.
Savitt then proceeds to show that the McMelloresque conclusion that (5) and (6) are logically incompatible requires a univocal assertion of the copula signifying predication throughout both claims. The bulk of his paper is dedicated to showing that a number of attempts to hold such univocal predication throughout (5) and (6) either places highly implausible interpretations of (6) in the A-theorist’s mouth, or so weakens (6) with atemporal BE-predication that the conjuncts of (5) (or (5*)) are all false under that univocality, or their commitments to these claims become logically innocuous, and hence no contradiction of the two claims can be obtained on behalf of the A-theorist in any case.
Savitt’s analysis of the possible senses of the copula is quite thorough, and serves indeed to show that the McMellor argument must explicitly embrace univocal predication in both (5) and (6) to carry its point. But even so, I have two comments to consider here: one, that any adequate account of univocal predication requires besides an explicit sense of the predicative copula an explicit sense of the predicates themselves in both (5) and (6); two, that it is possible that the MellSavittorian assumption that (5) and (6) are both purely conjunctive assertions may also be challenged.
Say for example that we hold the copula in (5) and (6) to Mellor and Savitt’s timeless sense of BE. Savitt suggests that such predication in (5) simply renders its conjuncts false, since any event that is timelessly one A-property is also timelessly all of them, as (6) apparently asserts. However, merely because the copula is divested of all temporal information, it is not equally clear that that the predicates P, N, and F are stripped of temporal information of a sort that might be relevant to the truth of (5). If P/N/F are type or universal predicates asserted for e, for example, then the conjuncts of (5) may all well be false, since the BE-fact of e’s having pastness is quite compatible with the BE-fact of e’s having presentness, for example. But what if P/N/F are instantiated token or particular predicates? In that case, then the BE-fact that e has P (for example) includes the temporal particularization of P, namely, P-at-tn . So, if e P-at-tx then it is true of that e so particularized that it is not (say) eN-at-ty . Interpreted this way, the conjuncts of (5) so modified (as (5**), say) are all true. But, even so, this would obviously not produce Mellor’s contradiction with the parallel variant of (6)
(6**) (eP-at-tx)&(eN-at-ty)&(eF-at-tz)
which is true for an appropriate "e" and compatible with (5**). (I might mention that it would be well to further specify whether the temporal predicates are best interpreted as monadic or relational in nature, although McTaggart is clear that he believes this to be moot since, in any case "the nature of the terms involves a contradiction." Still, we should attempt to be as clear as possible about the predicates to see if indeed this is the case. More of this in a moment.)
However, pace McTaggart, Mellor, et al, it occurs to me that A-theory may have another way to deal with (5) and (6). In particular, although (6) as stated earlier is best read as a purely truth-functional conjunction (and in that case would be logically equivalent to my (6*) by commutation), perhaps the statement (6*) would better express what A-theory means to assert if interpreted non-truth-functionally; namely, that the sense of the "&" relating the terms of (6*) is indicative of an asymmetrical relation, meaning something roughly like "and then" (and perhaps better represented by a symbol other than "&"). Hence (6*) would have an entirely different truth-semantics than that of conjunction, being true iff an event has (BE?) all the A-properties in some sort of definite sequence. For example, one might say that an event is part of an A-series iff it first is future, then present, and finally past, which (6*), but not (6) could satisfy. Such a non-truth-functional connective would appear to better capture the intuition of change that A-theory strives to enunciate. An added benefit of such an approach for the A-theorist is that it might provide a means of avoiding McTaggart’s claimed regress of the temporal properties, which Mellor also endorses:
The attribution of the characteristics past, present, and future to the terms of any series [events or times] leads to a contradiction, unless it is specified that they have them successively. This means, as we have seen, that they have them in relation to terms specified as past, present, and future. These again, to avoid a like contradiction, must in turn be specified as past, present, and future. And, since this continues infinitely, the first set of terms never escapes from contradiction at all.
If the semantics of A-statements could take advantage of the truth-conditions of a sequential connective, then McTaggart’s condition of sequentiality would be met without resort to a recursive application of the original temporal predicates, thus blocking the regress. I should note, however, such a sequential-connective form of (6*) remains compatible with (5) read conjunctively, or even with a (5*)’s "&" similarly revised with the univocal copula of (6*). So in a completely different way Savitt’s overall thesis would survive even here.
Not that criticism can so easily cease with these considerations. After all, given the prolific nature of our erroneous thinking about time, no vice-cop’s work ever seems done. What is the nature of temporal properties that events can acquire and shed them? What is the nature of the existence of events themselves that these statements of property change appear to quantify over that yields the timefullness of events by such property change? (In particular, what distinguishes events that actually have these properties from merely possible ones that do not become part of time?) What sequentiality is supposedly captured by the "and then" connective of (6*) that sequentially relates the terms? Is it somehow merely numerical? If so, what would constitute proper order (as opposed to a reversed version of (6*) that looks like (6) but simply has a different numerical order)? But if it is partly temporal, wouldn’t that introduce circularity into the account?
In closing, I must confess much agreement with Professor Savitt’s open cynicism about the entire McMellor project, and in general any property account of temporality on which it apparently depends. Recalling the title of this commentary, perhaps just because we are constantly reminded by the literature that McTaggart’s controversy is there, we tend to just drive-through the same old franchise of argument time and again. But besides that one established in 1908 by one trisyllabic ‘M’-guy, there is another from that same year that may have overall healthier conceptual fare for philosophers of time:
"Will Somebody Say ‘Minkowski’?"®