Fate, Time, and Language

by David Foster Wallace

  We may, for example, look at Bruce Aune’s “Fatalism and Professor Taylor,”17 which demonstrates formally that presupposition 5, expressed as:II-7) (∀p) (◊p → (∼(∃q)(p → q) ∧ ∼q))),

  reduces through proof to (◊p = p = □p), i.e., into a “collapse of all modal distinctions,” in which what we can do, we do do, and must do. Aune claims that “any premise which commits one to the logical equivalence of ... (‘can,’ ‘do,’ and ‘must’) ... is unacceptable and must be rejected.” But of course the fatalist can immediately respond: unacceptable to whom? and must be rejected on what grounds? The fatalist can perhaps agree with Aune that the Taylor problem has as an implication an equivalence of situational physical modals, but he can still say that what the situational equivalence of “can,” “do,” and “must” amounts to is simply fatalism, the idea that the only things we really can do are those which we must do. Thus Aune’s criticism seems to amount to nothing more than pointing out that Taylor’s argument has fatalistic consequences, which is exactly what Taylor himself was concerned to show.

  By what reason, other than mere habit or inclination, ought we to reject out of hand a modal system in which possibility, actuality, and necessity are collapsed? Would it somehow be meaningless or uninteresting? The fatalist can point out that no less a non-fatalist than G. H. von Wright does not think it would. In discussing a system with just such a feature, von Wright maintains that “This ‘collapsing’ of the distinction between the possible and the necessary does not make the system uninteresting as a modal logic. Quite to the contrary, speaking in the traditional modal terms, one can call it a modal logic of a universe of propositions which has no room for contingent propositions but in which every truth is a necessity and every falsehood an impossibility.”18 (In other words, a fatalistic modal logic.) Some philosophers19 have argued that the collapse of modal distinctions apparently implied by the Taylor problem results in the very concept of “necessity” itself becoming vacuous, and so renders the fatalist’s contention that everything that happens is “necessary” empty and benign. But the fatalist is clearly going to want to hold that since the relevant collapse is from possibility and actuality into necessity, it is only necessity which has any real meaning as a modal concept, and it is the others which are really empty. Where does this leave us? Again an attempted refutation of Taylor’s argument boils down to an attack upon a fatalistic intuition which we can only reject, not refute.

  Even some promising denials of the validity, rather than the soundness, of Taylor’s argument run afoul of this sort of problem. Raziel Abelson’s is a famous criticism of Taylor’s distribution of modal operators from whole entailments and disjunctions onto individual antecedents and consequents and disjuncts.20 It certainly seems legitimate to say □((O → B) → (~B → ~O)), but we are quite justified in wondering whence out of all this comes □(~O). Abelson urges us to be particularly suspicious of the move from □(O → B) to (~B → ~O), which he maintains is every bit as dubious as the famous modal fallacy:□(O → B)

  ∴ (O → □B).

  Abelson’s seem to be legitimate criticisms, but they have the disadvantage that they again force the fatalist into a corner in which it is very difficult to fight with him. Abelson claims that Taylor illicitly draws from:II-8) (O → B)

  the propositions:II-9) (O → B)

  and especiallyII-10) (~B → ~O).

  But Taylor’s public defenders21 claim strangely that what Abelson regards as the premise, (II-8), from which Taylor illegally draws the fallacious conclusions, (II-9) and (II-10), is really the conclusion gotten from (II-9) and (II-10), which it turns out are really Taylor’s premises. Steven Cahn writes that: “Taylor’s argument can be interpreted ... as saying that if O, then necessarily B, and if not-B, then necessarily not-O. Abelson transfers these individual necessities to the necessity of the entire proposition, ‘If O implies B and not-B, then not-O.’ This proposition is logically true, as is the first statement of the Chrysippus paradox ...1. □(p ∨ ∼p)

  2. ∴ (□p∨□∼p)[2]

  ... but whereas that paradox asserts a second statement that does not logically follow from the first, Abelson denies a second statement which, in fact, is the premise from which the first statement is deduced.”22

  What are we to say to this sort of defense? If the modalities involved here were alethic, Cahn’s reasoning would be demonstrably faulty. But we have seen that the modalities and relations in the Taylor problem are physical, causal. Does a cause render its effect a physically necessary thing? Does the absence of an effect render the presence of its cause physically impossible? (“Necessary” and “impossible” here in the strong sense implied by the distribution of the modal operator onto the individual antecedents and consequents.) The answer is simply not clear, largely because so very little work has been done on the formal, semantic and metaphysical properties of physical modalities. The difficulties in the Abelson attack and the Cahn defense seem to lie in the intrinsic ambiguities surrounding the notions of causation and causal “necessity,” surrounding the question whether any non-logical entailment can assure the appearance of the consequent or else the absence of the antecedent.23 The problem with arguing against the fatalists on this sort of level is that, given their metaphysical sentiments to begin with, they are instinctively and happily inclined to work their trade in this sort of confusing non-alethic modal neighborhood, to assert far more “necessity” than we (intuitively) think ought reasonably to apply to propositions, and simply to challenge us to refute them ... which we find so very difficult to do precisely because of the murky, disorienting ground on which the battle has been joined.

  A prime example of this sort of frustrating dilemma occurs with another of Abelson’s objections to Taylor’s argument, namely that since every event is by definition both a necessary and a sufficient condition of itself, the non-occurrence of an event would, under Taylor’s reasoning, mean that the event was impossible, and its occurrence would render it necessary, so that truth collapses into necessity and falsehood collapses into impossibility.24 We can easily see that, as against Aune’s formal objections, Taylor’s defenders will immediately reply here that this is exactly what they are arguing for, fatalism, the view that what does happen is necessary and what does not happen is impossible. Again they will say, with Cahn, that “To point out that it is strange is only to reject the conclusion; it is not to refute it.”25

  It looks as though a truly successful critic of Taylor’s argument must do more than show that his premises or conclusion have strange consequences, or merely assert that the conclusion is incorrect. Or rather I think he must do less. Taylor’s thesis is that a certain argument “forces” a fatalistic conclusion upon us. It’s clear that I cannot simply reject the conclusion out of hand, but it’s just as clear that neither need I accept it and then show somehow by, say, reductio that it is inconsistent in some way. To “refute” Taylor I think I need show only that his conclusion is not forced upon us by his argument—for this is his central claim. There is quite obviously something wrong with Taylor’s conclusion, but I cannot (and need not) make this fact the only premise on which to build. I think I need show only that the four-step argument out of Taylor’s six presuppositions does not actually yield what Taylor thinks it yields, that his argument is invalid. If intuitive rejections of premises and conclusion can be replaced by charitable interpretation, at least semi-rigorous argument, and a demonstration that fatalism follows not even from the most generous way of understanding Taylor’s reasoning, the Taylor problem can actually be “solved,” or at the very least the burden of argument and proof can be shifted from the opponent of fatalism to its proponent. In the next section I am going to try to show that Taylor gets his fatalist result only by equivocating between two different tensed physical-modal propositions, propositions that are inequivalent for truly interesting reasons that bear on the sorts of semantics I think are required for the coherent interpretation of statements involving situational physi
cal possibility and necessity.

  III. INTRODUCTION TO THE TAYLOR INEQUIVALENCE.

  If Taylor’s fatalistic argument uses apparently non-controversial premises and appears internally valid, yet results in an obviously defective conclusion, it seems reasonable to suspect that the fatalist engages in some equivocation of his premises, or else some equivocation in the move from what is posited to what is concluded. I think it is possible to argue that Taylor engages in both. What I regard as the most successful and valuable general criticism of the Taylor argument existent in the literature, Charles Brown’s “Fallacies in Taylor’s ‘Fatalism,’”26 attacks Taylor’s presuppositions 2, 3, 4 and 5 on just such grounds of equivocation.

  Brown maintains that since Taylor is clearly talking about physically necessary and sufficient conditions, rather than their logical counterparts, it is important to draw a distinction, temporally and modally, between events and states of affairs that are necessary consequences of other events and states of affairs, on the one hand, and events and states of affairs that are necessary preconditions for other events and states of affairs, on the other. Brown argues that Taylor not only never recognizes or acknowledges this distinction, but depends on an equivocation between the two different kinds of necessity to make his argument go through at all. Taylor commits the sin of equivocation, according to Brown, “by the seemingly innocuous ‘prepositional shift’ from logically standard ‘necessary (sufficient) condition of,’ to ‘necessary (sufficient) condition for.’”27

  Brown’s moves toward a solution to the Taylor problem depend on a conviction I regard both as correct and as resting on the surface of some very deep and interesting questions about the relations between physical modalities and time. The conviction is that once we leave the (comparatively) clear arena of purely logical relations between propositions, and enter into discussions of physical and causal entailments between actual events and states of affairs, there are at least two different ways for a state of affairs q to be “necessary” for a state of affairs p: under one interpretation, q’s absence necessitates that p cannot occur, while on the other, q’s absence necessitates only that p does not occur. That is, it is appropriate now to begin thinking about potential differences between the propositions: “It is the case that p cannot happen,” and “It cannot be the case that p does happen,” between: “It was the case that p could not happen,” and “It cannot be the case that p did happen.”

  An expansion of Brown’s quite right-headed criticisms provides the first step toward an analysis of the really deep and interesting problems in the Taylor argument. Consider the following two instances of what we’ll assume to be valid, non-logical, physical implications:III-1) (I give orderO→Sea-battle B tomorrow)

  III-2) (Combustion → Presence of fuel).

  In both these instances, the antecedents are “sufficient” for the consequents, and, more important, the consequents are “necessary” for the antecedents. Yet we should very quickly be able to see significant differences between the internal relations in the two entailments. We can see that, in (III-1), battle B is a necessary consequence of order O. But would we want to say, with regard to (III-2), that the presence of fuel is a necessary “consequence of” combustion? Not really: it would be more natural and sensible to say instead that it is necessary for combustion. In (III-1), the antecedent brings about, causes, gives rise to the consequent. In (III-2), though, the fire does not “bring about” the presence of fuel; it looks rather as though the presence of fuel was one of the things that actually brought about the fire (fuel together with, say, sufficient local temperature, the presence of a conductive atmosphere, the absence of local flame-retarding agents, etc.). We may, it appears, legitimately say that the consequent in (III-1) is an instance of a condition that is “necessary-of,” and that the consequent in (III-2) is an instance of a condition that is “necessary-for.”

  We might draw a similar sort of distinction between the two antecedents. The order O is sufficient for the battle B tomorrow. But in the case of the combustion, it does not seem right to say that it is sufficient for the presence of fuel, since it certainly didn’t have anything to do with bringing about the presence of fuel (the fire actually uses up fuel, causes fuel to be absent); rather we are more inclined to say that combustion is simply an infallible physical indication of the presence of fuel—since if there was no fuel, there most certainly would be no fire.

  We should now be able to see a certain reciprocity between the of’s and the for’s in the two different entailment-relations. Something that is causally sufficient for a consequent takes the consequent as a necessary consequence of it (e.g., III-1). An antecedent that is an infallible physical indication of the presence of its consequent is so only because the presence of the consequent is a necessary condition for the presence of the antecedent (e.g., III-2). Here we should probably notice that necessary consequences of their antecedents seem generally to post-date their antecedents, while necessary conditions for antecedents tend to precede (or at least do not post-date) those antecedents. We might also notice that none of these sorts of considerations appear to apply to logical entailments like ((p ∧ q) → p) and (p → (p ∨ q)); questions of time, of the differences between of’s and for’s, do not seem to enter into discussions of logical relations and the propositions that express them.

  As I read him, Professor Brown is accusing Taylor of equivocating and treating an entailment like (III-1) as if it were exactly the same as (III-2). Why might this be an effective criticism? It looks as though it will be effective only if (III-1) and (III-2) can be shown to behave differently under a modus tollens operation (a deny-the-consequent-and-see-what-happens-to-the-antecedent operation), since this is the operation via which Taylor proposes to show the impossibility either of O or of O′. Now, if we deny the consequent in (III-2), we are absent a precondition necessary for combustion to occur. It certainly seems reasonable to say that if a precondition necessary for some state of affairs to obtain is lacking, then that state of affairs cannot—in a situational-physical-modal sense of “cannot”—under these circumstances obtain; it looks to be physically impossible for combustion to take place without fuel. So (III-2) appears to accord perfectly with Taylor’s presupposition 5; it appears perfectly legitimate to say, with respect to some time t1, that: (t1(~Fuel)) → (t1 (∼◊Combustion)).

  The case of a modus tollens operation on (III-1) appears very much harder, though. If there is no sea-battle on day 2, what does that say about the physical possibility of the battle-order being given on day 1? This case is just not as clear as (III-2). If a causally necessary condition for some state of affairs is lacking, then that state of affairs indeed cannot occur, but what if a causally necessary consequence of a state of affairs is lacking? Or ought we to say not “is lacking,” but rather “will be lacking”? Would this make a difference?

  You can see right away that there are time ambiguities involved in a modus tollens analysis of (III-1) that were not involved in the analysis of (III-2). In the case of (III-2), it was possible to evaluate both the absence of the consequent and the possibility of the presence of the antecedent at, and with respect to, the same time—t1. We cannot do this in the case of (III-1). Why not? Because in (III-1) the relevant presence or absence of the necessary consequence must occur, and be evaluated as occurring, at a different, later time than the possibility of the occurrence of the antecedent. Here there seem to be at least two different times involved: t1, at which the order is or isn’t or can or can’t be given; and t2, at which the battle does or does not take place.

  Once we notice this, I must take a moment to point out something important. In order for me to evaluate what might be called the physical-possibility-at-t1 of the antecedent in (III-1) under a modus tollens operation, I must be able to pretend, since an event-at-t2 is alleged to bear on that possibility either that it is already somehow tomorrow, t2, and that I am looking out at the peaceful sea and analyzing the possibility of order O having bee
n given at t1; or that it is later than t2 and I know what’s happened; or that I am in some artificially privileged epistemic position and know, at some time prior to t2, that the relevant battle will in fact not occur at t2. (It is crucial to see that these epistemic considerations matter only to my ability to analyze the results of a modus tollens operation on (III-1), and have no bearing whatsoever on what those results in fact are; as Taylor cooks his case, it is not necessary that anyone involved in the naval operation know what will happen at any future time. I, though, in my formal modus tollens/contraposition analysis of the situation, denying the consequent’s truth-at-t2, must either be at or beyond t2, or in a position to know what is true- or false-at-t2.) Let’s assume in this analysis of (III-1) that it is now tomorrow, t2, and I am watching the peaceful sea. This means that I will talk about “yesterday” from my evaluative standpoint. (Exactly the same analysis can be carried out using the time-markers t1 and t2.)

  So here it is today, t2, and there is no sea-battle. Given that order O yesterday would have been sufficient for the sea-battle today, and that thus the battle-today seems to be “necessary” for there to have been an order O given yesterday, what are we to say about the possibility of order O having been given yesterday, given no battle today? Now, I hold that there are not one but two possible interpretations of Taylor’s situation, two possible contrapositives of the original entailment-proposition, given no battle today and a modus tollens operation on the original physical entailments:MT1) Today(∼B) → Yesterday(∼◊O)—or t2(∼B) → t1(∼◊O)