Fate, Time, and Language

by David Foster Wallace

  Clearly, as the expression is ordinarily used—as it is used by anyone interested in defending assumption (B)—“doing A is within my power” does not have these absurd consequences. For not only would one never say that it is not within a person’s power to do twenty push-ups unless he has already done nineteen of them (on the ground that doing nineteen of them is a necessary condition of doing twenty), but if a man should say that he can swim, or that he has the ability to swim, he would surely take it as a poor joke if someone replied, “No, you cannot swim: you lack the ability to do this because you are not now in a pool or lake.”

  Apart from this sort of difficulty, (5) has other consequences of philosophical interest. For example, it seems clear that doing A will always be a necessary condition of itself; that is, it will always be a necessary condition of one’s doing A that one actually does A. But in conjunction with assumption (5) this has the consequence that if A is indeed within my power, in Taylor’s sense, then I must actually be performing A—for if I am not, something necessary to my performance of A, namely my performance of A, fails to obtain. Since it is clear that if I actually perform A, A is within my power—at least in the sense of “power” defended by Taylor—it turns out that doing A is within my power if, and only if, I am actually performing A. But because this last assertion presumably follows from necessary premises, either logical truths or analyses of concepts like necessary condition and within one’s power, it must be accepted by Taylor as necessarily true; and this means that he is committed to the idea that no circumstances could possibly arise in which one could distinguish the possession of a power from the exercise of that power. Such an idea is of course absurd when measured by any normal use of the words “power” and “ability”—in particular, when measured by the use of these words in assumption (B).

  Necessary and sufficient conditions. In connection with my last argument, Taylor might object that A’s occurring is a necessary condition of itself only in the logical sense, and he was not concerned with the logical sense of “necessary condition.” But the fact is, Taylor never really explained what sense of “necessary condition” he was concerned with. In stating assumptions (2) and (3) he apparently thought he was exhibiting “the standard manner” in which the concepts of necessary and sufficient condition are “explicated” (compare his commentary on the two assumptions); but because assumptions (2) and (3) are simply conditional statements, having the form(2′) If A is sufficient for B and A and B are logically independent, then A cannot occur without B

  (3′) If B is necessary for A and A and B are logically independent, then A cannot occur without B,

  it is clear that neither provides an explication, in any useful sense, of the concepts in question. Indeed, (2′) and (3′) are not even sufficient to derive assumption (4), which Taylor asserts “is but a logical consequence of the second and third presuppositions”; for (4) has the form(4′) A is a sufficient condition of B if, and only if, B is a necessary condition of A,

  and this plainly does not follow from the two conditionals mentioned above—unless, of course, (4′) is taken to be analytically true, so that it “follows” from any assumptions whatever. Of course, if we clearly understood the sense of “can” in (2′) and (3′), we could infer, if we knew both that A and B were logically independent and that A could occur without B, that A is not a sufficient condition of B and B is not a necessary condition of A. But (i) the sense of “can” here is by no means clear—surely no clearer than the notions of necessary and sufficient conditions—and (ii) we would still be in doubt about when we could legitimately assert that A is sufficient for B and B is necessary for A.

  It is clear, then, that Taylor has not carefully delimited the extension of the term “necessary condition,” as he uses it in his argument. We simply do not know, for example, whether the fact that the occurrence of A is a logically necessary condition of itself disqualifies it from being a necessary condition of itself in Taylor’s sense. But because the admission of such necessary conditions would have serious consequences for his argument, Taylor may very well want to exclude them. His grounds for this might be that the necessary conditions he has in mind are those on which the occurrence of an event or action physically depend. Since it sounds very odd to say that the occurrence of A physically depends on its own occurrence, he might naturally want to exclude this case. Unfortunately for him, however, the oddity of saying this is scarcely a satisfactory, or even a legitimate, defense of his position; for it sounds every bit as odd to say, as he does, that what a man does depends on the physical consequences of what he does.

  Actually, the question whether certain logically necessary conditions might also be physically necessary conditions leads us to the very heart of Taylor’s argument. For after stating assumption (5), the assumption I have been calling into question, Taylor remarks that it, (5), simply follows “from the idea of anything being essential for the accomplishment of something else.” Since he used the idea of one state of affairs as being essential for another as an alternative way of expressing assumption (3), his contention seems to be that assumption (5) is just a logical consequence of (3). This suggests, however, that the “can” in assumption (5) is none other than the “can” of assumption (3), a “can” that is presumably connected with the natural, or physical, modalities. Hence, if assumption (5) is true, it involves a sense of “can” that is opposed to the “must” of physical, or natural necessity; and thus any attempt to appraise the truth of (5), let alone its relation to (3), must become enmeshed in the problems of the logic of the physical modalities.

  One question of central concern to the logic of the physical modalities is the relation between logical and physical, or natural, necessity. For reasons already mentioned, Taylor would probably want to maintain that (7) (p ⊰ q) ⊃—(p → q), where “→” represents physical, or natural, implication. Yet when one considers that no one would want to maintain that a logically impossible state of affairs could still be physically possible, the falsity of (7) becomes apparent at once. For beginning with the premise that physical possibility entails logical possibility, that is, beginning with (8) “PM(p) ⊃ LM(p)” (where “M” represents “possibility”), we may infer (9) “—LM(p) ⊃—PM(p).” And then, since it is impossible that p if, and only if, it is necessary that—p, we may obtain from (9) the equivalent (10) “LN(—p) ⊃ PN(—p).” Since (10) holds for all values of “p,” we may substitute “(p.—q)” for “p” and then infer (11) “LN(p ⊃ q) ⊃ PN(p ⊃ q).” But because (11) may also be written as (12) “p ⊰ q: ⊃ : p → q,” it is clear that we are committed to deny that logical necessity never entails physical necessity. Thus, given that “A ⊰ A” is true, we must also accept “A → A” as true; and this contradicts the result we get from the assumption, held by many philosophers today, that logical necessity never implies physical necessity.

  If this argument is acceptable, and I do not see how one could reject it without committing oneself to the idea that there might be physical possibilities which are also logical impossibilities, then not only is it true that in Taylor’s sense of “power” no distinction can be drawn between having a power and exercising that power, but it is possible to show that assumption (5), interpreted as concerning what it is physically possible for a person to do, leads to the abolishment of all modal distinctions. This latter contention, the implications of which I have worked out in detail elsewhere,3 may be demonstrated as follows. Taken in its most general form, assumption (5) may be expressed as (5′) “(p) [PMp ⊃—(∃q) ([p → q].—q)],” which is equivalent to the more perspicuous (6′) “(p) (q) ((p → q).—q: ⊃ :—PMp).” Now it is easy to show, for an arbitrary “p,” that “PMp ⊃ p” follows from (6′). To prove this, simply instantiate both “p” and “q” in (6′) to “p.” The result of this operation is “(p → p).—p: ⊃ : PMp.” Since “p ⊰ p” is clearly true, infer “p → p,” and then, by sentential logic, conclude with the desired result, “PMp ⊃ p.” Since the conver
se of this last formula is obviously true, (7′) “PMp ≡ p,” which holds for all values of “p,” is also true. Taking advantage of the law that if p ≡ q, then—p ≡—q, (7′) may be transformed into “—PMp ≡—p,” which in turn yields the law “PN—p ≡—p.” The law of double negation then permits the inference of “PNp ≡ p.” Since, with (7′), it may be concluded that p ≡ PNp and PNp ≡ PMp, it is obvious that the premise which led to this, namely (5′), leads to the abolishment of all modal distinctions. For when (5′) is taken as a necessary truth, a result of logical analysis, then the following statements must all be logically equivalent: (i) he performs A; (ii) he can perform A, or it is physically possible for him to perform A; and (iii) he has to, or physically must, perform A. I think it can be taken without further discussion that any premise which commits one to the logical equivalence of (i), (ii), and (iii) is unacceptable and must be rejected.4

  The Efficacy of time. Having, I hope, shown that Taylor’s assumption (5) is untenable, and that his assumptions (2), (3), and therefore (4) are somewhat unclear, I feel reasonably free of commitment to his fatalistic conclusions. But because the issue of fatalism is perennially perplexing, I want to make a remark or two about his assumption (6), for it, too, is far more questionable than it appears at first sight.

  On the face of it, assumption (6) seems perfectly straightforward; yet it contains the curious expression, “the mere passage of time.” What is a mere passage of time? Could time possibly pass without something, somewhere, changing—without the tick of a clock, the movement of a planet, the twitch of a muscle, or the sight of a flash? Apparently not: for not only is the chronometry of time determined by changes, but its very topology is defined by changes—by events, happenings, and the like. Surely it is no news that time implies change and change implies time: a timeless world is one in which everything has come to a stop, where even the dissenting thoughts of philosophers are arrested. But if time cannot exist without change, then every temporal interval requires the existence of change—somewhere, somehow. Hence “the mere passage of time,” unless it is meant to include change, is a contradiction in terms; it makes little sense to speak of such a thing.

  Although a duration is inconceivable without change, it does make sense, at least, to speak of individual things, or groups of them, persisting through time unchanged. No one thing must change in a given interval, but something or other must change. Thus, although the world changes over a period of time, I might remain unmoved, unaffected. After such a period of timelessness (for me), I would be the same as before: I could still swim, I could still do twenty push-ups. But these are abilities, not “powers” in the sense of Taylor. For the passage of time, which implies the existence of some change or other, does affect one’s powers or the things it is physically possible for one to do. For suppose that during my changeless, timeless state the change that time required—suppose it is the only change—dried up the lake in which I was standing. I would still have the ability to swim—and even, perhaps, the opportunity, if another pool of water, twenty feet from where I was standing, was unaffected by the change. But I would not have the power to swim at the time—since something necessary to my swimming, namely my actually being in water, fails to obtain. Given, moreover, that is takes time to move, it seems clear that it would then be physically impossible for me to exercise my ability to swim as well. The moral of this can be put very simply: assumption (6) is true only if the agent or thing that has the power is unaffected by change—not if no change occurs at all, which is impossible—and only if the word “can” is used in the sense of “ability.” It is false when the word is used in the sense of Taylor’s “power”; for this sense, being akin to, if not identical with, a confused sense of “physical possibility,”5 is radically different from the sense of “can” involved in “I can (am able to) swim” or “That copper can corrode ( = is capable of corroding)” or “I can do twenty push-ups, though I have not yet completed nineteen of them.”

  Although in rejecting thesis (B) Taylor seems to be concerned with abilities and capacities, his only assumption clearly concerned with abilities, and hence directly relevant to the truth of (B), is assumption (6), an assumption which actually had little to do with his argument for fatalism. Assumption (5), on which the main thrust of his argument hinges, is patently unacceptable. It is obviously false when the “can” it contains is taken to refer to abilities and capacities; and when it is taken to refer to physical possibilities, it leads to the abolishment of all modal distinctions. I have not myself tried to give an acceptable analysis of abilities, nor have I claimed to elucidate the problematic concept of physical possibility. My purpose here has been entirely negative: to destroy the plausibility of the chief assumptions on which Taylor’s argument rests, and in so doing to discredit the basis for his fatalistic views.

  NOTES

  1 Richard Taylor, “Fatalism,” Philosophical Review, LXXI (1962), 56-66.

  2 Ibid., p. 61. I have replaced the pronoun “my” in this passage by “his.”

  3 In “Abilities, Modalities, and Free Will,” forthcoming in Philosophy and Phenomenological Research.

  4 I have given detailed reasons for this assertion, which should be obvious anyway, in the paper mentioned in note 3.

  5 This sense is confused, because, as already mentioned, it leads to the quashing of all modal distinctions.

  7

  TAYLOR’S FATAL FALLACY

  RAZIEL ABELSON

  RICHARD TAYLOR has argued that we must either become fatalists or abandon the law of excluded middle and/or the inefficacy of time. In his ingenious essay “Fatalism,” Taylor formulates six plausible “presuppositions” and deduces from them a fatalistic theorem to the effect that, for a given act, either it is not in one’s power to perform the act or it is not in one’s power to refrain from the act.1 Taylor concludes that the only way to avoid this fatalistic consequence is to jettison his first presupposition (the law of excluded middle) and possibly also his sixth (the inefficacy of time). Now I should not like to give up either the law of excluded middle or the atemporality of the laws of nature. Fortunately, there seems to be an easier alternative, namely, to show that Taylor’s other presuppositions are at fault. For the sake of brevity and easy reference, I shall list and paraphrase Taylor’s six presuppositions:P1. A or not-A (excluded middle).

  P2. If A is sufficient for B (although “not logically related to” B), then A cannot occur without B also occurring.

  THE PHILOSOPHICAL REVIEW, VOL. 71, NO. 1, 1963.

  P3. If B is necessary for A (although “logically unrelated” to A) then A cannot occur without B also occurring.2

  P4. If A is sufficient for B, then B is necessary for A.

  P5. “No agent can perform any ... act if there is lacking, at the same time or at any other time, some condition necessary for that act” (my italics).3

  P6. “Time is not by itself ‘efficacious.’”4

  Taylor then sets down the perfectly reasonable hypothesis that, if an admiral orders a sea battle for tomorrow, then the battle will take place, and if he orders his ships to avoid battle, then the battle will not take place. This makes ordering the battle today (O) a sufficient condition for the battle taking place tomorrow (Q), and it makes not-O a sufficient condition for not-Q. It follows from P4 that Q is a necessary condition for O and not-Q is a necessary condition for not-O. Taylor’s deduction of his fatalistic theorem then follows:5 If Q, then not-O is impossible (that is, not within the admiral’s power to do), and if not-Q, then O is impossible.

  Q or not-Q (excluded middle).

  Therefore either O is impossible or not-O is impossible.

  Now this argument is formally valid by the rule of constructive dilemma, yet we cannot accept the fatalistic conclusion, so something must be wrong in the premises. Taylor blames the law of excluded middle and the inefficacy of time. He should, I think, have blamed the first premise of his fatalistic deduction, above. This premise is supported by the hyp
otheses: If O then Q and if not-O then not-Q, together with P2 to P5. Since there is nothing wrong with the hypothesis, there must be something wrong with P2 to P5. This is what I think is wrong:

  In P2-P5, Taylor systematically equivocates between the logical and causal senses of the modal terms “necessary,” “sufficient,” “can,” “power,” and “efficacious.” He employs these expressions in a hybrid way, combining some features of their logical use with some features of their causal use,6 thus providing us with an instructive demonstration of the importance of keeping these two uses clearly separated. Taylor’s stipulation in P2 and P3 that the states of affair A and B are “logically unrelated” seems to indicate that his modal terms are to be understood in their causal sense. On the other hand, Taylor’s phrase in P5, “at the same time or at any other time,” repudiates the causal sense for which the direction of time is essential.7 Again, when he asserts in P6 that “time is not ‘efficacious,’” one is left to wonder whether he means causally or logically efficacious. Of course time is not causally efficacious; time is not an agent that produces or influences events. But surely time is logically efficacious, since it often has a lot to do with the truth of what we say. As Gilbert Ryle once observed, “She took poison and then died” may be true while “She died and then took poison” is bound to be false.

  Taylor’s disclaimer of the logical interpretation of his modal terms is made speciously plausible by the fact that, given the material conditional “If A then B,” B is said to be a necessary condition for A even though there is no relation of entailment between A and B. But when the “necessity” of B for A is independent of time, it refers, I think, in an elliptical way, to a more complex entailment, between the premise “If A then B, and not-B,” and the conclusion “Not-A.” To put it in another way, “Necessarily, if A implies B and B is false then A is false” is a truth of logic. Thus the modal term “necessarily” applies to the inference from “If A then B, and not-B” to “not-A,” and does not modify “not-A” all by itself. It is therefore wrong to claim, as Taylor’s P5 in effect claims, that if B is a necessary condition for A (that is, “If A then B” is true), then if B is not the case, A is impossible (that is, not-A is necessary). For to make this claim is to transfer necessity from a modus tollens inference to one component of it (not-A). We are thus lured into believing that, since not-A is a contingent state of affairs, its necessity and the corresponding impossibility of A are nonlogical modalities. It may be of interest to note that a similar error lies at the root of the famous paradox of Chryssipus: A man necessarily either does X or does not do X (excluded middle). Therefore either he necessarily does X or he necessarily does not do X.8