WILLIAM HASKER
In 1985 David Foster Wallace, then a senior at Amherst College, decided to devote his philosophy honors thesis to the issues raised by Richard Taylor’s paper “Fatalism,” published two decades earlier. Taylor’s paper had generated a storm of discussion, most of it critical of his argument. (Apparently, no one actually considered the argument to be sound, not even Taylor.) Wallace, however, found all of the previous criticisms to be inadequate in one way or another, so he set out to provide a new refutation, creating in the process a new system of formal logic to deal with what he termed “situational physical necessity and possibility.”
Now, Wallace’s thesis does not by any means represent a turning point in recent philosophy; indeed, its very existence was known to only a few before its publication in the book to which this present volume is a sequel (Wallace 2011). Nevertheless, I believe there is a good deal to be learned from a reexamination of Taylor’s argument, the various criticisms of it, and Wallace’s response. Considering these matters can throw light not only on Taylor’s and Wallace’s philosophical positions but also on the general philosophical climate of the period. I will begin by presenting Taylor’s argument, followed by a selection from the criticisms made of it and the reasons Taylor and Wallace, as well as Taylor’s defender Steven Cahn, found them inadequate. This will be followed by a summary of Wallace’s system and the criticisms of Taylor’s argument that emerged from it; these criticisms are compared with those that had been made previously. Finally, I offer a few comments on the guise in which these problems present themselves in our own time.
The narrative of Taylor’s argument for fatalism is best begun not with his article of that name (Taylor 1962a) but with an earlier article, “The Problem of Future Contingencies” (Taylor 1957). This was a carefully argued defense of Aristotle’s view that assertions concerning future contingent events are neither true nor false; it also included a proposed revision of the traditional theological doctrine of divine omniscience. The article is well-balanced, reasonable, and contains excellent scholarship on Aristotle; furthermore, it makes a good (though perhaps not airtight) case for its conclusion. In spite of these merits, however, the article fell mostly on deaf ears, to the extent that it reached any ears at all (often a moot question concerning scholarly publications!).
The failure of this article to elicit a greater response may well have been a motivating factor for the subsequent publication, in 1962, of Taylor’s essay on fatalism. The strategy of the argument (though not its explicit form) would seem to have been a kind of reductio ad absurdum: “If you won’t accept Aristotle’s and my argument concerning future contingents, see what you will be stuck with in its place!” What appeared in place of the Aristotelian conclusion was precisely fatalism, which Taylor described thus:
A fatalist—if there is any such—thinks he cannot do anything about the future. He thinks it is not up to him what is going to happen next year, tomorrow, or the very next moment. He thinks that even his own behavior is not in the least within his power, any more than the motions of the heavenly bodies, the events of remote history, or the political developments in China. It would, accordingly, be pointless for him to deliberate about what he is going to do, for a man deliberates only about such things as he believes are within his power to do and to forego, or to affect by his doings and foregoings.
(Taylor 1962A, 41)
Taylor proposed to deduce fatalism from a set of six “presuppositions made almost universally in contemporary philosophy” (Taylor 1962a, 42). I give these presuppositions in his own words, though with some omissions where nothing essential is lost thereby.
First, we presuppose that any proposition whatever is either true or, if not true, then false.…
Second, we presuppose that, if any state of affairs is sufficient for, though logically unrelated to, the occurrence of some further condition at the same or any other time, then the former cannot occur without the latter occurring also. This is simply the standard manner in which the concept of sufficiency is explicated.…
Third, we presuppose that, if the occurrence of any condition is necessary for, but logically unrelated to, the occurrence of some other condition at the same or any other time, then the latter cannot occur without the former occurring also. This is simply the standard manner in which the concept of a necessary condition is explicated.…
Fourth, we presuppose that, if one condition or set of conditions is sufficient for (ensures) another, then that other is necessary (essential) for it, and conversely, if one condition or set of conditions is necessary (essential) for another, then that other is sufficient for (ensures) it. This is but a logical consequence of the second and third presuppositions.
Fifth, we presuppose that no agent can perform any given act if there is lacking, at the same or any other time, some condition necessary for the occurrence of that act. This follows simply from the idea of anything being essential for the accomplishment of something else.…
And sixth, we presuppose that time is not by itself “efficacious”; that is, that the mere passage of time does not augment or diminish the capacities of anything and, in particular, that it does not enhance or decrease an agent’s powers or abilities.…
(Taylor 1962A, 43–44)
Of these presuppositions, P2, P3, and P4 are essentially definitions; apart from minor quibbles, they are effectively beyond challenge. P6 is seriously ambiguous,1 but this is not too important inasmuch as it is not actually employed as a premise in the proof Taylor offers. His own inclination is to reject P1, the assumption of bivalence; as we shall see, he had a surprise awaiting him in this territory. Much of the criticism by other philosophers, however, was centered on P5. But before getting into that, we need to look at Taylor’s proof of fatalism.
Taylor takes as his example (with a tip of the hat to Aristotle) the occurrence or nonoccurrence of a naval battle on a particular day. First, he considers the situation the day after the naval battle either occurred or failed to occur. He assumes that
conditions are such that only if there was a naval battle yesterday does the newspaper carry a certain kind (shape) of headline—i.e., that such a battle is essential for this kind of headline—whereas if it carries a certain different sort (shape) of headline, this will ensure that there was no such battle.2 Now, then, I am about to perform one or the other of two acts, namely, one of seeing a headline of the first kind, or one of seeing a headline of the second kind.
(Taylor 1962A, 44)
Now, for me to read the headline stating that no battle occurred, the nonoccurrence of a naval battle yesterday is a necessary condition.3 And it follows from P5 that, this necessary condition being absent—that is, if a battle did in fact occur—it is not in my power to perform the action of reading that sort of headline. And on the other hand, for me to read the headline stating that the battle had occurred, a necessary condition is the occurrence of the battle. Once again, it follows from P5 that, if this necessary condition is absent—that is, if no battle occurred—it is not in my power to read a headline stating that the battle had occurred. So, given the situation as described, I have no control over which sort of headline I will be reading. Taylor goes on to say, “this conclusion is perfectly in accordance with common sense, for we all are… fatalists with respect to the past” (Taylor 1962a, 45). For future reference, call this Argument I.
Next, Taylor considers the situation the day before the battle would occur or fail to occur. Now we are to imagine that
I am a naval commander, about to issue my order of the day to the fleet. We assume, further, that, within the totality of other conditions prevailing, my issuing of a certain kind of order will ensure that a naval battle will occur tomorrow, whereas if I issue another kind of order, this will ensure that no naval battle occurs.
(Taylor 1962A, 46)
Now, my issuing an order of the first kind is sufficient (given the other conditions that prevail) for a naval battle to occur; it follows from this (by P4) that the occurrence of the battle is a necessary condition of my issuing such an order. But now it follows, given P5, that in the absence of this necessary condition—that is, if no battle occurs—it is not in my power to issue an order of that particular sort. And on the other hand, my issuing an order of the other sort is sufficient to ensure that no naval battle occurs; thus, (by P4) the nonoccurrence of a battle is a necessary condition of my issuing an order of this second sort. And once again it follows, given P5, that absent this necessary condition—that is, if a battle does occur—it is not in my power to issue an order of this second sort. But either it is true that a naval battle will occur, or it is true that no naval battle will occur (by P1)—and whichever of these is the case, I have no control over which sort of order I will issue. And this result, extended to cover each and every one of my actions, is fatalism. Call this Argument II.
Before we address the criticisms that were made of these arguments, it seems appropriate to call attention to some dramatic but misleading rhetoric in Taylor’s article—rhetoric, I surmise, that was put in place in order to enhance the “shock effect” of his thesis and elicit a more forceful response from his readers. The conclusion of the article4 manages to suggest, without actually stating, that Taylor either accepted fatalism or was strongly inclined in that direction, something we know was not the case. Even more egregious, however, is his initial characterization of the fatalistic hypothesis. It is already misleading to say that we have no more control over our own behavior than over the motions of the heavenly bodies. As compatibilists on free will have pointed out at great length, even if our behavior is causally determined it is controlled by our own desires, intentions, and decisions, something that obviously does not apply to the heavenly motions or the events of remote history. And the claim that it would be pointless for us to deliberate is simply false. People who seriously believe in fatalism (a.k.a. determinism),5 such as theological Calvinists, are often at pains to deny that our deliberations, decisions, and exertions of effort are pointless. All of these things, they rightly point out, make a difference in the world because they make a difference to our actions. It’s true enough that, as we consider the matter from a detached perspective, we will conclude (if we are determinists) that no other course of action was really possible. But that does not mean that our efforts are in vain. Taylor’s description may capture the connotations of “fatalism” as the term is often used, but it goes far beyond anything that is warranted by the fatalistic doctrine he argues for.
At this point I propose to skip ahead a bit and address an objection to Taylor’s argument that appeared at a slightly later stage in the discussion. In 1964 Steven Cahn published an article (Cahn 1964) in which he defended Taylor’s argument from some of the more common objections raised against it. However, he added a new objection of his own, an objection that has the distinction of being the only objection that Taylor himself ever recognized as having any validity. The point made by Cahn is one that we might feel, in retrospect, ought to have been obvious all along. The fact remains, however, that for a considerable period of time it was not obvious, either to Taylor or to any of the highly qualified philosophers who had undertaken to refute Taylor’s argument.
Here, in brief, is Cahn’s point:6 It is, as we have seen, a necessary condition of the admiral’s issuing a certain order that there is a naval battle the following day. Now, suppose that, as he is considering what to do, the proposition “There will be a naval battle tomorrow” is neither true nor false. It follows from this, trivially, that “There will be a naval battle tomorrow” is not true, and because it is not true, a necessary condition for his issuing that order is lacking, and it follows (by P5) that no such order can be issued. On the other hand, however, it is a necessary condition of the admiral’s issuing a different sort of order that there shall be no naval battle on the following day. But once again: the proposition “There will be no naval battle tomorrow” is, by hypothesis, neither true nor false. It now follows trivially that this proposition also is not true, and because it is not true, a necessary condition of his issuing that other sort of order is lacking, and it follows (by P5) that he cannot issue this kind of order either. This argument is easily generalized to arrive at the conclusion that, on the assumption that future contingent propositions are neither true nor false, it is never possible for any person to perform any action whatsoever. But this conclusion is not merely repugnant (as many find fatalism to be) but very obviously false and absurd.
Now, in one way Cahn’s objection actually strengthens Taylor’s argument, by showing that it does not depend on a premise (namely, P1) that it had formerly seemed to depend on. However, the objection creates a severe problem for Taylor. Undoubtedly his original motivation for the argument was to support the Aristotelian conclusion that future contingent propositions lack classical truth values. But now it appears that rejecting classical truth values for future contingents not merely fails to avoid the fatalistic conclusion but in fact makes things a great deal worse. The upshot is that Taylor is still confronted with his own argument for fatalism, but with no apparent way to escape from the argument’s conclusion. In a response to Cahn’s article, Taylor states, “I feel obliged to concede… that it may be quite unhelpful to try modifying the traditional interpretation of the law of excluded middle. Perhaps some of my other presuppositions are doubtful, but I can imagine no reason for rejecting any of them other than the one so frequently brought forth; namely, that they seem to have fatalistic implications” (Taylor 1964, 110). Nevertheless, Taylor did not abandon his argument but continued to include it, in an altered form, in the next edition of his Metaphysics.7 It may be that Taylor came to regard his argument as a conundrum—a philosophical puzzle for which a solution is required, but for which none seems to be available.8 On the other hand, the way the argument is discussed in the second edition of Metaphysics could lead one to think that by 1974 Taylor had come to embrace fatalism or at least to consider its truth as a strong possibility.9
We now turn to the objection concerning which Taylor said that it “is so familiar that I have come to anticipate it every time I hear this discussed” (Taylor 1962b, 57). Taylor credits John Turk Saunders for having stated the objection best, so we shall begin with Saunders’s statement. He wrote:
Taylor errs… in supposing that no agent has within his power an act for which a necessary condition is lacking. I suspect that he is led to make this supposition by equivocal reasoning of the following sort. He sees that (1) no agent can perform an act if a necessary condition for that act is lacking. But this means only that (2) as a matter of logic, if condition x is necessary for the occurrence of act y and x is lacking, then no agent performs y. The expression “can” functions only to indicate that the consequent of the second formulation follows logically from its antecedent. Taylor may then have equivocated with respect to “can,” taking it this time to mean the same as “has the power to.” In this way he may have become convinced that no agent has the power to perform an act if a necessary condition for that act is lacking.
(Saunders 1962, 54)
Saunders then argues that this supposition of Taylor’s is erroneous:
My knocking upon a thin wooden door with my fist is a sufficient condition for the door’s shaking. Hence the door’s shaking is a necessary condition for my knocking upon the door. But the door’s shaking is not a necessary condition for my ability to knock upon the door. (If it were, then my mere ability to knock upon the door would suffice to make it shake.) I may decide not to knock and the door may not shake, but it does not follow that I did not have it in my power to knock.
(Saunders 1962, 54)
Now we may solve (or dissolve) Taylor’s problem by noting that he is not entitled to conclude: Either it is not within my power to issue order O [the order that would lead to the naval battle], or it is not within my power to issue order O′. The occurrence of a naval battle on the morrow is a necessary condition of O but not of the ability to issue O; and the non-occurrence of a naval battle on the morrow is a necessary condition of O′ but not of the ability to issue O′. (To suppose otherwise, as Taylor does, is to adopt a position which logically implies that my ability to issue O is a sufficient condition for a naval battle on the morrow and that my ability to issue O is a sufficient condition for the nonoccurrence of a naval battle on the morrow.)
(Saunders 1962, 55)
This reasoning is apparently straightforward, but the dialectical situation is really quite complex. On the face of it, Saunders is rejecting Taylor’s premise P5, which states that “no agent can perform any given act if there is lacking… some condition necessary for the occurrence of that act.” His reason for doing so is that this premise violates the ordinary usage of language, by understanding “I have the power to do y” as entailing “I do y,” when the expression “have the power,” as ordinarily used, has no such entailment.10 Now, this may seem to invite the response (which was actually offered by Taylor—see Taylor 1964, 107) that the assertion that I have the power to do y if and only if I actually do y is simply the fatalistic doctrine itself. It seems, then, that Saunders’s objection to Taylor’s argument amounts to pointing out that the argument has fatalism as its conclusion. But of course that is precisely Taylor’s point, so this does not seem to amount to much as an objection.
To respond to Saunders in this way, however, overlooks an important element in the situation, namely that Taylor’s argument is supposed to be based on “presuppositions made almost universally in contemporary philosophy” (Taylor 1962a, 42). Now presumably philosophers who make those presuppositions intend, in making them, to be using language in the normal, everyday way, not in some special way that is peculiar to fatalism. So if the presuppositions, the premises of Taylor’s argument, require such peculiar uses of language to be adjudged as true, this is an excellent reason for rejecting his claim that these presuppositions are almost universally made.
How might Taylor respond to this point? On the face of it, two types of answer seem to be possible. One might, on the one hand, argue that the way the presuppositions are understood by Taylor does indeed correspond to normal usage, albeit a different usage than the one Saunders takes to be normative. Or, one might provide an independent argument showing that philosophers must, on pain of irrationality, accept Taylor’s premises as they stand, whether or not this involves a deviation from standard usage. (This assumes, to be sure, that standard usage may at times be involved in confusions and contradictions.) If Taylor can do either or both of these things, he can rebut Saunders’s charge that his position is based on fallacious reasoning. As it turns out, Taylor avails himself of both types of responses.
Taylor admits that Saunders’s point is correct with regard to “the usual sense of ability, which consists in having the skill strength, equipment, or knowing how” (Taylor 1962b, 57). However, he believes that there is another sense of ability that is relevant. Now, Taylor is certainly right in contending that there is more than one sense of “ability” that may be relevant here. Take the situation that concerns one’s ability to read a headline in today’s paper. We ask the person whether he is now able to read a headline stating that there has been a naval battle. One perfectly understandable and sensible response might be, “Of course! My eyes are just fine, the light is adequate, and I am fully able to read any headline whatever.” Or, he might respond, “Well, I can’t do that now, because I have seen today’s paper and there is no such headline.” The second response, unlike the first, uses “able” in a sense that takes into account the circumstances in which the person finds himself—circumstances that preclude his being able to read that sort of headline. And now we ask the admiral on that same day (the day after the battle would have occurred), “Were you able, the day before yesterday, to give your ships order O?” He might reply, “Of course I was able! I am entrusted with full authority to command the fleet, and if I chose to give such an order I could certainly have done it.” Or, he might conceivably reply, “Actually I couldn’t give such an order the day before yesterday, because my ships were not in the initial positions they would need to be in for such an order to be executed.” Here again, the second reply understands “ability” in a way that takes account of circumstances. So far, so good. But suppose the admiral were to say, “No, I was completely incapable of giving such an order. For if I had given that order, there would have been a naval battle yesterday, and as you can see, there was no such battle.” In that case, I think we would have to conclude that the admiral was joking—or perhaps, that he had taken up philosophy! I trust the point is clear: while there is indeed more than one sense of “ability,” there does not seem to be any ordinary sense of that word in which this latter statement on the part of the admiral would make sense. But that is what would be needed for Taylor’s premise P5 to pass muster before the bar of ordinary language.
However that may be, Taylor has another arrow in his quiver. He quotes Saunders’s argument (given above) about knocking on a thin wooden door, which concludes that “I may decide not to knock and the door may not shake, but it does not follow that I did not have it in my power to knock.” Taylor replies, “This is initially most persuasive, but to see how it fails, we need only to produce the same argument to show that I have it within my power to make something happen in the past which did not happen. Thus,
My reading a certain kind of headline is a sufficient condition for there being a naval battle yesterday. Hence there being a naval battle yesterday is a necessary condition for my reading such a headline. But the occurrence of such a battle is not a necessary condition for my ability to read such a headline. (If it were, then my mere ability to read such a headline would suffice to make the naval battle occur yesterday.) I may decide not to read such a headline and the battle may not have occurred yesterday, but it does not follow that I do not have it in my power to read such a headline.
Now if Saunders’s argument against my fatalism is a good one, this argument refutes fatalism with respect to the past, for it is the same argument, with only a difference of tenses. But this argument obviously does not refute fatalism with respect to the past, nor does Saunders’s argument refute it with respect to the future.
(Taylor 1962B, 59)
Saunders, however, was unconvinced by this. Here is his rejoinder:
Taylor wrongly takes me to argue that, even though a door does not shake, I did have it in my power to make it shake (by knocking upon it). This leads him to say that the same sort of argument will show that I have it in my power to make something happen in the past even though it did not happen. But I argued, not that I did have it in my power to make the door shake, but only that it does not follow from the door’s not shaking that I did not have the power to make it shake. Thus I am not thereby committed to arguing that I have the power to make an event happen in the past. Let me, then, rephrase Taylor’s charge so that it will apply to my position: if the non-occurrence of an event in the future does not entail my lack of power to bring about that event, then neither does the non-occurrence of an event in the past entail my lack of power to bring about that event. So phrased, I must say that I agree, at any rate to this extent: it is not due to the non-occurrence of an event in the past that I lack the power to bring about that event.
(Saunders 1962, 67)
In his defense of Taylor, Steven Cahn notes Taylor’s contention that “if Saunders’s argument does indeed refute fatalism in respect to the future, then it also refutes fatalism in respect to the past.” He then cites Saunders’s reply (quoted above) but says, “this does not at all seem to refute Taylor’s charge.… Is there some actual difference between the past and the future which would account for making this distinction? If Saunders wishes to answer Taylor’s charge he must point out such a difference, for it is the denial of such a difference upon which Taylor’s argument essentially rests” (Cahn 1964, 99–100).
As Cahn correctly observes, Taylor is challenging Saunders to point out some relevant difference between what we have termed Argument I, which establishes fatalism concerning the past, and Argument II, which establishes fatalism concerning the future. And Cahn is right: Saunders offers no such difference. But what Cahn apparently fails to see is that Saunders has a different response to Taylor’s challenge. Rather than providing a way to distinguish between Argument I and Argument II, Saunders concludes that both arguments are unsound. (Apparently he is well advised to do so, since he rejects Taylor’s premise P5, which is an essential part of both arguments.) Saunders says, furthermore, that he is not concerned, in his argument against Taylor, either to refute or to establish “fatalism concerning the past”—nor, for that matter, is he concerned to refute fatalism concerning the future. What he is concerned to do is to refute Taylor’s argument for fatalism concerning the future, and this he is satisfied has been successfully done. If the question were to arise, why we cannot bring about past events, some other approach would be required.11 An important point concerning this exchange, by the way, is that both Taylor and Cahn seem to assume that Taylor’s opponents must undertake the task of refuting fatalism—that is, of establishing that we do in fact have free will in the sense in which the fatalist denies this. But of course, this is an enormous task; the controversy has already raged for two millennia and shows little sign of abating. Fortunately, the opponent of Taylor’s argument need do no such thing. For an opponent such as Saunders, the task is merely one of refuting that argument—a task Saunders takes himself to have successfully performed.
Nevertheless, Cahn can still argue that Taylor’s opponents need to provide some explanation for the difference in the apparent cogency of the two arguments. “The power of Taylor’s approach is that the first argument seems acceptable until the second argument is produced. Then the first argument loses its appeal” (Cahn, private communication). This does seem to be a relevant challenge; I propose to meet it by elaborating slightly Saunders’s example of knocking on a door. This example will also help us see more clearly why Taylor’s premise P5 is defective. So here is the example: You and Saunders together came to visit a friend’s apartment, and Saunders pushed the doorbell button several times with no response. He turned away in disappointment, and you followed him out of the building. But then it occurred to you to ask, “Don’t you think you ought to have tried knocking on the door? I didn’t hear the doorbell actually ring; it may not be working.” He responds, “No, I was quite unable to knock on the door. For a necessary condition of my knocking on the door is that the door should shake—and as you could see, it did not shake the whole time we were there.” Of course this statement is absurd, but why is it absurd? A very little reflection should reveal the reason: Although the door did not in fact shake, it was fully within Saunders’s power to make it shake, simply by knocking on it. And this suggests the needed revision to P5: “No agent can perform any given act if there is lacking, at the same or any other time, some condition necessary for the occurrence of that act, unless it is also in the agent’s power to bring about that necessary condition.” It is, I think, completely obvious that this, rather than the original P5, is the correct principle—but this principle will fail entirely to yield Taylor’s fatalistic conclusion. Furthermore, the expanded example helps us understand why Taylor can make his (specious) claim that P5 is almost universally accepted. If we are inclined to accept it, this is because we do not ordinarily think of something like the door’s shaking as a condition of someone’s knocking on it (even though it is that, given Taylor’s definition of “necessary condition”). Rather, we would think of the door’s shaking as a consequence of the knocking. The “almost universal acceptance,” insofar as it obtains at all, is based on an understanding of P5 that is different than the one Taylor requires for his argument.
At this point considerations of space prompt us to move on, leaving undiscussed many more twists and turns in the debate over Taylor’s argument. So we turn to Wallace’s evaluation of the debate and of the objections to Taylor that had appeared in the literature. His comments on those objections occupy only a small part of his thesis, but they are significant because they have a bearing on his claim to have offered new objections that are more successful than those made previously. Many of his remarks echo replies already offered by Taylor and by Cahn, but one point that calls for special mention12 is Wallace’s diagnosis of (what he takes to be) the failure of Saunders’s objections.
It is important to see why Saunders’ seemingly plausible objections do not really succeed in refuting the fatalist. They amount to the claim that Taylor’s argument has implications which go against our intuitions about the world and about language. But see that the fatalist does not share our intuitions. He has metaphysical intuitions of his own about the way the world operates and the way language ought to be used to characterize those operations. He also has an argument for his intuitions here, Taylor’s. Because intuitions are obviously not refutations, mere claims that the premises or conclusion of the Taylor argument has counterintuitive implications or requires counterintuitive reasoning of some sort cannot by themselves refute the argument.
(Wallace 2011, 155).
Unfortunately, this passage contains multiple confusions of the sort we have already seen in previous answers to objections. First of all, it is not at all incumbent on the critic to refute fatalism—that is, to show that fatalism is false. The critic’s task is merely to refute Taylor’s argument. Intuitions can very well contribute to this in a major way, by showing that the near-universal agreement claimed by Taylor for his premises is a sham; in order to arrive at his conclusion, he must understand the premises in a different way than any that would be acceptable to the philosophers he is claiming in support. Furthermore, Taylor’s argument has force in overruling the intuitive objections only if the argument is based on premises that really can claim widespread acceptance. But some of the objections show that it is very doubtful that such a claim can be made on behalf of the premises as Taylor understands them.
However this may be, Wallace is very clear about the nature of his own response to Taylor:
where most have tried to justify [their] rejection by disallowing one or more of the presuppositions that serve as the explicit or implicit premises of Taylor’s argument, here I am going to try to bend over backwards to accept Taylor’s premises, to grant him everything he seems to want in the argument, and then to show that the conclusion he desires still does not follow validly from that argument. This is the project in outline.
(Wallace 2011, 151)
This is admirably explicit; we need to see how the plan is executed.
The core of Wallace’s response to Taylor consists in a formal logical system, “System J,” which was devised in order to address situations such as those involved in Taylor’s argument for fatalism. It should be said that System J was not a solitary accomplishment on Wallace’s part. He consulted extensively in setting it up, but clearly the initiative and most of the energy and effort came from Wallace.13 There is not the space here for a full treatment of System J (that would require an entire article by itself), but I will try to give enough of an account of it to enable the reader to see how it addresses Taylor’s argument.
The purpose of System J is to give an account of “physical-modal” propositions; crucially, these propositions speak about what is physically possible or impossible at a time, given the physical situation as it obtains at that time. (It is assumed that the laws of nature are those that hold in our actual world.) Wallace illustrates the difference between this sort of modality and other kinds with a series of examples: “It is not possible for me to be both a human being and a quartz crystal”—this is logical impossibility. “It is not possible for me to travel faster than the speed of light”—this is physical impossibility simpliciter. “It is not possible for me, now in Champaign, Illinois, to be touching a building in Massachusetts thirty seconds from now”—this is physical impossibility given the constraints of time and situation (Wallace 2011, 149). It is this latter sort of modality with which System J is concerned, and the familiar “□” and “◊,” as used here, will be taken to refer to this sort of modality.14 A typical proposition of System J has the form “tm ◊ tn E,” where E designates a kind of event, and “m” and “n” are temporal indices; the proposition states that “At tm it is possible that E occurs at tn.” It is important that “n” and “m” may have either the same or different values; this is because the truth value of “◊ tn E” may vary, depending on the time at which the possibility in question is evaluated. Once again, Wallace offers a helpful pair of examples:
In “It couldn’t rain last night; last night a high-pressure ridge was keeping all rain-clouds away,” we are evaluating the modal character of rain-last-night in light of the conditions we know to have obtained last night. But in “It can’t have rained last night; there are no puddles on the sidewalk this morning,” we are evaluating the modal character of rain-last-night quite obviously in light of the puddle-free conditions we know to obtain now.
(Wallace 2011, 173)
It is important to realize that only the first of these two sentences says anything about whether or not rain was possible last night.
Wallace develops his case against Taylor by setting out what he terms the “Taylor Inequivalence” (Wallace 2011, 159), an inequivalence between two propositions that can be symbolized as follows:
(A) t2 ~ ◊t1 O
(B) t1 ~ ◊t1 O
Here “O” represents the event of the admiral’s giving order O (the order that would result in a naval battle),15 t1 is the time immediately before such an order would have been issued, and t2 is a time the following afternoon, when the battle, had it occurred, would have been in progress. So the two propositions, spelled out in English, are as follows:
(A′) As of t2, it is impossible that order O is given at t1.
(B′) As of t1, it is impossible that order O is given at t1.
Now, Wallace makes three claims about these two propositions. First, the two propositions are not equivalent: (B) entails (A) but not vice versa. Second, what Taylor needs for his argument is (B); (A) does not suffice. But third, only (A) can be properly derived, so Taylor’s argument fails. I believe Wallace is correct in all three claims. (A) describes the situation as we “look back” from the afternoon of the second day, when no battle has occurred. We conclude, quite properly, that it cannot be the case that the admiral gave order O on the previous day, because if he had done so there would be a battle in progress, and there is no such battle. But this apparently has no bearing on the admiral’s power or ability to give such an order at t1. (B), on the other hand, describes the situation at t1 and asserts that at that time it was impossible for order O to be given—but if that was impossible, then the admiral lacked the power or ability to give such an order, which is precisely the fatalistic conclusion. If we follow Wallace’s discussion of the situation (which on the whole is quite persuasive), I believe we will conclude that he has established his three claims. Furthermore, the same result can be derived more formally from the full, “official” exposition of System J (Wallace 2011, 190–198), which for reasons of space we can’t go into here.16
So far, then, Wallace is doing well. But what of his claim that his objection to Taylor is successful where others have not been? Or his claim that, rather than contesting Taylor’s premises, he has granted the premises and shown the argument to be invalid? The first thing to notice is that the “Taylor Inequivalence” is extremely similar to the objection first posed by Saunders. According to Saunders, we recall, Taylor
sees that (1) no agent can perform an act if a necessary condition for that act is lacking. But this means only that (2) as a matter of logic, if condition x is necessary for the occurrence of act y and x is lacking, then no agent performs y.
This corresponds closely to proposition (A): Since no sea battle has occurred, we conclude that it cannot be the case that the admiral gave order O. However, Saunders goes on,
Taylor may then have equivocated with respect to “can,” taking it this time to mean the same as “has the power to.” In this way he may have become convinced that no agent has the power to perform an act if a necessary condition for that act is lacking.
This conclusion, which Saunders takes to have been illegitimately inferred, is essentially the same as proposition (B), which states that at the time when the order would have been given it was impossible for such an order to be given and therefore not in the admiral’s power to give it. The two objections are, if not strictly equivalent, nearly enough so as to make little difference.
Now, if Wallace’s objection and the one offered by Saunders are virtually the same, Wallace can claim to have succeeded where Saunders failed only if he has some new, decisive support for his objection that was not provided by Saunders. And indeed, he seems to think that this is the case. With respect to a “physical-possibility-structure diagram” on p. 186, he claims that it “allows us to justify this claim [viz., about the Taylor Inequivalence] in something more than an intuitive way” (Wallace 2011, 187). Is Wallace correct in this claim? In one way, he is. Certainly the diagram in question and System J as a whole flesh out the objection to Taylor’s argument in a way that Saunders never did. However, Wallace may be overlooking the point that formal logical systems rest on intuitive foundations. At least, this is true of the systems we seriously rely upon to guide our thinking. If we couldn’t see intuitively that modus ponens is a valid form of inference whereas affirming the consequent is invalid, we would have no basis for using the propositional calculus as a guide in our reasoning. And the same is true of System J; Wallace’s explanation of and advocacy for System J rely heavily on examples in which he appeals to our logical intuitions. So while that system does a good deal to work out systematically the sort of reasoning involved in the objection to Taylor’s argument, it by no means manages to escape from the ultimate reliance on intuition. But perhaps System J is more effective in spelling out those intuitions and enforcing their consequences? This may possibly be so; whether Taylor would have been convinced, had he been able to study System J, must remain an unanswered question.
To this extent, then, Wallace’s claim to have succeeded where others had failed must be left unresolved. However, the same cannot be said about his other claim, to have granted Taylor’s premises and shown that the argument is nevertheless invalid. In his extensive discussions it is entirely clear that he has failed to grant Taylor’s premise P5 in the sense in which Taylor understood it (Wallace 2011, 168–170). In fact, if we grant that premise Taylor’s argument can easily be shown to be valid—though in the end this does him little good, since the premise so understood is false.17
How then shall we assess Wallace’s response to Taylor’s argument? On the one hand, his creation of System J, and his articulation of his reply to Taylor in terms of that system, must be recognized as a splendid achievement, one that is not diminished by the help he received in formulating that system. (Any philosopher attempting such a task, of whatever training and experience, would be well advised to confer and consult with colleagues in the process.) On the other hand, his claim to have pointed out a fundamentally new objection, quite different from those made previously, and his claim to have granted Taylor’s premises and shown his argument to be invalid cannot be sustained. But there is one more thing for which he deserves credit: he realized, in the end (Wallace 2011, 212–213), that the real project was not to “refute fatalism” but simply to turn back Taylor’s argument; there remains the opportunity, for Taylor and other fatalists, to present a different sort of argument for fatalism should they choose to do so.
What does all this tell us about the overall philosophical climate during the years when Taylor’s argument was being debated? Probably a number of things, but what stands out to me is the lack of a developed practice of modal reasoning. That is not to say that philosophers were unaware of the notions of possibility, necessity, contingency, and the like; of course they were aware of such things. But in those years of the 1960s, philosophy was just beginning to rid itself of the graveclothes of logical positivism, and modal reasoning was far from the center of attention. It was widely assumed that the only respectable notion of necessity was that of analyticity—and Quine, notoriously, did a great deal to undermine even analyticity. The classic work on modal logic by C. I. Lewis was already available, but modal reasoning did not enter the mainstream philosophical dialogue until about 1970, through the work of Kripke and others. (Wallace cites Kripke and Montague in developing his own system—see Wallace 2011, 177–182.) Wallace was very much on target when he concluded that a detailed, explicit treatment of the relevant sort of modality was called for, even if, in the end, he only systematized notions that others had previously put forward in a more inchoate, less systematic form.
What has become of these topics today, a quarter-century after Wallace’s thesis? Taylor-style arguments for fatalism do not seem to be much in evidence, but in other respects the issues raised here remain very much alive. The question of truth values for future contingents comes to the fore in the context of the philosophy of time known as presentism: what exists (at any given time) is what exists now, and the truth-makers for future contingent propositions do not exist. Furthermore, insofar as the states of affairs are genuinely contingent, it is not yet decided whether these truth makers will exist or not. For this reason J. R. Lucas termed such propositions “valedictory truths”—they can be recognized as such only retrospectively, from the standpoint of a later time when the events either have or have not occurred. Many have concluded that such peculiar “truths” as these do not deserve the name, and they have opted for truth-value gaps where future contingents are concerned.18
On the other hand, the philosophy of time known as eternalism or four-dimensionalism (also the “stasis theory”) offers the prospect of a revival of fatalism. According to this view, all the events of all times coexist in the four-dimensional spacetime continuum, and there is no such thing as a privileged present moment that is “now.” The four-dimensional continuum by definition cannot change; such change as exists consists in the fact that different states of affairs obtain at different temporal indices within the continuum. It would certainly seem (though this is sometimes contested) that, on this view, there is no room for the “alternative possibilities” that are essential for free will as understood by Taylor, Wallace, and in general by advocates of libertarian free will. Four-dimensionalism, then, offers the fatalist everything she needs; no further argument is required. The threat of fatalism has by no means gone away.
NOTES
My thanks to Steven Cahn for his assistance at a number of points during the preparation of this paper. He is not, of course, responsible for my conclusions or for my remaining mistakes.
1. Raziel Abelson (1963, 79) gives a “minimalist” interpretation of P6, as asserting “the atemporality of the laws of nature.” On a maximalist interpretation, P6 implies that an occurrence can just as well be rendered impossible by a later event as by an earlier event—an explicitly fatalist implication. And there are other possibilities.
2. Clearly, allowing the claims here concerning necessary and sufficient conditions requires a bit of idealization. We are to assume, among other things, that there is zero probability of a breakdown of the presses, as well as a zero probability that some misguided humorist will print up a paper with a fake headline as a practical joke. Such idealizations will typically be required in the examples used; in general we will let them pass without notice.
3. To save space, I am paraphrasing Taylor’s argument here; the reader may be assured that I do not distort his intent or the logic of the argument.
4. “Apart from subjective feelings of our power to control things, there seem to be no good philosophical reasons against this opinion, and very strong ones in its favor” Taylor 1962a, 51).
5. A reader of the manuscript correctly points out that fatalism is often distinguished from determinism, with fatalism involving some additional consequences that are not implied by determinism as such. Taylor’s argument, however, is really an argument for determinism, so for purposes of this essay I treat the two as equivalent. (As the text points out, Taylor in his rhetoric invokes some of the connotations of “fatalism” that are by no means supported by his argument.)
6. Once again, in order to save space I am omitting Cahn’s elegant and precise formal presentation of his objection, which can be found in Cahn (1964, 103–105).
7. See Taylor (1963, 1974). There is a striking difference in the presentation of the argument for fatalism in the two editions. The first edition follows closely the exposition in the original article and points to the rejection of P1 (bivalence) as the most promising way to escape from the fatalistic conclusion. The exposition of the argument is quite different in the second edition, where Taylor describes the rejection of bivalence as an “arbitrary fiction, resorted to for no other reason than to be rid of the detested doctrine of fatalism” (1974, 70). It may be, however, that in the second edition Taylor was being deliberately provocative, in an attempt to draw the reader into the argument and that his apparently favorable view of fatalism does not reflect his considered opinion.
8. Cahn (1967, 86n) proposed a revision of Taylor’s P5 that, he claimed, avoids the difficulty stated by Cahn and still allows Taylor’s argument for fatalism to go through. Taylor never responded to this suggestion, and it was never considered by Wallace, so it will not be discussed further here.
9. “We shall say, therefore, of whatever happens, that it was going to be that way. And this is a comfort, both in fortune and in adversity. We shall say of him who turns out bad and mean, that he was going to; of him who turns out happy and blessed, that he was going to; neither praising nor berating fortune, crying over what has been, lamenting what was going to be, or passing moral judgments” (Taylor 1974, 71). Wallace does not seem to have considered the version of the argument in the second edition.
10. Later on, Saunders states, “[Taylor’s] position amounts to nothing more than the suggestion that we cease to use ‘in one’s power’ in the ordinary ways, and begin to use it in his way.… Taylor has, in effect, recommended that we add a meaning rule to those which already govern ‘in one’s power,’ viz. the rule: if it is in one’s power to bring about the situation then that situation occurs” (1962, 66).
11. Saunders gives what is apparently his own answer to the question: “I have no such power because we so use our language that it is false or nonsense to say that one has the power to bring about any event whatever in the past” (1962, 67). Whether this answer is adequate will not be discussed here.
12. There is one other point that perhaps deserves passing mention, since it may account for Wallace’s belief that he has shown Saunders’s objection to Taylor’s argument to be unsuccessful. Referencing pp. 64–66 of Metaphysics, Wallace states, “Taylor maintains that the occurrence of the battle tomorrow is obviously a necessary condition only of my giving the order today, not of my having the ability to give the order today, for, were the latter true, my mere ability to give the order today would by itself be a sufficient condition for the occurrence of the battle tomorrow, which looks to be absurd” (2011, 152). Now, if Taylor had indeed said this, that would constitute a major blunder on his part because it would immediately render his argument invalid. The mistake, however, is Wallace’s; no statement can be found on those pages supporting the attribution of this view to Taylor. (Perhaps Wallace was misled by a passage in which the view is attributed by Taylor to his opponents.)
13. The chief collaborator was Jay Garfield, then on the faculty of Hampshire College, who was asked by Willem de Vries, Wallace’s thesis advisor, to confer with Wallace. Here in part is Garfield’s description of their meetings: “It is hard at this point to say with any certainty who introduced what ideas into those conversations, and would probably have been difficult to do so at the time. These were discussions among colleagues, not ordinary supervision meetings between teacher and student.… I am pretty sure, but not positive, that I proposed system J and the broad sketch of its semantics (that is probably the reason David calls it J); I am also pretty sure, and a little more positive, that as soon as I did, David ran with it and showed both how it solved the central problem of demonstrating the invalidity of Taylor’s argument… and how treating time and physical modality this way makes sense of a number of other puzzles about physical modality and time. His philosophical instincts were sure; his thought was precise. The thesis came together in a matter of a few weeks” (Garfield 2011).
14. In Fate, Time, and Language “□” and “◊” are printed with a strikethrough to distinguish them from other sorts of modalities. In this essay they will be used only to refer to Wallace’s physical modalities, so there will be no ambiguity.
15. Wallace develops a new example of his own, concerning a group of terrorists who might or might not detonate a nuclear device on the Amherst College campus. For present purposes, I think it is simpler to stay with Taylor’s original example.
16. There is an error in the semantic rules for System J, as printed on p. 191 in the first printing of Fate, Time, and Language. In Rule 2, the two disjunction signs (“∨”) need to be replaced with conjunction signs (“∧”), and the same should be done with the one disjunction sign in Rule 4. Rule 2, written out in English, says in effect: “At tn, it is possible that p is true at tm if and only if there is a causal path jx and a world W′ such that W (the actual world) at tn lies on jx OR W′ at tm lies on jx OR p is true in W′ at tm.” Rule 4 says, “At tn, p will be true in the future if and only if there is a causal path jx OR there is a time tm such that W (the actual world) at tn lies on jx and W at tm lies on jx and tm is later than tn and p is true in W at tm.” In each case, it is evident that “OR” needs to be replaced with “AND” for the rules to make sense. (I have been informed by Steven Cahn that the errors do not occur in Wallace’s original manuscript. The mistakes were printer’s errors and were corrected in the e-book version and in all subsequent printings.)
17. Wallace’s mistake here may be attributable to his misreading of Taylor’s remarks in Metaphysics; see note 12 above.
18. This question has attracted interest especially among the adherents of “open theism,” a movement in philosophical theology that seriously embraces a revised conception of divine omniscience similar to the one suggested by Taylor in his 1957 article. (The movement is not, however, directly indebted to Taylor.) For discussion, see Tuggy (2007) and Rhoda (2011).
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