which has the form in the logic of J:(b”) to~◊tnE (where o = (n + one day)).
And (b”) is true iff no situation yesterday in which an explosion took place is physically compatible with the low-radiation situation in the actual world today; that is, if there is no path jy from the actual world today to a world yesterday in which there occurred an explosion.
(a′”) and (b”) are clearly compatible in some structure Φ, namely that Φ in which there is a path jx from the actual world a few moments before yesterday to a possible world contemporary with yesterday in which there was an explosion, but no path jy from any yesterday-world in which there occurred an explosion to the actual low-radiation world today. This particular Φ is precisely the structure visually represented in the diagram-analysis of the terrorist case on page 47 [this volume, page 186—eds.]. What we now have are rules and translation-procedures that formalize the sort of common-sense analysis captured by that diagram.
The reader should be able to see that precisely the same formal procedure can be used to demonstrate the Taylor inequivalence, the semantic difference between (t4∼◊t3O), (t3∼◊t3O) and (t2∼◊t3O), by demonstrating the compatibility within the ∅-structure of the truths now of both:(c) Yesterday it was possible for the admiral to issue order O.
and(d) It is not possible today that the admiral did issue order O yesterday.
This compatibility can obviously be demonstrated in exactly the same way that (a) and (b) were shown to be compatible.
The above formal characterization of the system this essay proposes for properly understanding physical modality may serve to make apparent what is probably for many philosophers the most radical and least intuitive feature of that system. It is that it allows for no alternative presents in the context of a given actual present. While there could easily be on my account alternative pasts—pasts which did not in fact occur but whose occurrence would be physically, causally compatible with the situation that obtains in the actual world now—and while there definitely are on my account alternative futures—alternative future-situations all physically, causally compatible with the features of the situation that obtains in the actual world now—there are here really no “alternative presents,” no “worlds” contemporary with the actual world now, and with at least one feature different from the features of the situation that obtains in the actual world now, which are nevertheless physically compatible with the situation that obtains in the actual world now. Whereas in no recognized modal system dealing with alethic modalities is (p → ~◊~p) a valid inference, in the system I propose for dealing with physical modalities: V-3) ((tnp → (tn~◊~tnp))
and soV-5) ((tnp → (tn□ tnp))
are valid.
This feature may appear to be objectionable in two ways. First, it may appear to accord exactly with the fatalist’s thesis that everything that occurs occurs necessarily and that everything that does not occur cannot possibly occur; that is, it might be claimed that in developing a semantics to defuse Taylor’s semantic argument for the metaphysical doctrine of fatalism, I have somehow semantically stumbled into accepting precisely the most distasteful metaphysical claims of the fatalist. A related but more general objection would be that the feature does violence to our most basic modal intuitions. We tend to understand possibility and actuality to be objective features of our lives, and our lives are lived in the present. Holding out the promise of “possibility-in-the-future” does not seem terribly comforting in light of system J’s apparently entailing that once we actually get to any point in that future, possibilities for alternative sorts of events and states of affairs, even those caused by us, melt away. Regardless of any metaphysical or ethical objections, philosophers schooled in modal logic are apt to regard any sort of system in which p seems to entail necessarily-p as at best empty and at worst crazy.
I believe that both sorts of objections can be convincingly rebutted. An answer to the first will lead directly into an answer to the second. In answer to the objection that I have somehow bought fatalism as a consequence of system J, I say that it is simply not true. Yes, in system J, (t2p → t2~◊~t2p) is a valid inference, but this is not a fatalist inference. A fatalist inference would be something like (t2p → t1~◊~t2p), and this is not a valid inference in J. As Richard Taylor characterizes fatalism, “A fatalist is best thought of, quite simply, as someone who thinks he cannot do anything about the future.”37 Thus the fatalist’s core assertion is something like: “Everything that is going to happen must happen; it is not now possible for anything to happen except what is actually going to happen.” The assertion licensed by J’s supposedly distasteful feature, on the other hand, is merely: “Given a situation actually obtaining now in which something is happening, there is no situation that could be obtaining now, and is physically compatible with the situation that actually obtains now, in which that thing is not happening.” And this is not fatalism; I happen to think it’s simply a logical consequence of a thoroughly common-sense way of understanding physical possibility.
Nor does this apparent denial of any mutually accessible alternative presents (the denial that there are now any different ways the world “could” be now, given the way the world actually is now) mean that such statements as “It is physically possible for p to be occurring now” are necessarily either false or meaningless at moments when p is not occurring. Quite to the contrary, I maintain that such statements can be true, but simply not in the context of the situation that obtains now. For example, it is as a matter of fact not raining right now. Consider the proposition: “It is possible for it to be raining now.” Where “possible” denotes physical possibility, I hold that the proposition is now neither meaningless nor necessarily false. But I do hold that the proposition: “It is possible for it to be raining now” is properly represented as actually containing two temporal operators. One operator designates the temporal location of the event the modality is asserted to range over. The other operator, which is actually suppressed in natural language, designates the temporal location of the conditions with which the given event is or is not compatible.
If “It is possible for it to be raining now” is to be true in the absence of rain now, the temporal location of the conditions with which rain-now is asserted to be compatible must be some point in the past of a path causally connected to the actual present. That is, if we’re now rainless, “It is possible for it to be raining now” really makes sense only if interpreted as: “The actual conditions in the world-n-units-ago are not physically incompatible with the occurrence of rain now,” or as: “n units ago it was possible that it would be raining now.” And a statement like: “It is not raining now, but it is possible for it to be raining now,” can make sense only if interpreted as actually asserting something like: “It is not raining now, but there was nothing in the actual relevant conditions n units ago that rendered it impossible that it could be raining now.”
Were the statement: “It is not raining now, but it is possible for it to be raining now” to be regarded as true in the context of the situation that obtains now, viz., an absence of rain, we would be committed to saying that the situation now, in which it is not raining, is somehow physically compatible with a situation-now in which it also is raining. That is, we would really be saying that it is physically possible that it is both raining here and now and not raining here and now. Needless to say, tn◊(p ∧ ∼p) is not derivable from the rules of system J, nor of course should it be. It thus looks to me as though the denial of any alternative presents in the context of an actual present, far from being absurd, actually avoids an absurdity. It does not, however, commit us to fatalism, for “alternative presents” are still possible with respect to and in the context of other situations-at-times in the future and past.
The center of my position here, and the way perhaps to convince remaining skeptics that system J is neither fatalistic nor at all modally counterintuitive, has to do with how I’ve defined and understood physical possibility. Again, I und
erstand physical possibility always to be relative to some situation-at-a-time. I understand it to be a relation of physical compatibility between situations, sets of conditions, joined in appropriate causal relations through time. This conception most closely resembles an epistemic-modal understanding of possibility in terms of coherent model-extension.38 The conception of possibility held by those philosophers weaned on a Kripke-/ Montague-type of modal model is very different, and this is perfectly understandable, given that Kripke/Montague semantic theories concern logical modalities, modalities which seem to be neither time- nor evaluative-context-sensitive. These philosophers understand possibility as a synchronic relation between cotemporal, ideally existing worlds. They think of “alternative presents” in terms of an infinitely long row of alternative logically possible worlds intersecting a horizontal time-axis at “now.” They think of evaluating “present possibilities” in terms of ranging along that row of simultaneous worlds, rather as one might scan a shopping list. When they feel they are being denied any alternative presents, these philosophers may be inclined to see their row of worlds suddenly collapsing into a single constraining actuality-turned-necessity, and so they may believe that violence is being done by system J to their intuitions about what is now-possible.
Their fears would be well-founded were system J to include as a feature the impossibility of alternative logically possible presents. But it includes no such feature, for the system is designed only to work toward a conceptual grasp and representation of what is physically possible, and physical possibility is, I have tried to argue, properly understood in a significantly different way from logical possibility. A “physical possibility,” if it obtains, always obtains, and is to be evaluated in the context of, an index and a situation. It is to be understood as a relation of causal, physical compatibility between indices and their respective situations through time. It is true that in system J what is now-actual is also now-physically-possible, but this is a physical, not an alethic, relation; it is to be understood as holding simply for the reason that what is actual now is, quite obviously, physically compatible with what was actual a few moments ago and gave rise to what is actual now.
So whenever it is asserted that this or that is “physically possible,” I hold that we are entitled and indeed required to ask in response, “Physically possible relative to what?” A physically possible situation is always physically possible relative to some other situation, and physical possibility is always to be understood as a relation of trans-temporal, causal, physical compatibility between situations.
So, to the philosopher who objects to the claim that, relative to a given actual present situation, there is no alternative physically possible situation, my challenge is this: Given a present situation that includes the feature p, give a coherent account of the claim that there could obtain at present a simultaneous situation, physically compatible with the one actually obtaining, that includes the feature not-p. Or, in roughly epistemic terms, given a model in which, say, it is at this moment raining, come up with a coherent, consistent extension of this model in which it is at this moment also not raining. I feel (I think with good reason) that this simply cannot be done. Nor need it be done, for system J captures the semantic implications of, and operates successfully in, a non-fatalist universe in which physical possibility is a real and prominent feature: it is simply a physical possibility relative to temporally distinct situations whose features often neither necessitate nor rule out alternative flows of events through time.
I also think a little reflection will reveal that system J actually captures rather nicely the thinking implicit in our everyday use of physical-modal language. If, for example, I am now on a train to St. Louis, and I say, “I could just as easily be on a train to Chicago right now,” I am talking about the compatibility of my presence on the Chicago-train with certain physical conditions. What conditions is it asserted to be compatible with? Certainly not the conditions that obtain right now, for then I would really be saying that I could be on both the St. Louis- and the Chicago-train at the same time. The conditions I am referring to here are most plausibly characterized as those obtaining at some point in the past—say, when I was on the train platform, between the entrances to the two trains, with the conductors shouting “All aboard!”, with me trying to decide where I wanted to go. It is just this sort of construal of “I could just as easily be on a Chicago-train right now” that system J captures, licenses, endorses ... a construal which neither necessitates my trip to St. Louis nor rules out my trip to Chicago, a construal and a system that demonstrably resists fatalism by allowing agents freedom of choice and action in the context of the physical-situations-at-times with which choices and actions in the appropriate causal relations.
VI. FURTHER APPLICATIONS OF SYSTEM J TO ANALYSES OF PROBLEMS INVOLVING PHYSICAL MODALITY AND TIME.
One of the truly ingenious features of Richard Taylor’s “Fatalism,” and a big reason why the paper has proved so resistant to effective criticism, is that it actually contains two situations, two arguments for two different kinds of fatalism, of which we’ve thus far examined only one. Taylor’s other argument—the first presented in his paper—concerns fatalism and the past.
Taylor argues sensibly that we are all “fatalists” with respect to the past, that we feel we have no control over or power to change what has already happened: “We all believe that it is not in the least now up to us what happened last year, yesterday, or even a moment ago.”39 This seems quite true, that we all think about the past the way a bona fide fatalist thinks about the future, as something not in our power actually to alter. Taylor offers an argument for the inescapable truth of fatalism-about-the-past. The argument is, in form, very similar to his argument for fatalism-about-the-future, the argument we’ve already looked at. Taylor claims that the two arguments in his paper are in fact more than very similar; he claims that: “The very reasons that can be given for being a fatalist about the past can be given for being a fatalist about the future.”40 And, indeed, many of the objections that have been advanced against Taylor’s future-fatalism argument can, as he cheerfully points out, be advanced with just as much force against his past-fatalism argument, a consequence that is obviously less than desirable. One advantage of system J and the tools of analysis it affords us is that we can use them to demonstrate the non-validity of the fatalism-about-the-future argument, while at the same time showing easily that Taylor’s past-fatalism argument goes through perfectly.
Taylor’s six presuppositions here are the same. The situation and argument are now this. Suppose I am about to sit down with a newspaper and read a certain sort of headline, in order to see whether a sea-battle occurred yesterday. Only if there was in fact a sea-battle yesterday will I read a battle-headline today. Call the occurrence of the battle yesterday B, and my reading the battle-headline today H. Only if there was not in fact a sea-battle yesterday, designated B′, will I read any other kind of headline, an action designated H′. As Taylor sets up this case, my doing H today will “ensure” that B obtained yesterday, will be sufficient for B, and my doing H′ today will be sufficient for B′ yesterday. (We might note with Professor Brown that here the “sufficiency-relation” is different from the sufficiency-relation that obtained in the other case between order O and battle B, but I’m going to ignore this, at least on the face of the matter.)
So (H → B) and (H′ → B′), and thus B and B′ are necessary for H and H′, respectively. We ask whether, as I sit down with the paper, it is now within my power to do H if I choose and also now within my power to do H′ instead if I choose. Not surprisingly, Taylor’s answer is no:VI-1) If B is true, then it is not in my power to do H′ (for if B is true, then there is, or was, lacking a condition necessary for my doing H′, namely the condition of there being no sea-battle yesterday.
VI-2) But if B′ is true, then it is not within my power to do H (for a similar reason).
VI-3) But either B is true or B′ is true (LEM/PB app
lies to a past-tense proposition).
VI-4) So either it is not within my power to do H, or it is not within my power to do H′.
Remember that the formal and structural features of system J allowed me to present a reasonable instance in which Taylor’s future-fatalism conclusion, that it is either physically impossible for the admiral to give order O or else impossible for the admiral to give order O′, did not follow. The neat thing is that the same features allows us to see that in this past-case the “fatalistic” conclusion does follow. Assume that there was in fact a sea-battle yesterday, and that, as Taylor cooks his example, the newspaper I am about to open is unprecedentedly efficient and conscientious (not to mention battle-fixated), and thus that only if there were no battle yesterday would there be anything other than a glaring battle-headline for me to do H′ with now.
Let’s see whether it is physically possible now for me to do H′ in the context of the occurrence of the battle yesterday, or rather whether the proposition:VI-5) Today~◊H′
is true. Well, see first that the proposition (VI-5) is as yet not well-formed in the language of J. It requires two temporal operators, for we can see that it contains an operator denoting physical possibility, and under the rules of J physical possibility is defined in terms of a diachronic accessibility relation between world-situations-at-times. This means that we can determine the truth-value of (Today~◊H′) only in terms of some earlier actual state of affairs that stands in an appropriate causal relation to (that gave rise to) the actual situation today. So we go back to the actual world, say, yesterday, to look for actual conditions that would rule out, be physically incompatible with, my doing H′ today. We’ve supposed that one feature of the actual world yesterday is B. Recall that B is the same as not-B′. Recall that, in Taylor’s example, only if B′ obtaine dyesterdaycan I do H′ today. Thus the absence of B′ yesterday represents perfectly a condition in the context of which H′-today is physically impossible, a condition with which H′-today is incompatible. Since under the rules of J the most plausible way to evaluate (Today~◊H′) is in the context of what actually obtained at some point in the past, and since we are using the point-in-the-past denoted by “Yesterday,” the rules of J license our transforming (Today~◊H′) into:VI-6) Yesterday~◊TodayH′ .