MT2) Today(∼B) → ∼◊(Yesterday(O))—or t2(∼B) → ∼◊(t1O).
This essay will argue that MT1 and MT2 are not equivalent, that MT1 → MT2 but MT2 ↛ MT1. It will argue further that Taylor’s situation and argument, under their very most charitable reading, do allow us to derive MT2, but that under no plausible analysis do they allow us to derive MT1. It will argue further that Taylor’s really interesting mistake in his argument for fatalism lies in his equivocating (unconsciously or otherwise) these two tensed physical-modal entailments, in believing and asking us to believe that he has shown that MT1 is true when he has really shown only that MT2 is (or might be) true. And whereas the valid derivation of MT1 from Taylor’s argument would, I believe, indeed entail fatalism, this essay will try to show that under the most plausible reasoning about the nature of physical modality, the valid derivation of MT2 from Taylor’s argument does not entail fatalism at all.
Taylor’s mistake rests on a very complex and interesting confusion. It takes us into a discussion of the semantic interactions between tense operators/time-markers and physical-modal operators, an area in which practically no work has ever been done. The interactions between times and physical modalities are so interesting and so complex precisely because, as I argued above, situational physical modalities vary with and depend on time and world-situations and sets of conditions in a way that, for instance, logical modalities do not. On an intuitive level we may say that this is so because what is situationally physically possible and necessary at any given moment is a function both of the general physical laws that characterize and govern the operations of our world, and of the particular set of relevant physical conditions and circumstances and considerations (we may call such a set simply a situation) that obtains at that moment ... and situations change from moment to moment. What it was physically possible for me to do in my situation three weeks ago—e.g., with respect to touching Johnson Chapel—is so obviously different from what it is physically possible for me to do in my Illinois-situation now, that the fact that the situational-physical-modal character of events and states of affairs is capable of changing over time seems to me really to require no further argument.
I will be making a case for the claim that situational physical possibility is best understood in terms of compatibility between sets of physical circumstances under unvarying natural laws. Since the sets of circumstances that bear on the modal character of an event or state of affairs usually can and do vary with the passage of time, and since thus the physical-modal character of some event or state of affairs may very well change from time-and-situation to time-and-situation, it is not surprising to find that scope problems of significant complexity arise when we try to formalize and interpret tensed physical-modal propositions. It is precisely such a semantic scope confusion that I think Taylor, offering a semantic argument for a metaphysical conclusion, has fallen for, and would have us fall for. An analysis that can show that MT1 and MT2 are not equivalent, why they are not equivalent, that MT2 and not MT1 follows from Taylor’s argument, and that only MT1 would actually force fatalism on us, should represent a significant step toward solving the Taylor problem.
Since there exists in the philosophical literature to date no real semantic device for handling the sorts of modalities we are concerned with here, this essay will attempt to introduce and formalize some of the features I believe such a semantic device should include. Intuitive use will be made of some aspects of the modal semantics introduced by Saul Kripke28 and extended by Richard Montague’s work in intensional logic.29 The tense-operator terminology will be that used by Robert MacArthur (following A. N. Prior) in his Tense Logic.30 The very simple tense-operator mechanisms needed for this essay’s analysis will now be introduced, alongside a quick demonstration of how important tense’s scope with respect to other operators can be for assigning interpretations and values to certain types of propositions.31
Tense-operators serve to remove tense from the interpretation of the main proposition to be evaluated and “pack the tense into the prefix.” F is the operator that denotes the future, and P is the operator that denotes the past. Fp translates: “p at some time in the future,” where the future is any moment or interval after the assertion of Fp. Pp means: “p at some point in the past,” with the past being any time before the assertion of Pp. Let’s now look at the following two propositions:III-3) P~p
III-4) ~Pp.
(III-3) means (III-3′) At some point in the past, not-p.
(III-4) means (III-4′) At no point in the past p.
(III-3) and (III-4) are thus clearly not equivalent. See for instance that (P~p) is perfectly compatible with (Pp), while (~Pp) and (Pp) are contradictory.
The scope of these indeterminate past- and future-operators relative to the scope of modal operators is just as important. Though we have not yet had a chance to examine the complex interactions between tense- and physical-modal operators, we can take a common-sense look at these two propositions:III-5) P(~◊p)
III-6) ~◊(Pp).
Let p be the proposition that Smith runs a mile in six minutes. Then (III-5) meansIII-5′) At some point in the past (it is not physically possible for Smith to run a mile in six minutes).
And (III-6) meansIII-6′) It is not physically possible that (Smith runs a six-minute mile at any point in the past).
Here (III-5) and (III-6) can easily be shown to be inequivalent. Suppose Smith actually did run a six-minute mile in high school, but that he was in an accident last year and has for months been a paraplegic. In this case, (III-5) would be true: at the point in the past designated “yesterday” it was not physically possible for the paralyzed Smith to run a six-minute mile. Yet (III-6) would now be false: Smith actually did run a six-minute mile at some point in the past, and though things are really more complex than I can represent at this point in the essay, it is transparently true that if something did happen in the past, it is physically possible that it happened in the past.
There is an obvious indeterminacy of reference to the F- and P-operators: they refer only to some point or interval in the future and past. Reference to specific intervals or moments is made possible by the introduction of metric indices. These are written as superscripts and permit reference to any specified moment by designating the number of some selected units away from the present the state of affairs named in the proposition is asserted to obtain. Pnp means: “P n units ago.” Fnp means: “P n units from now.” The asserted occurrence of p is thus fixed at some determinate point in the past or future (of course the same interpretive effect can be achieved with time-marker operators like t1 and t2, as long as some marker is designated “now”). A specificity in temporal reference is important for our purposes, because, as we’ll see, it renders even more complex the semantic analyses of tensed physical-modal propositions—it is just these complexities with which this essay is concerned.
IV. ARGUMENT FOR THE TAYLOR INEQUIVALENCE.
We’re now in a position to represent Taylor’s alleged equivocation more formally. Let the metric index here equal one unit, and let a unit be a day. Our rival contrapositives of the original (O → B) entailment become:MT1′) (~B→P1~◊(O))
andMT2′) (~B→~◊P1(O)).
To show that these two contrapositives of the original entailment do not yield equivalent results, I obviously need to show that the following two tensed physical-modal propositions are not equivalent:IV-1) (P1(~◊O))
andIV-2) (~◊P1(O)).
Demonstrating this inequivalence, in terms of both fatalistic implication and semantic evaluation, is thus clearly vital to my attempt to defuse Taylor’s argument. The demonstration proves so difficult precisely because no satisfactory system of rules—or device for representing such a system—concerning the scopes and interactions of tense- and physical-modal operators exists right now. I think I have three main tasks in this essay from here on out. The first is to show why, Taylor’s confusing case aside, we should want to say that (IV-1) is not equivale
nt to (IV-2). The second will be to introduce a rich and workable formal semantic device, which I call system J, for showing that (IV-1) and (IV-2) are indeed not equivalent. The third will be to defend this formal system J on its own merits as providing the tools for solving other vexing problems in the semantics of tense and physical modality, and as capturing nicely the ways in which we all actually do think and talk about physical possibility and time in the course of everyday life.
The first task will be undertaken by presenting what I hope will be a fairly compelling intuitive analysis of a situation of my own construction. Note, please, that it does not differ in any really significant ways from Taylor’s own example, except for the clarity of some of the claims involved.
Suppose that the day before yesterday a group of terrorists brought a completely assembled and fully functional nuclear weapon onto the Amherst College campus. Suppose further that yesterday the head terrorist, completely healthy and physically functional and not constrained in any way, sat next to the weapon, with his finger on the weapon’s fully functional triggering mechanism, all day, but did not press the trigger and so did not cause a nuclear explosion to occur, and so that a nuclear explosion did not in fact occur on campus yesterday. Suppose further, since we’re trying to be as Taylor-ish as possible, that a nuclear explosion on the Amherst campus yesterday would be an occurrence causally, physically sufficient for the presence of radiation in excess of, say 20 rads on the Amherst campus today:IV-3) □(P1(E)→ (R>20)).
Suppose further, as is I hope true, that there is not radiation in excess of 20 rads on the Amherst campus today:(IV-4) ~(R>20).
Since the explosion yesterday would have been sufficient for, “causally ensured,” (R>20) today, (R>20) today is precisely in Taylor’s sense “some condition necessary for” the occurrence of the explosion (E) yesterday. But is it not more appropriate, remembering Charles Brown’s argument, to say rather that the radiation today is a “necessary consequence of ” the explosion yesterday? This does indeed seem more appropriate: (IV-3) looks to be an instance of a (III-1)-, not a (III-2)-, type of entailment.
Does this fact have repercussions for the result of a modus tollens operation on (IV-3)? The answer is yes. What it means in a nutshell is that the denial of the consequent’s obtaining today means only that it cannot today be the case that yesterday the explosion did occur, not that it was the case yesterday that the explosion could not occur. We might say, more naturally if less perspicuously, as we enjoy the relatively low radiation today, that the explosion “can’t have” occurred yesterday, not that it “couldn’t” occur yesterday.32This is an absolutely vital sort of distinction. Compare the following sentences, and think of the kinds of “impossibilities” they really express: “It can’t have rained last night; there are no puddles on the sidewalk this morning,” vs. “It couldn’t rain last night; last night a high-pressure ridge was keeping all precipitation-causing clouds out of the area.” “He can’t have gone for a drive in his car an hour ago; the hood of the car’s not even warm,” vs. “He couldn’t go for a drive in his car an hour ago; an hour ago his car was broken.”
It seems reasonable to say that, given the way we use everyday modal language, “can’t have p” usually translates into the proposition ~◊Pnp, and that “couldn’t p” translates into Pn~◊p. I assert that the difference between the two types of propositions is enormous. Consider the terrorist case, with the low radiation today and so “necessarily” no explosion yesterday. For the purposes of argument, we may grant Taylor’s rather odd modal claims: that □(P1E → (R>20)), and so that □~(P1E∧~(R>20)), and so that when we acknowledge the truth today of ~(R>20), we are somehow justified in concluding that it is not physically possible that P1E and ~(R>20) are, as we have cooked the case, incompatible—physically incompatible—and of the fact that ~(R>20) obtains today.
So in this case we have granted everything Taylor would seem to want us to grant. But we are still able reasonably to deny the fatalistic conclusion. This is because we can point out that in the absence of the high radiation today we evaluate P1E’s possibility relative to what occurs now, today, at a time later than that designated by P1. We can say that this allows us to conclude only that, given what obtains today, it is not today possible that P1E. Were we, however, to say something different, that at P1 it was not possible for E to occur, we would be evaluating the possibility of E at and relative to P1, not at or with respect to any other time, viz., now. But it is this second sort of conclusion that Taylor seems to want us to derive from everything we have been willing to grant him thus far. It means basically that we would be saying that, given the set of circumstances that obtained yesterday, E was not physically possible yesterday. We would be saying not that it is not now possible that E occurred at P1, but rather that at P1 it was not possible for E to occur. And this would have as a consequence our buying the following: that yesterday, during the whole time the healthy and efficacious terrorist sat unconstrained with his limber finger on the fully functional triggering device of the fully operational nuclear weapon, it was somehow physically impossible for the explosion to occur. And this is clearly just plain wrong: I have constructed the case in just such a way that under any halfway-reasonable definition of situational physical possibility it is physically possible, at the time designated P1, for the explosion to occur at P1. And please see that if Taylor or Cahn were now to respond that, though the conclusion might seem absurd, it is what the argument forces upon us, we are now in a position to claim with some reason that it is not what the argument forces upon us at all. For it looks as though the terrorist case, with the low radiation today, allows us to conclude that:
but not that:
and that thus (IV-5) and (IV-6) are certainly not equivalent, and that thus the exactly similar (IV-1) and (IV-2) are not equivalent, and that thus MT1′ and MT2′ are not equivalent, and that thus the legitimate conclusion of Taylor’s argument can only be that, given the absence of a battle today, it is not today possible that I did give order O at P1, not that at P1 it was not possible for me to give order O if I chose to do so.
What accounts for the substantial difference between tensed physical-modal propositions like (IV-5) and (IV-2), on the one hand, and (IV-6) and (IV-1), on the other? It seems to be this. Remember that situational physical modalities (the truth-values of physical-modal propositions) vary with time and with the physical situations that obtain at different times. Therefore the evaluation of any physical-modal statement is going to be an evaluation relative to a time and to the physical situation obtaining at that time. Thus we may say that any physical-modal operator in a really well-formed physical-modal formula should appear within the scope of, and be evaluated in the context designated by, a tense-operator or time-marker specifying some time-situation index. When no tense-/time-operator appears to govern a physical-modal operator in a well-formed proposition, the relevant time-and-situation index of evaluation should be understood as an implicit “now.” Once this is understood, we can say that the time-and-situation relative to which a physical-modal proposition is to be evaluated is determined by the scopes of the explicit operators that appear in the proposition. If an explicit tense-operator or time-marker—Fn, Pn, tn—is given wide scope over a proposition containing a physical modal, this fixes the moment relative to which the modal is to be evaluated at the moment designated by the tense-operator. If, however, a tense-/time-operator is not given wide scope over the physical modal, if no explicit tense-/time-operator appears in a wff to range over the physical modal, this fixes the moment relative to which the modal is to be evaluated at the present—the time of the assertion of the proposition—and fixes the situation in the context of which the modal is to be evaluated at the situation that obtains now.33
That a physical-modal operator given explicitly wide scope, as in ~◊P1E, might bear on the modal character of an event or state of affairs asserted to obtain in, say, the past, matters not a bit (except that it makes analysis more confusing);
the moment at and with respect to which we evaluate the possibility that the past event did take place is in this case still now, and the situation in the context of which we evaluate the possibility that the past event did take place is still the situation that obtains now (not the situation that obtained at the time designated by P1, since P1 in ~◊P1E has scope only over an event, not over the possibility of the event). Again, the thing to see is that every properly used physical-modal operator appears, and is to be evaluated as appearing, within the scope of an index-specifying tense-operator (or time-marker); when no tense-/time-operator is explicitly designated, it takes as a default assignment the index “here and now.” The reader should be able to see that this perhaps strange-looking condition actually reflects the way considerations of tense, time and modality are used in our everyday thinking and speech. (For instance, 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.)
Fate, Time, and Language Page 17
