ACCIDENTAL NECESSITY AND LOGICAL DETERMINISM*
Journal of Philosophy 80 (1983): 257-278
Alfred J. Freddoso
This paper attempts to construct a systematic and plausible account of the necessity of the past. The account proposed is meant to explicate the central ockhamistic thesis of the primacy of the pure present and to vindicate Ockham's own non-Aristotelian response to the challenge of logical determinism.
Take some truth about the past, e.g., that Socrates drank hemlock. It is natural to believe that this proposition is necessary, i.e., no longer possibly such that it will be false. But just what kind of necessity are we dealing with here? It is clearly not logically, i.e., metaphysically, necessary that Socrates drank hemlock. Nor is this physically necessary, where a proposition is physically necessary just in case it is a law of nature. Of course, a causal determinist might contend that it is now causally necessary that Socrates drank hemlock, where p is causally necessary at t just in case, for some q (relevant causal conditions), q is true at t and it is physically, but not logically, necessary that if q is true, then p is true. But it should be clear that the sort of necessity in question here is independent of any special assumptions about causality. It attaches to the past simply in virtue of its being past.
Medieval logicians commonly called this modality necessity per accidens, i.e., accidental necessity. My goal in this paper is to construct a systematic and plausible account of accidental necessity. In so doing I will follow the lead of William of Ockham, who fashioned in rough outline a theory of per accidens modality which was explicitly intended to yield a non-Aristotelian response to the challenge of logical determinism.1 However, despite the fact that the recent literature on logical determinism contains a few detailed, as well as many superficial, discussions of the Ockhamistic position, no one has formulated a convincing version of that position.2 Specifically, /258/ the philosophers in question have failed on two counts. First, they have not articulated precisely the central Ockhamistic thesis of the primacy of the pure present. And, second, they have not drawn clearly the important distinction between the necessity of the past and causal necessity. These failures are all the more lamentable in view of the fact that the Ockhamistic response to logical determinism is actually much more attractive than its more popular competitors--or so, at least, I shall argue.
In section I of this paper I will first describe some general features of per accidens modality and then show how the most common construal of the claim that the past is necessary leads directly to a very strong argument for logical determinism. Then in section II will show that the Ockhamistic solution to this argument, with its insistence on the primacy of the pure present, has a firmer intuitive foundation than any other proposed solution. Next, in section III I will take up the neglected task of giving a precise analysis of the notion of the pure present, and then I will use this analysis to formulate an account of accidental necessity which thwarts the argument for logical determinism, but which, as I will show in section IV, is clearly neutral with respect to the debate over causal determinism.
The first thing to notice is that accidental necessity is as respectable and well-behaved a modality as logical, physical, or causal necessity. To make this clear I will begin with the simplifying assumption that all propositions are tensed.3 Though this assumption seems to me both natural and true, it is not crucial to my argument. But I will leave it to the friends of "tenseless" propositions to translate what I will say into their own idiom. The assumption in question has two consequences that will be relevant below. The first is that some logically contingent propositions may be true at some times and false at others. Examples are the present-tense proposition that David is sitting, the past-tense proposition that Plato taught Aristotle, and the future-tense proposition that someone will cook an omelet. The second consequence is that some present-tense propositions can be true at just one moment. Examples are the proposition that Mary is reading at T, and the proposition that T is present [or: that it is (now) T], where T is a single determinate moment of time. These propositions can be true only at T. /259/
Let me now list some of the basic properties of per accidens modality. First, a proposition that is necessary per accidens is, as the name suggests, such that its being necessary is an accidental feature of it. So only logically contingent propositions can be necessary per accidens or, consequently, impossible per accidens. This is a property that accidental modality shares with physical and causal modality as characterized above.
Second, as we should expect, a proposition's being necessary (impossible) per accidens is relative to a time, since a proposition typically becomes necessary (impossible) per accidens after not having been necessary (impossible). For instance, it is, let us assume, now necessary per accidens that Socrates drank hemlock, but this proposition was false when Socrates was a child. Similarly, it is now impossible per accidens that Socrates never drank hemlock, but this proposition was true when Socrates was a child. So accidental modality resembles causal modality and, arguably, physical modality in being time-relative.
From these first two points it follows that, for any moment t, logically contingent propositions may be divided into three jointly exhaustive and mutually exclusive groups, viz., those which are necessary per accidens at t, those which are impossible per accidens at t, and those which are neither necessary per accidens at t nor impossible per accidens at t. We can say that each of the members of the last group is temporally contingent at t.
Third, a proposition's being necessary (impossible) per accidens at a moment t entails that it remains necessary (impossible) per accidens at every moment after t. This, again, is what we should expect to be true of the necessity of the past. And since it seems logically possible for a proposition to be a law of nature at one time and not at some later time, this feature of accidental necessity distinguishes it from both physical and causal necessity. (This is an important point to which I will return below.) So some logically contingent propositions, e.g., that Socrates drank hemlock, are not now and never will be possibly false, and their negations are not now and never will be possibly true, where the impossibility in question is accidental impossibility. One corollary is that if p is necessary per accidens at t, then no one can have the power at or after t to bring it about that p is or will be false; and if p is impossible per accidens at t, then no one can have the power at or after t to bring it about that p is or will be true. In short, the unalterability of the past follows from its necessity.
Fourth, when we limit the consequents to logically contingent propositions, then accidental necessity, like other kinds of necessity, /260/ is closed under entailment.4 That is,
(A) If p entails q, and q is logically contingent, and p is necessary per accidens at t, then q is necessary per accidens at t.
Moreover, given what was said in the preceding paragraph, it is evident that the conjunction of (A) with the obvious truth that no one can have the power to make a logically necessary proposition false, entails:
(B) If p entails q, and p is necessary per accidens at t, then no one has the power at or after t to bring it about that q is or will be false.
(B) is unassailable. If p cannot be false at or after t, then no proposition entailed by p can be false at or after t--and so no one has the power at or after t to make such a proposition false. Likewise, it is easy to show that if p is impossible per accidens at t, then no proposition that entails p can be true at or after t--and so no one has the power at or after t to make such a proposition true.
What has been said so far provides us with a framework for talking about the necessity of the past, but it does not answer the question of just which propositions are in fact necessary per accidens at any given moment. And, of course, this is the heart of the matter. Some philosophers, appealing to the alleged possibility of time travel, have recently argued, in effect, that very few propositions are either necessary per accidens or impossible per accidens.5 For many true past-tense propositions are, they claim, at least conceivably such that someone may now have the power to make them false. For instance, a time traveler might now transport himself to Socrates' death scene and find himself in a position to prevent Socrates from drinking the hemlock. We now know, of course, that he will (did?) not exercise this power, but he may have such power nonetheless. However one reacts to such flights of fancy, their coherence invariably depends on further metaphysical assumptions, e.g., about the structure of time or the nature of persons, which most sober-minded thinkers would find outlandish at best. Though oddity /261/ does not entail falsity, it is at least fair to say that the philosophers in question have not won many converts.
In fact, the most popular rendition of the thesis that the past is necessary goes in just the opposite direction. Philosophers from Aristotle to Arthur Prior have, at least implicitly, accepted the following:
(C) If p is true at t, then the proposition that p was the case is necessary per accidens at every moment after t, and the proposition that p was never the case is impossible per accidens at every moment after t.
That is, if p is true now, then it will always be necessary afterwards that p was once true, and always impossible afterwards that p has never been true. And, the proponent of (C) contends, this amounts to saying, in possible worlds jargon, that, in every world just like ours up to and including the present moment t, the proposition that p was the case is true at every moment after t. Given (G), we can go on to state the thesis that the past is necessary succinctly as follows: for any p, if it is now the case that p was once true, then the proposition that p was true is necessary per accidens now; and if it is not now the case that p has never been true, then the proposition that p has never been true is impossible per accidens now.
The popularity of (C) forces us to acknowledge the initial plausibility of this conception of the necessity of the past. At the very least, there is no plausible alternative that stands out clearly. Yet, a moment's reflection reveals that the combination of (B) and (C) gives us all we need to construct the strongest possible (and, to my mind, the clearest possible) argument for logical determinism. In fact, I think it is fair to say that there is no strong argument for logical determinism which does not presuppose the truth of both (B) and (C). Take an arbitrary proposition describing what we would ordinarily consider to be a free action performed at a given moment, e.g., Katie's washing her car at some determinate moment T. Then we can formulate the deterministic argument as follows:
(P1) The proposition that Katie will wash her car at T is true now, long before T. (assumption)
(P2) So the proposition that it was the case that Katie will wash her car at T will be necessary per accidens at every future moment, including every moment that precedes or is identical with T. (from (P1)and (C))
(P3) But the proposition that it was the case that Katie will wash her car at T entails the proposition that if T is present, then Katie is washing her car. (assumption) /262/
(P4) Therefore, no one (including Katie) will have the power at or before T to bring it about that it is or will be false that if T is present, then Katie is washing her car. That is, no one will have the power at or before T to bring it about that it is or will be true that Katie is not washing her car when T is present. (from (P2), (P3), and (B))
Given (C), the move from (P1) to (P2) is straightforward. (P3) simply reflects the usual assumption that if it has ever been the case that p will be true at a moment t, then either p has already been true at t or p is true now (at t) or p will be true at t--depending on whether t is now in our past, our present, or our future. In short, if it has ever been the case that p will be true at t, then p is true whenever t occurs. But if this is so, then, given (B), the necessity of the past-tense proposition that it was the case that Katie will wash her car at T entails our inability to affect the present truth-value of the proposition that when T is present, Katie is washing her car. So (B) and (C) enable us to reason validly from the present truth of the proposition that Katie will wash her car at T to the conclusion that no one will ever have the power to bring it about that it is false at T that she is washing her car. (Notice that this is so regardless of whether the notion of power is given a libertarian or a compatibilist interpretation.) Further, this argument is perfectly general, since similar deterministic consequences follow whenever we substitute for the proposition that Katie will wash her car at T any other future-tense proposition whose present-tense counterpart can be true at just one moment.
There are only three philosophically interesting lines of response to this rather compelling argument. "Aristotelian" responses all deny assumption (P1), claiming either (a) that where p is a future contingent proposition, both p and its negation are neither true nor false, or (b) that where p is a contingent proposition, it is false both that p will be true and that the negation of p will be true. The first claim is commonly attributed to Aristotle, while Prior is responsible for the second claim.6 The fact that such claims have issued readily from the mouths of contemporary as well as classical philosophers should not blind us to how counterintuitive they are. Both (a) and (b) commit their proponents to saying, for instance, /263/ that even if the present-tense proposition that Katie is washing her car turns out to be true at T, it is still not true now (before T) that Katie will wash her car at T. But what else, we want to know, could the future-tense verb signify? When we begin to notice that these philosophers mean by 'will be true' what most of us mean by 'is now inevitable', it is hard to suppress the suspicion that they have merely changed the subject without helping us understand why we were disturbed by the deterministic argument in the first place. Moreover, the mere fact that we can construct formal logical systems in which (a) or (b) can apparently be accommodated without inconsistency is not sufficient to allay our discomfort.
A second line of response, suggested by Peter Geach in some recent work on divine omniscience, is to deny assumption (P3) on the ground that all assertions ostensibly about the future are really only about present intentions, dispositions, tendencies or trends.7 So, for instance, it might have been true before T that Katie was going to wash her car at T, even if the present-tense proposition that Katie is washing her car is false when T occurs. For she may have intended to wash her car at T, but then changed her mind. This response has more initial appeal than the first, since we often do use future-tense sentences, e.g., 'I will wash my car tomorrow' or (perhaps) 'Jones is going to do well on the upcoming exams', to express propositions about our present intentions or about ways in which the world is presently tending. Still, it seems reasonably clear that we also use sentences of this sort in ways which are not so readily amenable to such an analysis. When Katie, full of self-knowledge, ruefully admits "Though I now intend to quit smoking tomorrow, I probably won't," she is, for all her weakness of will, hardly in as peculiar a logical position as she would be if she were to say "Though I will quit smoking tomorrow, I probably won't." And when a latter-day Hobbes brashly predicts "Someday I will square the circle," we can be confident that he has uttered a falsehood even if we don't doubt for a moment his intention to make his prediction come true.
These brief and somewhat tendentious remarks are not meant to constitute a refutation of any of the positions discussed so far. I simply want to contrast their initial implausibility with what I take to be the initial attractiveness of the Ockhamistic alternative. It is, after all, hard to imagine that anyone would embrace either /264/ version of the Aristotelian response willingly, i.e., without being compelled to in the face of a very strong argument for determinism. And, perhaps to a slightly less degree, the same is true of the response adumbrated by Geach.
The Ockhamistic solution, put simply, is to deny the inference from (P1) to (P2) on the ground that (C), despite its popularity and prirna facie plausibility, is a needlessly and unacceptably strong explication of our pre-analytic beliefs about the necessity of the past. For, the Ockhamist claims, from the fact that it is true now before T that Katie will wash her car at T, it simply does not follow that the proposition that it was the case that Katie will wash her car at T is necessary per accidens at every future moment. And, in general, from the fact that it is the case before a given moment t that p will be true, it does not follow that the proposition that it was the case that p will be true is necessary per accidens at t and every moment after t. That is, it does not follow that in every possible world just like ours prior to t, it is true at t and every moment after t that it was the case that p will be true. The most pressing task facing the Ockhamist, then, is to explicate the phrase 'just like ours prior to t' in a way which is (a) strong enough to preserve the claim that the worlds in question share the same history at t and (b) weak enough not to engender deterministic consequences when combined with assumptions like (P1) and (P3).
Although, as we shall see, the detailed articulation of this position is rather complicated, the intuition which grounds it is the familiar, but often misunderstood, claim that a future-tense proposition is true now because the appropriate present-tense proposition or propositions will be true in the future. For example, the future-tense proposition that Katie will wash her car at T is true now because the present-tense proposition that Katie is washing her car will be true at T. But, as many an undergraduate will hasten to assure you, the converse does not hold. That is, it is false that the present-tense proposition that Katie is washing her car will be true at T because the future-tense proposition that Katie will wash her car at T is true now. So there is an asymmetric dependence of the truth-values of future-tense and, as we shall see, past-tense propositions on the future and past truth-values of the appropriate present-tense propositions. And, as I have argued elsewhere, this insistence on the centrality of present-tense propositions is the salient feature of Ockham's own account of the truth conditions for past-tense and future-tense propositions.8 However, this is not to /265/ say that the past and future are not "real," since the Ockhamist holds that every past-tense and every future-tense proposition is either true now (even if in principle unverifiable) or false now (even if in principle unfalsifiable).9 Rather, we can characterize the Ockhamistic position most accurately by the assertion that the pure present is metaphysically primary, since what is true at any given moment t is true at t because of what, at t, has been or is or will be purely present. With this insight in hand, the Ockhamist then substitutes for (C) the claim that p is necessary per accidens at t just in case p is a logically contingent proposition that is true at every moment at or after t in every possible world which shares all of our world's "presents" prior to t. And this, as I will show in more detail below, invalidates the move from (P1) to (P2).
As I noted above, however, the basic insight in question is often misunderstood. The reason is that the occurrences of the term 'because' in the preceding paragraph are frequently taken to signal a causal dependence of the past and future on what has been or will be purely present. Ockhamists themselves sometimes make this mistake and then sit in embarrassed silence when badgered with questions like: How can the future truth of a present-tense proposition have causal effects now? And, even if it can, doesn't this in itself show that the future is already 'real' in a sense which has deterministic consequences? The inability of the Ockhamists in question to give convincing replies to these queries accounts in part for the specious plausibility which has been assumed by the other responses to the argument for logical determinism.
The correct reply, however, is simply to deny that the asymmetric dependence in question is causal. It may seem evasive to insist that this 'temporal' dependence is sui generis, but many philosophers today accept, willingly or not, the similar claim that causal dependence is itself sui generis. Moreover, as I hope to show, our intuitions about temporal dependence are fine-grained enough to enable us to analyze this dependence in terms of more familiar notions. Regrettably, Ockhamists have not, as far as I can tell, successfully carried out this analysis before now. Some have even been content to take the notion of the pure present as primitive. So it is not surprising that their opponents have suspected them of preferring, in Russell's words, the advantages of theft over honest toil. But once we have such an analysis, it is hard to imagine what more /266/ could be demanded. The Ockhamist, as we have seen, is operating from a position of strength, since his conception of the necessity of the past has a firmer intuitive foundation than any of its competitors. Once these intuitions are articulated coherently in a way which thwarts the determinist's argument, the most reasonable course will be to accept the Ockhamistic response to that argument.
The Ockhamist, then, holds that every future-tense proposition is either true now or false now (pace Aristotle), that some contingent propositions are now such that they will be true (pace Prior), and that at least many future-tense sentences are commonly used to express propositions "about" the future rather than simply "about" the present (pace Geach). Moreover, as just noted, the Ockhamist's central thesis is that the pure present is metaphysically primary. This thesis, I hope to show, can serve as the basis for a plausible analysis of what it is for two possible worlds to share the same history at a given moment, and hence as the basis for an intuitively satisfying explication of accidental necessity.
It will be helpful here to outline my general strategy informally before introducing the modicum of formal machinery that I will use in what follows. I take the claim that the pure present is metaphysically primary to be tantamount to the assertion that for any moment t and any logically possible world w there is a set k of purely present-tense propositions such that (a) each member of k is true at t in w and (b) k determines what is true at t in w in a temporally independent way, i.e., in a way which does not temporally depend on what has been or will be true at moments of w other than t. I will call this set the submoment of t in w, and I will say that a given submoment obtains when and only when each of its members is true. Then, to put it roughly, I will claim that two worlds share the same history at a moment t just in case they share all and only the same submoments, obtaining in exactly the same order, prior to t. Finally, building on this claim, I will say that a proposition p is necessary per accidens at t in w just in case p is true at t and at every moment after t in every possible world which shares the same history (in the above sense) with w at t.
Given this general strategy, my first task is to specify which propositions are themselves purely present-tense, i.e., temporally independent, and thus eligible for membership in some submoment. To avoid confusion, I will hereafter call such propositions 'immediate' rather than 'present-tense'. For, as Ockham himself realized, some grammatically present-tense sentences are used to express propositions about the past or about the future. /267/
The division of propositions into immediate ones and non-immediate ones will be guided and constrained by what I take to be our shared intuitions about the notions of temporal dependence and independence. Roughly speaking, the truth or falsity of an immediate proposition is temporally (as opposed to, say, logically or causally) independent of what has been or will be true, while the truth conditions of a non-immediate proposition involve an essential reference to what has been true at past moments or will be true at future moments. Alternatively, the immediate propositions true at a given moment, unlike their non-immediate counterparts, determine what is "really occurring" at that moment and what will become part of our history after that moment.
To begin, it seems clear that every proposition which is either logically necessary or logically impossible is immediate, since the present truth or falsity of any such proposition is wholly independent of considerations about the past or about the future. But how are we to divide logically contingent propositions? Before we address this question directly, it will be helpful to list some intuitively obvious examples of immediate propositions which are logically contingent:
(1) David is sitting.
(4) David believes that Katie will travel to Rome next week.
(1) requires little comment, and there are innumerable simple propositions just like it. Again, although (2) is a complex proposition, each of its components is immediate, and its truth conditions are independent of what is true at times other than the present. (3) is somewhat more problematic, since one of its components is a proposition that is about the future and hence non-immediate. But on closer inspection we see that (3) is logically equivalent to its first conjunct, which is clearly immediate. (Note that the second conjunct of (3) is true if there are no future moments.) Hence, the truth or falsity or (3) depends only on what is immediately true in the present. Propositions like (4), which involve present-tense propositional attitudes directed toward non-immediate propositions, play an especially interesting role in the history of the Ockhamistic treatment of future contingents. Ockham himself seems to have counted such propositions as (to use my terminology) non-immediate and /268/ hence as ineligible for membership in submoments. But this is clearly a mistake--and one which would render implausible the Ockhamistic response to the argument for logical determinism. Immediate propositions, as noted above, are the key to determining what our history is at a given moment and which possible worlds share the same history with our world at that moment. But the past hopes, fears, beliefs, desires, predictions, etc., of historical agents are clearly unalterable elements of our past and must be counted as part of our history by any explication of what it is for two worlds to share the same history at a given time. No world w can claim to share the same history with our world now if in w Chamberlain did not fear that Hitler would not keep his word, or if in w Ernie Banks did not hope (and predict) every spring that the Cubs would win the pennant. So (4) must be counted as immediate if the Ockhamistic position is to retain its intuitive advantage over its competitors. On the other hand, the following logically contingent propositions are clearly non-immediate:
(5) David will sit.
(8) David mistakenly believes that Katie will be in Rome next week.
(5), like all simple past- and future-tense propositions, is obviously non-immediate. Its present truth or falsity depends on whether the immediate proposition that David is sitting will be true at any future moment. (6) is a bit more subtle, but its present truth-value does depend, at least in part, on whether the immediate proposition that Katie is in Rome has ever been true in the past. (7), though expressed by a present-tense sentence, clearly depends for its present truth-value on whether the immediate proposition that Katie exists began to be true 30 years ago. And (8), unlike (4) above, depends in part for its present truth or falsity on whether the immediate proposition that Katie is in Rome will be true at any time next week. (As a general rule, a proposition involving a present-tense propositional attitude directed at a past- or future-tense proposition is immediate unless it entails p or the negation of p. Hence, whereas:
(9) David believes that Katie will go to Rome.
(10) David fears that Katie has gone to Rome. /269/
are immediate, the propositions
(11) David correctly believes that Katie will go to Rome.
(12) David mistakenly fears that Katie has gone to Rome.
I will now introduce the formal mechanism which will allow us to systematize these intuitions. It consists of a propositional language L and a model theory for L. I will first describe it and then make some remarks about its intended interpretation. Suppose that L has a stock of letters representing propositions, together with the truth-unctions, an alethic modality M (logical possibility), and tenses P and F (past-tense and future-tense, respectively). Now let C be a linearly ordered set, the set of times, and let W be the set of logically possible worlds. A model structure R for L is a subset of the logical product W X C such that for every w W, the class of pairs (w,t), where t C, forms a sequence of C. (I am assuming, consistent with this model structure, that some possible worlds have a first moment of time and some have a last moment of time.) A model with model structure R is given by an assignment of classical truth-values, for each (w,t) in R, to the proposition-letters. The truth-unctional connectives behave in the usual way, while the tenses are given the following Ockhamistic definitions, where 'A' is replaceable by any well-formed formula of L:
P (A) is true at (w,t) iff for some t* < t, A is true at (w,t*)
F (A) is true at (w,t) iff for some t* > t, A is true at (w,t*)
In addition, the modality M is defined as follows:
M (A) is true at (w,t) iff for some (w*, t*) ∈ R, A is true at (w*, t*)
In order to give an intuitively adequate account of immediacy, it is necessary for us to make the following three stipulations about the interpretation of L under which that account is to be formulated:
First, the proposition-letters of L, which I will call its atomic constituents, represent only propositions that may be expressed in English by grammatically present-tense sentences. This stipulation is entirely natural, since the past-tense and future-tense counterparts of such propositions can then be adequately represented in L by formulas which involve operations on the atomic constituents of L.
Second, no proposition is represented by an atomic constituent of L if it is, intuitively, most properly represented in L by a formula /270/ which involves operations on L's atomic constituents. This stipulation is somewhat stronger and also somewhat more vague than the first. Nevertheless, it can be defended on intuitively attractive grounds. For instance, since L contains no operators that represent propositional attitudes, a simple present-tense proposition like
(13) David believes that Katie will at some time be in Rome.
is represented by an atomic constituent of L, say 'p'. But now consider the proposition:
(14) David correctly believes that Katie will at some time be in Rome.
How is (14) to be represented? Let 'q' stand for the proposition that Katie is in Rome. The second stipulation dictates that (14) be represented not by an atomic constituent of L but rather by the non-atomic formula 'pand Fq'. Again, even though
(15) David is standing and Katie is sitting.
is, arguably, expressed in English by a present-tense sentence, it is intuitively natural to represent it in L by a non-atomic formula like 'r and s'. While I realize that in some cases there will be disagreement about what the proper structural representation of a given proposition might be, I do not believe that any such disagreement will be sufficient to undermine my account of immediacy.10
The third, and initially the least intuitive, stipulation is that no atomic constituent of L represents a proposition whose proper philosophical analysis contains quantifiers, unless those quantifiers /271/ fall within the scope of a propositional attitude. Thus, no proposition like the following is represented by an atomic constituent of L:
(16) David has no true beliefs.
(20) David has more than three children.
On the other hand, propositions like
(21) David believes that every manatee is ugly.
(22) David fears that Katie is omniscient.
may be represented by atomic constituents of L. As I will explain below, this stipulation, despite first appearances to the contrary, has firm intuitive footing. Moreover, even though it limits the expressive power of L (since it has as a consequence that many propositions cannot be represented in L), this limitation is both necessary and harmless.12 I will return to this point shortly.
The account of immediacy that I will now formulate presupposes the interpretation of L determined by these three stipulations. Once we have an explication of immediacy, we can then resort to a less stringent interpretation under which L has the resources to represent any proposition.
It seems unproblematic to claim that any logically contingent immediate proposition is such that it, as well as its negation, is (a) possibly such that it is true at a first moment of time and (b) possibly such that it is true at a last moment of time and (c) possibly such that it is true at an intermediate (i.e., neither first nor last) moment of time. That is, a proposition is temporally independent only if its present truth or falsity is indifferent both to the question of whether there are any past moments and to the question of whether there are any future moments. Given our intended interpretation /272/ of L, we can define this notion of temporal indifference for the formulas of L as follows:
A is temporally indifferent iff either (a) A or its negation is not logically possible or (b) A, as well as its negation, is such that it (i) is true at some (w,t) where t is the first moment in w, and (ii) is true at some (w,t) where t is the last moment in w, and (iii) is true at some (w,t) where t is an intermediate moment in w.
Then we can say that a proposition is temporally indifferent if it is represented in L (under the intended interpretation) by a temporally indifferent formula.
Even though every formula of the form F(A) or P(A) is such that neither it nor its negation is temporally indifferent, not every temporally indifferent formula is also immediate (consider the formula representing the disjunctive proposition that David is standing or Katie has been to Rome). Nor is it the case that every atomic constituent of L is immediate (consider the atomic constituent representing the proposition that Katie is Tony's granddaughter). However, given the three stipulations made above, it does seem clearly to be the case that every temporally indifferent atomic constituent of L is indeed immediate. For each such formula represents a singular affirmative present-tense proposition which is also temporally indifferent.13 Conversely, it seems clear that, given our intended interpretation, the only non-immediate temporally indifferent formulas in L will be non-atomic. Such formulas will represent propositions like
(23) David correctly believes that Katie will never be
(25) David is standing or Katie will at some time be in Rome.
So we have a core of atomic formulas which are also immediate. Let S be the set of such formulas, and let V(S) be any valuation which assigns a classical truth-value to each of the members of S at a given (w,t). Then we can explicate immediacy as follows: /273/
A is immediate iff both (a) for any (w,t), if A is true at (w,t), then A is true at every (w*,t*) such that V(S) at (w*,t*) = V(S) at (w,t); and (b) if A is false at (w,t), then A is false at every (w*,t*) such that V(S) at (w*,t*) = V(S) at (w,t)
Intuitively, the truth-value of an immediate formula at any (w,t) is wholly a function of the assignment of truth-values for (w,t) to the temporally indifferent atomic constituents of that formula. Its truth-value, in short, does not temporally depend on what is true or false at other moments.
Finally, to revert to talk of propositions, we can say that a proposition p is immediate if and only if either (a) p is represented by an immediate formula of L, where L is taken under the interpretation determined by the three stipulations made above, or (b) p is logically equivalent to a proposition which meets condition (a).
The following consequences follow straightforwardly from this account of immediacy: (a) p is immediate if and only if the negation of p is immediate; (b) p and q are each immediate only if their conjunction and disjunction are also immediate; (c) p is immediate if and only if every proposition logically equivalent to p is also immediate; and (d) every logically necessary proposition is immediate, as is every logically impossible proposition. Each of these consequences is patently desirable. In addition, each of our original examples, (1)-(12), is classified correctly on this account of immediacy.
We can now see why the third stipulation made above is both necessary and harmless. Consider the proposition:
(26) David has no false beliefs and David believes that Katie will never be in Rome.
Intuitively, (26) is non-immediate, since its present truth-value depends in part on whether the immediate proposition that Katie is in Rome will ever be true. However, in the absence of the third stipulation, the first conjunct of (26) would be represented in L by a temporally indifferent atomic constituent of L, and so (26) itself would be represented by a conjunction of two immediate formulas. So without the third stipulation, (26) would turn out to be immediate, even though it is obviously non-immediate. But given the third stipulation, the first conjunct of (26) cannot be represented in L and so we are not forced to count (26) as immediate.
On the other hand, the limitation on L's expressive power imposed by the third stipulation is harmless. For even though the proposition that David has no false beliefs cannot be represented in /274/ L under the interpretation presupposed above, still its truth-value at any given (w,t) ∈ R is wholly determined by the valuations V(S) for every t* such that (w,t*)∈ R. Each proposition expressed by an English sentence of the form 'David believes that ______', where the blank is filled by a declarative sentence, is immediate. So even under the intended interpretation, L can express all truths about what David believes at (w,t). And the valuations V(S) for (w,t) and all the other moments of w are sufficient to determine whether or not all of the beliefs that David has at (w,t) are true. Similar considerations hold for (16)-(20) and other propositions involving quantifiers that cannot be represented in L under the intended nterpretation. Furthermore, even though a proposition like
(27) Every armadillo is vicious,
which is intuitively immediate and not troublesome in the way that the first conjunct of (26) is, turns out not to be immediate, still its truth or falsity at any given moment is completely dependent on the truth-values for that moment of the officially immediate propositions. Hence, nothing is lost by counting this proposition and others like it as non-immediate. Moreover, now that we have used our intended interpretation of L to isolate the set of immediate propositions, we can abandon this interpretation in favor of one under which L has the resources to represent any proposition.
We can now return to our main objective. Given the above account of immediacy, we can simply define the submoment for any (w,t) as the set of immediate formulas (or propositions) true at (w,t). (Below I will, for the sake of simplicity, speak of propositions rather than the formulas of L that represent them.)
In section II of this paper I noted that the Ockhamist rejects (C) as a needlessly and unacceptably strong construal of the necessity of the past. The underlying reason for (C)'s inadequacy is that it presupposes the following "natural", though ultimately implausible, explication of what it is for two possible worlds to share the same history at a given time:
(D) w shares the same history with w* at t iff for any t*< t, both (a) (w,t*) ∈ R iff (w*,t*)R, and (b) for any proposition p, p is true at (w,t*) iff p is true at (w*,t*)
(D) has as a consequence that if it is now a truth about the future that Katie will wash her car at T, then even before T it is part of our history that it has been the case that Katie will wash her car at /275/ T. The Ockhamist's opponents accept this consequence, but go on to deny that there are now any such (contingent) truths about the future.14 The Ockhamist, by contrast, insists that the consequence itself should be rejected because it reflects outrageously inflated ideas of actuality and history. Instead, he offers the following alternative to (D):
(E) w shares the same history with w* at t iff for any t* < t, both (a) (w,t*) ∈ R iff (w*,t*) ∈ R, and (b) for any submoment k, k obtains at (w,t*) iff k obtains at (w*,t*)
Though weaker than (D), (E) is clearly sufficient to capture the intuitive sense of the claim that w and w* share the same history at t. For suppose that they do share at t the same history in the sense explicated by (E). It then follows, for instance, that all and only the individuals that exist in w before t also exist in w* before t--and each has exactly the same life-story before t. Again, it follows that all and only the events which occur before t in w also occur before t in w*--and each occurs at exactly the same time in each world. Moreover, it follows that w and w* share all and only the same scientific laws at every time before t. Persons do exactly the same things at the same time, and have exactly the same things happen to them. The same political and social upheavals occur at exactly the same time in both worlds. In short, (E)--supported by the above explication of immediacy--seems to capture perfectly what philosophers or historians have in mind when they ask us to imagine a world "just like ours prior to t", or when they ask us to consider two worlds with "identical initial segments prior to t".
But, of course, from the fact that w and w* share the same history at t in this sense it does not follow that they also share the same present and future at t--even if we accept the law of bivalence and reject the views of Prior and Geach. That is, it does not follow from (E), as it does from (D), that all and only the same future tense propositions true at a given moment t*, before t, in w are also true at t* in w*. And so (E) provides us with the basis for an intuitively satisfying account of accidental necessity: /276/
(F) p is necessary per accidens at (w,t) iff (a) p is logically contingent and (b) p is true at t and at every moment after t in every world w* such that w* shares the same history with w at t (in the sense explicated by (E)).
So, for instance, the past-tense proposition that Socrates drank hemlock is now necessary per accidens, since the immediate proposition that Socrates is drinking hemlock is a member of some submoment which has already obtained. It follows that this submoment also obtains at some moment before T in every possible world which shares the same history with our world at T, where T is the present moment. So in every such world the proposition that Socrates drank hemlock is true at T and at every moment after T.
On the other hand, suppose that it is now the case, long before T, that the future-tense proposition that Katie will wash her car at T has always been true. Since T has not yet occurred, the immediate proposition that Katie is washing her car at T has not yet been true and hence is not a member of any submoment that has already obtained. So there is a possible world w that shares the same history with our world at the present moment and yet is such that it is never true in w that Katie will wash her car at T. From this it follows that the past-tense proposition that it was the case that Katie will wash her car at T, though now true, is not necessary per accidens now or at any other moment before T. But this, as claimed above, is sufficient to defuse the argument for logical determinism.
We can now see that the deterministic argument initially confounded us only because we could not immediately envision any plausible alternative to the construal of the necessity of the past embodied in (C) above. But at this point it should be clear that (C) was indeed the culprit, and so we are not forced to ingest the dubious remedies prescribed by Aristotle, Prior and Geach in order to ward off the determinist. Rather, a careful articulation of our natural response to the argument, viz., that it is now true (before T) that it was the case that Katie will wash her car at T only because it will be true at T that Katie is washing her car, has yielded a more palatable solution.
We are also in a position now to appreciate the often ignored distinction between per accidens modality and causal modality. Suppose that w and w* share the same history at a determinate moment T*. And suppose that prior to T* in w it is not only true but /277/ also causally necessary that Hurricane Xenophon will strike Key West at T*. Does it follow that:
(28) It was the case that Xenephon will strike Key West at T*.
is necessary per accidens before T* in w? Our previous discussion shows clearly that this does not follow. For even though w* shares the same history with w at T*, it is at least conceivable that the laws of nature change at T* in w*, or that God or some other supernatural agent intervene to save Key West at T* in w* by violating or suspending the relevant laws of nature. This suggests that the classical notion of a "future contingent" is insidiously ambiguous. In a weak sense p is a future contingent at t just in case p is future-tense and temporally contingent at t. In this sense (28) is a future contingent at T*. But to be a future contingent in the stronger sense p must also be causally contingent at t. Yet while this stronger sense is dominant in the philosophical literature, only the weaker sense is, strictly speaking, relevant to the issues surrounding the debate over logical determinism. In fact, it is precisely my use of the weaker sense that distinguishes my notion of accidental necessity from Prior's notion of what is "now-unpreventable.''15 My contention, in its barest terms, is that Prior and others have conflated questions pertinent to the debate over logical determinism with questions pertinent to the debate over causal determinism. But this conflation prevents us from coming to a deeper understanding of the relation between the two debates. This is clearly illustrated by the fact that we can use the proposed account of per accidens modality to formulate a necessary condition on an agent's power which is both (a) the strongest condition on power that can emanate from the mere claim that the past is necessary and (b) perfectly neutral with respect to the debate over causal determinism:
(G) S has the power at (w,t) to bring it about that p is true only if for some world w* such that w* shares the same history with w at t, at (w*,t) S brings it about that p is true.
We can then use (G) to formulate a corresponding condition for freedom. It should be clear that (G) expresses an extremely weak condition which is acceptable to both libertarians and compatibilists. The differences that separate these two groups surface only when we ask the further question of whether we can correctly add to (G) the condition that the causal laws shared by w and w* just /278/ before t are also shared by them (with no violations) at t. Libertarians will insist that we can add this condition, while compatibilists will deny this. But regardless of how we resolve this issue, the neutrality of (G) at least enables us to see clearly what is often obfuscated, viz., exactly how it is possible to be a causal determinist without at the same time being a logical determinist. Interestingly, a moment's reflection also reveals that a causal determinist can avoid being a logical determinist only by espousing an Ockhamistic response to the argument for logical determinism. For the responses suggested by Aristotle, Prior and Geach cannot even count as responses unless the truth-values of some future-tense propositions are not now fixed in the way demanded by a thoroughgoing causal determinism.
Finally, there are two further issues that would naturally be addressed here if it were not for lack of space. The first is whether my view commits me to the claim that we can have power over the past, specifically over those "future-infected" past-tense propositions that are neither necessary per accidens nor impossible per accidens at the present moment. In another paper I have argued that anyone who accepts an Ockhamistic account of accidental necessity should also accept the general thesis that an agent S has the power to bring it about that p is or will be true at t only if S has at the same time the power to bring it about that it has always been the case that p would be true at t.16 However, this argument involves assumptions that are not integral to an Ockhamistic account of the necessity of the past, and so dissenters on this issue need not reject what I have said above.
Second, my account of the necessity of the past has obvious relevance to the still lively debate over the alleged incompatibility between divine foreknowledge and human freedom. Briefly, if God is, as is frequently held, essentially omniscient, then it can be argued persuasively, I believe, that every proposition attributing to God a belief about the future is nonimmediate and hence not a member of any submoment. Thus divine foreknowledge would pose no new problems for one who accepts my explication of accidental necessity. But, of course, this contention requires more elaborate support, which I hope to provide in another place.
1. Several of the relevant texts are found in English translation in Marilyn McCord Adams and Norman Kretzmann, trans., William Ockham: Predestination, God's Foreknowledge, and Future Contingents (New York: Appleton-Century-Crofts 1969).
2. The most elaborate recent discussions of Ockham's position are found in the introduction to the Adams and Kretzmann volume and in Arthur Prior, Past, Present and Future (Oxford, 1967), esp. Chap. VII.
3. For a recent defense of the view that all propositions are tensed, see Nicholas Wolterstorff, "Can Ontology Do Without Events?," in Ernest Sosa, ed., Essays on the Philosophy of Roderick Chisholm (Amsterdam, 1979), esp. pp. 183-188.
4. I will say that p entails q just in case it is logically impossible that there be a moment at which p is true and q is false. Similarly, p is logically equivalent to q just in case it is logically impossible that there be a moment at which p and q differ in truth value.
5. See, e.g., Jack W. Meiland, "A Two-Dimensional Passage Model for Time Travel," Philosophical Studies 26 (1974), 153-173; and David Lewis, "The Paradoxes of Time Travel," American Philosophical Quarterly 13 (1976), 145-152. To corroborate a point made below, Meiland's argument presupposes that there can be two independent time dimensions, and Lewis' argument presupposes that a person is (literally) a mereological sum of temporal parts, two of which could confront one another in a time travel scenario.
6. See Aristotle, On Interpretation, chap. 9; and Prior, Past, Present and Future, pp. 128-136, and "The Formalities of Omniscience," Philosophy, 32 (1962), 119-129. I will assume for present purposes that this traditional interpretation of Aristotle is correct.
7. See Peter T. Geach, Providence and Evil (Cambridge, 1977), pp. 40-66. The most thorough explication of this position that I know of is contained in an unpublished paper by Jorge Garcia entitled "The Elimination of the Future."
9. Geach contends that those who hold (A) that there are propositions "about" the future are committed to the dubious thesis (B) that there is a "futureland" populated by merely future beings. See Providence and Evil, pp. 51-57. But I have argued in the place cited in footnote 8 that (A) is compatible with the negation of (B) and, further, that there are good reasons for thinking that Ockham himself rejected (B).
(a) David is now such that he will visit Rome.
(b) Katie is now such that she has been to Rome.
are not represented by atomic constituents of L. This assumption is reasonable, since (a), for example, seems best analyzed as:
(c) David now exists and David will visit Rome.
which can be adequately represented in L by a formula like 'p and Fq'. Second, I accept the claim that if God exists, he is essentially ominiscient--so that necessarily, God believes p just in case God correctly believes p. For present purposes I will simply assume that no proposition attributing a belief to God is represented by an atomic constituent of L. This will allow me to discuss logical determinism without having to tackle the problem of divine foreknowledge as well. However, it is important to note that the assumption in question would require a separate argument if we were dealing with divine foreknowledge. In short, the argument for determinism from divine foreknowledge is, contrary to what some have claimed, more difficult to contend with than is the argument for logical determinism.
12. At this point someone might suggest that it would be better for me to use a predicate language rather than a simple propositional language in explicating immediacy. However, as far as I can tell, this would simply complicate my presentation without making it any more accurate.
13. By a 'singular' proposition I simply mean one which involves no quantifiers or truth-functions which do not fall within the scope of a propositional attitude. Moreover, any proposition represented by an atomic constituent of L is affirmative, since any negative proposition representable in L is best represented (in accord with the second stipulation) by a formula involving the negation operator. I should also point out in passing that among the propositions represented by atomic constituents of L there will be many which ascribe dispositional and other 'scientific' properties to individual objects.
14. The Aristotelian view is usually stated in such a way that bivalence is denied only for causally contingent future-tense propositions. So suppose that it is now causally necessary that Mt. Vesuvius will erupt at T, where T is in our future. Then, since they presuppose (D), most versions of Aristotelianism are committed to the claim that it is now part of our history that it has been true that Vesuvius will erupt at T. This result is by itself sufficient to cast doubt on both (D) and these versions of Aristotelianism. I will discuss the relationship between accidental and causal modality in more detail below.
16. See my "Accidental Necessity and Power over the Past," Pacific Philosophical Quarterly 63 (1982), 54-68.