## ACCIDENTAL NECESSITY AND LOGICAL DETERMINISM*Journal of Philosophy 80 (1983): 257-278
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 Medieval logicians commonly called this modality necessity In section I of this paper I will first describe some general features
of
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 Let me now list some of the basic properties of Second, as we should expect, a proposition's being necessary (impossible)
From these first two points it follows that, for any moment Third, a proposition's being necessary (impossible) 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 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 (B) is unassailable. If 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 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 That is, if 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 (P1) The proposition that Katie will wash her car at (P2) So the proposition that it was the case that Katie
will wash her car at (P3) But the proposition that it was the case that Katie
will wash her car at (P4) Therefore, no one (including Katie) will have the
power at or before 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
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 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 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 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 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 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
The Ockhamist, then, holds that every future-tense proposition is either
true now or false now ( 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 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. and: (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 (5) David will sit. and (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 (9) David believes that Katie will go to Rome. and (10) David fears that Katie has gone to Rome. /269/ are immediate, the propositions (11) David correctly believes that Katie will go to Rome. and (12) David mistakenly fears that Katie has gone to Rome. are non-immediate.) I will now introduce the formal mechanism which will allow us to systematize
these intuitions. It consists of a propositional language
In addition, the modality M is defined as follows: M ( 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 First, the proposition-letters of Second, no proposition is represented by an atomic constituent of (13) David believes that Katie will at some time be in Rome. is represented by an atomic constituent of (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 (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 The third, and initially the least intuitive, stipulation is that no
atomic constituent of (16) David has no true beliefs. and (20) David has more than three children. On the other hand, propositions like (21) David believes that every manatee is ugly. and (22) David fears that Katie is omniscient. may be represented by atomic constituents of The account of immediacy that I will now formulate presupposes the interpretation
of 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
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 (23) David correctly believes that Katie will never be
in Rome. and (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
Intuitively, the truth-value of an immediate formula at any ( Finally, to revert to talk of propositions, we can say that a proposition
The following consequences follow straightforwardly from this account
of immediacy: (a) 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 On the other hand, the limitation on (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 We can now return to our main objective. Given the above account of
immediacy, we can simply define the 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) (D) has as a consequence that if it is now a truth about the future
that Katie will wash her car at (E) Though weaker than (D), (E) is clearly sufficient to capture the intuitive
sense of the claim that But, of course, from the fact that (F) So, for instance, the past-tense proposition that Socrates drank hemlock
is now necessary On the other hand, suppose that it is now the case, long before
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 We are also in a position now to appreciate the often ignored distinction
between (28) It was the case that Xenephon will strike Key West
at is necessary per accidens before (G) 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 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 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.
* I wish to thank Thomas Flint, Richard Foley, Jorge Garcia, James Garson, Penelope Maddy, Philip Quinn, and an anonymous referee for their helpful remarks on earlier versions of this paper. 1. Several of the relevant texts are found in English
translation in Marilyn McCord Adams and Norman Kretzmann, trans., 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, 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., 4. I will say that 5. See, e.g., Jack W. Meiland, "A Two-Dimensional
Passage Model for Time Travel," 6. See Aristotle, 7. See Peter T. Geach, 8. See my "Ockham's Theory of Truth Conditions,"
in Alfred J. Freddoso and Henry Schuurman, trans., 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). 10. There are two points which merit special attention here. First, I am assuming that propositions like: (a) David is now such that he will visit Rome. and (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 11. I am assuming that the correct analysis of (17)
is this: for any proposition 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 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 15. Prior develops this notion in the places alluded to in footnote 6. 16. See my "Accidental
Necessity and Power over the Past," |