The year 1970 was critical. Saul Kripke presented his “Naming and Necessity” lectures at Princeton University,2 David Lewis published his papers “Anselm and Actuality” and “General Semantics,”3 and Richard Montague wrote “Pragmatics and Intensional Logics.”4 Fifteen years later, when Wallace began work on his thesis, these formal resources had entered the mainstream (note that Michael Loux’s book, The Possible and the Actual, cited in Wallace’s notes, is a textbook). How did Wallace employ these new tools? Let us turn to his monograph.
Section 1 sets up the problem of fatalism and identifies the philosophical options as Wallace sees them. He then presents Taylor’s argument and discusses the modalities (the types of possibility and necessity) involved.
The heart of Wallace’s reply to fatalism is the concept he introduces of “situational physical modalities.” As Wallace explains, a distinction should be drawn between logical (alethic) and causal (physical) possibility and necessity. He further distinguishes physical possibility and necessity from situational physical possibility and necessity: What is situationally physically possible and necessary at any given moment is a function both of the general physical laws that govern the operations of our world, and of the particular set of relevant physical conditions ... and considerations ... that obtains at that moment ... and situations change from moment to moment.
(THIS VOLUME, 165)
In other words, while physical modalities concern invariant physical laws and are atemporal, situational physical modalities are not.
Section 2 presents a review of the literature regarding Taylor’s argument. Wallace agrees with Cahn that attempting to refute Taylor’s argument by showing that it has fatalistic consequences will not work.
In section 3 Wallace introduces what he terms “the Taylor Inequivalence.” He emphasizes the difference between the following two claims:(a) The absence of a sea battle today entails that yesterday it was impossible to order the battle
and(b) The absence of a sea battle today entails that it was impossible yesterday to order the battle
Note that the word “yesterday” is placed differently in the two sentences. In (a) the impossibility regards the order, and in (b) the impossibility regards the time. Wallace argues that Taylor’s argument yields (b) but not (a), and while (a) entails fatalism, (b) does not.
Wallace suggests that the fatalist argument trades on both the sort of error cited above, which is called “scope ambiguity,” and underdescription in the available formal languages. In other words, a richer formal language must be developed with its own alphabet, grammar, and rules of inference. That system then needs to be given a semantics or interpretation.
In section 3 Wallace explains his unique approach: 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 Kripke and extended by Richard Montague’s work in intensional logic.
(THIS VOLUME, 165-66)
However, while Montague’s semantics provides a way to evaluate modalities at certain times, Wallace finds it insufficiently fine-grained. It cannot account for the difference between (1) the evaluation of a modality at a time (the time at which a modality is evaluated) and (2) the evaluation of modality-at-a-time (the time to which the modality asserted is said to apply.)
To deal with this problem, Wallace introduces System J.5 He offers a visual representation of how System J assigns truth values to statements of future contingencies. He diagrams his own example (a nuclear explosion at Amherst College) and seeks to demonstrate the fallacy inherent in the fatalistic argument. Then Wallace defends his view of situational physical modalities and their interpretation in System J:
Physical modalities are understood as sensitive to time and sensitive to world situations causally joined in mother-daughter relationships, as part of causal paths. And this understanding of physical modality seems to point to a way to solve the Taylor problem, to show that even under the most generous acceptance of his premises and reading of his argument, the fatalist conclusion he wants to “force” upon us does not validly follow.
(190)
Keep in mind that certain paths in the past, now closed in the present, had once been open, while possibilities now open will be closed in the future. To map out these various possibilities at each of the times they were possible, Wallace uses System J.
He argues furthermore that System J better captures physical-modal expressions in our natural language:
If, for example, I am now on a train to St. Louis and I say, “I could
just as easily be on a train to Chicago right now,” I am talking about
the compatibility of my presence on the Chicago-train with certain
physical conditions. What condition is it asserted to be compatible
with? Certainly not the conditions that obtain right now, for then
I would really be saying I could be on both the St. Louis-train and
the Chicago-train at the same time. The conditions I am referring
to here are most plausibly characterized as those obtaining at some
point in the past—say, when I was on the train platform ... with me
deciding where I wanted to go. It is just this sort of construal of “I
could just as easily be on the Chicago-train right now” that System
J captures.
(209)
This is only a brief overview of the strategy Wallace employs to try to come to grips with Taylor’s argument. Granted, these matters are not simple, and following Wallace’s argument is not easy. But his work is well worth careful study not only by Wallace scholars but also by metaphysicians. For here Wallace demonstrates more than the deep familiarity with philosophical ideas, themes, and texts shown in the works he published during his life. This essay isn’t merely about philosophy; it is philosophy. Wallace was a gifted philosopher, and the conclusive evidence for that claim is found in the essay that follows.
NOTES
1 Steven M. Cahn, Fate, Logic, and Time (New Haven, Conn.: Yale University Press, 1967; rprnt., Eugene, Ore.: Wipf and Stock, 2004).
2 Saul Kripke, Naming and Necessity (Cambridge, Mass.: Harvard University Press, 1970).
3 The two papers are reprinted in David Lewis, Philosophical Papers, vol. 1 (New York: Oxford University Press, 1983).
4 Reprinted in Richmond Thomason, ed., Formal Philosophy: Selected Papers of Richard Montague (New Haven, Conn.: Yale University Press, 1974).
5 Logical systems, like Wallace’s, combining modality and tense had appeared in specialized journals during the late 1960s and 1970s but did not become widely known until after 1985. See Richmond H. Thomason, “Combinations of Tense and Modality,” in Handbook of Philosophical Logic, vol. 2, ed. D. Gabbay amd F. Guenthner (Dordrecht: Kluwer Academic Publishing, 1984).
15
RICHARD TAYLOR’S “FATALISM” AND THE SEMANTICS OF PHYSICAL MODALITY
DAVID FOSTER WALLACE
ACKNOWLEDGMENTS
Thesis dedicated to James Donald Wallace and Sally Jean Foster Wallace.
Thanks go to the following people for helping me in various ways with this project:Bruce Aune
Joseph Epstein
W. E. Kennick
Lily Knezevich
Fred Landman
David Shwayder
Richmond Thomason
Robert Wall
James D. Wallace
Corey Washington
Robert Wengert
• Special thanks to Professor Willem de Vries for being my thesis advisor. I could not have wished for a better one.
• Special thanks to Mr. Jamie Rucker of Hampshire College for his help with the formal features of this essay.
• My very special thanks to Professor Jay Garfield of Hampshire College. In
a spirit far beyond the call of any 5-College duty, Professor Garfield gave generously of his time and talent, provided good advice and good ideas at every turn, and made this thesis a lot better than it would have been without his help. His influence is on almost every page of this essay, though he is of course in no way responsible for errors or problems here.
I. INTRODUCTION TO THE TAYLOR PROBLEM AND ITS CONTEXT
The famous and infamous Taylor argument is without doubt a classic modern contribution to the philosophical problem of future contingents. This problem, in a nutshell, is whether we can allow contingent future-tensed propositions to take standard truth-values without doing violence to our belief that parts of the universe enjoy at least some degree of causal contingency and that persons enjoy at least some control over what does and will happen to them. The problem is at least as old as Aristotle and has received the attention of many famous philosophers and theologians.1
Probably the most important and influential twentieth-century work on the problem of future contingents has been done by Jan Łukasiewicz and Richard Taylor. Łukasiewicz, according to Susan Haack, regarded the problem as the primary motivation for his pioneering work in the metatheory of many-valued logics.2 His 1930 “Many-Valued Systems of Propositional Logic” includes this concise characterization of a standard form of the problem and its potential implications for logical theory:I can assume without contradiction that my presence in Warsaw at a certain moment of next year, e.g. at noon on 21 December, is at the present time determined neither positively nor negatively. Hence it is possible, but not necessary, that I shall be present in Warsaw at the given time. On this assumption the proposition ‘I shall be in Warsaw at noon on 21 December of next year,’ can at the present time be neither true nor false. For if it were true now, my future presence in Warsaw would have to be necessary, which is contradictory to the assumption. If it were false now, on the other hand, my future presence in Warsaw would be impossible, which is also contradictory to the assumption. Therefore the proposition considered is at the moment neither true nor false and must possess a third value, different from ‘0’ or falsity and ‘1’ or truth. This value we can designated by ‘½.’ It represents ‘the possible’ and joins ‘the true’ and ‘the false’ as a third value.3
Richard Taylor is not concerned to avoid Łukasiewicz’s difficulty by amending standard two-valued logic. Taylor’s aim is rather to present a particularly powerful modern argument for the claim that the extension of standard semantic values to tensed propositions has results which are incompatible with the idea that persons as agents are capable of influencing the course of events in their world.4 Taylor’s claim is that the doctrine of fatalism is forced upon us by valid argument from only a very few standardly accepted, common-sense philosophical presuppositions.
It is obviously necessary to an informed examination of Taylor’s argument that we get some idea of what exactly fatalism is. Most of us know that it is a metaphysical thesis characterizing the world as working in a certain sort of way, in which everything that did happen had to happen, everything that does and will happen must happen, and in which persons as agents can do nothing but go with the flow over which they enjoy absolutely no influence. As Taylor portrays him, the fatalist thinks of himself and his role in the world in a curious sort of metaphysical way:A fatalist is best thought of, quite simply, as someone who thinks he cannot do anything about the future. He thinks it is not up to him what will happen next year, tomorrow, or the very next moment. He thinks that even his own behavior is not in the least within his power, any more than the motions of distant heavenly bodies, the events of remote history, or the political developments in faraway countries. He supposes, accordingly, that it is pointless for him to deliberate about anything, for a man deliberates only about those future things he believes to be within his power to do and forego. He does not pretend always to know what will happen. Hence, he might sometimes try to read signs and portents, or contemplate the effects upon him of the various things that might, for all he knows, be fated to occur. But he does not suppose that, whatever will happen, it will ever have been really avoidable.5
So Taylor’s central claim, the Taylor problem, is that just a few basic logical and semantic presuppositions, regarded as uncontroversially true by most philosophers, lead directly to the metaphysical conclusion that human beings, agents, have no control over what is going to happen. The first of Taylor’s presuppositions is what he calls the law of the excluded middle, LEM: “We presuppose that any proposition whatever is either true, or, if not true, false.” It is perhaps worth noting that this is actually not LEM, but rather the principle of bivalence; a system for which LEM holds is a system in which (p ∨ ~p) is a theorem.6 The important thing, though, is that Taylor’s presupposition proposes to extend what we’ll call LEM/PB to all propositions, including those having to do with events and states of affairs that do not yet obtain: future contingents are treated within the semantic boundaries of standard two-valued logic.
Taylor’s second, third and fourth presuppositions explicate the commonly accepted relations of necessity and sufficiency among states of affairs: if some state of affairs p is sufficient for some other state of affairs q obtaining at the same or any other time, then p cannot obtain without q at some point obtaining, too: if some state of affairs q is necessary for some other state of affairs p obtaining at the same or any other time, then, again, p cannot obtain without q at some point obtaining, too; and if p is sufficient for q, q is necessary for p, and if q is necessary for p, p is sufficient for q.
The fifth presupposition is that no state of affairs can obtain if there is absent, at the same or any other time, any other state of affairs necessary for it to obtain. In Taylor’s language of human action, “... no agent can perform any given act if there is lacking, at the same or any other time, some condition necessary for the occurrence of that act.” The sixth presupposition is that “time is not by itself efficacious,” that time does not by itself increase or diminish the powers of anything.7
In his problem, Taylor presents us with a situation and an argument. Suppose that I am an admiral. Suppose that, in the context of the totality of circumstances obtaining, if I issue a certain kind of naval order, a sea-battle will inevitably occur tomorrow. The giving of such an order we designate O, the state of affairs in which a battle occurs tomorrow we designate B, and the relation in which O is sufficient for B we designate (O → B). Suppose further that, if I issue any other kind of naval order, here including no order at all, this will ensure that no sea-battle takes place tomorrow. We designate the any-other-kind-of-order O′, the state of affairs in which there is no battle tomorrow B′, and the sufficiency-relation between the two we designate (O′ → B′). By presupposition 4, since O is sufficient for B, and O′ is sufficient for B′, then B is necessary for O—this means that (~B → ~O)—and B′ is necessary for O′—meaning (~B′ → ~O′). And presupposition 1 allows us to import LEM/PB to say that either it is true that there will be a battle tomorrow, B, or, if not, then it is true that there will not be a battle tomorrow, B′; that is, that either B is true or B′ is true: (B ∨ B′). We note that this is an exclusive disjunction, that if B is true then B′ will be false (since B′ is the same as not-B), and vice-versa. We also remind ourselves of Taylor’s presupposition 5, that no agent can perform a given act if there is lacking some condition necessary for that act, which certainly looks reasonable, and then as I stand on the deck of my destroyer we ask ourselves whether it is now in my power to do O if I choose and also now within my power to do O′ (instead) if I choose. Taylor’s answer is no:I-1) If B is true, then it is not in my power to do O′ (since if B is true then there is, or will be, lacking a condition necessary for my doing O′, namely the condition of there not being a battle tomorrow).
I-2) And if B′ is true, then it is not in my power to do O (for an obviously similar reason).
I-3) But either B is true, or B′ is true (since presupposition 1 licens
es the application of LEM/PB to future contingents).
I-4) So either it is not in my power to do O, or it is not in my power to do O′.
At least internally, this argument appears to be formally valid under the rule of Constructive Dilemma.
The fatalistic consequences of the argument are easy to see. Let’s use “□” and “◊” to stand for some intuitive sort of necessity and possibility, respectively. Since obviously under any analysis I have to do either O or O′ (since O′ is not-O), that is, since □ (O ∨ O′); and since by (I-4) it is either not possible that I do O or not possible that I do O′, (∼◊O ∨ ∼◊O′), which is equivalent to (∼◊∼∼O ∨ ∼◊∼O), which is equivalent to (□∼O ∨ □O), we are left with □(□O ∨ □∼O); so that it is necessary that whatever I do, O or O′, I do necessarily, and cannot do otherwise. This obviously means that whether the battle, characterized as the direct result of my personal choice and order, occurs or not tomorrow is not in my control, after all. If it is now true that there will be a battle tomorrow, it is not in my power to do anything to prevent it; if it is now false that there will be a battle tomorrow, it is not in my power to do anything to bring it about. This is so even though the occurrence or non-occurrence of the battle would appear, as Taylor sets up the case, to be the clearest sort of instance in which I, the admiral, do have some control over what is going to happen. And not only is some event tomorrow not in my control, my very act of giving an order does not seem to be open to deliberation or choice; it is necessitated by the occurrence or non-occurrence of the battle tomorrow. Hence fatalism: what I do is necessary, what I do not do is impossible, what does and will happen is not at all in my control. And hence the Taylor problem: a semantic argument out of six seemingly inoffensive presuppositions appears to force upon us a strange and unhappy metaphysical doctrine that does violence to some of our most basic intuitions about human freedom.
Fate, Time, and Language Page 14