David Foster Wallace (DFW) was a certified “genius” (a MacArthur grant recipient) who became famous as “one of the most talented fiction writers of his generation” in the words of philosopher Jay Garfield. Garfield contributes an appreciation of DFW in the posthumous book; Fate, Time, and Language. Garfield thought that DFW missed his calling. Instead of becoming a novelist, famous for manic novels like Infinite Jest and The Pale King, Garfield suggests that he could have been an even better philosopher. Garfield says that DFW’s essay contained in Fate, Time, and Language; ‘Richard Taylor’s “Fatalism” and the Semantics of Physical Modality’; which was one of DFW’s senior theses at Amherst, proves that “. . . had he lived, he would have been a major figure in our field.” The other senior thesis became The Broom of the System, which started DFW onto his career in literary fiction in 1985.
DFW’s philosophy thesis is directed against the modern philosopher Richard Taylor, whose article ‘Fatalism’ (The Philosophical Review, Vol. 71, No. 1, 1962) made the claim that six “presuppositions”, commonly accepted by modern day philosophers, lead to the conclusion that fatalism is true. The presuppositions:
1) Any proposition whatever is either true or, if not true, false.
2) If any state of affairs is sufficient for, though logically unrelated to, the occurrence of some further condition at the same or any other time, then the former cannot occur without the latter occurring.
3) If the occurrence of any condition is necessary for, but logically unrelated to, the occurrence of some other condition at the same or any other time, then the latter cannot occur without the former occurring also.
4) If one condition or set of conditions is sufficient for another, then that other is necessary for it and conversely, if one condition or set of conditions is necessary for another, then that other is sufficient for it.
5) No agent can perform any given act lacking some precondition for it.
6) Time does not enhance or decrease an agent’s powers.
Taylor’s other writings (including the article “The Problem of Future Contingents” included in Fate, Time, and Language) make clear that Taylor didn’t think that fatalism was true. Like Aristotle (and Lukasiewicz) he thought that proposition 1) above, a paraphrase of the Principle of Bivalence (PB), didn’t apply to future contingent events.
DFW takes a different approach: to demolish Taylor’s fatalism argument in support of an overall conclusion that “if Taylor and the fatalists want to force upon us a metaphysical conclusion, they must do metaphysics, not semantics.” How we get there is a longish story, all of which I won’t tell here, but the story follows a path through Aristotle, Lukasiewicz, and Hobbes to contemporary commentators on Taylor’s paper and finally to invention of a system to evaluate physical modalities based on the possible worlds modal logic of Kripke modified by Montague to include time. DFW calls this “System J”, presumably in honor of his thesis adviser, the above-mentioned Jay Garfield.
Fate, Time, and Language is about fatalism. Fatalism comes up in a very old argument in the never-never land between logic and metaphysics, Aristotle’s argument about the problem of future contingents: “For example, a sea-fight must either take place on the morrow or not. No necessity is there, however, that it should come to pass or should not. What is necessary is that it either should happen tomorrow or not.” (On Interpretation, IX, 19a, 29, Loeb translation by Harold P. Cooke). In Aristotle’s analysis of the problem, he appears to conclude that contingent future events are an exception to the normal rule that has come to be known as Principle of Bivalence (PB): “In regard to things present or past, propositions, whether positive or negative, are true of necessity or false.” (On Interpretation, IX, 18a, 28). He is led to that conclusion by an argument that finds that that if we assume PB for the case of future contingent events then fatalism is proved, a conclusion which Aristotle finds absurd (https://notesfrommylibrary.wordpress.com/2011/04/15/aristotles-future-contingents/).
PB is a crucial concept here, since Aristotle’s argument was not that fatalism is true, but that since it is obviously false, there seem to be some “things” (propositions, statements, or sentences) which are neither true nor false, thus contradicting PB. DFW goes to some pains to point out the difference between PB and the Law of Excluded Middle (LEM). He refers to Susan Haack in Deviant Logic (p 65): “I shall approach the question . . . by investigating . . . three principles: the principle of bivalence, the principle that every wff (well-formed formula) is either true or false (hereafter PB); the law of excluded middle, the wff ‘p or not p’ (hereafter , LEM); and Tarski’s material adequacy condition for the definitions of truth, the principle that ‘A’ is true iff (if and only if) A (hereafter, (T)).” (T) is not in scope here. But PB and LEM are at the heart of the issue that Aristotle and Taylor tried to address.
DFW complains that Taylor commits an “equivocation” between two sorts of non-logical, physical implications: 1) “necessary-of” and 2) “necessary-for” implications. “I give Order -> Sea-battle tomorrow” is a “necessary-of” implication. “Combustion -> Presence of fuel” is of the other variety. “Battle B is a necessary consequence of order O. But would we want to say with regard to 2) that the presence of fuel is a necessary consequence of combustion?” Why is this important? Because, according to DFW, 1) and 2) can be shown to “behave differently under a modus tollens operation (a deny-the-consequent-and-see-what-happens-to-the-antecedent operation.” DFW follows the criticism of Charles Brown’s “Fallacies in Taylor’s Fatalism” (reprinted in Fate, Time, and Language) that Taylor’s propositions 2, 3, 4 and 5 are invalidated by this “equivocation.” But, importantly, not (like Aristotle, Lukasiewicz, and Taylor) proposition 1, PB.
But we are still a long ways from DFW’s final argument here. In the course of this argument he shifts from the sea battle of Aristotle to a nuclear explosion on the Amherst campus. (See the manic mind at work here?) “Suppose that the day before yesterday a group of terrorists brought a completely assembled and fully functional nuclear weapon onto the Amherst College campus. Suppose further that yesterday the head terrorist, completely healthy and physically functional and not constrained in any way, sat next to the weapon, with his finger on the weapon’s fully functional triggering mechanism, all day, but did not press the trigger and so did not cause a nuclear explosion to occur, and so a nuclear explosion did not in fact occur on campus yesterday. Suppose further, since we’re trying to be as Taylor-ish as possible, that a nuclear explosion on the Amherst campus yesterday would be an occurrence causally, physically sufficient for the presence of radiation in excess of, say 20 rads on the Amherst campus today.”
But there is no radiation today. This is the condition (R>20) that in Taylor’s sense is “necessary for” the occurrence of the explosion yesterday. But, Wallace insists, that rather R>20 is a “necessary consequence of” an explosion yesterday. Does this matter? DFW thinks yes. “What it means in a nutshell is that the denial of the consequent’s obtaining today means only that it cannot today be the case that yesterday the explosion did occur, not that it was the case yesterday that the explosion could not occur.”
DFW says, “. . . we have granted everything that Taylor would seem to want us to grant. But we are still able to reasonably deny the fatalistic conclusion. This is because we can point out that in the absence of radiation today we evaluate P1E’s (“E” at some past time) possibility relative to what occurs now, today, at a time later than that designated by P1. We can say that this allows us to conclude only that, given what obtains today, it is not possible that P1E. Were we, however, to say something different, that at P1 it was not possible for E to occur, we would be evaluating the possibility of E at and relative to P1, not at or with respect to any other time, viz., now. But it is this second sort of conclusion that Taylor seems to want us to derive from everything we have been willing to grant to him thus far. It means basically that we would be saying that, given the set of circumstances that obtained yesterday, E was not physically possible yesterday. We would be saying not that it is not now possible that E occurred at P1, but rather that at P1 it was not possible for E to occur. And this would have as a consequence our buying the following: that yesterday, during the whole time the healthy and efficacious terrorist sat unconstrained with his limber finger on the fully functional triggering device of the fully operational nuclear weapon, it was somehow physically impossible for the explosion to occur. And this is clearly wrong . . . . “
Are we done yet? Not by a long shot. We haven’t even gotten to ‘System J’ yet. And we are not going to go there. The interested reader will need to consult the book, for ‘System J’ involves typography and “math logic” not available to the current author. Suffice it to say that one of the virtues of this approach in DFW’s mind is that it can be used to invalidate not just Taylor’s argument about future contingent events, but his further argument about past events as well.
I have already quoted DFW’s ultimate conclusion: that we cannot derive metaphysical conclusions by semantics. But this is perhaps the place to mention the conclusions of Lukasiewicz in an article contained in the book Polish Logic 1920 – 1939, edited by Storrs McCall. This book is referenced in DFW’s thesis, but for the famous article on “Many-valued systems of Propositional Logic.” The article that I want to mention is the article “On Determinism” that precedes the article quoted in Wallace’s thesis. For in this article Lukasiewicz addresses the same issue as DFW and comes to the same conclusion as Taylor in his subsequent work: that the principle of bivalence “cannot be proved. One can only believe it, and he alone who considers it self-evident believes it. To me, personally, the principle of bivalence does not appear to be self-evident. Therefore, I am entitled not to recognize it, and to accept the view that besides truth and falsehood there exist other truth-values, including at least one more, the third truth-value. . . . I maintain that there are propositions which are neither true nor false but indeterminate.” My own preference would be to extend the courtesy also to propositions that are both true and false; not all propositions, of course, but only those that lie on the margins of thought, iteration, or language.