Abstract
David Lewis’s analysis of “can” in “The Paradoxes of Time Travel” (Lewis, American Philosophical Quarterly, 13, 145–52, 1976) has been widely accepted both as a definitive analysis of “can” and as a successful resolution of the Grandfather Paradox for time travel. I argue that the central feature of his analysis puts it on all fours with a fallacy frequently imputed to fatalists such as Richard Taylor. I go on to consider two moves that might be made to avoid the fallacy, arguing that one of them leads to the unavailability of an all-things-considered “can” and the other to a new primitive modality, not analyzable in Lewis’s way.
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Notes
For my purposes here, I make the controversial assumption that ability can be represented as a modality: I can do it = it is possible (in a sense to be explained) that I do it. I shall thus pass back and forth (as Lewis does) between “can” talk and “possibility” talk—talk of what an agent can do and talk of what can happen.
I have not used one of the “six presuppositions” Taylor identifies in his argument, namely, that time is not causally efficacious. I am not sure what role that assumption plays. The argument I have given here reaches its conclusion without it.
Why the need for Q as a separate conjunct, a referee has asked. The exegetical reason is that we need it to express the idea of compossibility with a fact, something that is actually the case. ‘Fact’ is factive! There is also a logical reason, given below in n. 6. My attribution of CAN to Lewis may also be supported by noting its analogy to what he says about possibility operators as restricted existential quantifiers over worlds (Lewis 1973, 4-8). For example, nomological possibility (or possibility relative to the laws of nature) is truth in some world where the laws of nature are just as in our own. In other words, P is nomologically possible iff there is a world in which P and L both hold, L being a description of which laws hold in @. In other words, ◊(P & L) & L. Substitute Q (the facts in the compossibility class) for L and you get CAN.
The relativity is made explicit when Lewis says, “What I can do, relative to one set of facts, I cannot do, relative to another, more inclusive, set” (paragraph 29).
Here is a logical reason for including Q as a conjunct in the analysans: without it, Lewis would be drawing an inference from 3″ alone to 6″, which lacks even the appearance of validity.
Incidentally, the impossibility of Order & No Battle in Taylor’s argument is also presumably causal or nomic rather than logical.
An influential treatment very much in line with Lewis’s is that given in Kratzer 1977. According to Kratzer, what must be true is what must be in true in view of certain considerations, either explicitly asserted or provided by context, and “must be true in virtue of” amounts to “is entailed by.” Correlatively, what can be true is what is consistent with the considerations in question.
I believe this assessment remains true even when the compossibility class, the class of facts in view of which modal claims are assessed, disappears from the object language and functions behind the scenes as part of the semantics of “can” talk.
On certain assumptions, the two arguments would collapse into one—for example, the assumption that change in something is just variation across different temporal versions of it.
The example of Newton reminds us that the common inference from ‘x is F relative to parameter p1, but not F relative to parameter p2’ to ‘there is no such thing as being F absolutely’ is a non sequitur. Absolute Fness might be defined as Fness relative to some privileged parameter.
Actually, he says “disguised as relevant,” not “disguised as past,” but it is hard to see what besides pastness could be the relevance-maker.
Vihvelin argues that a necessary condition of someone’s being able to kill her infant self is that the following counterfactual be true: if she tried, she might succeed. She then argues that that counterfactual is not true.
There are two main ways to distill absolute possibility facts out of relative possibility or compossibility facts. One is by simple existential quantification: P is possible/impossible = df ∃Q(Q is a fact & P is/is not possible relative to Q). This is no good for Lewis’s purposes, of course, since a given P could then be both possible and impossible. The other is by reference to facts in a distinguished compossibility class: P is possible = df ∃Q(Q is a relevant fact & P is possible relative to Q). This is the tactic I am ascribing to Lewis in paragraphs 31–34.
Do we get a third way if we let distinguished facts be distinguished only by the fact that context has selected them? Not really, for then the question whether the crocodile-menaced man can escape has none but context-relative answers.
“It was true five centuries ago that I was not going to vote Republican tomorrow” (with its mixed tenses) would arguably not count as properly about the past.
In his article seeking to reconcile freedom with determination by past facts and laws, Lewis claims that although we cannot break the laws, we can do things such that if we did them, the laws would be broken (Lewis 1981). Strikingly, he does not suggest that we can do things such that if we did them, the past would be changed. Does he perhaps acknowledge here that there is an absolute sense in which the past cannot be changed?
I thank Kadri Vihvelin and an anonymous referee for helpful comments on an earlier version.
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Van Cleve, J. Lewis and Taylor as Partners in Sin. Acta Anal 34, 165–175 (2019). https://doi.org/10.1007/s12136-018-0367-2
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DOI: https://doi.org/10.1007/s12136-018-0367-2