April 25, 2007

Essences and Impossible Antecedents

The first issue of The Reasoner has just appeared online. Berit and I contributed a paper, "Why Counterpossibles are Non-Trivial", in which we give three reasons for rejecting a vacuous reading of counterpossibles. One reason is that a non-trivial reading facilitates an analysis of essences. While Kripke's wooden table, Tabby, is necessarily a member of the set {Tabby}, it is not essential to Tabby that it be a member of that set. Neither is it essential to Tabby that seven is prime. It is tempting to offer the following explanation. If there hadn't been sets, Tabby might still have existed; and if seven hadn't been prime, Tabby might still have existed. But this sort of explanation requires, for its non-triviality and informativeness, that counterpossibles be non-trivial and informative. At some of the closest (impossible) worlds where there are no sets (or numbers), Tabby exists. By contrast, Tabby fails to exist at all the closest worlds where there is no wood. It is essential to Tabby that he be wood, but not essential to Tabby that seven is prime. Generally, x is essentially F iff x would not have existed if nothing had been F

April 17, 2007

Lewis on Non-Trivial Counterpossibles

Lewis offers a number of reasons for his, the now standard, reading of counterpossibles--viz., that they are all vacuously true. He does not take his reasons to be decisive. Let's revisit the reasons. Lewis writes,

There is some intuitive justification for the decision to make a 'would' counterfactual with an impossible antecedent come out vacuously true. Confronted by an antecedent that is not really an entertainable supposition, one may react by saying, with a shrug: If that were so, anything you like would be true! Further, it seems that a counterfactual in which the antecedent logically implies the consequent ought always to be true; and one sort of impossible antecedent, a self-contradictory one, logically implies any consequent. [Counterfactuals 24]

There are two reasons given here. The first is difficult to disagree with. An antecedent that is not really an entertainable supposition, invokes triviality. If Socrates were a potato, then, sure, anything goes! I'm down with that intuition. But this is not an objection to the position that I'm more inclined to, which says that counterpossibles are sometimes non-vacuously true (and sometimes false). Lewis' point suggests incorrectly that all counterpossibles involve an antecedent that is not entertainable. Counterlogicals, such as 'if excluded middle were invalid, then double-negation elimination would be invalid too", sometimes express non-trivial consequences of alternative logics. The sincere entertaining of such logics is something that we really can, and often do, do. That said, I share Lewis' view about non-entertainable suppositions. In sum, the position that allows for a non-vacuous reading of some counterpossibles should also allow for the vacuous reading of others.

The second reason that Lewis articulates above says that a counterfactual whose antecedent logically implies the consequent ought always to be true. That is, it ought to be that logically strict implication implies counterfactual implication. Perhaps there is a pre-semantic-theoretic intuition here. But counterpossibles are strange animals from any point of view. It shouldn't be too much of a concern if they run contrary to a pre-theoretic intuition. Moreover, putting too much weight on the intuition would be question-begging. Anyone who is convinced that there are non-trivial counterpossibles will not share this intuition about the relation between strict and counterfactual implication. Lewis seems to have ruled out in advance that there might be impossible antecedents that we sincerely entertain. For this reason, I don't think that he was considering the more interesting candidates for the non-trivial reading. The bottom line is that the Lewis intuition just isn't shared by those who take seriously the idea that some impossibilities may be sincerely entertained counterfactually.

Lewis offers an explanation for why some of us believe in non-trivial counterpossibles. He hypothesizes a mistaken need to explain why some counterpossible that we do want to assert are true and others that we do not want to assert are false. He writes,
I do not think, however, that we need to discriminate in truth value among such counterfactuals. Of course there are some we would assert and some we would not:
If there were a largest prime p, p!+1 would be prime.
If there were a largest prime p, p!+1 would be composite

are both sensible things to say, but

If there were a largest prime p, there would be six regular solids.
If there were a largest prime p, pigs would have wings.

are not. But what does that prove? We have to explain why things we do want to assert are true (or at least why we take them to be true, or at least why we take them to approximate to truth), but we do not have to explain why things we do not want to assert are false. We have plenty of cases in which we do not want to assert counterfactuals with impossible antecedents, but so far as I know we do not want to assert their negations either. Therefore, they do not have to be made false by a correct account of truth conditions; they can be truths which (for good conversational reasons) it would always be pointless to assert. [24-25]

I agree that a willingness to assert the former, but not the latter, examples is not a good reason to hypothesize distinct truth-values. Indeed, it appears to me that all four examples have the same truth-value. The context of the latter two presumably invokes the trivial world where anything goes, and the context of the former two presumably invokes non-trivial reasons for thinking that the consequents obtain in the counterfactual circumstances described. What Lewis leaves out are cases where, in fact, we do want to assert the negation of a counterpossible. For instance, it is false that if intuitionistic logic were the correct logic, then excluded middle would still be valid. This counterpossible is not merely something that we wouldn't want to assert; it is something we should want to deny! Lewis' pragmatic explanation of the desire for non-trivial truth conditions does not appear to generalize.

April 15, 2007

Synthese Deadline Approaching

This is a reminder about the May 1 deadline for paper submission for the special issue of Synthese, "Knowability and Beyond", which aims to cover modal epistemic issues relevant to knowability, broadly construed. The issue will contain invited papers by Jonathan Kvanvig, Gabriel Sandu and Neil Tennant, but will also provide the opportunity for other authors to make original contributions. Submissions will be double-blind reviewed. If you have something but aren't sure whether it would be appropriate for consideration, email me.


April 12, 2007

Vonnegut 1922-2007

Kurt Vonnegut on the purpose of life: "to be the eyes and ears and conscience of the creator of the universe, you fool"