January 02, 2007

Modality at the APA

I realize that time is an illusion and that 07 will be more of the same, but nevertheless feel compelled to drink champagne and wish you all a very happy new year.

There were some interesting talks at the APA in DC. For instance, Alan Hajek argued that most counterfactuals are false. Let P and Q be contingent formulas and suppose that it is not the case that both P and Q. Then the argument goes something like this:

1. Might and would are dual operators. That is, P []--> Q (i.e., if it were that P, then it would be that Q) is equivalent to ~(P <>--> ~Q) (i.e., it's not the case that if it were that P, then it might be that ~Q).

2. For each counterfactuals, P []--> Q, there is some objective chance that P but ~Q. So if P were the case then it might be that ~Q.

By 1 and 2, it follows that

3. P []--> Q is false.

At that session Dorothy Edgington and Bill Lycan had very interesting things to say as well. Some of the debate centered around whether the argument might go through even if premise 1 were false. Something like this would be favorable to Hajek's positions since arguably 'might' is an epistemic modal and 'would' is not. There was also disagreement about whether a natural counterfactual contextualism, analogous to epistemic contextualism, might block the argument. Hajek remained skeptical.

In an altogether different session on modality, Michael Nelson responded to Michael Fara and Timothy Williamson's paper "Counterparts and Actuality", in which it is argued that Lewis' counterpart theory (CPT) should be rejected because it is incompatible with the logic of actuality. Michael Fara was the official commentator and Williamson commented from the audience. Needless to say, Fara and Williamson were not about to let Nelson off easy. The dialectic went something like this.

Fara and Williamson argue that claims like

A: "It is possible that everyone that is actually rich was poor."

, and

B: "n is a botanist, but is not actually a botanist.",

once translated into CPT augmented with an actuality operator, deliver propositions with the wrong modal status. Contrary to what is required, the CPT translation of B is consistent (since true in models of CPT in which the denotation of 'n' has no actual world counterparts) and the CPT translation of A is false (since false in every CPT model).

Nelson offered some ways to defend CPT against this line of argument (for instance, by going second order or by adopting a 2-dimensional semantics). F and W however objected that, at least, Lewis would not be happy with these amendments since one of the advertised benefits of CPT is that it allows us to explain modality with no more than standard first-order extensional semantics.


Mike said...

Hi Joe,

Quick questions on (2).

2. For each counterfactuals, P []--> Q, there is some objective chance that P but ~Q. So if P were the case then it might be that ~Q.

I guess I don't see why an objective chance that P and ~Q entails that (P <>-> ~Q). There is some objective chance that the sun rises tomorrow and that I de-materialize (and re-materialize elsewhere). But the chances are infinitesimally small. Why would we say that in some of the closest worlds to ours in which the sun rises, I dematerialize? I should think that that happens in none of the closest worlds. On a separate point, I guess I'm not sure that increasing the probability that (P & ~Q) will in general ensure that there are some similar (P & ~Q)-worlds. Does Hajek claim that it does?

joe said...

Hi Mike,

That's the right question. Consider the following version of the argument:

(a) If I were to play the lottery, I might win.


(b) it is false that if I were to play the lottery I would lose.

From what I remember from the talk, Hajek takes each argument against the truth of a counterfactual to share much in common with the above argument. He assimilates the relevant objective chance (of the antecedent conjoined with the negation of the consequent) to lottery-like possibilities. One way that he does this is by appealing to quantum mechanics, where we find standard expected possibilities to be no closer than the non-standard unexpected possibilities.

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