### Counterpossibles

Sorry I'm late posting on chapter 5...I just finished reading it today. I found this chapter more interesting than the rest of the book so far, but then again I also felt like Williamson was here just doing straightforward modal epistemology instead of furthering the overall project of the philosophy of philosophy. In any case, I like the suggestions he makes connecting the epistemology of counterfactuals with the epistemology of modality.

I'm unconvinced, though, by his responses to the counterpossible objection. The objection is that Williamson is wrong to say that counterfactuals with impossible antecedents are vacuously true since some such counterfactuals are false. For example, suppose you ask me what is the sum of 5 and 7 and I say '11'. Further suppose that I mistakenly think I said '13' and I then go on to assert: "If 5 + 7 were 13 I would have got that sum right." This counterfactual has an impossible antecedent, but it seems straightforwardly false. Since I actually answered '11', I would still have gotten the sum wrong even if 5 + 7 were 13. This seems right to me.

One of Williamson's objections is that when we think through the example, it falls apart. He says: "For example, if 5 + 7 were 13 then 5 + 6 would be 12, and so (by another eleven steps) 0 would be 1, so if the number of right answers I gave were 0, the number of right answers I gave would be 1." But I don't understand what Williamson is saying here. Is he saying that the friend of counterpossibles in this case has to say that if 5 + 7 were 13, then I would have got the sum right, since it would follow from my giving 0 right answers that I did give 1 right answer after all? If this is what he's saying, I'm not sure why the friend of counterpossibles has to follow him in reasoning this way. It's much less clear to me, for example, that if 5 + 7 were 13 then 5 + 6 would be 12, than it is that if 5 + 7 were 13 then I would have got that sum right. Moreover, his objection here seems to rely on the fact that this is a mathematical example. But surely there are plenty of other intuitively false counterpossibles. Suppose, as Joshua does below, that it is impossible for two objects to be co-located. Then isn't the following both false and a counterpossible: "If Joshua's finger and my finger were co-located, then Joshua would be my son"?

I'm unconvinced, though, by his responses to the counterpossible objection. The objection is that Williamson is wrong to say that counterfactuals with impossible antecedents are vacuously true since some such counterfactuals are false. For example, suppose you ask me what is the sum of 5 and 7 and I say '11'. Further suppose that I mistakenly think I said '13' and I then go on to assert: "If 5 + 7 were 13 I would have got that sum right." This counterfactual has an impossible antecedent, but it seems straightforwardly false. Since I actually answered '11', I would still have gotten the sum wrong even if 5 + 7 were 13. This seems right to me.

One of Williamson's objections is that when we think through the example, it falls apart. He says: "For example, if 5 + 7 were 13 then 5 + 6 would be 12, and so (by another eleven steps) 0 would be 1, so if the number of right answers I gave were 0, the number of right answers I gave would be 1." But I don't understand what Williamson is saying here. Is he saying that the friend of counterpossibles in this case has to say that if 5 + 7 were 13, then I would have got the sum right, since it would follow from my giving 0 right answers that I did give 1 right answer after all? If this is what he's saying, I'm not sure why the friend of counterpossibles has to follow him in reasoning this way. It's much less clear to me, for example, that if 5 + 7 were 13 then 5 + 6 would be 12, than it is that if 5 + 7 were 13 then I would have got that sum right. Moreover, his objection here seems to rely on the fact that this is a mathematical example. But surely there are plenty of other intuitively false counterpossibles. Suppose, as Joshua does below, that it is impossible for two objects to be co-located. Then isn't the following both false and a counterpossible: "If Joshua's finger and my finger were co-located, then Joshua would be my son"?

## 1 Comments:

Neal,

I also didn't understand this argument. I take it that your formulation is correct. The key premise is something like the following:

(KP1) If 5+7 were 11, then 5+6 would be 10 and 5+5 would be 9 and . . . 0+0 would be 1 and so 0 would be 1 and so if you had 0 correct answers to the math problem, you also had 1 correct answer.

It is a little difficult to see how to fill out the argument, but we need not worry about that. It seems clear that a person who believes in false counterpossibles should believe in impossible worlds. But, impossible worlds need not be closed under classic logical consequence. We might accept that there is an impossible world where 5+7=13 and yet deny that 5+6=12 in that world. And so, the key premise (KP1) is probably false (at least according to those who deny Lewisian account of counterpossibles).

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