Wolfgang Schwarz

I'm inclined to think that (iv) isn't valid (which isn't to say (ii) is alright.) Things like "p <-> @p" are theorems but are not, in general, unalterable.

For example, suppose there's going to be a sea battle tomorrow. Since it's true that if there's a storm tonight, there wouldn't be a sea battle tomorrow, presumably the sea battle is alterable. However if this holds, then it's also true that if there's a storm tonight it wouldn't be the case that there's a sea battle tomorrow iff there's actually a sea battle tomorrow. So "there's a sea battle tomorrow iff there's actually a sea battle tomorrow" must be alterable if "there's a sea battle tommorrow" is.

Hi Andrew,

interesting. You're right that there is a natural understanding of "alterable" on which (iv) fails. In this sense, a truth p is alterable if there is something one can do such that if one were to do it, then ~p. So understood, p <-> @p is alterable. But suppose you announce that you want to make it the case that ~(p <-> @p). Then it is absolutely certain that you will fail, no matter what you try. So you don't really have the power to make it the case that ~(p <-> @p). In this sense, p <-> @p is unalterable. This is the reading I had in mind.

It's interesting that, on your reading, whether or not the conclusion of this argument entails fatalism then seems to depend on whether you accept evidential decision theory. On your reading the move from: "it's unalterable whether I die in a sea battle tomorrow" to "I shouldn't bother preparing for battle" is not sound under CDT, whereas it seems to be on my reading.

This makes me prefer my reading, although, of course, the conclusion is paradoxical whether or not it entails fatalism.

Right, though it might depend on which version of CDT you pick. I think Lewis's version does support the move from "it is unalterable" to "I shouldn't bother" even on my reading of "unalterable".

(I) is the culprit. If something is possibly actually the case, it need still not be the case. Here´s why: At the time you wrote this rant, it was possibly actually the case, that you would write a smart rant, though of course you failed.
Any analysis of modality that gives rise to such absurdities as (I) should be rejected.

Thomas, I think there is a fifth principle implicit both with Wo and Bacon:
v. David Lewis says p -> p.
With the aid of this principle one can prove i.:
0. David Lewis says i. -> i..
So i. is valid.

Hi chaps,

Frank, Thomas - i) does look dodgy until you realise the logic of 'actually' being employed here. According to this logic, if p is actually the case, then 'necessarily, p is actually the case', 'p is actually the case' and 'possibly, p is actually the case' all coincide. That result is counterintuitive (maybe a bit less so when we are careful not to give 'possibly' an epistemic reading.)

Once you accept that 'actually' works this way, then I agree we need to reject ii). The question then is whether ii) can fail in a language without (this kind of) an actuality operator - I'm thinking it can't. If that's right, then we have the option of denying that the logic of 'actually' in English works as set out above, rejecting i) and preserving ii) as a fully general truth. This unfortunately involves rejecting plenty of rather neat modal logic.

Perhaps there's a middle way - we can interpret some occurrences of 'actually' in English as semantically vacuous, as providing additional emphasis or some other pragmatic effect, but not as making any difference to the truth-conditions of sentences in which they occur. This might explain why i) sounds bad - we (for whatever reason) tend to give the occurrence of 'actually' in it this vacuous reading, making it equivalent to the false 'something is the case if it is possibly the case'.

Maybe this picture is implicit in what wo and Andrew were saying, which would explain why they don't take seriously the objection expressed by Thomas.