In my original free will post, I took it for granted that to say someone "could have done otherwise" conflicted with determinism only if that 'could' was interpreted categorically, rather than hypothetically.
I originally thought Van Inwagen's argument (that "could have done otherwise" is inconsistent with determinism) was only intended to apply to categorical coulds, and so was a waste of time (since it's arguing for something which nobody disputes). But apparently Van Inwagen meant for the argument to apply to hypothetical 'coulds' also - which is a much more interesting claim.
Here's a summary of the argument: Saying "S could have done otherwise" is equivalent to saying "S could have rendered the current state of affairs (P) false". But according to determinism: the past state of the universe (P0), in conjunction with the laws of nature (L), together necessitate the present state of affairs (P). So to make P false, you must make either P0 or L false. But surely S could not change the state of the universe before he was born, nor break the laws of nature. So S could NOT render P false. Therefore, determinism implies that S could NOT have done otherwise.
But let's have another look at what "(hypothetical) could" means: S could have done X if he had wanted to. That is, if there had been a different past state of affairs (which led S to have different desires), then S would have chosen differently. This is fully consistent with determinism (obviously so, I would have thought!), so lets see where Van Inwagen's argument fails...
Van Inwagen's challenge is to resolve the apparent inconsistency of the following triad:
1) S could not have rendered false either P0 or L.
2) P0 & L necessitate P.
3) S could have rendered P false.
I want to argue that #1 is either false or unimportant(i.e. it doesn't conflict with #3). The key is, of course, the precise meaning of "could" as used here. Recall we're talking about hypothetical coulds here. To save me effort, let's introduce the abbreviation SDDT to represent the counterfactual proposition that S's Desires had been Different at time T. Now, whenever we say 'S could X' above, we really mean If SDDT, then S could X. But we need to make a further distinction, regarding what sort of power the 'could' is assigning to S (or rather, to S's desires): Causal power, or logical power.
a) Logical power: This merely requires that there be a logical connection between SDDT and X, such that the truth of SDDT guarantees X, i.e. if SDDT, then X. So to say "S could make P0 false" is simply to say that "if SDDT, then P0 would be false". But this is a true statement!*(see update) P0 must be false as a precondition of SDDT (if the previous state of affairs were not different, then S's desires could not be different either! [note: determinism is assumed true for the sake of the argument]). So, according to this interpretation of the hypothetical 'could', #1 is false, thus rendering Van Inwagen's argument unsound. This interpretation may strike you as implausible, because it effectively takes S out of the picture.
b) Causal power: This more natural interpretation requires a stronger connection, to the effect that SDDT causes X (or, to rephrase it with a greater focus on S, "if SDDT then S would cause X"). Now, #1 is surely true (the present might be able to guarantee the past, but it cannot cause it!), but it means that the set is no longer inconsistent. The key here is the distinction between immediate and ultimate causes.
Let's start with a simple analogy. Imagine you're ten-pin-bowling, and although you aim down the centre, the ball curves off to the left and so misses all the pins. Bugger, eh. Anyhoo, now suppose a friend had advised you to aim to the right instead, so that the leftward curve straightened the ball, resulting in a strike. Now, we surely recognise the following three statements can all be simultaneously true:
1') Your aiming to the right did not cause your friend to advise you thus.
2') Without the advice, you would not have bowled a strike
3') Your aiming to the right caused the strike.
To sum up the crucial point as simply as possible: you can cause an event without being the ultimate cause of it.
The appropriate response to Van Inwagen's argument should now be clear: #3 effectively says that "SDDT causes P to be false", which is true. #1 says that "SDDT does NOT cause the falsity of P0 or L" - also true. The fallacy is thinking that there is any conflict here. The implicit inference is something along the lines of "if X causes Z, and Y does not cause X, then Y does not cause Z". But such an inference is clearly invalid, as the bowling example demonstrates. You can have a causal chain X -> Y -> Z, or in our case: ~(P0 & L) -> SDDT -> ~P.
So no matter whether you interpret the hypothetical 'could' as conveying a logical power or causal power, Van Inwagen's argument fails.
As far as I can tell, the main weakness of my argument here is in forging the logical/causal dichotomy regarding interpretations of hypothetical 'could'. I'm concerned that it may be a false dichotomy. Perhaps there is an alternative, more appropriate, interpretation which I have not considered here. If you can think of any possibilities, please comment and let me know! (Just be careful not to sneak in any categorical notions - i.e. don't forget the 'if' part in "if SDDT, then S could X")
P.S. For any readers from my metaphysics class following Van Inwagen's extended argument as presented in our lectures, the 'logical' response denies premise 5 (F->G), whereas my 'causal' response denies premise 4 (E->(B->F)).
* Update: I made a slight mistake above. Technically, SDDT implies the falsity of either P0 or L. Above I assumed that the hypothetically false one is P0, but now I think L is actually the better option.
Recall that SDDT is the hypothetical situation we are considering. What I'm now asking, is how we are imagining this hypothetical situation to have come about. I previously assumed that we imagine the laws of nature (L) are held constant, but we change the original state of the universe (i.e. make P0 false) just very slightly, so that the situation of SDDT would come about with as little other deviations from historical reality as possible. But this may not be possible, given chaos theory - a tiny change in initial conditions can have momentous consequences (ya know, butterflies causing hurricanes and all that).
So I think the hypothetical situation of SDDT is best understood as follows: The past all progressed exactly as it did in reality, right up until the moment before time T. At this moment, the laws of nature are (hypothetically, remember!) broken, so that S's desires at T are different. That is, we make SDDT true by making L false, but P0 remains true.
What does this mean for my original argument? Well, the only part of my argument affected is that 'logical power' part. You simply need to take every mention of P0 (in that one paragraph) and replace it with "P0 or L". That fixes it. It's useful to consider the two possibilities separately though, which is why I've written this long update instead of making the simple replacement before anyone noticed ;)
Why is it useful? Because it effects my formal response to Van Inwagen. The original "P0 is (hypothetically) false" version leads to the denial of premise 5 (F->G, as noted in my post-script above). But the new "L is (hypothetically) false" option discussed here will lead to the denial of premise 6 (~G) instead.
So that's that. Sorry for being long-winded. From what I've heard (which is not much), denying 5 or 6 is the usual response to Van Inwagen. So I'm much more interested in my 'causal' response which denies 4 instead - I'm unaware of that being tried before.