Consider this claim:
Thesis: It is possible to have two worlds, w1 and w2, and a person x such that: (a) in w1, x is responsible for A, and (b) in w2, x is not responsible for A, but (c) there is no difference between what x is consciously aware of in w1 and in w2.
Here is an argument for the thesis. Note that "responsible" can be read as "morally responsible", "rationally responsible" and "epistemically responsible" as far as the argument goes. One can even replace "responsible" with "praiseworthy", "blameworthy" or "criticizable", in the moral, rational and epistemic senses. I shall assume that times can be represented with real numbers.
- (Premise) No human being is aware of any mental episode that lasts no more than d0=10−22 seconds.
- (Premise) There is a human being x and times t1 such that (a) x exists between t1−d0/2 and t1 inclusive, (b) x exists at t2, (c) x is not responsible for anything at or prior to t1 and (c) x is responsible for something at t2.
- (Premise) Whether there is something that x is responsible for at t does not depend on what happens after t.
- (Definition) Let T be the set of times at which x is responsible for something.
- All the members of T are greater than t1. (By 2c and 4)
- Let t* be the infimum of T, i.e., the largest real number t* with the property that every member of T is greater than or equal to t*. (t* exists by a standard theorem about real numbers as T is bounded below by 5.)
- t*≥t1. (By 5 and 6)
- (Premise) For some x satisfying the above premises, there are worlds w1 and w2 whose laws and arrangement of matter are such as to still satisfy (1) and (3) and that are such that (a) w1 is exactly like the actual world up to t*−d0/2 and at t*−d0/2, x's mind is wiped in such a way that x is never aware of anything (except perhaps some innocent bliss, if divine goodness does not permit eternal unconsciousness or cessation of existence) and is never responsible for anything; (b) w2 is exactly like the actual world up to t*+d0/2, and at t*+d0/2, x's mind is wiped such a way that from t*+d0/2 on, x has the same mental episodes in w2 as in w1.
- In w1, x is never responsible for anything. (For x is not responsible for anything in the actual world up to t*−d0/2, and by 8, w1 is just like the actual world up to t*−d0/2, and we have 3.)
- In w2, x is responsible for something at some time after t*. (For x is responsible for something in the actual world at some time between t* and t*+d0/2 by the definition of t*, and by 3 and 8, x is responsible for something at w2 at some such time.)
- x's mental episodes diverge between w1 and w2 only on an interval of times of length at most d0. (By 8)
- x is not consciously aware of anything different at w1 than at w2. (Because 8 guarantees that 3 holds at both of these worlds)
- Therefore, w1 and w2 differ in whether x is responsible for something but not in what x is consciously aware of. And that's the thesis.
I think the best way out of the argument would be to deny (1). I think (1) is pretty plausible if naturalism is true--d0 is less than the time it takes light to cross the Bohr radius of the atom--but since naturalism is false, it might be that (1) is false as well. Personally, I have little desire to get out of the argument. One might also think vagueness will get one out of the argument. But I do not think something as basic as moral, rational or epistemic responsibility is something there is vagueness about.