OK, so I am basically obsessed with this stuff about God’s omniscience and Free Will. I have been having some very interesting, and helpful, discussion about whether Plantinga’s defense, which I take it is the standard defense, of their compatibility is any good or not. I have a sneaking suspicion that the two are incompatible and I have been trying to construct a poof to that effect, with mixed results…but I think I got it this time…if it turns out that I don’t then I promise that I will give up!
It seems to me that the problem is that “If God knows what I will do before I do it then it is necessary that I do it” does not really capture what the person who says that God’s foreknowledge is incompatible with our free will is trying to say. This is because, as we have seen, it must be the case that all my actions are necessary, but this doesn’t sound right at all (however, I do think some people are committed to it).
So, to make it clearer what I am actually trying to say, let me introduce a new modal operator ‘@’ with the following truth condition, where ‘v(x,w)’ is the valuation of x at world w,
v(@a, w)=T iff v(a, actual world)=T
v(~@a,w)=T iff v(a, actual world)=F
this says that @a is true if a is in fact true at the actual world and ~@a is true if a is in fact false at the actual world (~@a<–>@~a) so there is no need to introduce a fourth operator). ‘’ and ‘<>’ are given their usual interpretations.
Then I can say that God actually knows before I do a certain action that I will in fact actually do it. To avoid getting involved in tense logic let us introduce a predicate ‘B’ for before (though I think we could define ‘B’ in terms of the standard tense operators F, P, H, and G). Let ‘k’ be ‘God knows that’ and ‘a’ be some action of mine, then I can symbolize ‘God actually knows before I do action a that I will in fact actually do action a’ as @B(k,a), then the proof goes as follows
1. @a & @B(k,a) (this says that God actually knows what I did before I did it)
2. @B(k,a) –> @a (necessary truth)
3. @a –> @B(k,a) (necessary truth)
4. @a (from 1)
5. @B(k,a) (4,3 MP)
6. @a (5,2 MP)
7. (@a & @B(k,a)) –> @a (1-6 conditional proof)
Since 7 says that if it is the case that I actually do a and God knows beforehand that I actually do a then it is necessary that I actually do a, and God’s actually knowing that I do a entails that I actually do a (7) reduces to
7′ @B(k,a) –> @a
which says that if God actually knows what I will do beforehand then it is necessary that I actually do it.
Now one may wonder what the difference between ‘a’ and ‘@a’ is. Ordinarily there will be no difference, but there will be a huge difference when we examine the modal properties of the two. a will be true iff a is true in all possible worlds, whereas @a will be true if @a is true in all possible worlds, or in other words if it is the case that at every possible world it is true that, in the actual world, I do a. This is why (3) above is a necessary truth but (3′) is not,
(3′) a –> B(k,a)
(3′) says that if I do a then in every possible world God knows beforehand that I will do a. This can be false because there are possible worlds where the antecedant turns out false because in that world I do not do a and so God does not know it. But (3) can’t be false. For if it were then it would be the case both that I actually do a and that God did not actually know beforehand that I did a, which is just to deny that God is omnicient (so enigman will be happy).
Whew! So, if this is right then God’s foreknowledge is indeed incompatible with my having free will. If not then I will finally have to admit that there is at least one metaphysical interpretation on which it can both be true that God knows what I will do before I do it and that I am free…and I will then actually be very depressed!