A while ago I was obsessed with trying to show that God’s foreknowledge of our actions was incompatible with Human free will. I have had some time to reflect on the issue and I want to take another stab at it.
So, let ‘K’ be ‘knows that’ and ‘G’ stand for God, and ‘R’ for Richard Brown (me). Then (1) says that if God knows that I will do some action then it is necessary that I do that action.
(1) (x)(K(G,R,x) –> (D(R,x))
(1) captures the intuition that God’s knowledge necessitates our actions. I think that this is true, so to prove it I tried to show that denying it leads to a contradiction and, since it can’t be false it must be true. Here is the proof.
1. ~(x)(K(G,R,x) –> D(R,x)) assume
2. (Ex)~(K(G,R,x) –> D(R,x)) 1, by definition
3. (Ex)~~(K(G,R,x) & ~D(R,x)) 2, by def
4. (Ex) (K(G,R,x) & ~D(R,x)) 3, by def
5. K(G,R,a) & ~D(R,a) 4, EI
6. K(G,R,a) 5, CE
7. K(G,R,a) 6, necessitation
8. ~D(R,a) 5, CE
9. (x) (K(G,R,x) –> D(R,x)) assumption (2′)
10. (K(G,R,a) –> D(R,a)) 9, UI.
11. K(G,R,a) –> D(R,a) 10, distribution
12. ~D(R,a) –> ~K(G,R,a) 11, contraposition
13. ~K(G,R,a) 8,11 MP
14. K(G,R,a) & ~K(G,R,a) 7,13 CI
15. (x)(K(G,R,x) –> (D,R,x)) 1-14 reductio
The main objection centered on step (lucky number) 7 and my use of the rule of necessitation. 7 says that it is necessay that God knows that I perform action a. That means that it would have to be true in every possible world that God (in that world) knows that you perform action a. This may seem unreasonable if one thinks that there is a possible world where you do not perform action a. But if actions are events that can be named then it is easy to show that they must necessarily exist, in which case I would have to perform that action in every world where I exist, and snce it is just as easy to show that I must necessarily exist it follows that God would indeed know that I perform action a in every possible world and so 7 comes out true. So if one accepts S5 then one should not have a problem with 7.
But suppose that one rejects, or modifys S5 to avoid the embaressment of necessary existence? Then 7 starts to look fishy again. But is it? Say that there is some world where I do in fact perform a and some other world where I do not. Call them ‘A’ and ‘~A’. The in A God knows that I perform a but in ~A He doesn’t know that I perform a because it is false that I perform a and God does not know falsehoods. But is it really true that in ~A God does not know that I perform a? He knows everything, so He knows what is possible and so He knows that there is a possible world where I do perform a. Yes, but that just means that He knows “possibly Richard performs a’ not ‘Richard performs a'”, or in symbols; he knows <>D(R,a) not D(R,a). This I admit, and so it seems that there is a conception of God’s foreknowledge that is compatible with Human free will. But there does seem to be a sense in which He still knows that I do a; He knows in which possible worlds I do it and in which I don’t. But maybe that isn’t enough to justify 7 and so enough to avoid the issue.
But notice that it is a conception of God as confined to particular possible worlds where he knows all and only the truths in that world that is the actual world. The possible worlds are not real worlds but formal descriptions or specifications of how the actual world could have been and God has maximal knowledge of that. If one were a modal realist and thought that the possible worlds were real worlds that exist then there would be a problem here. In each world God would know either that you perform action a in that world or that you perform it in world-x. In both cases He knows that you perform action a and so it will true in all worlds that He knows that you do a. So 7 would be true again.
So I conclude that there are some interpretations where 7 comes out true; in which case there are some metaphysical systems in which God’s omniscience is incompatible with Human free will. Or He’s a dialetheist…