Omniscience, Foreknowledge, and Free Will

S is omniscient =df for every proposition p, if p is true then S knows p

Boethius (480-524), The Consolation of Philosophy,

There seems to be a hopeless conflict between divine foreknowledge of all things and freedom of the human will.
Just as when I know that a thing is, that thing must necessarily be; so that when I know that something will happen, it is necessary that it happen. It follows, then, that the outcome of something known in advance must necessarily take place."

This suggests the following argument:

If God knows that S will do A, then it must be the case that S will do A.

If it must be the case that S will do A, then S isn't free with respect to A.
Therefore,

If God knows in advance that S will do A, then S isn't free with respect to A.

Boethius: God is "outside of time".

C. S. Lewis, Mere Christianity:

Everyone who believes in God at all believes that He knows what you and I are going to do tomorrow. But if he knows that I am going to do so-and-so, how can I be free to do otherwise? Well, here, once again, the difficulty comes from thinking that God is progressing along the Time-line like us: the only difference being that He can see ahead and we cannot. Well, if that were true, if God foresaw our acts, it would be very hard to understand how we could be free not to do them. But suppose God is outside and above the Time-line. In that case, what we call "tomorrow" is visible to Him in just the same way as what we call "today." All the days are "Now" for Him.

amphibole: grammatical (as opposed to semantical) ambiguity.

Save soap and waste paper.

Standing on the balcony he watched the fireworks go off in his pajamas.

(1') It's necessary that if God knows in advance that S will do A, then S will do A.

(1'') If God knows in advance that S will do A, then the proposition that S will do A is necessarily true.

K = God knows in advance that S will do A

D = S will do A

F = S isn't free with respect to A

let '□' stand for 'it's necessary that'

Interpretation 1

(1') □(If K then D)
(2) If □(D) then F
∴(3) If K then F

Interpretation 2

(1'') If K then □(D)
(2) If □(D) then F
∴(3) If K then F

Evaluation of Interpretation 1:

The form of Interpretation 2:

If p then ∴q
If q then r
∴If p then r

Evaluation of Interpretation 2: