This is a friendly puzzle for my friends over at the Choosing Hats website. I can imagine that contesting with village atheists can be an exasperating experience, so here is something a little different:
Presuppositional Apologetics can’t account for all Truth!
First, some definition:
P: Some proposition P
[_]x: Necessarily x
Vx: All of x
~>: if then conditional
(1) If the Christian God makes P true then, necessarily, if the Christian God exists then P is true.
I don’t think an Presuppostional apologist would disagree with (1), but this leads to a modal collapse if First Order Quantification and S5 modal logic hold:
(2) [_] Vx: F ~> Vx: [_] F (Converse Barcan Formula)
Now let us take an instance of CBF:
(3) [_] Vx: x exists ~> Vx: [_] (x exists)
Now (3) tells us that if it is necessary that everything exists, then everything exists necessarily! What (1) leads us to is that God can’t make a contingent truth, indeed, there could be no contingent truths.
(C) The Christian God cannot account for all Truth.
Amended: Another way to look at this is if the Christian God is a truth maker for any proposition P, and if the Christian God exists necessarily, then anything that is true is necessary., no contingent truth could have the Christian God as it's truth maker.