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David K Johnson's argument against free will

David K Johnson is a reductive materialist--as far as I can tell.  He has an interesting argument against freedom of the will: instead of arguing from the necessity of the laws of physics, he argues from the nature of truth.  It goes something like this:  Given that X has happened, then it it is true that X, then it cannot be false that X, then X is true necessarily, then the event described by X cannot be contingent, then if that event is an act of human choosing, then that human chose necessarily, then no human choice is contingent.  But such contingency is a necessary condition for freedom; hence no human choice is free.  I must be missing some of the subtleties that he would like introduced, but please excuse that for the moment, as I don't so much want to undermine the argument by looking at how its premises might fail to support its conclusion as much as I want to explore its implications.

Important:  to pull this off he treats propositions as atemporal.

If the combination of our desire to know the truth and the evidence and argumentation mustered in support of his conclusion cause us to accept his conclusion, then something other than a material process (i.e., the truth of the propositions, inference) can influence our behavior.  In such a case, the notion that all human actions are explained entirely in terms of material processes would be false.

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