A Problem for Plantinga's Proper Functionalism

The Argument: If theism is true, then, probably, none of our beliefs have warrant. But surely many of our beliefs do have warrant; therefore, probably, theism is false.

The Argument Expanded: If theism is true, then Plantinga's account of warrant is probably correct. Now, roughly, Plantinga analyzes warrant in terms of beliefs formed by properly functioning, (successfully) truth-aimed cognitive faculties in congenial epistemic environments. However, he rejects naturalistic accounts of function, instead requiring essential appeal to intentional design in any adequate account of function.[1] However, he also thinks God is a person with cognitive faculties, and that his faculties weren't designed. Therefore, on his own account, they lack functions, in which case, a fortiori, they can't function properly. But if not, then on his own account, God's beliefs lack warrant. But if God's beliefs lack warrant, then it's hard to make intelligible the notion of God as a competent designer of our cognitive faculties. Therefore, if theism is true, then our beliefs probably don't have warrant. But surely many of our beliefs do have warrant. Therefore, probably, theism is false.

UPDATE: I recently read an article in which (Christiian philosopher) R. Douglass Geivett and Greg Jesson raise roughly the same criticism against Plantinga's account of warrant. See their "Plantinga's Externalism and the Terminus of Warrant-Based Epistemology", Philosophia Christi 3:2, pp. 329-340.
[1] Plantinga argues for this claim in ch. 11 of Warrant and Proper Function (Oxford University Press, 1993). A more recent, explicit statement from Plantinga that proper function entails intelligent design, see Plantinga and Tooley, Knowledge of God: ". . . this notion, the notion of proper function, essentially involves the aims and intentions of one or more conscious and intelligent designers" (p. 29).  For a critique of Plantinga's claim here, see, e.g., Wunder, Tyler. "Anti-Naturalism and Proper Function", Religious Studies 44 (2008), pp. 209-224; and Bardon, Adrian. "Reliabilism, Proper Function, and Serendipitous Malfunction", Philosophical Investigations 30:1 (2007), pp. 45-64. (Btw, Bardon offers a nice revised version of Bigelow and Pargetter's naturalistic analysis of functions in the latter paper.)

The Argument from Logic

Rough draft: Post stub. The fact that orthodox theists, from at least Augustine and all the way to the present, have seen logic as the expre...