Richard Carrier's Argument from Specified Complexity

Noted pseudo-philosopher Richard Carrier has an argument which, he thinks, demonstrates that "we should think the supernatural is impossible." Specifically, he wants to claim that "God's mind appears to be logically impossible." His line of reasoning goes (more-or-less) as follows:

1. (Assume for contradiction) God's mind is simple and immaterial.
2. God's mind must be able to store and process information.
3. Information storage and processing require specified complexity.
4. Such complexity requires some material on which information can be stored and circuitry stamped.
5. God's mind is complex and material (from 2-4).
6. Contradiction (from 1 and 5). 

Unfortunately, Carrier seems to have gotten himself tripped up on the nature of God's knowledge. For he writes:

A god has to know things (store information), and think things (process information). But there is a difference between correct and incorrect information, present and absent information; between conflation and distinction. A god has to be able to distinguish one person’s face, from another; and correctly connect each face, with other information about the corresponding person, like that Joe’s face goes with Joe’s job in sales and wife of eleven years, and Mark’s face goes with Mark’s service in the military and husband of eleven years. That information could be connected up differently—wires crossed, and Joe’s face gets incorrectly linked to Mark’s husband, producing the false information that Joe has a husband, and so on. And notice how many different ways connections can be crossed up: the more information, the more different connections are possible. And most of them (in fact, all but one of them; out of effectively infinitely many) will be false.

However, as the physicist Aron Wall pointed out in response to a near-identical objection (ironically put forward by a couple of conservative Mormons), "This is only an issue if you assume that God's knowledge is, like ours, representational, that is, that it proceeds by means of making something like an image or duplicate of the object known, in some other physical system (in our case, the brain)." But of course, classical theism does not make such an assumption; rather, it has always held that God knows all things via direct awareness, simply by knowing Himself as creator and sustainer of all things (hint: this is part of what CTs mean when we say that God's knowledge, creative act, etc. are really all one thing). Thomas Aquinas provides a useful summary of this concept, when he writes:

Now, it is not repugnant to the simplicity of the divine mind that it understand many things; though it would be repugnant to its simplicity were His understanding to be formed by a plurality of images. [...] Inasmuch as He knows His own essence perfectly, He knows it according to every mode in which it can be known. Now it can be known not only as it is in itself, but as it can be participated in by creatures according to some degree of likeness.  But every creature has its own proper species, according to which it participates in some degree in likeness to the divine essence. So far, therefore, as God knows His essence as capable of such imitation by any creature, He knows it as the particular type and idea of that creature; and in like manner as regards other creatures. So it is clear that God understands many particular types of things and these are many ideas. (ST I.15.2)

The idea that God's knowledge does not consist in stored-up beliefs or mental images may also be found outside of the Thomistic tradition. For example, William Alston (1986), a critic of divine simplicity, was nevertheless a major proponent of the idea that God has no beliefs whatsoever, but rather knows all things via direct awareness. To quote:

A creature in our condition needs inner representations in order to be able to think about absent states of affairs, since the facts are rarely if ever directly present to our consciousness. But since God enjoys the highest form of knowledge He is never in that position, and so He has no need for inner representations that He can ‘carry around with him’ for use when the facts are absent. The facts are never absent from His awareness; thus it would be fatuous to attribute to Him any such mental map. When we have arrived at our destination we can fold the map away.

In a recent paper defending Alston's view, Saeedimehr (2021) discusses two non-propositional accounts of God's knowledge, each of which would seemingly allow us to avoid Carrier's argument. To quote:

Since God is absolutely simple, He (His essence) is identical with his knowledge. Therefore, God’s knowledge is totally simple and hence it is beyond any kind of complexity, including the complexity due to having a propositional structure.

Since Alston finds the principle of Divine simplicity quite problematic, he seeks another basis for the non-propositional position. He argues that as human beings, our propositional knowledge stems from two of our limitations: first we ‘cannot grasp any concrete whole in its full concreteness’, and second ‘we need to isolate separate propositions in order to relate them logically’ and then ‘extend our knowledge inferentially’. But since God is obviously beyond these limitations, His knowledge is not required to be propositional.

It would seem, then, that a non-propositional account of God's knowledge allows us to reject premise (2) of Carrier's argument; namely, that God's mind stores and processes information. God does not store information at all (or to quote Alston, "carry [it] around with Him"); rather, at any one moment He has an infallible intuitive grasp of all facts. Similarly, God does not need to "process information" (or to quote Alston, "isolate separate propositions in order to relate them logically"). We need to do that, because our cognition is fallible and limited; God, on the other hand, is far beyond such things.

One hopes that Carrier himself never gets wind of this post, lest I be subjected to his, uh... scholarly rigor.