One possible objection to Theism is this: in the case of human or animal minds, we think using our brains. This is a rather complicated chunk of matter, that has—at the very least—a rather large amount to do with determining what our thoughts are. Assuming that there is a divinity which transcends the material world, and everything else, it wouldn't and couldn't have anything like a brain. So how could God possibly think?
The problem is aggravated all the more if we decide that the fundamental reality should be simple in the sense of not being composed of any kind of parts (this is a technical term in theology, not to be confused with "simple" in the sense of easy to understand or unsophisticated). Since if it were composed of separable parts, it would be natural to seek some explanation further back about how these parts got to be stuck together.
Recall, however, that I only proposed that God is like a mind, not that his mind works in the exact same way that ours does. Because we have brains, our knowledge is necessarily limited (because there's a limit to the information capacity and reliability of a finite piece of matter) and also indirect (because we experience things in the outside world by representing them as particular patterns of firing neurons).
If God does not have a brain, then there is no physical mechanism to determine which things he knows and which he doesn't know. So it seems likely he would have to know either nothing or everything. (Aristotle stands up to propose the compromise that God knows only his own act of thinking, but let's ignore him.) Since our original motivation for Theism was that God is like a mathematician who can appreciate the mathematical elegance of the physical world, it seems only the omniscience option will do.
Unlike us, God knows things directly, rather than by the mediation of a perceptual apparatus and neural processing. For if an omniscient being knew things by representation, then he would need an exact identical copy of the entire Universe in his brain. If he is omniscient, the copy would be exactly like the original, which seems absurd on grounds of redundancy: everything in the world would exist twice, once in reality and once exactly the same in God's mind. Better to say that God just knows whatever is true, or rather that God is such that his knowledge and Truth are one and the same thing! (This, incidentally, also provides a general recipe for dispelling almost any supposed logical paradox about omniscience. Just replace all instances of “God knows X” with “X is true”, and then you will have a new paradox which must have a solution, even if you are an atheist. That solution is then also available to the theist.)
Some readers may think that this view of God is a form of Pantheism, because in some sense the world is a part of God's thoughts. But I don't think this is true. The views which I am articulating here are a form of Classical Theism, which has historically been the most important view of God in the philosophy of Judaism, Islam, and Christianity. This view might come a little closer to Pantheism than people think, but it differs in some essential details.
If God is the fundamental reality, then he exists quite apart from the world and does not depend on it for his existence. His wisdom and power are eternal, and eternally he knows himself. Because he is omniscient, and does not need representations, what he knows about a tree must be exactly the same as that tree (together with its context), but that is not to say that his pre-existing ability to know is identical to the tree, still less that he himself is made out of wood, like the idols that have no understanding.
A brief digression: In Christian theology, there is one possible exception to my argument here, namely that God's knowledge of himself might well still be representational. We believe that there is also a Divine Son who is the Word and Wisdom of God, that he eternally pre-existed with his Father before all Creation. “Word” (λογος) is a metaphor for an expression of some idea, and this suggests that in some sense the Son is involved in God's act of knowing himself. So, although this is getting into very deep waters here, maybe even God can't fully understand himself without recourse to a representation. Since God is omniscient, this representation is in some sense an exact copy; fully accurate to who he is, yet distinguishable by the fact that it is the copy, not the original.
In fact, we believe that God is so full of life that there are actually two distinct self-expressions springing up out of the Father's being, namely the Son and the Holy Spirit. When an artist paints a self-portrait, the image of himself is an expression of who he is, and in a different way his artistic style—the “spirit” of the work—is also an expression of who he is. Yet there is only one portrait, and there are not three artists but only one. Since as Monotheists we believe that God is also One, we do not regard these as three parts of God but rather use the language of three persons within the unique divine Being. (A person is something which can be in a loving relationship with another person.)
However, most Christian philosophers (e.g. St. Thomas Aquinas) have thought that the doctrine of the Trinity cannot be deduced from armchair reasoning alone! (Though after we learn the fact, we can say something about how it might make sense given God's loving nature.) Especially since it sits rather uncomfortably with the idea of divine unity; our theologians have their work cut out just explaining why the Trinity is consistent with the idea of Monotheism which we hold in common with Jews and Muslims, let alone demonstrating it from sound metaphysical reasoning. Thus these last three paragraphs are NOT part of my main argument; I cite them only to avoid some confusions about how what I've said might fit in with what God has revealed about himself in the Bible.