As Ryan Hedrich points out, while there are different ways of understanding the historic Christian doctrine of "divine simplicity", Gordon Clark typically understands it as having reference to the identity of all of God's attribute:
Augustus Toplady wrote, among other things, Observations on the Divine Attributes. The simplicity of God and the identity of all the divine attributes, used above to settle the relation between justice and sovereignty, Toplady expresses in the following words. “Although the great and ever blessed God is a Being absolutely simple ... he is, nevertheless, in condescension to our weak and contracted faculties, represented in Scripture as possessed of divers properties, or attributes, which though seemingly different from his essence, are in reality essential to him, and constitutive of his very nature” (p. 675, col. 1). Toplady, then, specifies “his eternal wisdom, the absolute freedom and liberty of his will, the perpetuity and unchangeableness, both of himself and his decrees, his omnipotence, justice, and mercy.” (The Atonement, 1996, pg. 134
The mystic view is that the doctrines are really false, colloquial accommodations to human limitations. But Anselm believed that God has revealed the truth and that this truth itself, not some ethereal negation of it, could be demonstrated. This must not be taken to imply that certain attributes cannot be denied of God. John Scotus had called God Sun, Star, Breath, and Water, only to empty them of all significance. Anselm keeps the significance and denies that these are attributes of God. But other attributes which are better than these belong to God. He is living, just, wise, powerful, and eternal. At the same time, Anselm is careful to point out that God is not wise or just by participation in a superior Idea. God himself is justice. That is what he is. As this line of reasoning applies to all attributes, so by them we know not merely what sort of being God is, but what God is. And is this not to know his essence, which the negative theologians said was unknowable? However, this concession, if it be a concession, must be made to negativism. Since God is one, without any composition, it follows that Justice is Life, Power is Eternity, and all attributes are the same. Obviously if Justice is God’s essence, and if God’s essence is Power, Just and Power are identical. Each attribute exhausts every other, “because whatever God is essentially in any way, this is all of what he is.” (Thales to Dewey, 2000, pgs. 204-205 – original date of publication: 1957)
It is the honorable view that all the attributes are identical in God, and sometimes visibly so in history for when God demolished the walls of Jericho, the single action was both an instance of grace and an instance of wrath. In greater generality, knowledge is power, omnipresence is omniscience, mercy and truth are met together, and righteousness and peace have kissed each other. (The Incarnation, 1988, pg. 64)
Since all of God's attributes are identical, and since God is identical with His attributes (both of which necessarily follow from the doctrine of divine simplicity, since apart from this view, God would consist of distinct parts, and would therefore not be "simple"), it is unsurprising that Clark can refer to God, not merely as "logical", but as "logic." Indeed, Clark wants to argue that God is logic because he believes that God's thought is logical and that as creatures made in the image of God, our thoughts must be logical in a way identical to God's thought in order for us to understand His divine revelation.
But it is not clear that such a view is compatible with the doctrine of divine simplicity that he wants to advocate. Indeed, although he accepts that our thoughts and knowledge are univocal with God's, he seems to concede that one of the most important advocates of divine simplicity is Thomas Aquinas, who sees his doctrine as the necessary development of the analogical doctrine of knowledge which Clark so strenuously (and rightly, I think) rejects:
The notion of analogy begins quite simply and innocently in Aristotle. He notes that when we call a book a medical book, and when we call an instrument a medical instrument, and when we call a man a medical man, the predicate medical does not bear exactly the same sense in the three instances. The term is not equivocal, as is the case when we call Argos the dog of Ulysses and when we call Sirius the dog in the sky; but on the other hand, the term is not strictly univocal. It is analogical.
This simple distinction was elaborated by the Scholastic and the Neoscholastics into a complicated theory, in which, it would seem, the original situation no longer serves as a solid basis. The motivation and intricacies of the theory are seen most clearly in the arguments for the existence of God and our knowledge of him. God, according to the Thomists, is an absolutely simple being: but a simple, eternal, and immaterial being cannot constitute an object proportionate to our human understanding. Simplicity and eternity are not factors in our world of experience, and therefore we have no positive concept of them. To say that God is eternal means nothing more than that God is not temporal. What eternity positively means remains unknown to the human mind. What man has in this instance may be called negative knowledge.
Similarly, when we call God wise and when we call a man wise, the term does not bear the same sense. God’s wisdom is not distinct from his essence or his being; but the wisdom of man is. In general, there is no affirmation whatever that can be made of God and of man in the same sense. The reason for this impossibility is not only that the predicates do not bear the same meaning in both cases, but that, far more radically, the copula is bears two different senses. In God essence and existence are identical: What God is and that God is are the same. In every case other than God this is not so. Accordingly, when we say God exists and when we say man or dog exists, the term exist does not mean the same thing. Therefore, no term, not even the copula, can be used univocally of God and man.
Now, if the only alternative to univocal predication were equivocal predication, knowledge of God derived by abstraction from experience would be patently impossible. When words are used equivocally there is no definite relationship between the meanings, and knowledge of God would be in a state similar to a knowledge of Sirius that would be based on an experience of Ulysses’ dog. To avoid this fatal difficulty, the Thomists are forced to find some intermediate between univocal and equivocal predication, and they appeal to analogy. Between Argos and Sirius there is no resemblance, but in the case of God, man resembles God, they say, though God does not resemble man. This resemblance permits us to attach some meaning to the statement God is, so that we are neither in complete ignorance, nor limited to negative knowledge, but have an analogical if not a univocal knowledge. Thus empiricism in its Thomistic form attempts to escape the limits of experience.
There seems to be a very serious objection to this theory of analogy. Aristotle’s original analogies cause no difficulty. The term medical, whether applied to a man, a book, or an instrument, is presumably derived from experience. In all three cases there is a relationship to the science of medicine. And for this reason there is a univocal basis for the analogy. The term medical might univocally be defined as “having to do with the science of medicine”; and in this univocal sense the man, the book, and the instrument are all medical. Similarly, all the analogies of common speech have a univocal basis. The paddle of a canoe is analogous to the paddles of a paddle-wheel steam boat; it may even be said to be analogous to a screw propeller. It is so because there is an area of common or univocal meaning. The paddle and the screw propeller are both devices for using power to make boats move through the water. The Neoscholastics list and classify different types of analogy; some are more complicated than the preceding. For example, it might be said that the mind is to the soul as the eye is to the body. Here there is analogy, possibly between the mind and the eye, or possibly between two relationships. But no matter how complicated, or what type of analogy, an examination must discover some univocal element. The two terms must be like each other in some respect. If there were no likeness or similarity of any sort, there could be no analogy. And the point of likeness can be designated by a simple univocal term or phrase. The Thomists admit the likeness or resemblance in analogy; they deny the univocal basis. They transfer analogy from the status of a literary embellishment or pedagogical aid to that of a serious epistemological method. But this removes every real distinction between analogy and equivocation. (A Christian View of Men and Things, 2005, pgs. 216-218 – original date of publication: 1952)
It is not difficult to see why divine simplicity would require the rejection of Clark's univocal theory of knowledge. If God's love and God's hatred, for example, are identical, both of these attributes must obtain in God in a manner radically different from the way they are possessed by humans. Clark seems to attempt to circumvent this real problem in his book on the incarnation, quoted above, by simply giving an example of Christ's crucifixion in which God's love and wrath meet. But this does not prove that these attributes are identical. It just proves that they are compatible, and what's more, that they complement one another. God discharged His wrath on His Son in order that He might exhibit His love to His elect, and later likewise glorify His Son according to His love (Heb. 1:3-4). If God's attributes are identical, God's love for His elect is also an instance of His hatred for them, and His hatred of the reprobate is also an instance of His love for them. This clearly makes no sense. I might expect a Van Tillian or perhaps a Barthian to argue something like this, but I don't see how it is compatible with scripturalism. It is essential for God's love for His elect to only be an instance of love, and not in any sense be an instance of His hatred, and it is necesssary for God's hatred of the reprobate to be solely an instance of His hatred for them, and not His love (Rom. 9:13).
If God's love is identical to His hatred, how can it also be the opposite? The Law of Identity is violated. It cannot be true, in such a case, that A = A, because A also = not-A. The law of non-contradiction is thus also violated. Likewise, if we say that it is "true" that God loves the elect, we must also be able to say that it is also false that God loves the elect, since hatred is the absence of love. The law of excluded middle is thus also violated. Thus, the three basic laws of logical thought are totally violated by this doctrine.