Objections to St. Thomas’s doctrine of divine simplicity get made from all sides. The objections are usually ones St. Thomas formulated himself, and so one can always got to the relevant texts to get a response. But he also formulated an interesting principle about the divine simplicity that he never used to respond to objections:
Because we know and name God from creatures, the names we give to God signify what belongs to material creatures…. And because in material creatures what is perfect and subsistent is compound… whereas names given to signify simple forms, signify a thing not as subsisting… for instance, whiteness signifies that whereby a thing is white. Therefore, since God is both simple and subsisting, we attribute to Him abstract names to signify His simplicity, and concrete names to signify His substance and perfection, although both these kinds of names fail to express His mode of being, inasmuch as our intellect does not know Him in this life as He is.
And so when we want to understand the divine simplicity, we should use abstract names as opposed to concrete ones, and so it follows that to the degree that we want to understand God as existent or as a subject with properties, we cannot understand his simplicity; and to the extent that we get a clear view of his simplicity, we lose sight of his actual existence. A theistic proof might show God is real, but the development of this proof requires seeing that God is reality. But the second horn of this dilemma must be kept as a real dilemma: it is too easy to simply collapse the abstract name down into the concrete one. If we took the statement that God is reality in a pantheistic way, for example, we would simply collapse the claim “God is reality” into “God is all these real things around us” which silently replaces the abstract name with a collective name (which is simply a mode of concrete existence). Again, if we understand “God is reality” or “God is truth” as meaning that God is some sort of property or feature of real things or of true thoughts, or even that he is some exemplar or supremely true or real being, we again silently replace the abstract with a concrete subsistent thing. In fact, saying “God is being/reality itself” can easily be understood as a vacuous honorific. The characteristic thomist divine title, Ipsum esse subsistens, is, for us, necessarily a dual idea: we cannot simultaneously understand Ipsum esse (Existence itself, which is the summit of his simplicity) and subsisting. The title has to be understood as specifying what is for us a duality which we can know reduces to a reality which we can only know as behind the duality.
And so on the one hand, if we are to have any sense of the divine simplicity, it has to be based on an account of why we think God exists at all; but on the other hand we have to recognize that we only understand this simplicity in the measure that we separate our ideas of simplicity from our ideas of what is concrete and existent. There is a divine uncertainty principle (purely epistemic) that stipulates we can understand either the divine existence or the divine simplicity, but not both with precision. To the extent we understand God as existing, we will be unable to see his simplicity, and vice versa. This could serve as a general response to many objections to the doctrine of divine simplicity.