In this post, I want to define the expression "divine simplicity" before attempting to refute it. According to the doctrine of divine simplicity, "God is radically unlike creatures in that he is devoid of any complexity or composition, whether physical or metaphysical. Besides lacking spatial and temporal parts, God is free of matter/form composition, potency/act composition, and existence/essence composition. There is also no real distinction between God as subject of his attributes and his attributes. God is thus in a sense requiring clarification identical to each of his attributes, which implies that each attribute is identical to every other one. God is omniscient, then, not in virtue of instantiating or exemplifying omniscience — which would imply a real distinction between God and the property of omniscience — but by being omniscience. And the same holds for each of the divine omni-attributes: God is what he has. As identical to each of his attributes, God is identical to his nature. And since his nature or essence is identical to his existence, God is identical to his existence" (See http://plato.stanford.edu/entries/divine-simplicity/)
David Burrell tries to illuminate this seemingly obscure or abstruse doctrine. He explains that (generally) no entity is identical with its nature (e.g. a square is not identical with squareness nor is a rectangle identical with rectangularity nor is a human being identical with the abstract property of being human). God is supposedly the only exception to this "rule" according to Burrell. See Burrell's text _Aquinas: God and Action_, pp. 5-7.
Thomas Aquinas himself insists that God is non-compositional or wholly simple in his Summa Theologica. In the prima pars of the Summa, Aquinas emphasizes this point in multiple ways:
ST I.3.1: "I answer that, It is absolutely true that God is not a body; and this can be shown in three ways."
ST I.3.2: "I answer that, It is impossible that matter should exist in God."
ST I.3.3: "I answer that, God is the same as His essence or nature."
ST I.3.4: "I answer that, God is not only His own essence, as shown in the preceding article, but also His own existence. This may be shown in several ways."
ST I.3.5: "I answer that, A thing can be in a genus in two ways; either absolutely and properly, as a species contained under a genus; or as being reducible to it, as principles and privations. For example, a point and unity are reduced to the genus of quantity, as its principles; while blindness and all other privations are reduced to the genus of habit. But in neither way is God in a genus. That He cannot be a species of any genus may be shown in three ways."
ST I.3.6: "I answer that, From all we have said, it is clear there can be no accident in God. First, because a subject is compared to its accidents as potentiality to actuality; for a subject is in some sense made actual by its accidents. But there can be no potentiality in God, as was shown."
ST I.3.7: "I answer that, The absolute simplicity of God may be shown in many ways. First, from the previous articles of this question. For there is neither composition of quantitative parts in God, since He is not a body; nor composition of matter and form; nor does His nature differ from His 'suppositum'; nor His essence from His existence; neither is there in Him composition of genus and difference, nor of subject and accident. Therefore, it is clear that God is nowise composite, but is altogether simple."
Another way of making the same point as the aforementioned authors is to say that God is non-mereological. That is to say that the doctrine of divine simplicity contends that God is timeless and non-spatial or utterly non-compositional: He has no parts whatsoever. And if God's essence is identical with God's existence, then the three persons of the Trinity presumably are not three beings, but one being. But yet the Persons are supposedly one being although they putatively are not identical one to the other (i.e. the Father is not the Son nor is the Son the Holy Spirit or the Father, etc). But how is it possible for three Persons to constitute one Being? In the next post, I will answer the question above and offer reasons why a Christian probably should eschew the simplicitas dei doctrine.