Does divine simplicity imply that God is identical to his attributes?

St. Thomas Aquinas's Compendium Theologiæ cap. 24 says:

God's simplicity is not contradicted by the multiplicity of the names applied to Him.

This enables us to perceive the reason for the many names that are applied to God, even though in Himself He is absolutely simple. Since our intellect is unable to grasp His essence as it is in itself, we rise to a knowledge of that essence from the things that surround us. Various perfections are discerned in these things, the root and origin of them all being one in God, as has been shown. Since we cannot name an object except as we understand it (for names are signs of things understood), we cannot give names to God except in terms of perfections perceived in other things that have their origin in Him. And since these perfections are multiple in such things, we must assign many names to God. If we saw His essence as it is in itself, a multiplicity of names would not be required; our idea of it would be simple, just as His essence is simple. This vision we hope for in the day of our glory; for, according to Zacharias 14:9, “In that day there shall be one Lord, and His name shall be one.”

Negative names applied to God, or signifying His relation to creatures manifestly do not at all signify His substance, but rather express the distance of the creature from Him, or His relation to something else, or rather, the relation of creatures to Himself.

But as regards absolute and affirmative names of God, as "good," "wise," and the like, various and many opinions have been given. For some have said that all such names, although they are applied to God affirmatively, nevertheless have been brought into use more to express some remotion from God, rather than to express anything that exists positively in Him. Hence they assert that when we say that God lives, we mean that God is not like an inanimate thing; and the same in like manner applies to other names; and this was taught by Rabbi Moses. Others say that these names applied to God signify His relationship towards creatures: thus in the words, "God is good," we mean, God is the cause of goodness in things; and the same rule applies to other names.

Both of these opinions, however, seem to be untrue for three reasons. First because in neither of them can a reason be assigned why some names more than others are applied to God. For He is assuredly the cause of bodies in the same way as He is the cause of good things; therefore if the words "God is good," signified no more than, "God is the cause of good things," it might in like manner be said that God is a body, inasmuch as He is the cause of bodies. So also to say that He is a body implies that He is not a mere potentiality, as is primary matter. Secondly, because it would follow that all names applied to God would be said of Him by way of being taken in a secondary sense, as healthy is secondarily said of medicine, forasmuch as it signifies only the cause of the health in the animal which primarily is called healthy. Thirdly, because this is against the intention of those who speak of God. For in saying that God lives, they assuredly mean more than to say the He is the cause of our life, or that He differs from inanimate bodies.

Therefore we must hold a different doctrine—viz. that these names signify the divine substance, and are predicated substantially of God, although they fall short of a full representation of Him. Which is proved thus. For these names express God, so far as our intellects know Him. Now since our intellect knows God from creatures, it knows Him as far as creatures represent Him. Now it is shown above (q. 4, a. 2) that God prepossesses in Himself all the perfections of creatures, being Himself simply and universally perfect. Hence every creature represents Him, and is like Him so far as it possesses some perfection; yet it represents Him not as something of the same species or genus, but as the excelling principle of whose form the effects fall short, although they derive some kind of likeness thereto, even as the forms of inferior bodies represent the power of the sun. This was explained above (q. 4, a. 3), in treating of the divine perfection. Therefore the aforesaid names signify the divine substance, but in an imperfect manner, even as creatures represent it imperfectly. So when we say, "God is good," the meaning is not, "God is the cause of goodness," or "God is not evil"; but the meaning is, "Whatever good we attribute to creatures, pre-exists in God," and in a more excellent and higher way. Hence it does not follow that God is good, because He causes goodness; but rather, on the contrary, He causes goodness in things because He is good; according to what Augustine says (De Doctr. Christ. i, 32), "Because He is good, we are."

Formulated in precisely this way (namely, that God’s essence is identical to His attributes), probably the best source is St. Thomas Aquinas.

For example, in his Summa theologiae, Ia, q. 3, a. 6, in which he asks the question, “Does God have any accidents?” Aquinas answers in the negative, and the first objection regards the Divine Attributes:

[W]isdom, virtue, and the like, which are accidents in us, are attributes of God. Therefore in God there are accidents. [Note that this is an objection that Aquinas later refutes.]

Aquinas explains in the responsum that God cannot have any accidents for a variety of reasons: first, because the substance-accident composition is an actuality-and-potentiality pair which is impossible in God (who is the First Cause and thus Pure Act); second, because God’s Essence is identical with His Being, and hence unfettered and unlimited, which prevents anything extraneous from being “added” to it; finally, because God cannot not have “properties” that are distinct from Himself, since these would be “part” of Him and yet caused by Him, but there is nothing caused in God.

In response to the objection, he simply observes that wisdom, virtue, and similar attributes are not predicated of God and of man in exactly the same way. Although such attributes would be accidents in man, they are not so in God.

It follows that these attributes are identical with God. (We see this idea confirmed in other parts of the Summa, for example, Ia, q. 13, a. 4.)

This idea, however, was expressed earlier by the Fathers of the Church. For example, St. Augustine affirms it in his De Trinitate, V, 2:

But other things that are called essences or substances admit of accidents, whereby a change, whether great or small, is produced in them. But there can be no accident of this kind in respect to God; and therefore He who is God is the only unchangeable substance or essence, to whom certainly being itself, whence comes the name of essence, most especially and most truly belongs.

However, this is not Augustine’s invention: it was the universal consensus of the Fathers, including Clement of Alexandria, Basil, Cyril of Alexandria, John Damascene, and Pseudo-Dionysius the Areopagite.