Divine Simplicity is one of the central doctrines in classical theology and metaphysics when we discuss The Being. It appears in the thought of philosophers and theologians such as Plato, Aristotle, Plotinus, Augustine of Hippo, Thomas Aquinas, etc.
At first glance it deceptively simple: God is not made of parts.
But what we mean when we say "parts"? They mean any kind of composition whatsoever. Divine Simplicity therefore claims that God is absolutely non-composite. There are no physical parts in God, no metaphysical parts, no distinct attributes together, no distinction between what God is and that God exists, no distinction between God's essence and God's power, wisdom, goodness, knowledge, or will. God is not a collection of properties but God is utterly one, utterly unified (note that not even internally diffrentated, as it can be discussed in a holistic framework).
It is important, because all composite things are ultimately dependent.
A house depends on bricks.
A molecule depends on atoms.
A body depends on organs.
A machine depends on components.
Whenever something is composed of parts, it appears to require some explanation for why those parts are together rather than apart. The more composite a thing is, the more it seems to depend on factors outside itself. Complexity, is indeed a problem.
Thus we reason that if God is supposed to be the ultimate reality—the final explanation of everything else—then God cannot be composite. If God were composed of parts, then one could ask: what explains the unity of those parts? What causes them to exist together? Something more fundamental would appear necessary. But God, by definition, is not supposed to depend on anything more fundamental, it is by which language downstream from. Therefore God must be metaphysically simple.
If God had parts, then He would be dependent on something more fundamental than Himself to explain those parts.
Plus, God is not composed of form and matter. This comes from Aristotelian metaphysics. A bronze statue consists of bronze (matter) and the statue shape (form). Matter is what something is made of; form is the organizing principle that makes it the particular thing it is. Classical theology says that anything composed of form and matter has unrealized potential and depends upon constituents. God, however, is Pure Actuality with no unrealized potential. Therefore God cannot be a compound of form and matter.
Furthermore, God is not composed of essence and existence. This is where Divine Simplicity becomes clear. God is its existence and essence. All identical.
Because God is utterly, purely, simpliciter.
For ordinary things, there seems to be a distinction between what a thing is and whether it exists.
Consider a unicorn. We understand what a unicorn is, a horse-like creature with a horn, even though unicorns do not exist. The essence can be conceived separately from existence.
Likewise, for humans, we can describe human nature without thereby proving that any particular human exists. The concept and the actuality are distinct.
According to classical theologians such as Aquinas, every created thing possesses this distinction. A creature has an essence which receives existence. The creature is not existence itself.
God is different.
God does not merely possess existence.
God is existence.
Aquinas famously describes God as ipsum esse subsistens, subsistent-being-itself.
There is no distinction between what God is and that God is.
Furthermore, as it now should be clear, God is not composed of substance and accidents.
In metaphysics, substances possess accidental properties. A person can be tall, short, tired, happy, angry, educated, or ignorant. These qualities can change while the underlying person remains.
You may become taller, wiser, richer, or poorer without becoming a different substance.
God cannot possess accidental properties because accidents are acquired or lost. Anything that gains or loses properties undergoes change. But as we know, God is unchanging. Therefore God cannot have accidents.
Importantly to repeat, Everything attributed to God must belong to God's very essence. Therefore, God's attributes are identical to God's essence.
Ordinarily, we distinguish many properties.
A person might be wise but not powerful.
Powerful but not good.
Good but not knowledgeable.
Knowledge, goodness, power, justice, mercy, and existence are distinct concepts.
In God, these distinctions exist only in our minds.
God's goodness is not one thing.
God's wisdom is not another thing.
God's power is not a third thing.
God's justice is not a fourth thing.
Rather, God is one utterly simple reality that our finite intellect analyzes from different perspectives. Thus, finite cannot totally understand the infinite, nor there cannot be any discursive way to know God.
Imagine viewing a brilliant white light through multiple colored filters. The filters separate red, blue, and green. Yet the light itself was not divided. The divisions arose from the way the observer perceived it.
God's infinite reality exceeds human understanding. Our minds therefore break God's perfection into concepts such as wisdom, power, goodness, and justice. These conceptual distinctions (not literal distinctions, very important) reflect our limited mode of understanding rather than actual divisions within God.
Divine Simplicity is closely connected to the doctrine of Pure Act (actus purus).
In Aristotelian metaphysics, everything in the world possesses both actuality and potentiality.
An acorn is potentially an oak tree.
A child is potentially an adult.
A cold cup of coffee is potentially hot.
Potentiality implies incompleteness. Something could become what it currently is not.
God, however, cannot have unrealized potential as been said.
If God could become more powerful, He would currently lack power.
If God could become better, He would currently lack goodness.
Any unrealized potential would imply imperfection.
If God could become more knowledgeable, He would currently lack knowledge.
Therefore classical theology concludes that God is Pure Act—fully actualized reality without potentiality.
Since composition often involves potentiality, Pure Act naturally leads toward Divine Simplicity.
As if said, Change requires a transition from potentiality to actuality. If God possesses no potentiality, God cannot undergo change. Therefore Divine Simplicity also means immutability. God eternally possesses the fullness of perfection.
This also affects how classical theology understands divine knowledge.
Humans know things by receiving information. We observe. We learn. We infer. We remember. But God does none of these. God knows everything by knowing Himself.
Since God is the ultimate cause of all reality, perfect self-knowledge includes knowledge of everything that flows from Him. So God knows all things and only has one thing to do so as pure existence and intellect, which is to contemplates the perfection, itself (no it isn't narcissistic).
God's knowing is identical with God's essence.
However, if you ask me, claiming God is simply partless is a far stronger claim then Divine Simplicity that insist to say existence or act or essence of intellect are all identical to God, however then we are moving toward another topic.