Divine simplicity is the doctrine that God is without composition of any kind: no parts, no distinction between God and God's attributes, no distinction between essence and existence. On this account God does not have goodness, power and knowledge; God is goodness, is power, is knowledge, and these are one reality distinguished only by our manner of speaking about it.
The motivation is not verbal. Whatever is composed of parts depends on its parts and on whatever composed them, and so is not ultimate; a God with real internal composition would be explained by something else. Simplicity is therefore a way of saying that God is the terminus of explanation rather than an item within it. It also secures uniqueness, there is no property God shares with anything else in the way two things share a nature, and it underwrites the traditions' insistence that language about God works differently from language about creatures.
Its classical statements run across all three Abrahamic traditions. Augustine and Anselm in Latin Christianity; Maimonides in the Guide of the Perplexed, who presses it into a thoroughgoing negative theology in which no positive attribute may be predicated of God at all, only negations and attributes of action; Ibn Sina and the Islamic philosophers on God as the being whose essence is its existence; and Aquinas in Summa Theologiae I.3, who establishes it immediately after the existence of God and makes it the hinge of everything that follows.
It has been contested throughout. In Islamic theology the argument over the divine attributes was fought on exactly this ground: the Mu'tazila held the attributes identical with the essence in order to protect unity, and the Ash'aris held them real and neither identical with nor other than the essence in order to protect what scripture says of God, the ninth-century dispute over whether the Qur'an is created was one front of this. In Christianity the doctrine has to be squared with the Trinity, and Eastern Orthodox theology, following Gregory Palamas, distinguishes the unknowable divine essence from the uncreated energies in which God is participated; Western scholastics generally rejected the distinction as introducing composition, and Orthodox theologians defend it as the only way to hold together God's unknowability and real communion with him. Among modern analytic philosophers the doctrine has been attacked as incoherent, Alvin Plantinga argued that it makes God identical with a property and therefore not a person, and defended by Eleonore Stump, Brian Davies and others on the ground that the objections assume a theory of predication that classical theism explicitly denies.