Apophatic theology (also known as negative theology) is an attempt to describe God by what cannot be said of Him. Many of the terms used to describe God’s attributes have within them an apophatic quality. For example, when we say God is infinite, we’re also saying is that God is not finite (i.e., not limited). Another example would be describing God as a spirit being, which is just another way of saying that God is not a physical being.
In church history, the apophatic method was popular among theologians such as Tertullian, St. Cyril of Jerusalem and the Cappodocian Fathers. The most influential proponent of apophatic theology was Pseudo-Dionysius (who was quoted many times in the Summa Theologica by Thomas Aquinas). Apophatic theology is also prevalent in Eastern Orthodox Christianity and is seen as superior to positive (or cataphatic) theology. Because of God’s transcendence, it is thought, further knowledge of God must be gleaned from a direct experience of Him. This leads to mystical approaches to attaining a knowledge of God.
Much of this seems to evolve from the debate between God’s immanence and His transcendence. God’s immanence sees God as intimately involved with His creation and taking a keen interest in the lives of people. To protect against an over-emphasis on God’s immanence, there are those who want to stress God’s transcendence, His "wholly otherness." But truth is not an "either/or" proposition in this case, but a “both/and” proposition. God is both immanent and transcendent. In His transcendence, it is appropriate to speak of what God is not (apophatic theology). We must also keep in mind that Christianity is a revealed faith and that, despite God’s transcendence, God condescended to reveal Himself to mankind. Therefore, we can make positive statements about God—that He is loving, gracious, and merciful. Such statements need to be seen analogically. In other words, we can understand what goodness and love and mercy mean, but when applied to God, they are understood to be applied in perfection, i.e., they are applied analogically, from the lesser (us) to the greater (God).