The name given to the theology based on the VIA NEGATIVA.
Converse of the VIA AFFIRMATIVA. The way of God through negation, a commonplace of all mysticism, whether Eastern or Western. No predicates attach to God; no words may legitimately be used to describe him. He is "not this, not that". But in stripping from our mind its delusions about God we prepare it for the truth, and in eliminating all that is not God, we begin to penetrate to the heart of the mystery. A magnificent expression of the via negative will be found under DIONYSIUS THE AREOPAGITE.
The way of affirmation is an approach to God through positive assertion about His attributes. He is good, just, wise, loving, and so on. From that point we know it we have to expand our concept from goodness as we know it to infinite goodness. Many theologians claim that the via affirmativa is inadequate without the via negativa, because it, can speak only of the attributes of God, never of His eternal nature.
John Ferguson - Encyclopedia of Mysticism
Finally, two different basic approaches to spirituality need to be clarified. In all traditions there is a way of viewing spirituality that emphasizes the importance of images, symbols, and sensations. This kind of spirituality, classically known as kataphatic, has always been the most popular. In it one seeks deeper realization of God through visions, feelings, imagery, words, and other sensate or symbolic forms of experience.
The second way emphasizes the truth of God that lies behind, beyond, or hidden within all sensory or intellectual representations. This is known as the apophatic way. Evangelical and charismatic Christianity, popular Hinduism, and much of Tantric Buddhism represent markedly kataphatic spiritualities. At the other extreme, one might find the Christian mysticism of John of the Cross and Meister Eckhart, the silence of Quaker Meeting, and the emptiness of Zen Buddhism, which are distinctly apophatic spiritualities.
In nearly all traditions one will find elements of both apophatic and kataphatic approaches, overlapping, but with one of the two in dominance. In most cases the kataphatic way will predominate, for as we shall see, there are elements of the apophatic approach that are deeply threatening from both psychological and spiritual standpoints. It should also be noted that most people who wind up with an apophatic orientation have passed through a number of kataphatic experiences or "phases" on their way.
Younger people and individuals just beginning the process of intentional spiritual searching almost invariably start off with a kataphatic orientation. They seek substantial experience, sensate assurance of their relationship with the Divine, and they expect this to occur though the usual and familiar media of senses, imagery, and thought. Some times people will continue to seek out such sensory experience for years before developing any deep attraction to the mystery behind and beyond experience.
I am aware that I have made the apophatic approach sound more sophisticated or "mature" that the kataphatic in this discussion. This is my bias, but it should be acknowledged that the ultimate value of a person's approach to spiritual growth is finally the business of that person and God. Regardless of orientation, it is important that spiritual directors have a deep appreciation of the benefits and risks of both kinds of spirituality. Extremes of the kataphatic approach can produce endless fascination with imagery or thought, thus obscuring the divine source of all experience. Similarly, apophatic extremism can lead to life- denying and anti-incarnational distortions.
Gerald May - Care of Mind Care of Spirit
Negative theology (sometimes called the apophatic tradition) means opening to the mystery of the divine presence within us which transcends the capacity of every human faculty. It is an important bridge in East-West dialogue, without which that dialogue is virtually unthinkable. Many who have gone to the East in search of spiritual wisdom have been able to return to their Christian roots upon hearing that there is a Christian contemplative tradition.
Thomas Keating -
Centering Prayer and the Christian Contemplative Tradition
And, since mainstream Protestantism is hardly more steeped in spirituality than Catholicism, it means that the general religious attitude of Western Christianity has been without a Via Negativa in the modern period. (Exceptions would have to be made for the more radical Protestant groups such as Quakers, Mennonites, and Moravian Brethren, and perhaps some minority Catholic groups such as the Catholic Worker Movement.)
What - if anything - did religions substitute for a Via Negativa? Asceticism was more often than not the response in Catholic spirituality; the effort at using will power to control one's feelings replaced a Via Negativa. Mortifications replaced meditations. Where meditation was encouraged it was so often of an active kind that it could easily drive out any temptations to contemplation.