Dictionary:

irrationalism

  (ĭ-răsh'ə-nə-lĭz'əm)

1. Irrational thought, expression, or behavior; irrationality.
2. Belief in feeling, instinct, or other nonrational forces rather than reason.

As a starting point, a view that accords authority to some other faculty than reason. However that might cover empiricism, since use of the senses is not the same as the use of reason. In a more restricted sense, then, a view which releases the deliverance of some faculty, such as faith, or intuition, from the critical scrutiny of reason. A characteristic stance of fideism in theology, and Romanticism in the general culture.