1. In the terminology of Kant, something is pure in so far as it is unmixed with elements derived from experience. Knowledge is usually made up of what we receive through impressions and what our faculty of knowledge supplies from itself; knowledge is absolutely pure if it is attainable completely a priori. Pure reason is reason unmixed with anything empirical or practical: that concerned with the forms rather than the substance of knowledge. A pure concept or notion is opposed to an empirical concept, as having its origin in the understanding alone, and not in experience. Pure concepts include those of time and space, that have application in experience. But there are also pure notions that transcend the possibility of experience: God, free will, and immortality.

2. In set theory, a pure set is one in the Zermelo hierarchy, constructed entirely from the null set, and sets of sets (see Zermelo-Fraenkel set theory).