Intuition
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6 - Antony Flew: A Dictionary of Philosophy

A form of uninferred or immediate knowledge. Two principal philosophical uses of the term may be distinguished:

1. uninferred knowledge of the truth of a proposition
2. immediate knowledge of a nonpropositional object.

In the latter sense, four kinds of nonpropositional objects have been claimed as intuitable:

1. universals
2. concepts, as in the case of correctly applying a concept without being able to state its rule of application
3. sensible objects, as in Kant's account of our immediate, nonconceptual relation to sensible objects
4. ineffable objects, as in Bergson's account of the inexpressible awareness of duration, or in certain religious accounts of our awareness of God.

Intuitionism:

1. (in ethics) The view that (at least some) moral judgments are known to be true by intuition.
2. The view that there are several distinct moral duties, that cannot be reduced to one basic duty, in contrast, for example, to utilitarianism. While both views can be, and are, held separately, they often go together.
3. (in mathematics) A system propounded by L.E.J. Brouwer, identifying truth with being known to be true, that is, proven. The main theses of intuitionism are:
   • that a mathematical entity exists only if a constructive existence proof can be given
   • that a (mathematical) statement is true only if there is a proof of it, and false only if a proof of its denial can be given.

Brouwer's idealist inclinations led him to describe mathematics as investigation of the (ideal) mathematician's "mental constructions". The view is notable for its rejection of classical (or realist) logic, in particular the law of double negation, the law of excluded middle, and classical reductio.