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Intuition in philosophy

In the philosophy of Immanuel Kant, intuition is one of the basic cognitive faculties, equivalent to what might loosely be called perception. Kant held that our mind casts all of our external intuitions in the form of space, and all of our internal intuitions (memory, thought) in the form of time.

Intuitionism is a position in philosophy of mathematics derived from Kant's claim that all mathematical knowledge is knowledge of the pure forms of the intuition.

Intuitionistic logics are a class of logics, devised and advanced by Arend Heyting and Luitzen Egbertus Jan Brouwer and more recently by Michael Dummett, to accommodate intuitionism about mathematics (as well as anti-realism more generally). These logics are characterized by rejecting the law of excluded middle: as a consequence they do not in general accept rules such as disjunctive syllogism and reductio ad absurdum. Intuitionism is a form of constructivism.

A situation which is or appears to be true but violates our intuition is called a paradox (a paradox can also be a logical self-contradiction). An example of this is the Birthday paradox.

A few systems act in a counter-intuitive way. Attempts to change such systems often lead to unintended consequences.

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