Critique of the Kantian philosophy
"Critique of the Kantian philosophy" is a criticism Arthur Schopenhauer appended to the first volume of his "The World as Will and Representation" (1818). He wanted to show Immanuel Kant's errors so that Kant's merits would be appreciated and his achievements furthered.
Intuition
Immanuel Kant finds intuition is thought of as basic sensory information provided by the cognitive faculty of sensibility (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 advanced by Luitzen Egbertus Jan Brouwer in philosophy of mathematics derived from Kant's claim that all mathematical knowledge is knowledge of the pure forms of the intuition – that is, intuition that is not empirical. Intuitionistic logic was devised by Arend Heyting to accommodate this position (and has been adopted by other forms of constructivism in general). It is characterized by rejecting the law of excluded middle: as a consequence it does not in general accept rules such as double negation elimination and the use of reductio ad absurdum to prove the existence of something.