Kant’s view comes to dominate West European philosophy and his theory of knowledge plays a crucial role in the foundation of mathematics.
A clear understanding of his notions of would do much to elucidate his epistemological approach. Kant’s theory of knowledge seems, hitherto, to have been analyzed by post modern philosophers, and some mathematicians, and it even seems directly to rage their conjectures through incontestably certain in the ultimate concern of its consequences.
Perry R.B. retrieves that Kant’s contributions to epistemological foundation of mathematics consisted in his discovery of categories and the form of thought as the universal prerequisites of mathematical knowledge.
According to Perry , in his Prolegomena to any Future Meta¬physics, Kant exposed a question "How Is Pure Mathematics Possible?".
While Philip Kitcher in Hersh R. shows that all three foundationist gurus Frege, Hilbert, and Brouwer were Kantians; that was a consequence of the influences of Kant’s philosophy in their early milieus, and the usual tendency of research mathematicians toward an idealist vewpoint.
The publication of Kant’s great works did not put an end to the crisis in the foundation of philosophy.
On the contrary, they raged about it more furiously than ever.
As two main schools found in the philosophy of mathematics, before and after Kant, the latent elements of them were discovered and brought to the higher level.
One school considered as the sceptical promoting of the new analysis, and proceeded to build its dome furnished by its material; the other took advantage of the positions gained by the ultimate champion and developed its lines forward in the direction of transcendental claim.
Kant lays the foundations of philosophy; however, he built no structure.
He did not put one stone upon another; he declared it to be beyond the power of man to put one stone upon another.
Kant attempts to erect a temple on his foundation he repudiated.
The existence of an external world of substantial entities corresponding to our conceptions could not be demonstrated, but only logically affirmed.
1 Perry, R.B., 1912, “Present Philosophical Tendencies: A Critical Survey of Naturalism Idealism Pragmatism and Realism Together with a Synopsis of the Pilosophy of William James”, New York: Longmans Green and Co. p. 139
2 Hersh, R., 1997, “What is Mathematics, Really?”, London: Jonathan Cape, p.132
3 Ibid. p. 129
4 ….., “Immanuel Kant, 1724–1804”, Retrieved 2004