The Quest for Mathematical Philosophy: Descartes, Spinoza, and Kant

Descartes and Spinoza believed that by following the mathematical method, philosophy would achieve its historical destiny, and provide the certain answers to the metaphysical questions which have been with mankind since ancient times. Kant desired to follow the path of Descartes and Spinoza—though he did not use the mathematical method, he was hopeful that mathematics, science, and philosophy could come together in a “historical singularity” which would create a knowledge revolution. He believed that through mathematics and science, the scope of philosophy could become limitless and infinite possibilities could be created for mankind. 

In his Preface to the Second Edition of his Critique of Pure Reason, Kant writes: 

“In the earliest times to which the history of human reason extends, mathematics, among that wonderful people, the Greeks, had already entered upon the sure path of science. But it must not be supposed that it was as easy for mathematics as it was for logic in which reason has to deal with itself alone to light upon, or rather to construct for itself, that royal road. On the contrary, I believe that it long remained, especially among the Egyptians, in the groping stage, and that the transformation must have been due to a revolution brought about by the happy thought of a single man, the experiment which he devised marking out the path upon which the science must enter, and by following which, secure progress throughout all time and in endless expansion is infallibly secured.”

In the same paragraph, after a few sentences, he writes: 

“A new light flashed upon the mind of the first man (be he Thales or some other) who demonstrated the properties of the isosceles triangle. The true method, so he found, was not to inspect what he discerned either in the figure, or in the bare concept of it, and from this, as it were, to read off its properties; but to bring out what was necessarily implied in the concepts that he had himself formed a priori, and had put into the figure in the construction by which he presented it to himself.”