Excerpt from The Philosophical Review, 1899, Vol. 8
Earlier thinkers had escaped this problem by treating mathe matics as a system of analytic judgments. Given concepts (def initions) of the various geometrical figures, they regard the demon strations of their properties and ... relations as mere acts of logical analysis. It is the merit of Kant, though Descartes and Locke may have anticipated his classification of judgments into analytic and synthetic, to have first discovered the true character of mathematics as a body of synthetic propositions, and to have pushed into the foreground of modern philosophy the problems of the possibility of synthesis. Now, whatever else may be nec essary for genuine synthesis, its sine qua non is perception. Thought alone is inadequate to its production. In the whole domain of pure reason, in its purely Speculative use, there does not exist a Single directly synthetical judgment based on con cepts.1 The synthetical judgments of mathematics, on the other hand, depend upon the construction of concepts,2 that is, upon acts of perception which enter alike into definitions, axioms, and demonstrations. But these percepts in which the concepts of mathematics are presented cannot be empirical, for.
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