18th-century Mathematics vs. Kantian Philosophy of Mathematics
Abstract
Modern methodology of mathematics bans any reference to any graphic representation in mathematical proofs. Kant, who assumed that mathematical judgments are synthetic and a priori judgments, consequently maintained that an appeal to a priori views is necessary in mathematical proofs. The Kantian assertion agreed with the factual situation of mathematics in the eighteenth century. At that time, analysis was very often based on geometrical and mechanical illustrations. In this article it is hypothesized that Kant assumed that mathematical judgments are synthetic a priori judgments (the consequence of which was that in mathematical proofs an appeal to a priori views is necessary) in order to theoretically explain the factual situation of mathematics in the eighteenth century.
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