On the Acquisition of Mathematical Concepts
Kant, Geometry, and Algebra
DOI:
https://doi.org/10.4013/con.2024.203.07Keywords:
Kant. Schematism. Algebra. Arithmetic. Geometry.Abstract
In the Kantian perspective, the possibility of knowledge arises from the conjunction or synthetic unity of the spontaneity of understanding (categories) with the a priori form of sensibility. The task is to understand how this conjunction or synthetic unity is accomplished by analyzing each of its conditions separately and as a whole. In the Critique of Pure Reason, specifically in the section “On the Schematism of Pure Concepts of the Understanding” (A 137-147 / B 176-187), this mechanism is demonstrated. With this in mind, this work has the following aims: first, to present the problematics of transcendental schematism; second, to describe the schematic construction of geometric concepts, and finally, to specify the position of algebra in Kantian philosophy of mathematics.
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