Mathematics in the Light of Transcendental Aesthetics: did Kant Create a ‘Philosophy of Mathematics’?
DOI:
https://doi.org/10.31649/sent44.02.058Keywords:
transcendental principles of mathematics, representation, productive power of imagination, mathematical objects, logistic models of mathematicsAbstract
The article is devoted to the criticism of the thesis about the existence of a special ‘Philosophy of Mathematics’ in Kant’s transcendental philosophy. Based on the analysis of the peculiarities of the formation of mathematical subjects, in particular in the fields of arithmetic, geometry, and algebra, as well as the role of imaging and the productive power of imagination, the synthetic nature of mathematics and its ability to produce new knowledge, which corresponds to the basic principles of transcendental philosophy, is proved. It is demonstrated that the Kantian position is represented by the establishment of a priori conditions for the possibility of mathematical cognition, not a logical justification of mathematical concepts. It proves that the Kantian transcendental approach to mathematical cognition does not require formal-logical justification, which is inherent in most modern models of the philosophy of mathematics.
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