Maimon's criticism of Kant's doctrine of mathematical cognition and the possibility of metaphysics as a science.

Abstract The aim of this paper is to discuss Maimon's criticism of Kant's doctrine of mathematical cognition. In particular, we will focus on the consequences of this criticism for the problem of the possibility of metaphysics as a science. Maimon criticizes Kant's explanation of the synthetic a priori character of mathematics and develops a philosophical interpretation of differential calculus according to which mathematics and metaphysics become deeply interwoven. Maimon establishes a parallelism between two relationships: on the one hand, the mathematical relationship between the integral and the differential and on the other, the metaphysical relationship between the sensible and the supersensible. Such a parallelism will be the clue to the Maimonian solution to the Kantian problem of the possibility of metaphysics as a science. Highlights • Maimon's criticism of Kant's doctrine of mathematical cognition is analyzed. • Said criticism sheds light on the relationship between mathematics and metaphysics. • Maimon finds in differential calculus the key to the cognition of the supersensible. • Maimon's solution to the Kantian problem of metaphysics as a science is discussed. [ABSTRACT FROM AUTHOR]