In arithmetic, if only because many of its methods and concepts originated in India, it has been the tradition to reason less strictly than in geometry, ...

T HE heart of Kant's views on the nature of mathematics is his thesis that the judgments of pure mathematics are synthetic a priori. Kant usually offers this as one thesis, but it is fruitful to regard it as consisting of two separate claims, a meta- physical subthesis and an epistemological ..

We cannot imagine two straight lines intersecting at two points even though they may do so. In this case our abilities to imagine depend upon our abilities to visualise.

According to Kant, “mathematical knowledge is the knowledge gained by reason from the construction of concepts.” In this paper, I shall make a few suggestions as to how this characterization of the mathematical method is to be understood.

Kant was centrally concerned with issues in the philosophy of natural science throughout his career. The Metaphysical Foundations of Natural Science presents his most mature reflections on these themes in the context of both his 'critical' philosophy, presented in the Critique of Pure Reason, and the natural science of his time. This volume presents a new translation, by Michael Friedman, which is especially clear and accurate. There are explanatory notes indicating some of the main connections between the argument of the (...) Metaphysical Foundations and the first Critique - as well as parallel connections to Newton's Principia. The volume is completed by an historical and philosophical introduction and a guide to further reading. (shrink)

This is the only work to provide a histori­cal account of Kant’s theory of arith­metic, examining in detail the theories of both his predecessors and his successors.

Kant's distinction between intuitive and discursive knowledge precludes his giving intuitions linguistic representation. Singular terms represent concepts given what kant calls a 'singular use' and are analyzable as definite descriptions. That the object described exists and that there is only one such object can be given linguistic representation only through an explicit assertion of existence and uniqueness. As an intuitionist in mathematics kant holds that mathematics proclaims the constructibility and not the existence of its objects.