How do we know necessary truths? Kant's answer

European Journal of Philosophy 6 (2):115–145 (1998)
Abstract
It is traditionally held that our knowledge of necessity is a priori; but the familiar theories of a priori knowledge – platonism and conventionalism – have now been discredited, and replaced by either modal skepticism or a posteriori essentialism. The main thesis of this paper is that Kant's theory of a priori knowledge, when detached from his transcendental idealism, offers a genuine alternative to these unpalatable options. According to Kant's doctrine, all epistemic necessity is grounded directly or indirectly on our capacity for clear and distinct rational intuition . Insight, in turn, depends upon functions of the imagination for creating “mental models” of necessary truths. This doctrine is well exemplified by Kant's account of our knowledge of simple analytic truths
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