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Extra resources for Salomon Maimon: Rational Dogmatist, Empirical Skeptic: Critical Assessments (Studies in German Idealism)

Example text

Maimon calls this act" creatio ex nihilo" (III, 58). We should qualify our understanding of geometry and construction in accordance with the stipulation Maimon poses. 43 He does indeed think that mathematical reasoning is dependent upon intuition. 44 However, he does not attribute intuition (in the sense ascribed to the finite intellect) to the infinite intellect. To explain this apparent dilemma, we cannot think of mathematics as perfect knowledge; it is subjective knowledge because of its dependence on pure intuition.

For instance, in order to construct an equilateral triangle we should formulate a rule which takes its point of departure from the concept 'triangle'. However, we know that this is not the rule of construction for an equilateral triangle. There are several possible solutions to this problem, but I do not see how any of them can be generalized so as to resolve this problem in a comprehensive way, and therefore I set them aside. 50 As I shall try to show briefly by comparing the principles and the philosophical picture delineated here with some of the elements of Hegel's philosophy.

In the first case we see iI1 pure intuition that the outcome of our rule of construction is something that the understanding is obliged to accept because of its emergence in pure iI1tuition, though it cannot justify it. This is not the case, 11owever, in the case of the circle. Here, Maimon claims, the understanding poses the rule by which the presentation is accomplished. Although it could not be accomplished were we not endowed with pure intuition, it is not the work of pure intuition that produces the circle.

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