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What are analytic and dialectic logic in Kantian philosophy? What's the difference between them and why can't we use analytic logic as an organon?

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The Transcendental Analytic is concerned with how pure concepts of the understanding (the categories) ground our objective access to reality through mathematical and dynamical principles. The mathematical principles elaborate on how quantitative and qualitative concepts are applied to the objects of our perception. Dynamical principles show how the relational categories provide the "root" or rather the "scaffolding" of a complete system of nature.

The Transcendental Dialectic then turns to examine the questions of completeness of this system more closely. Whereas the dynamical principles are, as Kant says, regulative in reference to intuition, they're constitutive in reference to experience, which, for Kant, is the process of the successive systematization and objectivization of our knowledge or the shift from mere possibility to necessity (in terms of the modal categories that Kant introduces). The ideas of reason, in contrast to the dynamical principles, are purely regulative. They represent the idea of the complete system of nature and thus guide our empirical investigations, yet aren't possible objects of experience. This leads to antinomies. There two approaches, finistic and infinitistic, to the issue of completeness of a system of nature are contrasted.

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