Kant's own theoretical philosophy bars synthetic a priori knowledge of how a noumenal freedom could interact with phenomenal nature, making the 'influence' claim unintelligible by his own critical standards.
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a priori(Frege treats 'analytic' as entailing 'a priori' for arithmetic.)
Knowable independently of empirical experience; here treated as a consequence of analyticity.
knowledge(Distinguished from mere true belief, which may be the product of indoctrination and need not exercise deliberative capacities.)
Justified true belief — true belief that has been arrived at through the exercise of deliberative capacities, including comparison of and deliberation among alternatives.
synthetic a priori knowledge(Kant's epistemology; distinguished from analytic a priori (conceptual analysis) and empirical a posteriori (experience-dependent) knowledge)
Knowledge that goes beyond the mere analysis of concepts — doing more than unpacking explicit or tacit definitions — yet legitimately claims universal and necessary validity.
unintelligible(as describing what would happen to Baumgarten's theory without this distinction)
Impossible to understand or make sense of; completely unclear or contradictory.