Synchronic Manifolds: The Axioms and Anticipations
This chapter talks about a concept that is essentially the sort of thing that can have instance, a one over against a potential many. A concept thus serves as a principle of unity for a manifold insofar as it collects the items that are subsumed under it. Correctively, however, concepts serve as rules for counting the items that are subsumed under them. The principle of the Axioms tells us something about all ‘intuitions’ and the principle of the Anticipations about all ‘appearance’, but an intuition or an appearance need not be an object. Pains, sounds, afterimages, and even feeling can qualify. The Axioms of intuition and anticipations of perception themselves are the synthetic a priori principles of mathematics whose objective validity is to be secured by those arguments. What we find in the Axioms, in other words, is in essence an argument from the subjective conditions of intuition to an objectively valid conclusion regarding intuited items. A conclusion that finds expression in, and thereby secures the epistemic legitimacy of, a synthetic a priori judgment about those items.
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