Since Kant himself acknowledges in the Paralogisms that inner sense does not give knowledge of the soul as a thing-in-itself, the reliability of memory-based temporal ordering cannot be secured from within Kant's own system.
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inner sense(Cited as the basis of the rival empiricist hypothesis against Kant's a priori synthesis)
Introspective experience from which empirical information about one's mental states is derived
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.
reliability(what induction is trying to prove about itself)
The quality of consistently producing correct or trustworthy results; something you can depend on to work.
thing-in-itself(Kant's distinction between appearances and things-in-themselves in the Second Antinomy)
An entity whose properties and divisions subsist independently of any act of experience or cognition, such that its decomposition into parts would form a completed (or completable) sequence.