If what is logically necessary to conceive, starting from existential premises such as the contingency of the phenomenal world or the existence of anything, is not applicable and necessary, then knowledge at every level of experience is impossible.
Knowledge exists only when it is rationally intelligible, resulting from a self-consistent application of the mind's categorical structure to the data of experience. Therefore, either what I must rationally conceive, on existential premises, is objectively the case, or no knowledge is possible.
But the position that knowledge is impossible is self-contradictory, since its truth involves its falsity. Therefore, what is rationally necessary to conceive, on existential premises, is objectively the case.