The Collaborative International Dictionary
Apodeictically \Ap`o*deic"tic*al*ly\, Apodictically \Ap`o*dic"tic*al*ly\, adv. So as to be evident beyond contradiction.
Wiktionary
adv. In an apodictical manner.
Usage examples of "apodictically".
As its concept, however, such as it is given, may contain many obscure representations which we pass by in our analysis, although we use them always in the practical application of the concept, the completeness of the analysis of my concept must always remain doubtful, and can only be rendered probable by means of apt examples, although never apodictically certain.
What we really insist on is this, that philosophical definitions are possible only as expositions of given concepts, mathematical definitions as constructions of concepts, originally framed by ourselves, the former therefore analytically (where completeness is never apodictically certain), the latter synthetically.
From concepts a priori, however (in discursive knowledge), it is impossible that intuitive certainty, that is, evidence, should ever arise, however apodictically certain the judgment may otherwise seem to be.
When such experience (anything as an object of possible experience) is presupposed, these principles are, no doubt, apodictically certain, but in themselves (directly) they cannot even be known a priori.
This can only be done in two ways, either by proving one's own proposition apodictically, or, if that does not succeed, by trying to discover the causes of that failure, which, if they lie in the necessary limits of our reason, must force every opponent to submit to exactly the same law of renunciation with reference to any claims to dogmatic assertion.
I also propose in this preface my own view of metaphysics, which has so many analogies with the Copernican hypothesis, as an hypothesis only, though, in the Critique itself, it is proved by means of our representations of space and time, and the elementary concepts of the understanding, not hypothetically, but apodictically.
As this would have to be proved by mere reason, and therefore apodictically, he would have to establish the impossibility of both, which I feel certain no rational being would venture to do.
They could never hope to prove apodictically the absolute reality of space, because they are confronted by idealism, which has shown that the reality of external objects does not admit of strict proof, while the reality of the object of our internal perceptions (the perception of my own self and of my own status) is clear immediately through our consciousness.