…we may infer its nature in accordance with what seems most plausible…. — Janus

Conventionally speaking, true enough. But what of those inferences we seek, regarding the nature of something for which we wish to obtain apodeictic certainty, for which the merely plausible isn’t sufficient?

Can anything we know except those things whose negation would be a logical contradiction be apodeictic?

You should accept the premise of the possible world, since in our relationship with the world, it is shown as something that is not given once and for all (the future is not given). — JuanZu

That's exactly why there is discontinuity. The past is given, the future is not. As you say, "the world is not given once and for all", only the past has been given. Therefore the present constitutes a discontinuity of time.

Your post discusses only the future and the possibilities of the future. Now, what about the actuality of the past, and the discontinuity between the possibilities of the future and the actuality of the past?

That, and the stronger version, that of which the negation is impossible.

Neither of these can refer to things we know, however. There can be no apodeitic certainty in empirical knowledge, at least that given from inductive inference, re: Hume, 1739.

That leaves me wondering what could be the criteria for logical impossibility other than contradiction.

And then what would be the criteria determining whether something would count as a physical or metaphysical impossibilty?