…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?

Hmmm. Good question. Insofar as logic regards only what we think, maybe logical contradiction has to do with the relation of conceptions to each other we think in a judgement, whereas logical impossibility has to do with the relation of judgements to each other we think in a cognition.

With respect to physical/metaphysical impossibility, the former has to do with the content, the latter with the form, of propositions in general? The physically impossible is e.g., that proposition in which there can exist no object to which conceptions may belong, and the metaphysically impossible merely exposes that this conception has no relation whatsoever to that conception.

Dunno. What say you?

Perhaps an example might help. It is not logically impossible that Mt Everest might detach form the Earth and float up into the sky. We might say it is physically impossible, given what we understand to be the laws of nature governing this Universe. We could say it is metaphysically possible since a Universe where the laws of nature or the lack of them allowed such a thing to happen is not a logical contradiction.

Is it possible that something could both be Mt Everest and not be Mt Everest in any imaginable world. It would not seem possible, since it is logically contradictory.

In any case, the point of my question was more concerned with understanding whether you think anything which is not logically necessary (or impossible) could be apodeictically certain.

Getting complicated, methinks. Logic talked about is in propositions; logic used in a cognitive method is in judgements, and the first presupposes the second.

The apodeictic certainty in Aristotle rests on either definition or self-evidence in propositions and is empirically demonstrable; the apodeictic certainty in Kant rests on judgement, and is merely thought. In Kant, the certainty which rests on definition or self-evidence, are termed analytic judgements. It follows that judgement antecedes and sets the ground for propositions.

That something is not logically necessary does not say it is not logically possible. The proof of that apodeictic judgement is in the truth of its negation: for that something which is logically necessary, that something must be possible.

Anyway….I think for the not logically necessary, there is apodeictic certainty in its logical possibility.

I agree there is logic used in "cognitive methods" (given that I'm understanding correctly what you mean by that), but that logic is not deductive, so I would say its results cannot be apodeictic. Rather the logic there is inductive (expectation based on observed regularities) and abductive (speculative inferences to what seem to be most plausible explanations, i.e. explanations most consistent and coherent with what has been currently accepted as knowledge).

So, I disagree with Kant that non-analytic judgements can be apodeictic. There can be no synthetic apriori certainty. I think what Kant was doing in working out the forms of intuition and the categories was phenomenology―that is he was reflecting on the nature of perception in order to establish its general characteristics. So, in that sense it's more of an observation-based inquiry. We can be certain of observationally confirmed judgements, but only within the appropriate context―the are not deductively certain and their negations are not logically self-contradictory.

That said I cannot, for example, imagine a non-spatiotemporal visual perception―visual perceptions are strictly defined in terms of spatiotemporality, so anything that doesn't comply would not be defined as such, and it can therefore be said to be, in that sense, an analytic judgement that all visual perceptions must be spatiotemporal.

I agree with you that something not being logically necessary does not entail it being logically impossible. If all the events in this world are not logically necessary, they must nonetheless be logically possible, so I also agree that there is apodeictic certainty in establishing what is logically possible―it's basically anything which is a non-contradiction. But the downside of that certainty is that it doesn't really tell us much about anything.

I agree there is logic used in "cognitive methods" (…), but that logic is not deductive, so I would say its results cannot be apodeictic. — Janus

There is a theoretical argument in which parts of the cognitive method, under certain conditions, as means to certain ends, is deductive, but the subject is not conscious of its functioning. I’d nonetheless agree the cognitive method in itself, insofar as it is not susceptible to empirical proof, wouldn't meet the criteria for apodeictic certainty. But the point of speculative metaphysical theory in general only extends to whether the parts of the method reflect certainty with respect to each other. It’s like….if this then that necessarily (the point)…..but…..there’s no proof there even is a this or that to begin with (beside the point).
————-

I disagree with Kant that non-analytic judgements can be apodeictic. — Janus

Non-analytic judgements are synthetic, and it is true no synthetic judgement possesses apodeictic certainty. But synthetic and synthetic a priori while being the same in form are not the same in origin.

There can be no synthetic apriori certainty. — Janus

Of course there can, provided the method by which they occur, which just is that difference in origin, is both logically possible and internally consistent. And is granted its proper philosophical standing.

Case in point: mathematics. How many pairs of straight lines would you have to draw, to prove to yourself you’re never going to enclose a space with them? After you’ve thought about it, maybe even drawn out a few pairs, why do I NOT have to tell you it cannot be done? And if you thought about it more narrowly, you'd discover you wouldn’t need to draw any pairs of lines at all to arrive at that conclusion yourself.

The form of that discovery;
…..(the judgement you made)….
The process by which the discovery manifests;
…..(a priori because you didn’t need the experience of drawing pairs of lines to facilitate the judgement)….
And the content of the discovery;
(The unrelated, thus synthetic concepts, “enclosed space” and “pairs of straight lines”, conjoined in the judgement)

…..gives exactly what you say there cannot be.

So even if this particular method is not accepted, it is still true, still necessarily the case, two straight lines cannot enclose a space. Is there another way, equally valid, to get this apodeictally certain kind of non-empirical knowledge?
—————-

…..doesn't really tell us much about anything. — Janus

True enough. Knowledge proper is in experience. Logic merely guides the system and limits the method by which experience is possible.
—————-

Have you heard about the observation of (the effects of) colliding black holes? Talk about paling in comparison, everything I just said…..

But the point of speculative metaphysical theory in general only extends to whether the parts of the method reflect certainty with respect to each other. It’s like….if this then that necessarily (the point)…..but…..there’s no proof there even is a this or that to begin with (beside the point). — Mww

So, what you seem to be talking about is not certainty, but consistency.

Non-analytic judgements are synthetic, and it is true no synthetic judgement possesses apodeictic certainty. But synthetic and synthetic a priori while being the same in form are not the same in origin. — Mww

I think we agree on this. Do you mean that syntheses are hypotheses, whereas synthetic a priori propositions are phenomenologically derived by reflecting on experience in order to establish its general characteristics?

There can be no synthetic apriori certainty.
— Janus

Of course there can, provided the method by which they occur, which just is that difference in origin, is both logically possible and internally consistent. And is granted its proper philosophical standing. — Mww

Now you seem to be contradicting what you said above. I don't see how either logical possibility or internal consistency can yield certainty. And I have no idea what "proper philosophical standing" could be.

Case in point: mathematics. How many pairs of straight lines would you have to draw, to prove to yourself you’re never going to enclose a space with them? — Mww

It is logically self-evident that a pair of lines cannot enclose a space, so I'd call that analytic, not synthetic.

Have you heard about the observation of (the effects of) colliding black holes? Talk about paling in comparison, everything I just said….. — Mww

I hadn't, so I searched on it...very interesting, said to confirm predictions made by Einstein and Hawking. The interesting thing about scientific theories is that it seems they cannot be confirmed to be true, even on account of their predictions being confirmed by observation.

Our intentional acts, as they are thrown into the possible and the non-given of the world, imply operationally a continuity between the measuring apparatus and that which is measured. For, after all, to act in a non-given world is to act in relation to something other than the presence of the present and the present of consciousness. There is, then, a relationship between our operational actions and the non-given of the world. That is, because non-consciousness is involved in operativity, there is a continuity between the measuring apparatus and that which is measured. This continuity is therefore beyond consciousness, just as the future is beyond the present (which is the form of consciousness). And our intentional acts such as "measuring" are also thrown beyond consciousness and the presence of the present.

There is no place here to talk about the past, since conscious and intentional acts occur in relation to a possible future. There may be a discontinuity in time (I leave the question open), but there is no discontinuity between the measuring device, that which is measured, and our intentional-operational act. All three are beyond what is given to consciousness. That is why subjectivist interpretations of quantum physics are wrong. Measuring here is seen as an act that is thrown into the possible and the not-given for consciousness. It is no coincidence that operativity is closely related to the body, and that the body has long been conceived as the other of the mind and consciousness.

The non-given, the body, intentional acts (measuring), and non-consciousness are all intertwined.

Our intentional acts, as they are thrown into the possible and the non-given of the world, imply operationally a continuity between the measuring apparatus and that which is measured. — JuanZu

I don't dispute the continuity between the measuring device and the physical world being measured. Both are part of the given world. The discontinuity is between the non-given possibilities of intention, and the givenness of the sensed world.

Nor do I dispute that there is a "relationship" between the non-given and the given. However, I assert that the relationship is one of discontinuity. In fact, the description as two distinct things, given and non-given, with a relationship between the two, itself implies a discontinuity. If there was continuity, it would be one continuous thing.

There is no place here to talk about the past, since conscious and intentional acts occur in relation to a possible future. — JuanZu

How can you say this? The reality of what you refer to as "the measuring apparatus and that which is measured" is supported by their existence in the past, and sense observation of them, in the past. Without their past existence, they are only future possibilities, needing to be created in a physical presence. "Physical presence" is a product of past observation, having no reality without past observation.

Any "measurement" itself, as the "quantity" or "value" derived, exists in the realm of intentionality, the non-given. And, there is a discontinuity between this, the non-given, and the givenness of the apparatus and object to be measured

I don't dispute the continuity between the measuring device and the physical world being measured. Both are part of the given world. — Metaphysician Undercover

The measuring device and that which is measured enter into a teleological operational dynamic. Here, it is the act of measuring. That is why neither can be excluded from the non-given of the world. This is even more so when things in quantum physics are decided from one moment to the next with the intervention of the measuring device.

How can you say this? The reality of what you refer to as "the measuring apparatus and that which is measured" is supported by their existence in the past, and sense observation of them, in the past. — Metaphysician Undercover

I can say this because it is essential for their participation in scientific practice that the world is not given once and for all. The creation of the entire experiment depends on it. Experimenting implies a relationship with the future, and so we create the conditions for an experiment just as we create a measuring device.

Experimenting implies a relationship with the future, and so we create the conditions for an experiment just as we create a measuring device. — JuanZu

Correct, but that relationship between the past and the future is discontinuous. That's why "the prediction" is never a statement of necessity, and this is fundamental to experimentation.