My solution is grounded on the assumption of the conditional truth of the existence of physical things. — Pieter R van Wyk

The proof….not merely the assumption of a conditional truth….for the existence of physical things relative to human perception, preceded you by about 250 years.

Even so, I don’t find a connection between the assumed conditional truth of the existence of things, and the prohibition of the collection of natural laws from mingling with the collection of human-based rules.

Perhaps a synopsis of the reasoning for this assumption to your proposed solution, is in order. I already agree with the conclusion, but from a rather different set of majors and minors, I’m sure. So…..for me, a simple matter of procedural interest.

The Demarcation Meridian then states that there exists no shared collection between the Rules of Man and the Law of Nature. — Pieter R van Wyk

Does this not beg the question…..is the statement formulated in accordance with the apodeictic principles of law, or the merely hypothetical principles of rule?

Wouldn’t whether or not one agrees with the statement depend entirely upon the ground of the prohibition?

If law and rule are equally human constructs, what is the commonality necessary for their determination, and from that, their distinction? And if they are not, there still remains the necessity for the justification of their relative distinction, which would be itself a human construct.

I agree there is no shared collection between law and rule, and grant time-variance, albeit tentatively, as the immediate mitigating condition, iff time does not belong to the objects of either, but only to that by which they are determined.

Interesting topic, so thanks for that.

Well said.

Yes, in order for my thinking to work, reason must be presupposed as a functional condition of the human intellect.

Problem is, even given something as presupposed in the human condition, there is nothing given in the mere presupposition, that it must be reason. As with mind, these pure ideas are only contingent, re: theory-specific, logical starting points, a way to deny to speculation its inevitable descent into self-contradiction.

Personally, I would attribute to reason the process, from which “mind” is one product of it.

I think mind is a conception, an abstract metaphysical representation based on the idea of complementary pairs.

What purpose can there be for anything, that isn’t reducible to the purpose of that intelligence from which it is given?

If it is said the purpose of philosophy is to guide the human intellect in its various pursuits, but it is that intellect by which the predicates of such guide are determined, and indeed even the conception which represents it by the same name, it seems obvious philosophy as such has no purpose, per se.

Philosophy is a doctrine, a prescriptive method, for the non-fallacious cum hoc ergo propter hoc use of human reason alone. It is to reason, a fundamental human condition, purpose belongs, philosophy being merely that by which reason attains toward its purpose.

Or not….it’s self-complicating.

Nonsense. You said it yourself, no one can even help you.

Given the thread topic, you’re equivocating the denial of help, with the impossibility of it.

I’m not at war. Not even conflicted.

Sorry if you are; can’t help ya.

….the sense of detachment from the physical world and the body can be terrifying…. — unenlightened

Dunno about all that. With respect to the transcendental ego, it is irrelevant anyway, for whatever that may be, in whatever form it may manifest, it has only to do with the rational being known by a subject as itself.

….in yourself, is the answer. — unenlightened

Absolutely, and from which follows necessarily, it must be done alone.

Is yours a private hill, or would you mind a visitor?

No pets, no bad habits, just me, a real human with real human attributes….however well-seasoned they may be….fully willing and capable of standing my own gawddamn ground.

intention matters
— Mww

Not in categorical morality, sorry. — Copernicus

I’d agree if categorical morality was a thing. But it isn’t; it is only a doctrine describing the justifications for the possibility for a thing. It is a product of pure practical reason, having no validity otherwise.

Just as in any metaphysical thesis.
————-

….elevated Aquinas' "intention" into a categorical "duty". — Colo Millz

….just like that.

I certainly didn’t mean to describe situational morality; not even sure what that is.

I’m just saying that even though that which is doctrinized must be followed, in accordance with a categorically conditioned moral philosophy, the contrariness of human nature itself, only becomes offset by the intention to follow.

I’m arguing that intention matters, insofar as without it, categorical morality, even while being a justified doctrine, is worthless without those actions determined by it alone. The ideal moral agent will always follow the categorical moral principles, which speaks to affirmation of his intent, but the ideality of any moral agent, merely from his basic human nature, is always contingent on circumstance, which speaks to the negation of his intent.

If a moral agent conditioned by deontological predicates doesn’t intent to be obligated by them, he is logically self-contradictory with regard to reason, and morally inept with regard to conscience, from which follows necessarily, that his intention regarding his moral principles, matters. Approval, on the other hand, is irrelevant.

Deontological doctrine doesn’t follow principles; it determines the origin of them and thereby what they may be. The acts, whatever they may be, judged as necessary for the properly deontological moral agent, follows them. Or, follows from them.

Anyway…..my two cents.

Since when did categorical morality depend on intentions? — Copernicus

One might say categorical morality depends on intentions, iff the agency in possession of an autonomous, self-determinant will, respects, without exception, such law as practical reason provides as legislation for its volitions. Respects the law without exception, makes explicit the fully voluntary intention to be obligated by it.

Deontological moral doctrine, which can be considered synonymous with categorical morality, doesn’t concern itself with saving, but only with the conditions for eliminating causal necessity for it.

All good, except….

….the conditions described at B132 to B138 are observed…. — Paine

….I think “observed” is out-of-place here. The listed pagination concerns the analytic of logical functions, not the aesthetic of empirical givens.

I have the feeling you appreciate the precision in recounting the text, with the same precision with which it was written, and meant to be understood.

But, as with , I know what you mean.
————-

….what determines whether a given object is treated in accordance with sensibility or in accordance with pure speculative reason. — Ludwig V

A given object is always treated in accordance with both sensibility and reason. What determines that such should be the case, is nothing but this particular version of speculative metaphysics.

An object in general, or a merely possible object, without regard to any particular one, constructed by the understanding hence that object not given to the senses but still related to possible experience, is called an empirical conception and is treated a priori by pure theoretical reason. For example, justice, beauty, geometric figures, deities, and the like.

That object without any empirical content whatsoever, and no possibility of it hence entirely unrelated to possible experience, both constructed and treated by pure speculative reason, and is called a transcendental object or idea. For example, the categories, mathematical principles, inferential syllogisms, and the like.

These are not proper objects, of course, not existent things, but merely indicate a position in a synthesis of representations in which they are contained. Rather than being objects as such, they are objects of that to which they stand in relation. Object of Nature is an appearance, object of intuition is a phenomenon; object of understanding is a conception; object of reason is an idea. Explanatory parsimony, if you will.

That’s what I get out of it, anyway. Loosely speaking.

Can’t argue with any of that. Except that absent any percipients thing; you seem alright with it, so I’ll leave it be. I know what you mean.

“….if the critique has not erred in teaching that the object should be taken in a twofold meaning,
namely as appearance or as thing in itself…”
(Bxxvii)

In other words, the Critique does teach the twofold aspect, but not of the object. It is the two-fold aspect of the human intellectual system as laid out in transcendental philosophy. It is by means of that system that an object is treated as an appearance in accordance with sensibility on the one hand, or, an object is treated as a ding an sich on the other, in accordance with pure speculative reason.

All that is perceived must exist, but it does not follow that only the perceived exists. Because it is absurd to claim only the perceived exists, insofar as subsequent discoveries become impossible, we are entitled to ask….for that thing eventually perceived, in what state was that thing before it was perceived?

Why? To defeat Berkeley’s “esse est percipi”, as prescribed by that “dogmatic” idealism predicated on subjective conditions alone.

Years ago, I found it much more advantageous to shy away from the A edition. Read it for context, but not study it for comprehension. I mean…there’s a reason the Good Professor made changes, so I just figured it best to go with what he himself thought as better.

Sidebar: the “a” in “….specifically a wholly distinct appearances…”, is a translator’s (not author’s) footnote indicator belonging to “specifically”; it isn’t the indefinite article of grammar spellchecker wants it to be.

I think it potentially very confusing to think of “I” as an appearance, as mentioned in A379, however specifically distinct it may be, especially if one has already understood the transcendental aesthetic in which appearance is only that empirically/physically/materially real thing from which sensation follows necessarily. One would naturally surmise that “I” is certainly no real thing therefore should not have been considered as an appearance at all.

But an appearance to the senses is that by which they are affected. To be consistent, then, regarding appearance, if I am an appearance it must be that I am an affect on myself, which, of course, is that very specific distinction he meant to convey in the text but only makes perfectly clear in a bottom-of-the-page asterisk.

Still, I’m sure you’re aware, all that is revised in the B edition, 157, where “that as I appear to myself” reduces to “only the consciousness (…) that I am”, which releases appearance as previously given in the Aesthetic, from the intuition which is proposed as necessarily following from it. And, which is kinda cool, by doing that he tacitly supports Descartes’ sum while not being quite so supportive of the “problematic” idealism explicit in the cogito ergo… part. Also, he belays the whole existence thing, relegating it to a category where it belongs, rather than connecting to the “I”, which is only a transcendental thought to which existence proper does not belong.

(I am)….not because I think, but because the (consciousness of thinking) represents that I am. Or something like that…. “synthetic original unity of apperception”, is what he’s trying to establish to modify or amend or basically replace the whole original cogito idea.

If you haven’t already, scroll all the way to the end of the text you’re referencing, to the translator’s comments, by text page-grouping, to see that Kant had trouble with this whole thing….getting what he wanted to say across to his readers. And if he had that much trouble with getting it out to us, it’s not hard to image how much trouble we have taking it in.

Or…it’s just me and I’ve completely missed the mark. (Sigh)

….painting a specific appearance. — Paine

I saw that, and the first thing that came to my mind was, to say the same thing….I’ll have to think about it.

Probably not what you meant, but, considering the currently discussed author and his original Prussian linguistic tendencies, I might be forgiven.

I shy away from the term 'self'. — noAxioms

As is your prerogative, being the thread host. I agree with the topical question….where’s the mystery….albeit for very different reasons apparently.

Postmodern philosophy has become like Big Pharma, in that the latter creates ailments to sustain medicinal inventions while the former creates scenarios bordering on superfluous overreach, and both thrive when the individual generally is, or artificially made to appear as, either pathetically blasé or pathologically ignorant.

First-person is a euphemism for self…
— Mww

I'm not using it that way. — noAxioms

To what else could first-person perspective belong?
————-

I personally cannot find a self-consistent definition of self that doesn't contradict modern science. — noAxioms

I don’t find a contradiction; a self-consistent definition of self isn’t within the purview of typical modern science to begin with. The so-called “hard” sciences anyway.

But you’re right to ask: where's the mystery? I don’t know why there should be one.

If every human ever is always and only a first-person….
-Mww

I don't understand this at all. First person is a point of view, not a property like it is being treated in that quote. — noAxioms

First-person is a euphemism for self, indeed a point of view; properties belong to objects, the self can never be an object, hence properties cannot be an implication of first-person subjectivity.

The frames of reference are incongruent. — Paine

The subject that thinks, is very different from the subject that describes thinking. Even myself, should I describe my thoughts, necessarily incorporate a supplement to that method which merely prescribes how my thoughts obtain.

If every human ever is always and only a first-person, doesn’t that make the first-/third-person dichotomy, false? Or, if not, at least perhaps a simplified NOMA, re: Gould, 1997?

Agreed on incongruent frames, even if from a different point of view.

The more things change the more they stay the same, re: translator’s intro, “…. how precarious Court favour then was….”, in juxtaposition to today’s White House.

Mid-1600’s, a numbered series of sentences; early 1900’s, a number series of paragraphs, neither of which satisfy the want of systemic philosophical theory. Which is fine of course, no set-in-stone way to do philosophy. Personal preference kinda thing.

Maybe he was more the anthropological moralist than metaphysical philosopher anyway.

I wasn’t familiar with the Duke, so thanks for the chance to check him out.

Not sure how to take it, but….thanks?

The Duke's influence on Kant doesn’t have much exposure, assuming there was any, but what you wrote sounds a lot like some of the foundational aspects of the second Critique.

I know Kant took a couple French Enlightenment thinkers quite seriously, so there is precedent.

Interesting you brought him up, regardless.

On this forum (…) I have a very hard time finding (…) intellectually informed people discussing Philosophy leisurely… — Ansiktsburk

One of the biggest gripes of philosophers is that folks like to cherry-pick what they write. I admit to it in this case, but I also found a reason: as a rule, intellectually informed people don’t discuss leisurely.

the echo of Aristotle's form-matter dualism. — Wayfarer.

250 years ago, Aristotelian logic ruled academia, from 1770 Kant held the chair of metaphysics and logic at U. of K., so could hardly dispense with it altogether. Thanks to Leibniz in the one hand and Newton on the other, though, Kant did, as you say, move the standardized matter/form duality from an ontological to an epistemological condition. He took it away from the object and gave it to the subject.

And his treatment of time…fascinating. At the expense of real things, no less, that which could actually kill us, relinquishes its importance to something having not the least effect on us at all.

Ballsy move, ya gotta admit, considering the relatively recent advent of the hard sciences, and it took 35 years or so (WWR, 1818) for a decent comprehension of what just happened.

What is an intuition? Empirically, it is the synthesis of the matter of a given appearance, with a form, the representation of which, is phenomenon.

“…. That which in the phenomenon corresponds to the sensation, I term its matter; but that which effects that the content of the phenomenon can be arranged under certain relations, I call its form. (…) It is, then, the matter of all phenomena that is given to us à posteriori; the form must lie ready à priori for them in the mind, and consequently can be regarded separately from all sensation….” (A20/B34)

This is what I was talking about above, where the matter of an object is irrelevant, because there isn’t an object, in mathematical judgements a priori. But it is a judgement, which requires a relation of conceptions.

Now, the matter of an empirical intuition is conditioned by space, but the form is conditioned by time, hence the two pure intuitions one hears so much about. Absent the need for the condition of space for lack of an appearance, but retaining the condition of time, we “…exhibit an empirical intuition a priori…” to ourselves, in order to cognize a relation of synthetical conceptions, which are represented in the judgement.

What is cognition? It is presentation to the subject the consciousness of a judgement, from which follows that mathematical judgements a priori are not in themselves yet cognitions. The missing piece is the intuition, which in the case of mathematical judgements in order to be cognitions, must get their intuition a priori as form alone.

Incidentally enough, there is a definitive conjunction here: the categories are all relations of time, and number is a schemata of the category of “quantity”, so it naturally follows that form is a representation of time. Not represented in time, but of time.

Remember, we were discussing a certain kind of judgement. By involving intuition we’ve moved on from mere synthesis of unrelated conceptions. While we are certainly authorized to think all connected to something like 7 + 5 = 12, thinking does not present any objective validity, and for which is required the invention and use of real objects.

The drawing of numbers or figures, associating them in accordance with operative demands, is the method of proof. When we draw a figure or number, that becomes the appearance, and that, conditioned by space, combined with time already established as present in the mind, and we have an actual phenomenon. Now the synthesis in intuition is space and time, the synthesis in understanding is phenomenon and conception, and experience of the determined mathematical cognition is given.

Oh what a tangled web we weave….right? While metaphysics cannot be a science, this is how it can be treated as if it were.

“…find the sum…” is the something reason directs understanding to do, in the synthesis of given conceptions; what the sum is requires intuition, because only from sensibility can an object representing what reason requires. Herein is counting, for the easy math, the development of formulas and equations for the not-easy, thereby obtaining empirical knowledge of that which originated in thought alone.

This is Kant's “…mathematical cognition….”, in which is what he calls the “….construction of conceptions….”, as opposed to philosophical cognitions, in which is the “… spontaneity in the production of conceptions…”, herein whatever intuition represents the synthesis of the two given constructed conceptions, which will eventually be constructed that elusive “12”.
(Constructed conceptions arise immediately as schemata of the categories, not mediately as representations belonging to mere thought)

There are no numbers naturally in Nature; all of them are put there by us, as objects of sensibility, hence numbers, when employed by understanding in mathematical cognitions, originate as intuitions a priori. How did that happen, you ask. Well…cuz reason switched gears on us, of course, by insinuating presupposing categorical schemata as a real object for what is usually mere phenomena given from a naturally occurring object.

The transcendental aesthetic prescribed the method required for the beginning of empirical knowledge. In keeping with that, if one were to use his fingers for counting, how did he get 1, 2, 3…and not finger, finger, finger….

Same with lining up rocks in aggregate with respect to the quantity: when you count rocks you don’t think, rock, rock, rock….

Stick an object up in front of your face, you experience all that from which is intuited in that object. Stick that object of experience now called a hand in front of your face, but this time, while still perceiving fingers as incorporated in the object called hand, you think them as numbers. Not only numbers, but numbers in succession, in exact relation to alternate fingers. Coolest part is…..you’re not the least confused by contradicting your own antecedent experience (finger) by determining something which should be impossible from it (number).

This is the construction of conceptions, and from them are the empirical intuitions a priori, and why this whole shebang must come from reason herself, a transcendental faculty, for if this arrangement originated in any cognitive, or discursive, faculty, we would be oh-so-confused by conflicting experiences, and in fact, most likely couldn’t even function in such manner at all.
(Keeping in mind, reason has nothing to do with knowledge as such but only provides the rules and principles, through “transcendental ideas”, for knowing successfully, that exclusively the purview of the logical faculties of cognition, re: understanding)

The differences in the text is so subtle.
….In the Aesthetic, we have intuitions which are given as “the matter of objects”;
….In judgement of mathematical cognitions, we have “….exhibition à priori of the intuition which corresponds to the conception…” for which the matter would be irrelevant;
….In judgement of philosophical cognition we have conceptions which conform to the intuition insofar as “…the intuition must be given before your cognition, and not by means of it.…”.

Now we see what ALL mathematical judgements are synthetic and ALL are a priori. Pretty simple really: we observe relations in Nature, the a posteriori, but represent them to ourselves with that which isn’t observed in Nature at all, the a priori.

Added bonus: because the intuition of number is exhibited a priori in correspondence to the conception from which it is given, that intuition can contain nothing more than that which is contained in the conception. Hence arises the apodeictic certainty of mathematical judgements.

Dunno if any of this helps or not, and it is all opinion, so…..

Careful what you ask for. I don’t have a problem with the Prolegomena because I don’t consider it the relevant text for the current discussion.

300 years after the fact, all there is, is opinion. My opinion is, most everybody, in concentrating on this or that, overlooks transcendental philosophy as a whole.

I can explain til I’m blue inna face, but there remains a serious problem: there’s no need for mathematical judgements or their synthetic a priori classification, when I’ve known all about them since I was knee-high to a grasshopper, thanks to my 1st grade teacher. It’s extremely difficult to comprehend the reason for them when rote instruction has removed the consciousness of their applicability. That being said….

1)….the human being has not evolved out of the condition he was in 300 years ago: he still perceives and he still thinks, from which it follows the tenets of transcendental philosophy still hold;
2)….from 1), regardless of current opinion concerning the system prescribed by transcendental philosophy with respect to human cognition, each part of the system remains fully dependent on all the others;
3)…..from 2, mathematics being synthetic judgements a priori is merely an example of what they are, where they reside in the system, and what they do for the system, but rely on something else for sufficient proof of their possibility.

It makes no difference if synthetic judgements a priori are accepted or not; within the theory they are required, which just means to reject that part is to reject the whole. Which is fine, things do move on, after all.
————-

In the case of the conception of a priori itself, Kant did not mean it with respect to time as such, but with respect to placement in the system as a whole. The systemic procedure in a nutshell, for knowledge of things, is perception through to experience. Kant allows a priori to be pure or impure, but stipulates….probably for the sake of his editors…when he writes the word, he means the pure version, always, without exception. The pure/impure signifies whether or not the subject under consideration is empirical, subject being the propositional form thereof, indicating what he’s talking about at the time: impure means, e.g., the subject conception is represented by a real thing, while pure, on the other hand, means, “….not such as is independent of this or that kind of experience, but such as is absolutely so of all experience….”.

Now, given the only two possible ways for the human cognitive system to work, either from perception of things, which is all the empirical side, or, from mere thinking of things, which is all the rational side, it follows that “independent from experience” makes explicit the term is restricted in its use to the rational side alone.

So, a priori means within, or restricted to, any internal systemic function in which there is nothing having to do with empirical predication. To then say a priori, as it relates to time is before experience, is not quite right, insofar as pure thought absent empirical conditions, is already that for which there never will be any experience anyway, so before experience or before the time of experience, in such case, is superfluous.

It is the entire point of transcendental philosophy, is to combat Hume’s reluctance to pursue pure rational thought as the ground of knowledge. In order to be successful, Kant had to demonstrate those conditions under which ALL knowledge stems, and that from the very condition Hume’s resolution was to “….consign it to the flames…”.
————-

To answer your question when do we know 7 + 5 = 12, we know it when we represent it to ourselves by empirical example. Yet beforehand, we know a priori there is nothing contained in the conception “7”, or in the conception “5”, from which we are given the conception “12”.

Because that is known with apodeictic certainty….
(when all you have is boards over there and nails over there)
….yet the are mathematical statements we know with equal certainty from experience….
(yet there’s houses everywhere you look)
….it remains to be undetermined how to get from one to the other….UNLESS….the cognitive part of the system as a whole, and in particular the part which reasons, does something with the two given conceptions…
(hammer the nails into the boards is the way to build a house; synthesis the “7” and the “5” in understanding is the way to judge the relation of two given conceptions having nothing to do with each other)

Full stop. You hammer all day long, you still don’t have a house; you synthesis the conceptions, you still don’t have the conception “12”. Now we see synthetic judgements a priori are only representations of a very specific cognitive function, a synthesis done without anything whatsoever to do with experience, and of which we are not the least conscious. It is all an act of reason, which is that systemic faculty not so much involved in knowledge itself, but provides the principles by which it becomes possible. At this point we don’t care about the 12, just as we don’t care the house isn’t done yet. All we want is proof for a way to get the house built, and proof of a way to get to whatever the relation of 7 and 5 gives us.

We think nothing of combining 7 and 5. We don’t think anything of the combining of them. But we stop dead in our cognitive tracks, when the very same synthesis is just as necessary but for which immediate mental manipulation is impossible. The rote mechanism of mere instruction doesn’t work for a vast majority of us, when the synthesis is of, like, numbers containing many digits, or of a different form of synthesis altogether, i.e, calculus. The principle is the same, though, for all of them.

And all that, is only half the story….

Cool. I figured, but confirmation is always best.

Need the year of publication, for whatever text you’re saying has Groundwork in its title. The Groundwork I’m familiar with is a treatise on moral philosophy, having nothing to do with mathematical judgements, and 7 + 5 is not discussed as far as I could determine, but that a categorical "ought" implies a synthetic a priori proposition, is.

And sec 281 doesn’t Google.

Thanks.

I'm not sure what you mean by "even if it isn't the case". — Janus

As you say, there are no synthetic a priori judgements, but as Kant says, that logical construct (proposition, judgement), in which the conceptions have no relation to each other but are connected in thought, are called synthetic a priori judgements, and are used by the cognitive faculties as principles. You may be correct, in that it isn’t the case the cognitive faculties use such judgements as principles, because there isn’t any such thing.

Thing is, even though I cannot prove the tenets or conditions supporting the theory, you cannot disprove them either. Of the two, my position is nonetheless stronger, in that the logic used in the construction of the theory cannot be shown to be self-contradictory, which is the only way to falsify the theory itself. Best you can do, is start over, with different sets of initial premises and thereby come to a different conclusion.

What will you do, then, to escape the fundamental starting point, the least likely to be wrong initial condition, that the shepard simply “sees” a two-poled fence won’t work? Granting that point, which seems the most reasonable, all that remains is the explanation for what it is to “see”.

Same as it ever was…..as my ol’ buddy Brain Eno used to say.

I don't see how a tautology could be independent of its conceptual content—can you give an example? — Janus

I said irrespective, not independent. It is impossible to even think, judge, cognize, reason…any of that stuff, independently of conceptual content. Even so, I probably could have worded it better, in that, while being independent of conceptual content is impossible, the fact the judgement warrants the title “tautology” indicates only a certain relation between them.

I meant to say it isn’t the conceptions themselves that earn the title, but the relation of them to each other. For those conceptions that don’t relate the title is lost, that’s all.
————-

if they put in just two parallel fence lines, it would have been obvious that would not keep the sheep in or the wolves out. — Janus

Actually, a good example. It shows since Day One, humans had this cognitive capacity, as simply a part of its general intellect. Those academically/philosophically/scientifically illiterate shepards knew something without having to do the work for experiencing it. All that was needed, a few centuries later when somebody stopped to think about it, was a system in which that knowledge was possible, followed by a theory to demonstrate how the system works.

It never was a question of it being done, but, how it is done. Kant’s Claim to Fame is that he assembled the first definitive exposè for this particular inherent human capacity, and no one has done it any better since. “Better” here meant to indicate more complete, beginning to end, front to back, top to bottom.

Why two straight lines cannot enclose a space, is no longer a mystery. Even if it isn’t the case, it is still a perfectly logical explanation.

It is logically self-evident that a pair of lines cannot enclose a space…. — Janus

Since the ancients that has been the case. It just makes sense that two straight lines cannot enclose a space but no one ever thought about the rational mechanism by which two unrelated, non-empirical conceptions can be conjoined to construct its own evidence, since Nature is never going to provide the universality and absolute necessity required for its proof.

….so I'd call that analytic, not synthetic. — Janus

Usually a judgement is termed tautological insofar as it is true by definition irrespective of its conceptual content, whereas analytical merely indicates that the subject/predicate conceptions as the content in self-evident judgements belong to each other, or that one contains the other within it.

The conception of a straight line, on the other hand, does not contain the conception of number, nor can the conception of a number be thought as belonging to the conception of a line, hence the judgement with “two straight lines” as its subject, is termed synthetical. In the judgement “every body is extended”, the conception in the subject is related to the conception in the predicate, in that you cannot think a body without the extension connected to it, so is analytical.
—————-

I don't see how either logical possibility or internal consistency can yield certainty. — Janus

Neither do I; in themselves they don’t. They are the conditions necessary in the form of a judgement, for the certainty in the relations of the conceptions which are its content. They don’t yield, or produce, certainty, so much as make it possible.

Sorry for the delay. I got doin’ Her Satanic Majesty’s Request, if ya know what I mean. Flower beds, of all things. The kinda thing the average joe’s hardly likely to get right.

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…..

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.