reliance on the ‘object’ in his third critique.
— Possibility

What ‘object’? — Mww

Nature, art, etc.

The base structure of Kant’s schema is the subject-object relation, with the subject bracketing out sensation, or affect/desire, as if it is irrelevant. Only what can be attributed to the object - either as concept or as aesthetic - is discussed with regard to the ability (of the subject) to make judgements in relation to an object. I would argue that beyond the fourth moment, where the artist or genius refrains from judging, there is no subject-object distinction, only inclusive relation.

The TTC, on the other hand, acknowledges affect/desire as the directional flow of energy through the entire schema, and advocates the disciplined practice of aligning this aspect of ourselves with that of nature in order to understand the Tao.

Our approach to understanding language is our approach to understanding everything - there is a necessary practical or relational aspect which cannot be attributed along subject-object or sensation-cognition lines.

I'm glad I seemed to have managed to express this well enough to make sense (for a change!).

It is probably one of the most common misconceptions of Kant's work I come across and some people just cannot see it likely because it is so blindingly obvious and they don't see the importance of stating something so obvious. Others are just atheists or theists trying to force views upon others by taking his words and terms out of context to justify some silly political view.

Re noumena, this, with passages from Kant, comes from Wikipedia:

Kant also makes a distinction between positive and negative noumena:[22][23]

If by 'noumenon' we mean a thing so far as it is not an object of our sensible intuition, and so abstract from our mode of intuiting it, this is a noumenon in the negative sense of the term.[24]

But if we understand by it an object of a non-sensible intuition, we thereby presuppose a special mode of intuition, namely, the intellectual, which is not that which we possess, and of which we cannot comprehend even the possibility. This would be 'noumenon' in the positive sense of the term.[24]

The positive noumena, if they existed, would be immaterial entities that can only be apprehended by a special, non-sensory faculty: "intellectual intuition" (nicht sinnliche Anschauung).[24] Kant doubts that we have such a faculty, because for him intellectual intuition would mean that thinking of an entity, and its being represented, would be the same. He argues that humans have no way to apprehend positive noumena:

Since, however, such a type of intuition, intellectual intuition, forms no part whatsoever of our faculty of knowledge, it follows that the employment of the categories can never extend further than to the objects of experience. Doubtless, indeed, there are intelligible entities corresponding to the sensible entities; there may also be intelligible entities to which our sensible faculty of intuition has no relation whatsoever; but our concepts of understanding, being mere forms of thought for our sensible intuition, could not in the least apply to them. That, therefore, which we entitle 'noumenon' must be understood as being such only in a negative sense.[25]*

^ Kant's words bolded

So Kant apparently rejects intellectual intuition; the kind of intuition which Plato claims gives access to the Forms.

What I obviously don’t understand, is how the ability to grasp novel facts through mathematics is not intellectual intuition.

Think of Dirac positing antiparticles purely on the basis of them ‘falling out of the equations’ only later to be empirically confirmed. The many predictions made by the theory of relativity which could only be confirmed decades later with the invariable headline EINSTEIN PROVED RIGHT AGAIN. How are these NOT examples of intellectual intuition? What am I not seeing? Anyone?

It's an interesting question, and I don't know the answer. Spinoza believed in intellectual intuition of a certain kind (understanding "sub specie aetermitatis", or "under the aspect of eternity"). Hegel, as I understand it, sought to restore the idea against Kant's rejection of it. Perhaps the issue is that there could be no way of demonstrating that such intuitions are yielding true knowledge.

As to mathematics, our understanding of it may be explained as rule following, or abstracting from empirical experience. It's obviously a complex subject, to which much more thought might be given.

I'm very suspicious about this element of Kant's philosophy.

One the one hand, in the SEP entry on Kant's philosophy of mathematics says this:

Kant argues that mathematical reasoning cannot be employed outside the domain of mathematics proper for such reasoning, as he understands it, is necessarily directed at objects that are “determinately given in pure intuition a priori and without any empirical data” (A724/B752). Since only formal mathematical objects (i.e. spatial and temporal magnitudes) can be so given, mathematical reasoning is useless with respect to materially given content (though the truths that result from mathematical reasoning about formal mathematical objects are fruitfully applied to such material content, which is to say that mathematics is applicable to and a priori true of the appearances (Shabel 2005). Consequently, the “thorough grounding” that mathematics finds in its definitions, axioms, and demonstrations cannot be “achieved or imitated” by philosophy or physical sciences (A727/B755).

But in another entry on Kant's view of mind and consciousness, we also read:

Kant aimed among other things to:

Justify our conviction that physics, like mathematics, is a body of necessary and universal truth...


Laying the foundation for pursuit of the first aim, which as he saw it was no less than the aim of showing why physics is a science, was what led Kant to his views about how the mind works. He approached the grounding of physics by asking: What are the necessary conditions of experience (A96)? Put simply, he held that for our experience, and therefore our minds, to be as they are, the way that our experience is tied together must reflect the way that, according to physics, says objects in the world must be tied together. Seeing this connection also tells us a lot about what our minds must be like.

This seems a contradiction to me, because mathematical physics is reliant on and intertwined with mathematics in modern science. So I think there's something basic that I'm not getting here, maybe I'll put this up on Philosophy Stack Exchange (after I finish moving house anyway.)

Perhaps, not in idealist (folk psychologist) terms, "intuition" is just (the perceptual – noninferential – aptitude of) pattern-recognition (e.g. gestalts).

Bab[ies] are born with a priori knowledge. — Dijkgraf

Our neonatal brains are evolved feedback systems endowed with aptitudes that develop competences for adaptively interacting with their environments like any other encephalized species. A biophysical (i.e. empirical) process – not a "transcendental condition of the possibility..."

Our brains are much more like a 'neural net wetware micro-subsystem' (of an environmental macro-system) than a monadic-modular hardware-O/S-software difference engine. No "pre-installation" necessary, like e.g. (Darwinian) cellular automata, autopoeisis, etc.

Our brains are much more like a 'neural net wetware micro-subsystem' (of an environmental macro-system) than a monadic-modular hardware-O/S-software difference engine. No "pre-installation" necessary, like e.g. (Darwinian) cellular automata, — 180 Proof

WTF? :chin:

reliance on the ‘object’ in his third critique.
— Possibility

What ‘object’?
— Mww

Nature, art, etc. — Possibility

Cool. Objects in general. Not the particular object. The hint was there; just making sure I understood it.
————

The base structure of Kant’s schema is the subject-object relation, with the subject bracketing out sensation, or affect/desire, as if it is irrelevant. — Possibility

With respect to the “....speculative metaphysics of Nature...” ** in the acquisition of “....theoretical knowledge of all things....” **, yes, absolutely. The judgements here are discursive, concepts relate to intuition, the imagination is “...reproductive...”, pure reason being the logical arbiter.
(**A841/B869)
————

The TTC, on the other hand, acknowledges affect/desire as the directional flow of energy through the entire schema, and advocates the disciplined practice of aligning this aspect of ourselves with that of nature — Possibility

In Kant, “directional flow of energy” aside, this affect/desire is separable, as affects on the subject, and desires of the subject, differences in principles, origins and manifestations being rather obvious, I should think. The judgements here are aesthetic, concepts relate to each other, the imagination is “...productive...”, practical reason being the logical arbiter.

Aligning ourselves with Nature arises from....

“....If pleasure is bound up with the mere apprehension of the form of an object of intuition, without reference to a concept for a definite cognition, then the representation is thereby not referred to the object, but simply to the subject; and the pleasure can express nothing else than its harmony with the cognitive faculties which come into play in the reflective Judgement, and so far as they are in play; and hence can only express a subjective formal purposiveness of the object...”
(CJ, Intro, VII)

.....which just say Nature has an affect on our subjective condition as well as our cognitive system.

The subjective desires, on the other hand, arise from a different causality that Nature, such that its manifestations are not merely affects on the subjective condition, but outright determinations of it. As such this is the domain of the Kantian metaphysics of morals, under the purview of principles derived from pure practical reason, as opposed to the affects of Nature on us, which is the domain of the metaphysics of Nature, which is under the purview of principles derived from pure speculative reason.

Oh, what a tangled web we weave......when we really can’t prove a damn thing.

I'm glad I seemed to have managed to express this well enough to make sense (for a change!).

It is probably one of the most common misconceptions of Kant's work I come across and some people just cannot see it likely because it is so blindingly obvious and they don't see the importance of stating something so obvious. Others are just atheists or theists trying to force views upon others by taking his words and terms out of context to justify some silly political view. — I like sushi

I don't know if you saw my previous emails about the similarities between Kant's noumena and the Tao as described in the Tao Te Ching. I think my familiarity with Lao Tzu makes me open to your way of seeing things.

So Kant apparently rejects intellectual intuition — Janus

Truth....
As he must, at least in humans, in keeping with his admitted metaphysical dualism. When he states that intuitions are sensible representations given from matter, and conceptions are intellectual representations given from thought, then intuitions cannot be intellectual without negating the very dualism on which his speculative metaphysics is constructed.
—————

....or Dare:
Intellectual intuition is merely a euphemisn for some possible phenomenon the understanding thinks a priori, in order to justify the construction of a conception it also thinks.

We wish to know about Nature;
Nature is composed of objects;
No object, hence Nature, can be known without being subjected to the categories;
One of the categories is quantity;
We know quantity relates to objects but we know quantity is not itself an object;
We construct objects a priori representing quantity, called schema, such that the relation can be determinable;
One schema of quantity is number, another is any general geometric figure, which are universal representations of a particular which is also a possible phenomenon;
That constructed schema is a “non-empirical intuition” ** by its a priori form alone, residing in imagination, having nothing whatsoever to do with sensibility, and the conception synthesized with it in understanding becomes a constructed conception, as opposed to a spontaneously generated concept arising from apperception;
As soon as the schematic object we imagine becomes an object in the world, it is no longer a “non-empirical intuition”, thus not subject to the categories alone but also to sensibility, and becomes a phenomenon;
Construction of conceptions in this way are synthetic a priori cognitions, and makes the science of mathematics, and the physical sciences grounded on it, possible.
** A714/B742

The mental image of a line as non-empirical intuition represents the line as a conception; the mental image of a number as a non-empirical intuition represents a unit of quantity as a conception, insofar as the certainty is given that the drawings on a piece of paper conforms exactly to both the images in imagination and the conceptions in understanding.

This is mathematical reasoning writ large, itself possible only from the category of quantity, from which its apodeitic certainty arises. There is no contradiction at all possible, from conceptions constructed from only a single category, just as there is no possible contradiction of identity, when matter is reduced to a single substance, the category in this case being quality. In Kant, these two are termed mathematical regarding their respective certainty, the other two are dynamic, regarding their respective contingency.

Can we call “non-empirical intuitions” intellectual intuitions? Sure...why not. While so doing removes the connection from Kant, it doesn’t do any real damage, as long as one is aware of the difference.

Perhaps, not in idealist (folk psychologist) terms, "intuition" is just (the perceptual – noninferential – aptitude of) pattern-recognition (e.g. gestalts). — 180 Proof

That certainly seems to be a possibility.

That constructed schema is a “non-empirical intuition — Mww

It is certainly arguable though that it could be an abstraction derivative of empirical intuitions. It seems to be one of those "chicken and egg" problems. Do you think we learn to see things as things via being taught to as well as possessing evolved constitutional aptitudes? As 180 says "seeing as" relies on a consitutional capacity for "gestalting". I don't think there's much question that animals also do it.

The term 'synthetic a priori' suggests that Kant thought these a priori intuitions are synthesized, which begs the question as to what 'material' they are synthesized from. It seems they become a priori only after the fact (of empirical experience), so to speak.

In any case when considering the question of intellectual intution, we are considering more abstruse (metaphysical) intuitions, such as Platos' Forms, Spinoza's one substance and Hegel's absolute spirit, and I think it's fair to say Kant had no truck with that kind of metaphysical intellectual "intuition" (speculation).

Thanks, that is helpful, but what of this?

Kant argues that mathematical reasoning cannot be employed outside the domain of mathematics proper

Doesn't that negate applied mathematics, which is so fundamental to science?

Do you think we learn to see things as things via being taught to as well as possessing evolved constitutional aptitudes? — Janus

Nowadays, it seems being taught is all we consider in the acquisition of knowledge, which is the same as “how we see things”, I’m guessing. Which is precisely why both Kant and Schopenhauer had such a hard-on for the schools, because any formal, rote instruction, including parental, neglects the means for the sake of the ends. But teach yourself something completely devoid of extant experience, or learn what no one else knows, by invention or accident, it becomes clear mere instruction is self-limiting, in that it turns reason into a mere passive skill rather than an active faculty.

The U.S used to rank first in the world for high school mathematical comprehension. Now we are 15th.
—————-

That constructed schema is a “non-empirical intuition”
— Mww

It is certainly arguable though that it could be an abstraction derivative of empirical intuitions. — Janus

Perhaps, but not in keeping with transcendental philosophy, in which is said, “intuition cannot think, and understanding cannot intuit”. If intuition is predicated on synthesis of empirical conditions, re: matter and form, given from sensibility, than intuition cannot think its representation, thinking is the properly the synthesis only of conceptions. It follows that if understanding cannot intuit, it cannot employ empirical conditions to abstract from.

So the question then becomes...why can’t understanding abstract from phenomena, which are the result of sensible empirical conditions. If this were the case, then we wouldn’t need to think the schema of the categories, because they would already be given as objects of perception. And even if there are numbers in the world, it is only because we put them there, which makes explicit their primal origin is in pure reason.

That conception of the transcendental seems to be based on the assumption that empirical intuitions are not always already conceptually mediated, even prior to conceptions becoming explicit.

On that alternate view the conceptual dimension of the empirical is not given transcendentally, but immanently. The transcendental view seems to rely on the existence of something otherworldly or divine; which would mean that the distinction between transcendentality and transcendence is moot. (Of course in its '"ordinary" sense, as something not empirically observable 'transcendental' retains its coherence). No way to prove any of this, but it's an alternate view.

And if we make definite claims about the occulted nature of the empirical and of empirical intuitions, then we would seem to be overstepping our bounds and indulging in the kind of speculation, which is neither emprically (obviously) or rationally justified, that Kant would want us to eschew.

Kant argues that mathematical reasoning cannot be employed outside the domain of mathematics proper

Doesn't that negate applied mathematics, which is so fundamental to science? — Wayfarer

In short, applied mathematics is demonstration of mathematical reasoning. Doing the math which grounds the physical sciences presupposes the axioms and definitions from which those sciences are even possible, and which can only develop a priori. You are well aware, it goes without saying, that while we observe relationships in Nature, the laws which explain that relationships are not given by the observation alone.

You are well aware, it goes without saying, that while we observe relationships in Nature, the laws which explain that relationships are not given by the observation alone. — Mww

They're deductive. Synthetic a priori, yes?

He approached the grounding of physics by asking: What are the necessary conditions of experience (A96)? Put simply, he held that for our experience, and therefore our minds, to be as they are, the way that our experience is tied together must reflect the way that, according to physics, says objects in the world must be tied together. Seeing this connection also tells us a lot about what our minds must be like.

Does this relate to Wigner's 'unreasonable efficacy of mathematics in the natural sciences'?

I know I'm grasping at straws.

The transcendental view seems to rely on the existence of something otherworldly or divine — Janus

I'm sure that that is not what Kant means by transcendental. Doesn't he go to the trouble of differentiating 'transcendental' from 'transcendent' to avoid that implication?

Layman's explanation: what is transcendental is what is always already the case, what must be assumed to be so by any supposition, what is implicit in experience without being visible to it.

That conception of the transcendental seems to be based on the assumption that empirical intuitions are not always already conceptually mediated, even prior to conceptions becoming explicit. — Janus

THAT conception? Not sure what conception you mean. If you mean my exposition of non-empirical intuitions, that is not a conception of the transcendental. The categories on which mathematical quantities are based are conceptions deduced transcendentally, but employed immanently, with respect to possible knowledge.

Empirical intuitions are not always conceptually mediated. All intuitions, as sensuous representations, depend on affections, which is the same as saying empirical intuitions are mediated by sensation. But yes, prior to conceptions becoming explicit, which occurs in the synthesis by imagination of phenomena to thought. We are not aware of the synthesis of matter and form that become phenomena; we only become aware of objects as particular empirical entities when they are thought under the explicit conceptions understanding thinks as belonging to them.
———-

On that alternate view..... — Janus

By alternative view you mean Plato, Spinoza and Hegel?

......the conceptual dimension of the empirical is not given transcendentally...... — Janus

Nor is it in Kant. The empirical is conditioned by the transcendental, by the categories, but the conceptual dimension is given from the spontaneous representations arising under the unity of apperception. Thinking. There is thinking transcendentally, but thinking is not itself transcendental.

.....but immanently. — Janus

Yes, even in Kant, immanently taken to indicate having to do with possible experience.
————

The transcendental view seems to rely on the existence of something otherworldly or divine — Janus

Sometimes, maybe, but not in Kant, who is quite adamant that the transcendental is not to be confused with the transcendent, which properly is otherworldly or divine.
————

in its '"ordinary" sense, as something not empirically observable 'transcendental' retains its coherence — Janus

Dunno about ordinary, but in Kant-speak, transcendental basically refers to the possibility of pure a priori principles, judgements and/or cognitions. So rather than “not empirically observable”, which is a partially correct, it would actually be not empirically possible. Technically, transcendental is the term applicable to the kind of reason which gives only a priori objects. Of all the terminology in Kant, that one warrants the most care.

I'm sure that that is not what Kant means by transcendental. Doesn't he go to the trouble of differentiating 'transcendental' from 'transcendent' to avoid that implication?

Layman's explanation: what is transcendental is what is always already the case, what must be assumed to be so by any supposition, what is implicit in experience without being visible to it. — Wayfarer

I am not saying Kant didn't make the distinction, but I am questioning whether the distinction holds in light of the implications of his philosophy. Think about the differences between phenomenology as presented by Husserl, Heidegger and Merleau Ponty and Kant's philosophy.

Phenomenology posits the "transcendental reduction", which, as I read it, is transcendental in the "ordinary" sense as I outlined in brackets in the previous post.The objects of sense are understood, in their pre-experiential rawness, as transcendental, which renders the empirical as not separate from the transcendental, and undermines the notion of a duality of ideality and reality that lingers in Kant despite his refutation of idealism.

For example the purely formal notion of the transcendental subject in Kant is replaced in Husserl with the embodied subject, thus establishing the a priori nature of materiality.

Schopenhauer's criticism of Kant in this, is that in calling the noumenal "things in themselves" he contradicts his denial that they could be spatio-temporal entities, since there can be no "things" without difference and no difference without spatial and temporal separation. — Janus

Firstly, Kant nowhere claims that differences must be spatiotemporal. One pure concept is different than another, & yet none of them originate a-posteriori in space & time; indeed, they couldn’t, because they’re in one’s possession a-priori & would still be had, as such, even if they’re never employed in relation to space & time. So Kant never contradicts himself in that respect.

Secondly, Schopenhauer is actually the one who contradicts himself in that respect. He claims that differences & multiplicity are spatiotemporal, & yet he posits that there are “eternal Ideas” or “Platonic Ideas.”

“..., Art, the work of genius. It repeats or reproduces the eternal Ideas grasped through pure contemplation, ... .”

“Time is only the broken and piecemeal view which the individual being has of the Ideas, which are outside time, and consequently eternal.”

“The pure subject of knowledge and his correlative, the Idea, have passed out of all these forms of the principle of sufficient reason: time, place, the individual that knows, and the individual that is known, have for them no meaning.”

Thus, Schopenhauer not only asserts that an Idea has “passed out of all these forms of the principle of sufficient reason: time, place,” but he also says that there’s a multiplicity of them when he speaks of “Ideas” in the plural form. Schopenhauer therefore maintains that there is a multiplicity of things that are “outside time” & have “passed out of all these forms of the principle of sufficient reason: time, place, ... .” In other words, he maintains that there are differences & multiplicity that transcend space & time; consequentially contradicting himself when claiming that difference & multiplicity is spatiotemporal.

Thanks and very interesting. Welcome. — Tom Storm

& I thank you for welcoming me. :up:

I think this line, despite the new questions it generates, probably answers all my original questions. — Tom Storm

Glad to hear that I could help you in finding any answers.

It was a paranthetical comment, not representative of what I think Kant says, but suggestive of an important point in its own right. — Wayfarer

Then I misunderstood you if you never tried to pass it off as being representative of what Kant says. Sorry, my mistake.

Yet to that point of yours. If, according to you, the brain constructs the world, then wouldn’t that brain itself have to already exist in order to do so? For, what’s non-existent can’t create, let alone do, anything, right? Consequentially, if so, the world, or both the materials out of which the brain is constructed & with which the brain interacts, would already exist & it couldn’t itself be a construction of the brain.

To try to understand Kant’s subject of the pure forms & concepts as the “hominid brain” completely undermines what Kant means when stating that we construct the phenomenal world.

For, in Kant’s sense, both the material & the formal elements of phenomena depend on such a subject & can’t exist without it; so that the subject is essential to the very creation, construction, or coming-into-being of such phenomena. Whereas in the sense of how the “hominid brain” is commonly understood, the world, or both the materials out of which the brain is constructed & with which the brain interacts, already exists independently of the brain; & therefore the world, or both the materials out of which the brain is constructed & with which the brain interacts, wouldn’t be a creation, construction, or come-into-being, because of the brain.

You're certainly entitled to that "opinon". — 180 Proof

... & you to yours. Yet are you unwilling to give your reason(s) for opining that Schopenhauer is a better Kantian than Kant?

Yet to that point of yours. If, according to you, the brain constructs the world, then wouldn’t that brain itself have to already exist in order to do so? For, what’s non-existent can’t create, let alone do, anything, right? — Mental Forms

I completely agree with your point. I'm not in the least a materialist-reductionist or a brain-mind identity theorist. I might well have said 'the mind constructs....' but was making the point with respect to the brain, because of the acknowledged fact that the human brain is the most complex and sophisticated known natural phenomenon. Read the next comment again: 'It creates a world, the only one you'll ever know'. By that I mean, the mind synthesises and creates the only world you will ever know, but by pointing to the acknowledged complexity and sophistication of the brain, was making a rhetorical point.

So:

For, in Kant’s sense, both the material & the formal aspects of phenomena depend on such a subject & can’t exist without it; so the subject is essential to the creation, construction, or coming-into-being of such phenomena — Mental Forms

Is exactly what I was getting at, and something I often say myself.

But the issue I'm having with Kant's philosophy of mathematics is another thing altogether.

I'm not in the least a materialist-reductionist or a brain-mind identity theorist. I might well have said 'the mind constructs....' but was making the point with respect to the brain, because of the acknowledged fact that the human brain is the most complex and sophisticated known natural phenomenon. Read the next comment again: 'It creates a world, the only one you'll ever know'. By that I mean, the mind synthesises and creates the only world you will ever know, but by pointing to the acknowledged complexity and sophistication of the brain, was making a rhetorical point. — Wayfarer

Oh, okay. If you might have well said “the mind,” instead of the brain, then I guess that I’d misconstrued your meaning due to what I perceived as being ambiguous; I thought that you were trying to say, in one way or another, that the mind is the brain. Again, my mistake.

the laws which explain that relationships are not given by the observation alone.
— Mww

They're deductive. Synthetic a priori, yes? — Wayfarer

Yes. The ubiquitous analogy......just from seeing five rocks here, and seeing four rocks there, it is impossible to cognize a certain totality of rocks from just those two observations alone. As well, the sensation on the back of your neck, an effect, allows you a cause via Hume-ian inference, but the sensation alone does not tell you what the cause is.
————

....for our experience, and therefore our minds, to be as they are, the way that our experience is tied together must reflect the way that, according to physics, says objects in the world must be tied together.....

Sorry to take so long, but I have trouble unpacking that comment. It seems so backwards to me. I mean...for our experiences and therefore our minds. Experience is determined by the mind, experience presupposes mind (or, more accurately, reason), mind is always antecedent to experience, so it should be, our minds, and therefore our experiences.

To be as they are....
We cannot say how they are, but only how this relates to that, iff they each work a certain way, according to a theory. Maybe...to be as they seem?

The way our experience is tied together....
Experience isn’t tied together. This and that are tied together in order for there to be an experience. Maybe...the way our experiences are tied to each other?

Must reflect the way that says how objects in the world are tied together....
From this armchair, that’s just wrong on transcendental accounts, even if it apparently holds in phenomenological accounts. We never can properly say how objects in the world are tied together, but only how reason ties the representations of them together in accordance with observations. It is my understanding that phenomenology regards objects in themselves as that of which experience concerns itself, the finer theoretical tenets of such a metaphysic being unfamiliar to me. From that point of view, I suppose it is reasonable to say, the way our experiences are tied together says how objects in the world must be tied together. Still, where is the room for pure a priori cognitions, therefore where mathematical reasoning, in a paradigm where objects in themselves are the objects of experience? Hume’s Dilemma in spades, methinks.

Anyway.....probably much ado about nothing, that is, my misunderstanding the comment, yet still spending time talking about it.

thanks for the explanation, it helps. I will go back to that passage on physics and track down the original reference, it might have been poorly paraphrased in the article I quoted.

We never can properly say how objects in the world are tied together, but only how reason ties the representations of them together in accordance with observations. — Mww

Physics does that, though. And chemistry. In such a way that their behaviours - the behaviours of objects - can be explained and predicted through mathematical and symbolic analysis. We predict from the laws of motion how two objects will react if they collide. That prediction is what I presume Kant would call synthetic a priori. I posted a question about this on philosophy stack exchange.

See my answer to Wayfarer, Mww. Hopefully that should answer your questions.

Firstly, Kant nowhere claims that differences must be spatiotemporal. One pure concept is different than another, — Mental Forms

I didn't say that Kant claimed that. Concepts differ in their semantic content; I was referring to the supposed differences between "things in themselves", which if they exist, are not concepts but real things. We cannot conceive of differences between real things that are not spatio-temporal differences.

The difference between abstract and intuitive cognition, which Kant entirely overlooks, was the very one that ancient philosophers indicated as φαινόμενα [phainomena] and νοούμενα [nooumena]; the opposition and incommensurability between these terms proved very productive in the philosophemes of the Eleatics, in Plato's doctrine of Ideas, in the dialectic of the Megarics, and later in the scholastics, in the conflict between nominalism and realism. This latter conflict was the late development of a seed already present in the opposed tendencies of Plato and Aristotle. But Kant, who completely and irresponsibly neglected the issue for which the terms φαινομένα and νοούμενα were already in use, then took possession of the terms as if they were stray and ownerless, and used them as designations of things in themselves and their appearance — Schopenhauer

The reason why Kant fails to understand noumena is because he is bound to the rigidity of categorical thinking. He is quite "manichean" on this: the world we can know is boundaried and closed to possibilities beyond the definitions allowed by the simple understanding that sensual intuitions are blind without concepts and concepts are empty without sensual intuitions. This is what you get when logic rules theory absolutely. All that matters is clarity. Kant would have made a good banker (or better, a good anglo-american analytic philosopher. Kant started both traditions, the analytic and the continental philosophies).

But this noumena, what are its boundaries? He imposes limitations on human knowing reasoning that since there are no sensual intuitions, there is nothing for a concept to be about, but why is this true? For surely the only reason he had to posit noumena is because he had no choice: representations had to be OF something. Look a little closer and you see that noumena must be posited only because there is something in the phenomenal presentation that insists. Now look at noumena and what it "is". There is nothing it is not, for how is there to be a line drawn? His my apperception of my hand in this occurrent event of typing to be excluded from the encompassment of noumena?

Kant doesn't see that noumena is just a term for what is in the phenomenological "presence". Experience itself is thoroughly noumenal. There is an insight here that is elusive, slippery. One way to say it is this: we live an breathe metaphysics. We think of metaphysics as being impossibly remote (like Kant does in the transcendental dialectic) but this is all wrong, simply put.

What stands in the way of realizing this in the perceptual encounter itself is, in philosophy, this Kantian intractability.

What is called wisdom is far remote from what professional philosophers do.

great answer, Astrophel. I would love to sit here and compose a reply, but I'm moving house for the next 2 days, but you can be sure I will come back to this.