we've subsequently discovered, per Relativity, that the geometry of space and time is non-Euclidean. Which means that Kant's (synthetic a priori) judgments about space and time have been falsified by experience. — Andrew M

First, Kant didn’t attribute any geometry to space, but rather, to objects in space. Kant was a “magister” in math and tutored university-level mathematics, so it is highly unlikely he wasn’t aware of non-Euclidean axioms, such that triangles on the surface of a sphere do not have angle summation of 180 degrees. But that fact does not negate the Euclid’s “the shortest distance between two points is a straight line”, which remains true even if one cannot get from A to B in a straight line. The truth that one cannot cut through the Earth to get from NYC to Hong Kong does not falsify the fact that cutting through the Earth is the shortest way.

Second, in order for experience to falsify “...Kant’s (synthetic a priori) judgements about space and time...”, one would have to show, 1.) he made any such statements, 2.) that if he did, how experience would falsify them, and most importantly, 3.) what synthetic a priori judgement actually is.

“....Judgements of experience, as such, are always synthetical....”
“....Mathematical judgements are always synthetical....”
“....mathematical propositions are always judgements a priori, and not empirical, because they carry along with them the conception of necessity, which cannot be given by experience....”

It is clear Kantian synthetic a priori judgements require necessity, which experience cannot deliver. Therefore experience cannot falsify them.

Consider, even though time dilation and length contraction have been shown to be the case, as regards relativity, all that began with pure mathematics, which are.......wait for it......all synthetic a priori propositions. Einstein had to think all this stuff before he ever wrote anything down, and had to wait years for technology to catch up enough to demonstrate the the truth in the math.

Also consider, no matter what relativity says, a guy doing geometric functions anywhere in the Universe can still use Euclid’s axioms. He’s still human and so was Euclid, so......

It’s always helpful to keep in mind just what relativity means.
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Did Kant think that our existing language that we use to represent the world and acquire knowledge somehow fails us?[/quote]

Could very well be, seeing as how he invented some for himself. Or at least reformed some extant meanings to suit himself. But generally I wouldn’t say he thought language fails us. That we use the same language doesn’t guarantee understanding, but does guarantee understanding is possible. And because the language of mathematics is the same for every human, understanding math is given, depending on experience with its use, of course.
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The stick example shows that one can be mistaken about what they think they've perceived. So the language term "appear" is introduced to represent that situation (e.g., the straight stick appeared to be bent). The problem it solves is to give us language for describing a naturally-occurring situation. Things aren't always as they appear to be. — Andrew M

That things aren’t always as they appear is certainly true, but it isn’t why Kant introduced the term “appearance”. Even if that which appears is not a false representation of the real state of affairs, it is no less an appearance than that which appears that is a false representation. Because the Kantian cognitive system is representational, there must be representations for each step in the procedure, so appearance is simply the first representation in the transition from external real physical to internal speculative theory. This is why I said “appearance” for Kant is like making the scene, being presented, and not meant to tell us what a thing looks like. Appearance serves the Kantian system equally to all five senses, which tends to eliminate what a thing looks like, when the thing being perceived doesn’t even have a look, but has instead a feel or an odor.

The stick appears bent is in the sense of what it looks like but really isn’t; the Kantian appearance of the bent stick is exactly that.....for all representational intents and purposes, the damn stick is bent!!! All the way through the cognitive system the stick retains the appearance of a bent stick, and it will be judged to be bent.....which is exactly what we see. It doesn’t matter to the system that light is being refracted, it doesn’t matter to the cognitive system that air density and water density are not the same, or even have anything to do with the perception of a stick in a peculiar condition.

Experience tells us the stick, appearing bent, really isn’t. The system only tells us what it has the capacity to tell us. If the laws of physics operate such that a stick looks to be bent, then the stick will appear bent. All the bent stick proves is that perception is passive, insofar as it makes no mistakes, but rather all errors in cognition are from judgement alone. We know the truth of this little tidbit, because the stick appears just as bent after we learn it isn’t, then before we learn it isn’t. And a crawly thing between your shoulder blades makes its sensational appearance without having a “looks like” appearance.
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But that shifts the question to be about his system as a whole. What problem is it solving? — Andrew M

Depends on what his system is thought to be. Actually, it is a speculative cognitive system, meant to show a possible method for the human intellect to arrive at an understanding of himself and his environment. Keyword...speculative. The theory was never meant to establish a truth about anything at all, except itself as such. Hence, the theory doesn’t solve any problems, except those the theory explores, and then only if one grants the tenets of it. The bent stick is a pretty lousy example of false knowledge, though, because somebody somewhere figure out real fast the illusion behind it. But no one in the normal living of normal life is ever going to have direct experience of time dilation, and the guy on the platform only makes his judgements based on his watch, not the watch the guy on the train uses.

We speak of things that happen IN time but it would be more exact to say that we measured things with time. Time without events and observers would vanished. — David Mo

Yes, things happen in time is a general statement, or a general condition of all measurable things. Still, when we say we are measuring things with time, we are merely denoting the amount of time IN which a thing happens.
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So, is invisibility a metaphysical idea? — David Mo

Depends on the metaphysical theory in play. According to Kant it is, because invisibility has no object of its own, so would be a concept of reason, hence, transcendental, which is itself in the metaphysical paradigm. Things may indeed be invisible and still present a sensation to the process of cognition, hence are subject to the categories, but the concept of invisibility, in and of itself, is not so subject. It is the thing by which we are affected, not the invisibility of it.

Thus,.......consider the geocentrists whose a priori view was that Earth was the center of the universe, might better be said.....whose prior view.
— Mww

Cool. So my suggestion is that this should similarly apply to absolute space/time and relativistic spacetime. — Andrew M

Yes, I see what you mean. Newtonian absolute space/time was the view prior to relativistic spacetime.

That is, through experience, Einstein's Relativity has replaced Newtonian Physics. Doesn't that contradict the Kantian view? — Andrew M

I’m not understanding what in Einstein would contradict Kant. Where did Einstein prove Kant wrong, in as much as they each operated from two distinct technological and scientific domains? Kant had no significant velocities other than a horse, and there were no trains, which together negate even the very notion of time differential reference frames, so there wouldn’t appear to be any reason for Kant to notice measurable discrepancies in rest/motion velocities.
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So it seems to me that Kant's notion of appearance is artificial. What problem does it solve that we haven't already solved with the natural distinction above. — Andrew M

What problem is there, that the natural distinction above solves? Appearance in Kantian terminology can’t be artificial in any sense, because it is a representation of sensation. If there is a sensation, there will be an appearance, period. And it is necessarily a one-to-one correspondence between sensation and appearance, otherwise there is no ground for the subsequent cognitive procedures, which falsifies the entire system. Appearance in Kant is like making the scene, as in “...that which appears...”, not what a thing looks like, because the advent of appearance in the system is long before cognition, which means there is nothing known whatsoever about the appearance except that one has occurred, been presented, to the system. Thus, it shouldn’t be said that that which is unknown at a certain time is thereby artificial.

I’m open to clarification on either of these, if you wish to provide it.

intuitions are not templates (a priori), they are the content of our ideas. Space and time are the templates of sensible intuition. — David Mo

Philosophy advances by the appropriation of terms, no doubt. Appropriation of terms into subsequent domains still should be legitimatized.

Intuition...content of ideas.
Space and time.....templates of sensible intuitions
Ergo....space and time are the templates of sensible content of ideas.

Could be, but....what is the sensible content of an idea? “Invisibility” is an idea, but hardly has sensible content. An object certainly has sensible content, but should such object then be merely an idea?
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The metaphysical error is to use space and time templates without sensible material. — David Mo

Certainly an empirical error, I’ll give you that. I wouldn’t go so far as to call it a metaphysical error to use time without sensible material, though, even while space would suit the case. All human thought is successive, a condition of time without material content. In fact, any first principle of relation necessarily implies time as an a priori template, re: cause and effect. Or, A cannot simultaneously be not-A.

Actually, it might be a metaphysical error to use the templates of space and time WITH sensible material, because metaphysically, space and time don’t have any sensible material conceived as belonging to them.

Don’t mind me.....just thinking out loud.

the (contingently) prior background — Andrew M

...is categorically opposed to the Kantian a priori meaning, for any contingently prior background is merely another way to say “experience”.

“....By the term "knowledge a priori," therefore, we shall in the sequel understand, not such as is independent of this or that kind of experience, but such as is absolutely so of all experience. Opposed to this is empirical knowledge, or that which is possible only a posteriori, that is, through experience...”

Thus,.......consider the geocentrists whose a priori view was that Earth was the center of the universe, might better be said.....whose prior view.
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An implication of the Kantian view is that two events that are simultaneous for one observer are simultaneous for all observers. — Andrew M

Two events for a guy and guy standing right beside him, will be simultaneous to both, yes. The difference between the observations will be immeasurable.

I’m thoroughly familiar with Einstein, 1920 (English)
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On sticks in water....

“.....It is not at present our business to treat of empirical illusory appearance (for example, optical illusion), which occurs in the empirical application of otherwise correct rules of the understanding, and in which the judgement is misled by the influence of imagination...”

Other "templates" are more particular and a posteriori. — David Mo

Yep.

Intuitions.

Man, that’s a lot of templates. If there are an immeasurably large number of possible experiences, each one with its own template......where’d they all come from?

Now if there were a certain number of templates to which every single possible experience must abide, that might be something to consider. Sorta like a mind saying......hey, screw this. If that which is presented to me doesn’t meet certain necessary conditions, I ain’t even going to bother trying to make something of it.

‘Course, still have to explain where a few necessary conditions come from, just as much as a veritable infinite number of templates. Down in the metaphysical weeds are things like innate ideas, forms, pure conceptions....all kinds weird stuff.

Consider the geocentrists whose a priori view was that Earth was the center of the universe and that the Sun moved across the sky. The heliocentrists replaced that with their own a priori view that it was the Earth that moved around the Sun. — Andrew M

What is it about those views that make them a priori?
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Kant's a priori view was Euclidean. But Einstein replaced that with spacetime relativity. — Andrew M

Even in Einstein, the observer in his own reference frame is in the Kantian view of Euclidean space and time.

Oh. Ok....never mind.

Kant tries to think logical and mathematical thought operations themselves and not just apply them to the world as a natural and true way to access things. — waarala

Well done!!! Pure reason writ large, yes?

Just as logic is predicated on the synthesis of major/minor/conclusion, so too is the theory of human knowledge, in this case transcendental idealism, predicated the synthesis of intuition/conception/judgement.

And, just as mathematics is predicated on law, which invokes the principles of universality and necessity, so too is reason, “....in obedience to the laws of its own nature...” speculated in such manner as to produce those laws.

Makes sense he would construct a logically, lawfully consistent theory based on the two domains in human experience that operate exclusively on those principles.

Per Kant, there's a real world but it's completely unknowable. — Andrew M

If taken from the principle of induction, this would be correct, but might should read....unknowable completely.

The world-in-itself is completely unknowable, taken as the totality of all possible thing-in-themselves, is the logically consistent proposition, wherein completely unknowable means not knowable at all. In that sense, the knowability depends solely on the human cognitive system, without any regard to empirical principles.

Kant's idea, which I assume, is that the a priori is something like a template that we apply to the world. — David Mo

Common interpretation, that. A template impressed on the world to which it must conform. I would rather think a priori reason is the mold into which the world is poured. The only difference, which is more semantic than necessary perhaps, is that template implies projection of the mind onto the world, and mold implies receptivity of the world into the mind. Just depends on one’s choice in understanding of the relationship between mind and world.
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An open question is whether we should assume some structural order in the world. — David Mo

What would the world look like if we didn’t? I’m not sure what you mean by a structure. Is it that we assume, e.g., atomic structure, because experiments support it?

In context, I am the non-academic, therefore it is I whose criticism is quite toothless.

That is not to say I don’t read, and appreciate the intelligibility of, non-academics; philosophy forums are full of ‘em, after all.
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he had read the best verses of his life in mediocre poets. I'm in. Why not you? — David Mo

Pure cognitive prejudice: he who has not the remaining time or eyesight left for luck, should limit himself to interest.

That was a great introduction. Although I couldn’t find when it was written; apparently, Pogson-Smith wasn’t famous enough for a wiki page of his own.

I am always fascinated by historical contexts, the influences of the time of the writing, as opposed to looking back from its future. I mean....who cares about the Papal Bull of 1570, but its effect on Hobbes was quite apparent. Descartes was talked about a lot differently then than now, as well.

Interesting.

children do not construct the concept of cause or substance by adding sensations, but by giving them an order. — David Mo

Children do not construct those concepts by adding sensation....agreed, absolutely

But if it is meant that the child does construct those concepts by giving them an order....I don’t know how that would work.
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We perceive something from a unique perspective and we don't know why it has to be that way. — David Mo

Dunno why not, we own that unique perspective, so we know why it has to be that way. Couldn’t be any other way.

If you mean we don’t know why the something we perceive, given our unique perspective, has to be the way we perceive it, then that is exactly right. Our unique perspective is not an authority on the way of something, but only how we think of it.

Reasoning tells us why it has to be this way and not otherwise, its necessity. — David Mo

Yes, but only from our unique perspective. We cannot project our sense of necessity if it arises from our own reason. If that were the case, we’d be effectively telling the Universe how it must be, rather than us merely trying to understand how it is. Besides, whatever necessities the Universe holds in itself, can only be given to us depending on how we ask about them. Except for sheer accident, of course.

“...Reason must approach nature with the view, indeed, of receiving information from it, not, however, in the character of a pupil, who listens to all that his master chooses to tell him, but in that of a judge, who compels the witnesses to reply to those questions which he himself thinks fit to propose...”

The Universe says, “I’ll tell you puny, know-nothing humans whatever you want to know. All you gotta do is figure out how to ask me the proper questions”

In a certain sense, child psychology has proved Kant right: children do not construct the concept of cause or substance by adding sensations — David Mo

Yes, and raises a very subtle point of Kantian metaphysics: it isn’t what we know, but how we know it. OK, so as the theory goes, there exist a priori principles in the mind, and an example is a geometric figure, Well, after a certain age, it is highly unlikely a person doesn’t already have a great experience with geometric figures, which makes it very hard to claim a priori principles. Ok, fine. Divide a priori into pure and impure, in order to save the one because of an apparent contradiction with the other, and reflect back to a time of very first experience. Problem is, no one can remember what was going on in their heads at some very first experience, that isn’t conditioned by something they already know. Which makes the Hume-ian argument against a priori knowledge so powerful.

But if we consider a child, who has absolutely minimal experience with everything to begin with, hence isn’t affected by memory, it becomes easier to see the necessary rational groundwork for reason in general and a priori reason in particular. Because a child does learn, and learns without conditioning experience, some kind of a priori principles or pure conditions must exist in the human system. But if a child, and therefore anyone, has some form of pure a priori conditions, they couldn’t be constructed, for there would be nothing to construct them from, that aren’t themselves the same kind of thing, or from experience, which he doesn’t yet have.

This is why Kant specifically, and many others somewhat less but still inclusively, claim for the faculty of understanding the ability to think, for it would appear, however magically it must seem, that these necessary conditions, like, as you say, cause, substance, existence, possibility, necessity, etc., must arise from the intellect itself.

Of course, no one has been able to explain how understanding can think pure a priori and thereby necessary conditions....the categories.....but if it does, then all else falls into place neat as the proverbial pin. The second major objection: metaphysical theories cannot be falsified.

The issue with subject/object dualism is that it affects (or infects, depending on one's perspective) the way people look at everything such that it is difficult to conceive of any alternative. — Andrew M

Yes, I suppose. We talk usually in the form, “We think....”, “You know...”, “I am....”, and so on, which makes explicit a subject/object dualism in general intersubjective communications. But I wouldn’t call that an issue as much as I’d call it linguistic convention. Nature of the beast, so to speak, and definitely makes it difficult to conceive an alternative.

Ooooo but my oh my how they try: universal consciousness, utilitarianism, being one with my fellow man.....(sigh)

If there is a real issue, I would attribute it to science, which is trying its damnedest to eliminate the subjective nature of the intellect.

I guess I'd like to hear what you have to say about the transcendental pretense (the assumption that we all have the same rational system.) — mask

My understanding of the alleged transcendental pretense is that fundamental subjectivity is a license for arrogance, or, that because there is a common rational system amongst humans, a common great and wonderful behavior should be constructed from it. And because Kant is the prime champion for the power of the person as subject, he is accused as the culprit for the rise of such pretense.

What a load!!!! Kant’s time was the Enlightenment, the cultural, political and religious upheaval of which contributed much more to Everydayman’s new-found dominance than the Kantian (1784) sapere aude ever did.
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Or in general what you think Kant had to take for granted in order to write CPR. — mask

Superficially: reality of the external world combined with the power of natural science to explain it; the inevitability of metaphysics combined with the failure of natural science to explain it.
Fundamentally: it is possible to discover, and rein reason to within, a proper boundary.
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....what did he not see? — mask

The intrinsic circularity of human reason itself, re: the evolution of a theory on reason, using reason to evolve it. It is hard to say he didn’t see it, but rather merely ignored it, seeing as how there is no choice in the matter.
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Do you have any criticisms of Kant? — mask

Nahhhhh. After 250 years, there’s not much left to be critical of, that hasn’t been beat to death by others. Besides, any criticisms a non-academic would have really is quite toothless.

A worth endeavor perhaps, but the nature of human subjectivity seems to prohibit, or at least seriously impair, its possibility.

The world is not a set of objects but the 'stage' or 'background' on which or against which all things exist. — mask

Yes, seems that way to me as well. A jar of jellybeans is not the jar.

There is another part that is outdated: mathematics is universal. — David Mo

I submit Kant means by universal, anywhere there is a human employing those principles in the same conditions under which they were imposed a priori. No matter where we go in the Universe, they must apply, and now that Voyager 2 has exited the solar system, the universality of mathematics seems to be confirmed. It still exists just as we built it.

A sheet of paper will be a plane anywhere a human is in the same plane. Mathematics as human know them will not hold in a black hole, but then.....neither will a human. 1 +1 = 2 no matter what planet we occupy. There may be different mathematics in the Universe, dependent on the rationality that forges them, but those rationalities wouldn’t be the same as ours.

If the language that the individual thinks in is forged socially, then Heidegger has a point with his being-in-the-world and being-with-others as a deeper layer than the epistemological theory of the individual mind processing sensation with an innate set of concepts. — mask

That may all well be, but it bears keeping in mind that peope don’t think qua think, in language; people think, meaning the private subjective rational activity, in images. Language only arises in discussions of thought, which is to say, the meaning of those images.

I think we do have the same rational system, more or less, but believing this seems to depend on experience — mask

The system is complete in itself; the content of the system is predicated on experience, yes. And it really doesn’t matter what name a theory subsumes the system under, as long as they all agree we as humans all have the same faculties.

Cool. Thanks. I admit to not thumbing far enough, or thumbing right over it. I lost my place in answering your question. Are you ok with the responses you got, or is there anything you’re still unsatisfied with?

Kant’s things in themselves, which correspond to Locke’s things themselves, affect our senses and in this sense they certainly bear a quasi-causal character. — Tomida

YEA!!! (Does the Happy Dance, a-la Snoopy.....feet just a-blur)

I appreciate your familiarity with the subject matter, and your arguments.

Things in themselves are not perceived, only thought. — David Mo

That things in themselves are only thought is correct, but everything a human perceives is also thought. On the other hand, to say a thing in itself is ONLY thought implies its existence is not necessary. If its existence is not necessary, it can have no necessary use. Isn’t its regulation of our knowledge a necessary use, insofar as at least instance of an unknownable, is informed by it?

But I take your intent with the proposition. The solution is to allow the determinations of the nature of the “-in-itself” to be different than the determination of the nature of the “thing” connected necessarily with it. See SS9-1.
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Your mistake was here. — David Mo

I won’t say I haven’t made one, except that if I did, it would have nothing to do with the ideality of space or transcendental appearances. I haven’t thought of things or things in themselves in that way. Nor have I involved subjective conditions as properties.

I do grant anything to which my empirical intuitions cannot apply a transcendental existence, which has absolutely nothing whatsoever to do with me in considering things met in perception alone. The transcendentalism only disappears iff something progresses into the faculty that represents it as an appearance, which perception is never tasked to do.

I understand what you’re trying to say, by saying the thing-in-itself is not perceived. Things perceived do not vacate their space simply because they are impressed upon us, the thing remains even while we are thinking about it. Nevertheless, the thing thought about merely represents the thing that remains in its space, and THAT is the thing-in-itself.

When the face in the toast is the focus of attention, the toast itself fades to background)
— Mww

I'm afraid I don't understand the example of the toast. This raises a question about your conception of the thing in itself (noumenon). The face on the toast is just a phenomenal illusion. — David Mo

Agreed. The point being, the manner it which it became an illusion.

I categorical reject the symbolism implicating the thing-in-itself should equate to noumenon.
I find it telling that it is so difficult to fathom, that the discursive faculty of understanding is the sole originator of any kind of likeness between them, and then only because they are misunderstood. They are utterly and completely different in form and matter, they are differently logically and they are different conceptually. The only commonality shared between them is knowledge and the lack thereof.
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Things in themselves refer to objects such as substance, God, cause, soul, etc. that have no appearance. — David Mo

Yes, things in themselves and all those “such as” are the same as far as the faculty of sensibility is concerned, because none of them appear to us, but they all can still be thought by us. That does not mean the thing in itself refers to them, or, that those “such as” are even objects, in the manner in which a thing in itself is an object.

Does Kant really think there are basketballs out there? — mask

Linguistic convention says there are basketballs out there; transcendental idealism says there are objects out there only called basketballs because the human represents the object to himself as such.
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.....ordinary reality is a kind of intersubjective representation.... — mask

Correct. Given that all humans incorporate the same rational system, all reality in general should be consistent among them. A basketball is such for me as it is such for you. Even if I have no experience of them, if you tell me about one, I should understand what you’re talking about and form a representation of it a priori for myself. This is for the most part because of the categories, which permits conception of an object in general without all the the necessary intuitions given from perception.
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A small point. Can geometry really be saved this way? — mask

My doctrine of the ideality of space and of time..... — Kant

I can’t find this passage. To tell the truth, I don’t even recognize it, my keyword searches don’t lead me to it, and because I’m too lazy to peruse all my literature even after thumbing through some of it, would you please refer me to its source? I’m not sure what geometry is having to be saved from, unless you meant illusory appearance. That has an affirmative answer, but I’m going to withhold it because I don’t want to confuse the contexts.
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The truths of Euclid seem to depend on shared practices. Trying to ground science on an individual mind seems iffy. — mask

Synthetic propositions of geometry indeed require practice to prove their truth, consistent with their specific objects. Analytic propositions of logic, on the other hand, do as well, but require only objects in general be given to them.

The science of relativity is grounded in Galileo’s mind alone, isn’t it? Einstein may or may not have thought SR and GR on his own, even if there never was a Galileo, but he didn’t.

Representations of our sensibility is an affect on our senses. An affect on our senses is a perception. A perception requires what we call an outward object. Outward objects are outward things. Outward objects in themselves are things-in-themselves. Outward objects in themselves are perceived. things-in-themselves are perceived. That which is merely perceived is unknown to us. Things-in-themselves are unknown to us.
— Mww

Your argument is wrong. To think that an undetermined "something" has caused A is not the same as knowing the cause of A. Moreover, Kant says countless times that we cannot perceive things in themselves. This is the main point of CPR. — David Mo

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“...objects are quite unknown to us in themselves, and what we call outward objects, are nothing else but mere representations of our sensibility...”
(B45)

Simple substitution, object in itself for thing in itself. It is done by the author repeatedly. Please show how my argument is wrong.
— Mww

In this paragraph Kant is criticizing the "ordinary" representation of things in themselves, purely empirical. His criticism begins from "But if we consider..." The idea is that the in thing itself cannot be reached through the generalization of the senses. — David Mo

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I still don’t see how my argument, that paragraph ending in things-in-themselves are unknown to us, is wrong. Your “But if we consider....” is in B63, which has to do with transcendental objects. B45 isn’t treating objects of perception as transcendental objects.

I understand “objects are quite unknown to us in themselves” (B45), but I don’t think that is meant to imply objects unknown to us in themselves, are not the objects of perception. If such should be the case, we must have two distinct and locally separate objects...the one we perceive, and the exact same singular entity left behind because it is unknown to us. That would be like.....if we don’t know what they are, we can’t see them, which is logically absurd. Or, which is just as silly.....we can’t see them because we don’t know what they are.

I would appreciate a reference for your “...Kant says countless times that we cannot perceive things in themselves. This is the main point of CPR....”. I would agree we cannot perceive any transcendental object, and if the thing-in-itself is considered as one, we wouldn’t be able to perceive it with our representational system. But that does not say spacetime objects are only considered transcendentally.

True enough, actually. But, man......those paragraph-long sentences.....I have to start over by the time I get to the end of some of them, I swear.

But you are right, all in all. He lays a very basic set of pre-conditions, in the introductions, to be sure.

YES!!! I mean....the guy’s tough, sure. Sometimes confusing, absolutely. But it’s all in the book, if a guy wants to dig it out bad enough.

Read Kant in full. — I like sushi

YES!!! And get several translations. Sometimes comparing them helps with one’s comprehension.

Anyway, Kant only say in these sentences that noumena cannot be explained by sensibility because they point to an impossible-pure knowledge of metaphysical entities. — David Mo

Understood, and all well and good. Some groundwork, if I may:

Thought. A thought. Full stop. No ways and means, no object, no terminology. Just a split-second instance of what a human does as a private rational agency. A form of something as yet without content. Then, consider its spontaneity. The proverbial, “it just popped into my head” kinda thing. Granting this actual occasion is sufficient reason for Kant to speculate this, as the second theoretical tenet:

“....Our knowledge springs from two main sources, the first (receptivity for impressions); the second is the (spontaneity in the production of conceptions). Through the first an object is given to us; through the second, it is thought....”

And because of that tenet, these consequences are justified as following from it:

“....we call the faculty of spontaneously producing representations, understanding.....”
“.....Conceptions, then, are based on the spontaneity of thought...”

Thus is given that concepts are representations, and as such, arise spontaneously from the faculty of understanding, which makes explicit understanding is the faculty of thought itself. In other words, it is meant to justify that understanding thinks. From that, and with various support found within the theory, thought is cognition by means of conceptions.
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Now, that being what the understanding is, it remains to be said what the understanding does.

“.....But the conjunction of a manifold in intuition never can be given us by the senses, for it is a spontaneous act of the faculty of representation. And as we must, to distinguish it from sensibility, entitle this faculty understanding; so all conjunction (...) is an act of the understanding. To this act we shall give the general appellation of synthesis, thereby to indicate, at the same time, that we cannot represent anything as conjoined in the object without having previously conjoined it ourselves....”

Thus is given that understanding is the faculty that thinks, and in empirical thought, thinks a synthesis of conjoining representations of its own spontaneous creation to the representations of a manifold in intuition. Or, conceptions to intuitions, hence the adage, “...Thoughts without content are void; intuitions without conceptions, blind....”

Sidebar: This......we cannot represent anything as conjoined in the object without having previously conjoined it ourselves......is the oft-abused, but fundamentally critical “Copernican Revolution”.
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The onset of the noumenal problem arises here:

“....understanding which is occupied merely with empirical exercise, and does not reflect on the sources of its own cognition, may exercise its functions very well and very successfully, but is quite unable to do one thing, and that of very great importance, to determine, namely, the bounds that limit its employment, and to know what lies within or without its own sphere....”

The entire foray into noumena is justified by this one thing:

one may see a piece of toast, but one may also see a piece of toast with a face in it.

All this is, is the faculty of understanding turning itself into the faculty of imagination, insofar as there is created a phenomenon from that which no such phenomenon should be contained.

And the problem is caused by the understanding itself:

“......The understanding, when it terms an object in a certain relation phenomenon, at the same time forms out of this relation a representation or notion of an object in itself, and hence believes that it can form also conceptions of such objects....” (B306)

Without the direct references, it shall be given that the conceptions understanding thinks as belonging to a mere notion of an object in itself already established as a phenomenon from the faculty of sensibility, it calls a noumenon, thus nothing but an intelligible concoction dreamed up by understanding simply because it has voluntarily exceeded its empirical mandate in the employment of its spontaneity.

In effect, understanding represents to itself, on its own accord, the notion of a thing, terms it noumenon, but stops right there, without also thinking schema that would then be synthesized to it in order for such notion to have reality.

Understanding here thinking to or within itself, not with respect to sensibility thus without empirical content, therefore it is the pure understanding. The only conceptions belonging to pure understanding are the categories. The categories can only apply in empirical thought having to do with objects of sensibility, and the notion of an object in itself understanding thinks for itself, is no such thing. The only concepts with which pure understanding has to synthesize......which is its job after all.....are the categories, but synthesis of pure conceptions with mere notions cannot give a cognition. Therefore, noumena are nothing but logically possible, pure thoughts of the understanding, and most certainly not a thing in itself.

It now should be clear that.....

“.....giving the name of noumena to things, not considered as phenomena, but as things in themselves, hence is compelled to cogitate them merely as an unknown something....” (B310, 1985)
“....the concept of noumena, not to be thought as objects of the senses, but as a thing-in-itself, solely through a pure understanding....” (B310, 1929)

.......is simply an elaboration of B306, in which the original thought of the pure understanding as “object in itself”, is thoroughly interchangeable with the thing in itself of B310, and only is meant to advocate noumena have no possibility of ever being a cognized empirically just as the actual, real physical ding an sich outside us has no possibility, and not that they should ever be thought as being the same thing. The difference in consideration as to why they cannot, lays in the consequences of noumena being the off-shoot of a mere notion, but the ding an sich stands as an unknowable, albeit a real, physical object. The former is objectively valid as a thought, the latter is objectively real as an object.
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In the case where it is said noumena are the limit on appearance, or sensibility, derives from the following:

Phenomena are the result of the synthesis of appearance to intuition by the imagination. Understanding synthesizes phenomena with conception. Pure understanding attempts to synthesize a notion of an object in itself already given as phenomenon, which already has an appearance as its predicate. The notion of an object in itself deletes phenomenon proper......

(When the face in the toast is the focus of attention, the toast itself fades to background)

.......thus the appearance used in the synthesis of them, is likewise deleted. Keeping in mind understanding unites intuition with conception, it follows the deletion must be appearance, because if understanding thinks to delete intuition, it doesn’t work at all, a contradiction. The limit on sensibility is then, that upon the thought of noumena, the faculty of sensibility ceases to function as the source of empirical knowledge. It is the toast that is real, not the face.

The devil for some, and the nonsense for others, is in the details.

There are many devils in the details.

Yeah.....just think of how many meanings can be changed merely by gutting a quotation.

Kant has anything to do with Science generally. — Galuchat

FYI, and of no particular import, Kant demonstrated the refutation of Newtonian absolute space and time (1786), advanced the first iteration of the nebula theory of star-generation (1755), the first iteration of plate tectonics (1756), the first to use “quantum” in its current meaning as “minimally discrete”. The absolute space thesis was metaphysical, having no mathematical proofs so not really science, the nebula essay inspired LaPlace and is still the core principle, the plate tectonics was way off-base, the point being he was the first to think what would eventually become current science.

Things and things-in-themselves are equal as objects, just not as knowledgeable objects. Things as they are in themselves are still spatial-temporal things.
— Mww

This doesn't make any sense I'm afraid. The thing-in-itself is exactly what Kant, repeatedly, says is what cannot be known. — Xtrix

You continue to confuse, or equate, the knowledge of a thing with the existence of it. A thing to be known must exist, but a thing that exists may not be known. Things existing before knowing beings, are the very same things existing and known by humans. Merely adding thinking subjects to the total of reality makes no difference to the thing. The thing doesn’t give a hoot about humans, it will remain always just itself.
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We label objects as thing-in-themselves only to tell us we have no way to prove that what we know about objects is what they actually are.
— Mww

"Actually are" apart from our way of knowing them, which is spatial-temporal. There's nothing left over, hence why we cannot say anything about it. — Xtrix

The subtlety is.....our knowledge of a thing may be exactly what it is in itself. But without proof, which we don’t have and can’t get, because we have nothing with which to compare, we can’t know with apodeictic certainty. And we don’t have and can’t get proof because we don't know things, in themselves or otherwise, because we only know representations of things. It follows that our representations may perfectly exemplify things as they actually are in themselves, but once again, we can’t prove it.

All human empirical knowledge is grounded in the principle of induction. The more we know about a thing, the more conceptions we can logically understand as belonging to it, the closer we are to total knowledge of it, knowing exactly what that thing is. We cannot possibly have complete knowledge of some things (the quantum, the cosmological, because we have no idea what conceptions might even apply), which makes explicit the difference between what we do know and what there is to know, is exactly the same difference between the thing known and the thing in itself unknown.

Yes, what effects us from outside corresponds exactly to what we sense. That which effects our eyes exactly corresponds to what we see; that which effects our ears corresponds exactly to what we hear, etc. We have to have consistency between incoming data and what the cognitive system works with.
— Mww

Then the stimuli would be the thing in itself, not representation. — Xtrix

Correct. We can shorten thing-in-itself to just object or thing, without changing anything but the words.
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All kinds of things are outside us, but they are not representations, they are real, physical objects of experience,
— Mww

Saying they're real physical objects and representation is the same thing. Of course they're representations. — Xtrix

No. Things outside us are real physical objects that become represented in and by the system. They cannot be representations antecedent to the system that causes them.

Now, if you wish to call representations and objects the same thing, you certainly can. But can you say how the representations are determined, if they reside outside the mind, as objects reside outside the body? If you use the Kantian system, you end up with representations of representations, which is catastrophic to the system itself.
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you're arguing some kind of correspondence theory of truth. Again, that's not Kant. — Xtrix

I wouldn’t know, and really don’t care. Kant is concerned with knowledge, and says very little about truth qua truth in his knowledge thesis.
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I say we don't perceive objects in themselves (which is obvious), then you disagree and quote Kant and the first thing he says is "objects are quite unknown to us in themselves" — Xtrix

That was supposed to show perception of objects in themselves is actually true where you say it is false, and it is actually the case that knowledge of objects in themselves that is false.

Object are quite unknown to us in themselves says exactly the same as objects in themselves are quite unknown to us.
— Mww

Sure. So you agree? — Xtrix

Of course; I wrote it. You’re talking about perception of, I’m talking about knowledge of. You’re saying it’s obvious objects-in-themselves are not perceived when they actually are. Perception, and the faculty of sensibility cannot tell the difference between a thing and a thing in itself. There is no difference in the data received from a thing and the data received from that very same thing in itself. Which is probably why we just call it an object. Reconciles the whole mess.
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Reducing experience to "empirical" experience is pretty limiting, and not very clear. — Xtrix

The theory is touted by its author as being “...complete and self-contained, with nothing not of account...”. Best way to do that is keep everything in a place exactly created for it, so nothing overlaps and gets in the way. Commonly called self-contradiction. Experience is called one thing, in order to prevent it from being something the conditions for that one thing, simply won’t allow. So, yes, it is limited, intentionally.
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The initial response was about my saying the subject/object variation I was thinking of was Kant's. — Xtrix

It is. Or, it can be. Kant goes to great length to give a dissertation on logic and how logic is the form of all a priori cognitions of pure reason. And of course, all logical propositions are constructed on the subject/object dualism. We got side-tracked by the present discussion on different topics that don’t require a subject/object dualism for understanding them, but they would come into play when discussing what the subject himself is actually doing when he thinks, without getting as far as knowledge and experience, which is what phenomena/noumena and things in themselves are all about.

I’ll love weeds. Metaphysical weeds, not common garden variety weeds.

"The concept of a noumenon, (...) as a thing in itself" (B310) — David Mo

Your (...) leaves out the most important part, that act having its own special name.

“.....giving the name of noumena to things, not considered as phenomena, but as things in themselves...” (B310, 1985)
“....the concept of noumena, not to be thought as objects of the senses, but as a thing-in-itself...” (B310, 1929)

Your comment says what a noumenon is like, the author says how it should be treated. The two iterations are very far from being consistent with each other,

Thanks, and a tip of the pointy hat in your general direction. (Grin)

Representations of our sensibility is an affect on our senses. An affect on our senses is a perception. A perception requires what we call an outward object. Outward objects are outward things. Outward objects in themselves are things-in-themselves. Outward objects in themselves are perceived. things-in-themselves are perceived. That which is merely perceived is unknown to us. Things-in-themselves are unknown to us.
— Mww

Your argument is wrong. — David Mo

All of mine you quoted above is assembled from my quote below:

“...objects are quite unknown to us in themselves, and what we call outward objects, are nothing else but mere representations of our sensibility...”
(B45)

Simple substitution, object in itself for thing in itself. It is done by the author repeatedly. Please show how my argument is wrong.