I agree that Kant does not say much about noumena and uses it in different ways.
However let's look at the main interpretation of noumena, "the thing in itself."

Strip all perceptions from an object and something still remains.
My only point is that this is not a gray nothingness but must have an existence external to us.

Unless we are willing to believe that all existence is in our minds, as the good Bishop Berkeley believed, we must postulate an external reality upon which our reality is based. Otherwise everything is in our minds.

My main point, is that there is a fundamental basis of reality which we can never be aware of but which is represented by perception and an implicit order in perception which is based upon an implicit order in noumena. This is beyond what is stated Critique but I believe it can be extrapolated from it.

Kant studies phenomena or what is human knowledge. What is not studied is what characteristiics noumena might have. This is a subject worth looking into.

One of the fundamental points about noumena is that it is absolutely separate from awareness.
In the terms of set theory the set of awareness (phenomena) is disjoint from the set of noumena (external truths), but there is a relationship between them which we will never know.
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I believe, and this may be only my opinion, that noumena is what exists when we are not. Deprive all perception from an object or eliminate, a more extreme example, all conscious life from the universe and a universe will still exist, a noumenal universe beyond any possibility of our ever perceiving it.

Why? Because "our world" depends upon perception. The universe exists without any perception of i and we will never of any idea of what it is.

Ref : Mww
Thanks for your response. What I am exploring is how "real" is quantum field theory."

Kant seems to give a low priority to sensation stating that it is meaningless without the apriori concepts of space and time.

But there is one thing that I am confused about.

The only bridge there is between us and noumena is sensation. There must be an implicit order given given by noumena to sensation, otherwise even the unity of sensation with the apriori concepts could never give meaning

Since this order already comes peep prepackaged with sensation, we can, as with noumena, never be aware of it. Only that it is there.

All this says simply that the real external world has order and structure. Sensation and this "inherited' order come to us already prepackaged.

As an analogy: we are given a book of numbers. If the listing of numbers is random, we can never make sense of it. If the listing of numbers have order to it, we can create our own order from it.

As an aside: Kant states that space and time are apriori concepts that make sense of sensation.
Judging how space and time are handled in quantum field theory, Kant may have a point. We can speculate that the mathematics of quantum field theory are like sensations and it is only with our apriori concepts of space and time that we can make sense of them. Space and time have no external reality within quantum field theory.

Ref:MWR Can you please advise where these pages are.

Thanks

From what I understand noumena is the external reality, "the real of the "real." We can never have knowledge of noumena. You are right, we have no use to us other than it is the external reality upon which our reality is based. We can never have an appearance from nothing. It must come from something (Kant's statement) and that something is the "thing in itself," one view of noumena.

The question then is how do we get phenomena from noumena. It must first be given by senation (Kant's word).

Thanks for the comment. I was looking a little more deeply into the concept of nonmena on Utube. One presentation gave the example of a sunset. Perception sees it as the color yellow (as an example).
However if we look at the science yellow is in the electromagnetic spectrum I thing (and I could be wrong) in the range of 500 nm,

Many would say this is the noumenal interpretation of the color yellow, However how is a nm? It is a measurement in space. What is space? It would be Kant's interpretation that an inherent quality of our mind, a seed, in consort with perception, to give order to our perceptions (phenomenal objects in space).

Or space could very well be (not Kant's interpretation) of something in noumenon..

Electric and magnetic fields were based on Faraday's perceptions and thought.
Perceptions are representations of noumenon. The external real gives, with the interaction of the mind, the phenomenal real (what's in our minds).

I would guess that giving noumenon a conscious representation is some how a part of evolution. Somewhat along the line evolution and maybe something else kicked in to improve our chances for survival.

To say that what we see is really out there is a questionablel assumption. To say that what we see is what represents what we cannot see may be a more reasonable assumption

Another Utube presentation was given by Amy HABER,The Noumenon of Kant gives a very enlightening discussion of this. Crudely put she discusses noumenon as triparte:
1. It is the utterly unperceivable interacting with the mind to give the perceivable. The external reality and the mind interacts to give the world reality,

One interesting point that feeling of "outside" is a mental impression (Kant). This simple short statement
knocks the wind out of a lot of stuff.

2. The noumenon of the I, "das ich."

3. Tjhe noumenon of the whole (I could be wrong on this one).

Kant, at the start stated the concept of the "thing in itself." Later on, one of the uses of noumena is
what exists when all perception is taken from from the "observeables". It would seem that it is the remarkable capability of the mind to take what is utterly beyond awareness and give it an appearance in awareness. How this can happens is one of the great ignored questions.

Bishop Berkley had previously that that it is ridiculous to believe that anything exists outside our minds since everything we see is inside our minds. God is the great coordinator. Kant got us out of this annoying statement by the very logical statement that there is a real existence outside our minds which is given an appearance inside our minds

Kant did not write a lot about noumena other than it is there. What I am doing is simply exploring and speculating further what noumena is. This is not part of Kant. But this is an exploration and speculation of idea.I claim nothing else.

My main point is that physics have studied phenomena with remarkable success. Physics explains, predicts and is experimental verified. If noumena is the actual external reality, it should be calling the shots. This is an contradiction of two statements that are obviously true.

My major point is not the limitations of Newtonian physics but a simple statement made by Kant:

"Physics is valid within the limits of human reason."
I would change one word:
Physics is valid within the limits of human awareness.

"At the core of all physics is a mathematical expression of observation and then expanded."

The key word is observation which is perception-phenomena.Delete all perceptual qualities, and something still exists, the thing in itself, noumena. Noumena and noumenal processes are what is there when we are not, It is the actual external reality independent of consciousness.

That something is there, which is given representation to our minds as phenomena, I believe is a statement hard to dispute.

We study phenomena, which are based on noumena and awareness. In a way it can be said we are studying representations (to us) of actual external realities, not these realities itself.

The question then is how is physics so successful when in a sense we are studying what we see in our minds, not what is actually out there.

Another point: If all that a physicist know about physics is what he is conscious of and yet we have no idea what consciousness is, then what is physics?

Another point is consciousness is a very real part of the universe, yet we seem to separate it from physics. It is most likely that it is impossible that it can be included, but we should at least remember it is there and that a full understanding of the cosmos is therefore not possible.