He says what appears in your sensibility can be dealt by reason, but what doesn't appear in your sensibility, but what you can think of, are Thing-in-itself. — Corvus

It seems to me that in the section on Refutation of Idealism, Kant does argue that we can use reason to transcend our sensibilities.

B275 - The proof that is demanded must therefore establish that we have experience and not merely imagination of outer things, which cannot be accomplished unless one can prove that even our inner experience, undoubted by Descartes, is possible only under the presupposition of outer experience.

B276 - Theorem - The mere, but empirically determined, consciousness of my own existence proves the existence of objects in space outside me.

B276 - Proof - I am conscious of my existence as determined in time. All time-determination presupposes something persistent in perception. This persistent thing, however, cannot be something in me, since my own existence in time can first be determined only through this persistent thing. Thus the perception of this persistent thing is possible only through a thing outside me and not through the mere representation of a thing outside me. Consequently, the determination of my existence in time is possible only by means of the existence of actual things that I perceive outside myself. Now consciousness in time is necessarily combined with the consciousness of the possibility of this time-determination: Therefore it is also necessarily combined with the existence of the things outside me, as the condition of time-determination; i.e., the consciousness of my own existence is at the same time an immediate consciousness of the existence of other things outside me.

He argues that we can prove using reason the existence of objects in space outside our sensibilities.
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If you really have to brand him what he was, he would more likely had been a transcendental realist. — Corvus

Kant was not a Transcendental Realist. From the SEP article Kant’s Transcendental Idealism

One promising place to begin understanding transcendental idealism is to look at the other philosophical positions from which Kant distinguishes it. In the “Fourth Paralogism”, he distinguishes transcendental idealism from transcendental realism:

Transcendental realism, according to this passage, is the view that objects in space and time exist independently of our experience of them, while transcendental idealism denies this.

Transcendental realism is the common-sense pre-theoretic view that objects in space and time are “things in themselves”, which Kant, of course, denies.
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Now that is Berkeley's immaterial idealism, because you deny the existence in the world, but think they all exist in your mind. — Corvus

As an Indirect Realist, I believe that a mind-independent world exists, which is the Realism part of Indirect Realism.

Reason can only deal with the objects appearing in our sensibility via experience, and that is the limit of pure reason. — Corvus

This sounds like Berkeley's Subjective Idealism, which denies the existence of material substance in the world and contends that familiar objects like tables and chairs are no more than ideas perceived by the mind, and as a result cannot exist without being perceived. IE, reason is limited by what we are able to perceive. (Wikipedia - George Berkeley)

However, Kant differentiated himself from Berkeley in not denying the real existence of objects distinct from our representation of them. From the Introduction to the CPR:
Specifically, he differentiated his position from Berkeleian idealism by arguing that he denied the real existence of space and time and the spatiotemporal properties of objects, but not the real existence of objects themselves distinct from our representations, and for this reason he proposed renaming his transcendental idealism with the more informative name of "formal" or "critical idealism," making it clear that his idealism concerned the form but not the existence of external objects.

Within the Refutation of Idealism is the argument that pure reason is not limited by experiences within our sensibilities, and whereas Idealism assumes that our only immediate experiences are inner experiences Kant shows that we also have immediate access to outer experiences.
B277 - Idealism assumed that the only immediate experience is inner experience, and that from that outer things could only be inferred, but, as in any case in which one infers from given effects to determinate causes, only unreliably, since the cause of the representations that we perhaps falsely ascribe to outer things can also lie in us. Yet here it is proved that outer experience is really immediate, * that only by means of it is possible not, to be sure, the consciousness of our own existence, but its determination in time, i.e., inner experience

As the Wikipedia article on Critique of Pure Reason writes:
In order to answer criticisms of the Critique of Pure Reason that Transcendental Idealism denied the reality of external objects, Kant added a section to the second edition (1787) titled "The Refutation of Idealism" which turns the "game" of idealism against itself by arguing that self-consciousness presupposes external objects.

Kant uses the idea of time to prove that external objects may be perceived directly enabling pure reason to transcend experiences within our sensibilities.
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If Thing-in-itself exists in the empirical world, and thought to appear in phenomenon, then it would be contradiction. — Corvus

For the Direct Realist, the thing in itself in the world does appear in appearance as phenomena, ie, when we perceive the colour red there is a colour red existing in the world. This is why Kant is not a Direct Realist.
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It doesn't make sense to me, when you say, the postbox exist in the empirical world, but the red patch exists in your mind. — Corvus

Perhaps because that's not something I said. As an Indirect Realist, as the colour red exists in the mind and the not the world, the postbox also exists in the mind and not the world.

For the Direct Realist, as the colour red exists both in the mind and the world, the postbox also exists in both the mind and the world.

in the sense of transcendental idealism, is it not the case that the unity of perceptions of a given object actually represent a 'whole' object rather than merely a set of properties — AmadeusD

In Transcendental Idealism there is a priori pure intuition of space and time and a priori pure concepts of the understanding, ie, the Categories

Therefore, Transcendental Idealism applies to appearance in the mind not objects in the world. ie Transcendental Idealism applies to phenomena not noumena (though whether the Category of cause can apply to noumena is debated).

Yes, as the unity of perception of a given object is about an object that appears in the mind not as it actually is in the world, Kant's unity of perception is about a whole rather than a disparate set of parts.
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'Horseness' doesn't consist in any properties of the horse, but the totality of those properties, under certain concepts. Take away the 'brownness' and it's still a horse. Take away 'horse-hairy-ness' and it's still a horse. Take away the mane, the hoofs etc.. In parts, and Horseness remains. — AmadeusD

If there is something in the world which doesn't have the properties of brownness, horse-hairy-ness, mane and hoofs, would anyone looking at this something think that it was actually a horse?

Solid ground for infallible knowledge is about the objects in the empirical world. Noumena is for the A priori perceptions which have no objects in the world of appearance. Noumena has nothing to do with the solid material existence in the empirical world. — Corvus

Then where does Kant get his solid ground for infallible knowledge of solid material existence in the empirical world?
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It gets all strange, if you place the ordinary objects like cups or trees into Noumena, and say they are Thing-in-itself, which are unknowable and cannot be talked about. — Corvus

For the Indirect Realist, the colour red exists in the mind but not the world, though there is something in the world that caused our perception of the colour red. When the Indirect Realist talks about the colour red, they are referring to two distinct things, the known colour red in the mind and the unknown something in the world that caused our perception of the colour red.

For the Direct Realist, the colour red exists both in the mind and the world, When the Direct Realist talks about the colour red, they are referring to one thing.

Do you believe that the colour red exists in the world?

1. You are talking about only the things in your mind. It will not give you any further knowledge on the external world itself. You say you are seeing the red postbox, but it is in your mind, and it doesn't exist in the world. So it is not an empirical knowledge, but it is your belief in your mind, which you admit that it doesn't exist in the world. — Corvus

As an Indirect Realist, from the Indirect part of Indirect Realism, the red postbox exists in my mind and not the world. From the Realism part of Indirect Realism, something exists in the world which may or may not be the same as what exists in my mind.
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2. There is also high possibility of illusion and hallucination on the perception and also talking about them, which are not the reality in the empirical world. — Corvus

Yes, The Argument from Illusion against Direct Realism

The Argument from Illusion, found in Berkeley, Hume, Russell, and Ayer, begins from the familiar fact that things sometimes look other than they are (perceptual relativity, illusions, hallucinations) and concludes that we only directly (or immediately) perceive our own ideas (or sense data).

(Lecture II The Argument from Illusion - Penelope Maddy)
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3. These are not what Kant thinks how perception works. He was seeking to establish a solid ground for infallible knowledge. He would be seriously worried to see someone looking at things not existing in the world, and keeps talking about them as if they do exist in the world, and at the same time saying they don't exist in the world — Corvus

Where does Kant get his solid ground for infallible knowledge of noumena?

It sounds gross self-contradictory to say "matter existing in the world is noumena", and then keeps going on "noumena cannot be cognized, it cannot therefore be talked about"......................How can "matter" be talked about as "unknown causes"? Do you mean they are the same? How so? — Corvus

"Matter" and "red" are words in language and concepts in the mind. As I perceive a red postbox in the world, I can also perceive solid matter in the world.

I can talk about red postboxes in the world even though what is referred to as the colour red doesn't exist in the world. Similarly, I can talk about solid matter in the world even though what is referred to as matter doesn't exist in the world.

From an innate belief in the Law of Causation, the Principle of Sufficient Reason, an appearance has a prior cause. If a known appearance in the mind is named "red", the unknown cause in the world can be named "X". "X" does not refer to a known thing in the world but refers to an unknown prior cause of a known effect. This prior cause can have happened at any time and can have been of any kind. For convenience within language, "X" is re-named "red".

So how were you able to talk about "the matter of the Eiffel Tower", if you couldn't know it? Is it possible to know what "the matter" means? — Corvus

For Kant, matter existing in the world is noumena, and as noumena cannot be cognized, it cannot therefore be talked about

From the SEP article on Kant’s Critique of Metaphysics
Throughout the Analytic Kant elaborates on this general view, noting that the transcendental employment of the understanding, which aims towards knowledge of things independently of experience (and thus knowledge of “noumena”), is illicit (cf. A246/B303).

From the SEP article Kant’s Transcendental Idealism:
In the section “On the ground of the distinction of all objects into phenomena and noumena”, which he substantially revised for the B Edition, Kant reiterates his argument that we cannot cognize objects beyond the bounds of possible experience, and introduces a complex distinction between phenomena and noumena....................Clearly, we do not cognize any noumena, since to cognize an object for us requires intuition and our intuition is sensible, not intellectual.

As Kant wrote:
A249 - if, however, I suppose that there be things that are merely objects of the understanding and that, nevertheless, can be given to an intuition, although not to sensible intuition (as coram intuiti intellectuali), then such things would be called noumena (intelligibilia).

I can talk about "matter" as unknown causes are named after known appearances

I can talk about seeing a red postbox in the world, even though the colour red doesn't exist in the world, but only in the mind. The cause of an appearance is named after the appearance, in that if the appearance is red, the cause is named red.

As the SEP article on Kant’s Critique of Metaphysics writes:
Filling this out, Kant suggests that to take ourselves to have unmediated intellectual access to objects (to have “non-sensible” knowledge) correlates with the assumption that there are non-sensible objects that we can know. To assume this, however, is to conflate “phenomena” (or appearances) with “noumena” (or things in themselves). The failure to draw the distinction between appearances and things in themselves is the hallmark of all those pernicious systems of thought that stand under the title of “transcendental realism.”

In practice, unknown noumena are named after known phenomena. IE, if our perception is named red, the unknown cause of our perception is also named red. The word red then has two distinct meanings, first as the known perception in the mind and second as the unknown cause in the world. Problems arise when these two distinct meanings are conflated. IE, when I talk about seeing a red postbox in the world, what I am talking about is not an unknown something existing in the world but a known appearance existing in the mind.

The Eiffel Tower is indeed an idea, which has been realized (made real) in iron. Without the idea, no such thing could have been wrought. The resulting artefact is an ideal exemplar of the synthesis of matter and form. — Wayfarer

For Kant, we know the form of the Eiffel Tower from its appearance as phenomena. However, we cannot know the matter of the Eiffel Tower from Sensible Intuition, as it is noumena.

A249 - Appearances, to the extent that as objects they are thought in accordance with the unity of the categories, are called phaenomena. If, however, I suppose there to be things that are merely objects of the understanding and that, nevertheless, can be given to an intuition, although not to sensible intuition (as coram intuiti intellectuali),then such things would be called noumena (intelligibilia).

Are things more than their parts? — AmadeusD

If all the metal was removed from the Eiffel Tower, what would be left. An idea of the Eiffel Tower would be left.

If by "thing" one means an idea in the mind as well as physical parts in the world, then, yes, things are more than their physical parts.

The question he has is somewhat similar to mine.................his question is Kant's use of the word 'experience' with regard to delineating between 'understanding' and 'intuition'. He is asking why Kant thought he could get away with the premise that het two are necessarily distinct and why, with regard to Humean/Leibnizian alternatives, he thought it could not be argued against. — AmadeusD

Robert Paul Wolff

Wolff said "the foundation of the distinction is that Kant thinks that through sensibility we are placed in direct relation with individual things, and through conception and understanding we are placed in indirect relation through general concepts to individual things. IE, we can look at a particular horse, but we need to bring it under the general concept of horse, the particular falls under the general. He doesn't think this can be reduced to the same thing but they are different things"

The difference between the particular and the general

There is a difference between a particular and the general. For example, we look at a field and see at one moment in time and one particular position in space a particular set of shapes and colours. We can then generalise, ie, conceptualise, a horse .

We can only come up with the general concept of a horse after seeing several particular example of a horse.

For Kant, an Intuition can be i) Sensible Intuition, ie, phenomena - ii) Non-sensible Intuition, ie, noumena - iii) Pure Intuition, ie space and time. What all these have in common that it is intuition of one particular thing, ie, a set of shapes and colours we see in the field at one moment in space and time

For Kant, our Principles of Understanding can be discovered from our Concepts of Understanding, ie the Categories, For example, such Principles of Understanding would include: i) the conservation of energy ii) qualities inhere in substances iii) things don't happen randomly. What all these have in common is that the concept is not about one particular thing, but is about a set of particular things under the umbrella of a single idea.

The question is, after seeing several particular sets of shapes and colours in a field through space and time, how do we understand that they are connected in some way under the single idea of a "horse".

The Empiricists Hume and Locke thought that we discover the concept of horse just from the experience of seeing several instantiations of a horse. Kant thought that we can only discover the concept of horse from a combination of a priori knowledge independent of experience together with empirical experience.

For Hume, we would infer the concept of horse from the constant conjunction of states of affairs in the world. For Kant, we would know the concept of horse because our experiences fulfilled an a priori understanding.

Does the colour red exist in the world or the mind

The question is how we establish general concepts from several particular example. For example, we see the colour red when looking at wavelengths between 620nm and 750nm.

Are the Empiricists correct when they propose that we have learnt the concept of red from looking at all the wavelengths from 620nm to 750nm and finding a similarity in them. Are the Innatists correct when they propose that we know the concept of red a priori, before even looking at wavelengths, and only need to look at a single wavelength, say 700nm, in order to recognize it as the colour red. (Accepting that it is disputed whether or not Kant endorsed concept innatism)

If the Empiricist are correct, the colour red exists in the world and we discover it. If the Innatists are correct the ability to perceive the colour red exists in the mind which we then recognize in the world.

Objects are sets of properties

An object such as a horse is a set of properties, such as colour, texture, smell, taste, etc. In fact, an object is only its set of properties, in that if all the object's properties were removed, then no object would remain.

If the Innatists are correct in that the ability to perceive the colour red exists in the mind prior to experiencing the world, a similar argument can be made for all the other properties. Butt as an object is no more than its set set of properties, then our understanding of what an object is, as illustrated by the CPR, is dependent not only what we experience but also on an a prior ability in being able to recognize what we experience.

(Kant's Categories - Daniel Bonevac)
(Leibniz on Innate Ideas and Kant on the Origin of the Categories)

You couldn't possibly have the concept without the phenomena — AmadeusD

Some concepts are innate prior to any phenomena

Suppose you touch sandpaper and feel a rough sensation and then touch silk and feel a smooth sensation. You have the concepts of rough and smooth and you have the phenomenal experiences of sandpaper and silk

Why is it when touching sandpaper you feel a rough sensation rather than a smooth sensation? Is it because i) within the phenomena there are already sensations that will be subsequently experienced or ii) the sensations pre-exist any experience of the phenomena ?

I would suggest that concepts such as rough and smooth are innate and pre-exist any phenomena subsequently experienced.

One assumes that if what Kant says is true in the CPR, then it must be understandable in ordinary terms, otherwise it isn't relevant.

Trying to understand Transcendental Idealism and Empirical Realism using the analogy of colour:

1) For Kant, there are the a priori pure intuitions of space and time and the a priori pure concepts of understanding, ie the Categories. Although both a priori, the pure intuitions of space and time precedes and provides the framework for the pure concepts of understanding, in that I can imagine space and time with no objects within it but I cannot imagine objects not in a space and time.
2) Space and time are intuitions because singular, and the Categories are concepts because general.
3) Of the four Categories, quantity, quality, relation and modality, colour is within the Category of quality.
4) Kant's Innatism, in the belief in a priori knowledge is a counter to Locke's Empiricism, in that the mind is a "Tabula Rasa" at birth.

5) I am born with the ability to see the colour red when looking at a wavelength of 700nm
6) I am not born with any ability to see a colour when looking at a wavelength of 300nm
7) Necessary, because when looking at a particular wavelength, I always perceive the same colour, in that I cannot decide sometimes to see the colour green and other times to see the colour blue. Universal, because in whatever space and time I happen to be in, when looking at a particular wavelength, I always perceive the same colour.

8) It is a Sensible Intuition in the sense that I perceive the colour red when looking at the single wavelength of 700nm
9) It is a Concept in the sense that I perceive the colour red when looking at wavelengths from 620nm to 750nm
10) I am not born with the Concept of the colour red or a Sensible Intuition of the colour red, in that when not looking at a wavelength between 620nm and 750nm I cannot imagine the colour red. I am born with the ability to perceive colour only when looking at a particular wavelength of light.

11) Perceiving a colour requires neither Judgement nor Understanding.

12) When we perceive colour, we are perceiving something as an Appearance, a Phenomenon. We are not perceiving the cause of that Appearance, a Noumenon.
13) However, from our inherent belief in the Principle of Sufficient Reason and the Law of Causation, we believe that something must have caused the phenomena that we perceive, and we can name these unknown things noumena
14) Even though noumena are the cause of phenomena, this does not mean that a phenomenon is the same as the Noumenon that caused it. For example, even though I perceive the colour red, the colour red doesn't exist in the world, what exists in the world is a wavelength 700nm.
15) From my belief in the Principle of Sufficient Reason, my belief in a wavelength of 700nm as the cause of my seeing the colour red is a Non-Sensible Intuition.

It must be the case that if the CPR is true, no matter how complex it is as a book, its truth must be applicable to simple examples.

I am not sure if your justification using innate-ism were coherent for your premises or conclusions. — Corvus

Kant doesn't justify his premise that we have a priori pure intuitions and a priori pure concepts of the understanding.

I suggest that his premise can be justified by the Principle of Innatism, a natural consequence of 3.5 billion years of evolution.

Is there a better justification for his premise?

whatever judgements are made about the world, the mind provides the framework within which such judgements are meaningful. So though we know that prior to the evolution of life there must have been a Universe with no intelligent beings in it, or that there are empty rooms with no inhabitants, or objects unseen by any eye- the existence of all such supposedly unseen realities still relies on an implicit perspective. What their existence might be outside of any perspective is meaningless and unintelligible, as a matter of both fact and principle — Wayfarer

Although my position is from Indirect Realism, can it be true that the content of all the scientific literature about the Universe prior to life can be dismissed as meaningless and unintelligible?

After all, Kant was neither a Berkelian Idealist nor Phenomenalist.

The origin of A priori ideas in biological psychological sense would be in the interest of the evolutionary science rather than Philosophy. — Corvus

Surely good philosophy needs to justify its premises.

If I said that aliens from Mars are running all governments, and made no attempt to justify my statement, I would get nowhere.

Similarly, if I based a philosophy on the premise of a priori pure intuitions and a priori pure concepts of the understanding without attempting to justify my premise, my philosophy has been based on a weak foundation and will thereby be unpersuasive to many.

'Objective and independent' stands in contradiction to 'within language'. — Wayfarer

Isn't it admirable within philosophical language to be objective and have an independent point of view?
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We cannot consider a mind-independent world, because to consider anything is to make it the subject of thought. You refer to 'the mind dependent' and 'mind independent' as if these are two separate realities, but that is comparison that can't be made. — Wayfarer

Yet we consider a mind-independent world every time we talk about the Universe before life began on Earth. For example, The Origins of the Universe by Michael Greshko
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I'll bow out now unless I have something to add specific to the text. — Wayfarer

The question is, is a discussion about the terms "mind dependent" and "mind independent", which Kant didn't use, relevant to a text that does refer to "phenomena" and "noumena"?

Kant was saying that pure intuitions and concepts are the the properties of our minds which work with pure reason in CPR. He is not interested in where they came from — Corvus

Possibly, but his philosophy isn't complete without asking where these a priori pure intuitions and a priori Categories came from.
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For example 2+2=4 is A priori knowledge, which is universally and necessarily true in the whole universe.----------------That sounds like extreme idealism. We are talking about the universally and necessarily true knowledge, and it exists. Again it is nothing to do with the physical universe. Knowledge exists in our understanding. Universally doesn't mean the physical universe. It means "under all conditions". — Corvus

When you refer to "universe" do you mean a universe within the mind or a universe external to the mind?
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You just committed a self-contradiction here. You shouldn't even be able to write about it, if above were true. — Corvus

From the Principle of Sufficient Reason, an appearance must have a cause, which may well be unknown. This unknown cause can be called "x", or even "Thing-in-Itself".
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But I know they exist, because I read about them. Just because I know something doesn't mean that I must believe in it too.-----------------I have demonstrated how the official definitions could be false, but you have gone back to the false official definition ignoring the real life demonstration and evidence. — Corvus

How can you know atoms exist, yet not believe in their existence?

When you say "Innatism", it denotes psychological or biological nature rather than epistemic, conceptual nature, and it has nothing to do what Kant was meaning for A priori. — Corvus

For Kant there is a priori pure intuition of space and time and the a priori pure concepts of the understanding (the Categories)

These are necessary for the possibility of experience, and are priori to experience. They don't come from the mind but are part of the mind.

My question is, where did these pure intuitions and pure concepts come from?

From a perspective of today, I can explain them using the concept of Innatism, in that we were born with them as part of the structure of the brain as a consequence of 3.5 billion years of evolution.

If not from Innatism, where do you think our pure intuitions and pure concepts came from?
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For example 2+2=4 is A priori knowledge, which is universally and necessarily true in the whole universe. — Corvus

For Kant there is a priori pure intuition of space and time and the a priori pure concepts of the understanding (the Categories).

For example, the Categories include quantity, quality, relation and modality, and quantity includes such things as all, both, most and some.

This allows us when looking at a set of objects to make judgements such as "all the objects green", "both objects are blue", "most of the objects are orange" and "some of the objects are purple".

Then, given ten objects of which six are orange, some of these statements will be true and some will be false. For example, the statement "most of the objects are orange" will be true.

As no situation can be imagined whereby given ten objects of which six are orange, the statement "most of the objects are orange" will not be true, meaning that it is universally and necessarily true.

However, the Categories don't apply to unknown Things-in-Themselves, but only to known Appearances.

As this is the case, then what does universal and necessary refer to. They cannot refer to the world of Things-in-Themselves, as these are unknowable, but can only refer to the world of Appearance, as only this is knowable, and the world of Appearance only exists in the mind of the perceiver.

Therefore, it is true that a priori knowledge is universally and necessarily true in the whole universe, but this universe only exists in the mind of the perceiver, not in any world that exists outside the mind of the perceiver.
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Justified true belief has stronger ground than a knowledge via heard through the grapevine. I really don't believe the electrons, atoms and Andromeda galaxies exist, because I have never seen them, or been there. But I know they exist, because I read about them. — Corvus

Knowledge is justified true belief, so knowledge has a stronger ground than belief.

If from the grapevine one hears the belief that atoms exist, and the grapevine justifies the claim, and in fact atoms do exist, then, and only then, is this knowledge.

But that is an oxymoron — Wayfarer

If the concept of "apple" didn't exist, how could we be talking about the concept of "apple"?
If the word "apple" wasn't real, how could we be writing about the word "apple"?
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Werner Heisenberg, who aside from being one of the architects of quantum theory, also wrote on its philosophical implications, said that electrons 'do not exist in the same way that flowers or stones do' — Wayfarer

Consider the mind and a mind-independent world.

As regards a mind-independent world, as flowers and stones are sets of elementary particles, flowers and stones must exist in the same way that elementary particles exist.

As regards the mind, as flowers, stones and elementary particles are concepts in the mind, elementary particles exist in the same way that flowers and stones do .

It is true that elementary particles, flowers and stones exist differently in the mind to how they exist in a mind-independent world.

As regards a mind-independent world, Plato's Forms are aspatial and atemporal, which is not the case for elementary particles.
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I too am an empirical realist - there really are apples - but I also recognise the sense in which they exist for a subject. Another kind of being might not see them at all, or might see them in a completely different way. It doesn't mean that they don't exist, but that they don't have inherent existence — Wayfarer

Yes, for the Empirical Realist, the apple that is perceived is a mere representation, not something that is mind-independent.

When you say the apple exists, but doesn't have inherent existence, what do you mean?

I don't think your depiction of a priori as subjective is correct — Wayfarer

I agree that my innate ability to see the colour red when looking at a wavelength of 700nm is not a subjective ability, although my seeing the colour red is a subjective experience .
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The problem with that view is that the manner in which electrons can be said to exist is not at all straightforward.........................We have to get our head around the role of the mind-brain in constructing/creating what we perceive as reality. — Wayfarer

Do electrons really exist?

It depends what you mean by "exist". The Merriam Webster Dictionary includes "exist" as "to have real being whether material or spiritual".

It depends what you mean by "real". The Merriam Webster Dictionary includes "real" as "having objective independent existence".

From my belief in Neutral Monism, I could ask the same question about apples: "Do apples really exist?"

My answer would be that yes, "apples" and "electrons" do exist, and they exist as concepts in the mind.

My answer would also be that "apples" and "electrons" are real in that they have an objective independent existence within language.

If A priori is just innate to you, and all different from person to person, then what is the point of A priori? Would it not better just as well call it as Relative concept rather than A priori? There must be some universality and necessity in truth on A priori, and that was what Kant was after in CPR.........................I can't know what your perception of WL700nm would be like, and that was the point. — Corvus

The point of the a priori is that it distinguishes two very different approaches to the relationship between the mind and the world.

It distinguishes between Innatism, the philosophical belief that one is born with certain ideas and knowledge, and Locke's idea that the mind at birth is a blank sheet, a tabula rasa, devoid of all ideas or knowledge, where all our ideas and knowledge arrive from experience.

For Kant, the mind has a role in constructing what we perceive as reality:
A239 - We can only cognize objects that we can, in principle, intuit. Consequently, we can only cognize objects in space and time, appearances. We cannot cognize things in themselves.

I agree that there is the question as to the universality and necessity of such a priori ideas and knowledge :
Introduction - Kant also sought to defend against empiricists its underlying claim of the possibility of universal and necessary knowledge - what Kant called a priori knowledge, knowledge originating independently of experience, because no knowledge derived from any particular experience, or a posteriori knowledge, could justify a claim to universal and necessary validity.

As Hume showed, no a posteriori knowledge can justify a universal and necessary validity, in that a scientist can draw a conclusion from 1,000 measurements, yet that conclusion may be negated by the 1,001st measurement.

It is true that for me, my a priori ideas and knowledge, because they are a priori, ensure a universality and necessity to what I cognize. However, humans do not exist as a hive mind but as separate individuals.

My a priori ideas and knowledge ensure a universality and necessity to what I cognize, and your a priori ideas and knowledge ensure a universality and necessity to what you cognize. The question is, is there any reason to believe that your a priori ideas and knowledge are the same as my a priori ideas and knowledge. If not, even though there is a universality and necessity to our individual ideas and knowledge, our separate ideas and knowledge don't necessarily share a common universality and necessity.
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I know the Andromeda Galaxy exists, but I don't believe it exists. — Corvus

I think that this should be the other way round: "I believe the Andromeda Galaxy exists, but I don't know it exists"

The SEP article on The Analysis of Knowledge discusses knowledge as justified true belief. First one has a belief, and then one tries to justify this belief, and if one's belief is true, then one has knowledge

IE, belief comes before knowledge.
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Yes, but my question was how do you know it is real or illusion? — Corvus

The Merriam Webster Dictionary includes the meaning of "illusion" as
1a1 - a misleading image presented to the vision
1a2 - something that deceives or misleads intellectually
1b1 - perception of something objectively existing in such a way as to cause misinterpretation of its actual nature

If I perceive a tree, how do I know there is a real tree in the world or the tree only exists in my mind.

The Direct Realist would say that they perceive a tree, and the Indirect Realist would say that they perceive a representation of a tree.

For the Indirect Realist, if "illusion" means 1a2 or 1b1, then the tree is an illusion as the viewer is being misled in thinking that what they perceive of necessity actually exists in the world. If "illusion" means 1a1, then the tree is not an illusion, as the viewer is not being misled in thinking that their perception doesn't exist.

A priori means that it is universally true under all circumstances. — Corvus

The IEP article on A Priori and A Posteriori writes: An a priori concept is one that can be acquired independently of experience, which may – but need not – involve its being innate, while the acquisition of an a posteriori concept requires experience.

A Priori does not mean universally true for all people at all times. A priori means in a sense innate within a particular person. My private subjective experience of colour when seeing a wavelength of 700nm is innate to me.

How can you know that when you are look at a wavelength of 700nm, your private subjective experience of colour is the same as mine?
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How / Why do you justify your belief in something that you cannot prove it exists? — Corvus

I cannot prove that electrons exist, yet I believe they exist. I justify my belief from the numerous scientific articles that I have read that say that electrons do exist.

Do you believe that the Andromeda Galaxy exists? Can you prove that it exists?
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what is the relation between the colour you perceive (red), and the WL700nm? — Corvus

Totally mysterious. What do you think the relationship is?
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How does he know for certain what he is conscious of is not an illusion? — Corvus

Isn't this the argument against Direct Realism, in that if Direct Realism was true, the external world would be exactly as we perceive it. However, in the case of illusions, there is an obvious difference between our perception and reality. For example, when a pencil is placed in a glass of water, it can look crooked. But it isn't really crooked.

Kant was definitely not a Direct Realist.

How does the Direct Realist know when looking at something in the world, such as a tree, that what they think they are looking at is just an illusion?
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Does this mean, if something was conscious of itself, then it could be inside him? — Corvus

Not everyone agrees with Kant's Transcendental Argument.

If I am conscious of the passing of time, then I must be conscious of two different moments in time. But how is this possible if I only exist at one moment in time?

Any popular media based information will be flatly rejected as propaganda in all philosophical discussions unless proved and verified otherwise — Corvus

Yes, every source is open to doubt, even the SEP, which is the premier reference work in philosophy.

We know it is the premier work in philosophy because the Stanford Department of Philosophy says so. They write: The Stanford Encyclopedia of Philosophy (SEP) is the premier reference work in philosophy, and covers an enormous range of philosophical topics through in-depth entries.
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When you say, we impose space and temporal forms on the sensory experiences, it does imply we can also choose not to impose as well. — Corvus

No, because this imposition is a priori, and as priori is beyond choice. In the same way that when I see the wavelength of 700nm I have no choice as to what colour I perceive .
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Wasn't Kant refuting the rationalists rather than idealism? If it were idealists, who were they? — Corvus

As the Wikipedia article on Transcendental arguments concludes: He has not established that outer objects exist, but only that the concept of them is legitimate, contrary to idealism

From the Britannica article on Rationalism: Rationalism, in Western philosophy, the view that regards reason as the chief source and test of knowledge.

From Routledge Encyclopedia of Philosophy:Idealism is now usually understood in philosophy as the view that mind is the most basic reality and that the physical world exists only as an appearance to or expression of mind, or as somehow mental in its inner essence.

In B275, Kant mentions Berkeley as an example of a Dogmatic Idealist, someone who declares the existence of objects outside us to be either false or impossible

Kant is refuting Idealism as a belief rather than Rationalism as a method .
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What is the proof of the legitimacy of the concept that things exist independently of the mind? — Corvus

Speaking as an Indirect Realist, none. I believe that things exist independently of the mind, and can come up with reasons to justify my belief, but cannot prove it. Such is the nature of Indirect Realism.

This is a question for the Direct Realist, who does believe that they directly perceive things that exist independently of the mind.
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Any relevant quotes for this argument from CPR? — Corvus

In B275 is the section on The Refutation of Idealism

He includes the Theorem: The mere, but empirically determined, consciousness of my own existence proves the existence of objects in space outside me.

In B276 is the section Proof

I am conscious of my existence as determined in time. All time-determination presupposes something persistent in perception. This persistent thing, however, cannot be something in me, since my own existence in time can first be determined only through this persistent thing. Thus the perception of this persistent thing is possible only through a thing outside me and not through the mere representation of a thing outside me. Consequently, the determination of my existence in time is possible only by means of the existence of actual things that I perceive outside myself. Now consciousness in time is necessarily combined with the consciousness of the possibility of this time-determination: Therefore it is also necessarily combined with the existence of the things outside me, as the condition of time-determination; i.e., the consciousness of my own existence is at the same time an immediate consciousness of the existence of other things outside me.

In other words:

1) I am conscious of my existence in time
2) Therefore I am conscious of something persisting in time
3) But this something that persists in time cannot be inside me, as this something cannot be conscious of itself
4) Therefore as this something that persists cannot be a representation inside me, this something that persists must be outside me.
5) Concluding that there must be something outside me, refuting Idealism which believes there is nothing outside me.

I don't subscribe to the most of Wiki info. — Corvus

As with most sources, whether Fox or CNN, whether the BBC or Talk TV, one has to make a personal judgement as to whether the source makes a logical and reasoned case.
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From the traditional logic perspective, they insist that contents is not dealt by logic. Fair enough on that. But from all the other logic, content itself is important part of logic. If you read Bolzano's Theory of Science, you would agree. — Corvus

What is a Transcendental argument

From the Wikipedia article on Transcendental arguments, which presumably uses transcendental logic, Kant used transcendental arguments to show that sensory experiences would not be possible if we did not impose their spatial and temporal forms on them

In the Critique of Pure Reason (1781) Kant developed one of philosophy's most famous transcendental arguments in 'The Deduction of the Pure Concepts of the Understanding'.[8] In the 'Transcendental Aesthetic', Kant used transcendental arguments to show that sensory experiences would not be possible if we did not impose their spatial and temporal forms on them, making space and time "conditions of the possibility of experience".

An example of a Transcendental argument is used by Kant in his refutation of idealism. Idealists believe that things have no existence independently of the mind. His Transcendental argument does not prove that things exist independently of the mind, only that the concept that things exist independently of the mind is legitimate.

Kant argues that:
1) since idealists acknowledge that we have an inner mental life, and
2) an inner life of self-awareness is bound up with the concepts of objects which are not inner, and which interact causally,
3) then we must have legitimate experience of outer objects which interact causally.

I can make a similar Transcendental argument:
1) A postbox emits a light having a wavelength of 700nm, and because I have the innate ability to perceive the colour red when looking at a wavelength of 700nm, I perceive the colour red.
2) I perceive the postbox as red not because the postbox is red but because I perceive the postbox as red.

My argument doesn't prove that the postbox is not red, but only the possibility that the postbox is not of necessity red.

Is "bachelors are unmarried" an analytical statement

As regards the statement "bachelors are unmarried men", when thinking about what the words refer to, as both "bachelor" and "unmarried men" refer to the same thing, the statement is analytic. However, when thinking about the sense of the words, as the sense of "bachelor" is different to the sense of "unmarried men", they don't refer to the same thing, and so is not an analytic statement.

IE, the content or sense of the words must be taken into account , not just their form or reference.

They sounded to have read somewhere about the traditional logic, and it is the only form of logic in existence, and have been opposing on the view that Logic can require contents for its operation. :roll: — Corvus

The SEP article on Kant’s Transcendental Arguments, section 3, shows that Kant is still relevant today.

Kant-inspired transcendental arguments against scepticism about the external world were developed with vigor in the mid-twentieth century, notably by P. F. Strawson, most famously in his Kantian reflections in The Bounds of Sense (1966). These arguments are often reinterpretations of, or at least inspired by, Kant’s Transcendental Deduction and his Refutation of Idealism.

The article writes that Strawson’s most famous transcendental argument in 1966 is modelled on the Transcendental Deduction, where Strawson's target is sense-datum experience.

However, according to the Wikipedia article on Logic, logic only deals with the form of an argument and not the content of an argument:
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or logical truths. It studies how conclusions follow from premises due to the structure of arguments alone, independent of their topic and content.

However, the Wikipedia article assumes the possibility of the separation of form from content. But that cannot be the case, in that if all the content was removed, what form would be left. If all the metal was removed from the Eiffel Tower, what would remain?

What pitfalls must i avoid in reading this section? — AmadeusD

I would say that the biggest pitfall is reading it in isolation of secondary sources, which might include:

IEP - Immanuel Kant: Logic
He insists that formal logic should abstract from all content of knowledge and deal only with our faculty of understanding (intellect, Verstand) and our forms of thought.

SEP - Kant’s Transcendental Arguments
Among Immanuel Kant’s (1724–1804) most influential contributions to philosophy is his development of the transcendental argument. In Kant’s conception, an argument of this kind begins with a compelling premise about our thought, experience, or knowledge, and then reasons to a conclusion that is a substantive and unobvious presupposition and necessary condition of this premise.

The Generality of Kant’s Transcendental Logic - Clinton Tolley - University of California
Unlike the traditional logic, which focuses only on the form of thinking and judging, Kant intends his new transcendental logic to focus on the content of thinking and judging, albeit in a very abstract manner.

Generation Online - Transcendental Logic
Kant defines transcendental logic, on the other hand, as a subdivision of general logic, and distinguishes it from general logic in so far as transcendental logic does not abstract from all the contents of knowledge, but takes from transcendental aesthetics the forms of pure intuition of space and time into consideration, thus abstracting from empirical contents, whilst still accounting for pure intuitions.

These secondary sources point at a distinction between the importance of the form of a logical statement in traditional logic and the importance of the content of a logical statement in transcendental logic

Perhaps this means that a logical stalemate is as much dependent on its content as its form.

Once again….red is not a thing. Wavelength is a thing, but is not an sensation. — Mww

Of course, sensations in the mind are caused by things in the world. Au revoir.

I’ve never seen 700nm. — Mww

Exactly, the object perceived in the mind is not of necessity the same object in the world causing the perception. Knowledge of the phenomena does not of necessity give us knowledge of the noumena, as the Direct Realist insists it does.

For over 300,000 years, humans did not know that the cause of their perception of the colour red was the wavelength of 700nm. Only in the last 200 years have humans discovered that the colour red they perceived in the mind doesn't actually exist in the world. Perhaps coincidentally, about 200 years ago, Kant wrote CPR.

That objects don’t exist contradicts the human experience. — Mww

1) When we perceive the colour red, the colour red doesn't exist in the world, what exists in the world is a wavelength of 700nm.
2) When we perceive a bent-stick, there is no bent-stick in the world, it is a straight stick in water.
3) When we perceive an elliptical coin, there is no elliptical coin in the world, it is a circular coin on its side.
4) When we perceive a mountain to be the same height as a person, a person the same height as a mountain doesn't exist.
5) When we perceive the two sides of a road approaching each other in the distance, the two sides of the road in the world are in fact parallel.
6) Whe one perceives a pink elephant, there is no pink elephant in the world, only an hallucination caused by delirium tremens.
7) When we perceive an apple, apples don't exist in the world, what exists in the world are
fundamental particles and fundamental forces existing in space and time.

The object that we perceive in our mind is not of necessity the same as the object that exists in the world, meaning that the object we perceive in our minds does not of necessity exist in the world.

Only the Direct Realist would say that the phenomena we perceive in our minds is the same as a noumena that exists in the world.

JMD Meiklejohn version CPR is only 500 pages long (the 2nd edition only). All the other versions are 700 - 800 pages because they combined the 1st and 2nd Editions into one book. — Corvus

I am using the Cambridge Edition, translated and edited by Guyer and Wood, which includes the first and second editions.

Now all you gotta do is figure out exactly what that means, and how it reflects on the human cognitive system overall. — Mww

What does it mean that we have an a priori pure intuition of space

As with the colour red, where we have the innate ability to perceive the colour red when looking at a wavelength of 700nm, it means that we have the innate ability to perceive objects in space when looking at the world.

It means that neither the object nor the space that we perceive actually exist in the world, but there is definitely something in the world that we can name for convenience as object and space that has caused our perception of an object in space.

As you say, on the other hand, the pure physicalist may insist the extension of objects, and the relation of objects to each other, is impossible without the necessary condition of empirical space. But in CPR no pure physicalist excuses are to be found, except the natural existence or possible existence of real things. — Mww

Kant in his Prolegomena made clear that he believed space is empirically real

In the Introduction to CPR by Paul Guyer and Allen W. Wood is the statement that, for Kant, space and time are empirically real.
Kant's thesis that space and time are pure forms of intuition leads him to the paradoxical conclusion that although space and time are empirically real, they are transcendentally ideal, and so are the objects given in them.

From the SEP article section 2.3 on Kant’s Transcendental Idealism, Kant in the Prolegomena was apoplectic that Feder and Garve had claimed that his Transcendental Idealism was just a Berkeleyan or Phenomenalist idealism, and pointed out that in the CPR bodies exist in space and that we have immediate, non-inferential knowledge of them.

In his Prolegomena, Kant wrote that space is real and exists outside of ourselves:
Here’s something else that can be proved ·as a requirement for the intellectual management· of experience, but can’t be shown to hold of things in themselves: Our outer experience not only does but must correspond to something real outside of ourselves. That tells us this much: there is something empirical—thus, some phenomenon in space outside us— ·the existence of· which can be satisfactorily proved. ·That’s all it tells us·, for we have no dealings with objects other than those belonging to possible experience; because objects that can’t be presented to us in any experience are nothing to us. What is empirically outside me is what appears in space.

It is true that in the CPR Kant writes that we have an a priori pure intuition of space

Kant argues that our perception of space is not a posteriori derived from experience, but must be a priori in order to underlie all experience.

A24/B38 - 2) Space is a necessary representation, a priori, which is the ground of all outer intuitions. One can never represent that there is no space, although one can very well think that there are no objects to be encountered in it. It is therefore to be regarded as the condition of the possibility of appearances, not as a determination dependent on them, and is an a priori representation that necessarily grounds outer appearances.

Understanding A24/B38 using the analogy of perceiving the colour red, we can only perceive the colour red because we have the innate ability to perceive the colour red when looking at a wavelength of 700nm. The fact that we perceive the colour red doesn't mean that the colour red exists in the world. In fact, it is the wavelength of 700nm that exists in the world, and this wavelength of 700nm is the cause of our perception of the colour red.

The fact that we do perceive the colour red suggests that there is in fact something in the world causing such perception, which may for convenience be called" red". There is a dualism in reference, in that red may refer either to what we perceive or the cause of what we perceive. It should be noted that what is referred to by the same term are of different kinds.

The fact that we do perceive space as an outer intuition suggests that there is in fact something in the world causing such perception, which may for convenience be called "space". There is a dualism in reference, in that space may refer either to what we perceive or the cause of what we perceive. It should be noted that what is referred to by the same term are of different kinds.

Where does Kant write in the CPR that space is not empirically real?

There is a dualism in reference of the word space, in that space may refer either to what we perceive or the cause of what we perceive. Whilst Kant does discuss space as referring to what we perceive, where does Kant in the CPR write that space as referring to the cause of what we perceive doesn't exist?

By second-handing the content of the original, the poster is merely holding with the opinion of the secondary author, rather than presenting his own in accordance with the actual reading of the text. — Mww

The poster presents their own opinions as to both the primary and secondary sources

The OP of this Thread suggests a reading group of the CPR, reading the book and sharing thoughts about it. There is no restriction within the OP that only the primary source must be used.

To ignore secondary sources about such a complex book would be foolhardy, in that very few of us have had the time to read the almost 800 pages, analyse and study the almost 900 paragraphs, and compare and contrast the CPR within the body of his other works.

As long as these secondary sources are referenced, and on the assumption judged worthy of inclusion, reasons should given for sources that support one's position and reasons given against sources that don't support one's position.

The use of secondary sources shows that one is not trying to reinvent the wheel, but is constructively building on different debates and different perspectives of academics over a period of 200 years who have devoted their careers to this particular topic.
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Please refrain from repeating yourself — Mww

"Repetition is the mother of learning"

I try to make my posts complete, and if a particular quote or idea helps to make the post understandable then I will use it, regardless of how many times I have used it before.

Nevertheless, it is true matter depends on a source outside the mind, an external thing appearing to the senses. — Mww

I agree, otherwise Kant's Transcendental Idealism would just be a Berkeleyan or Phenomenalist idealism.
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Irrelevant. Color is just another sensation, given from an undetermined appearance..................................So you’re saying the something we perceive might not be the something that caused our perception. So what? — Mww

Yes the colour red is a phenomena, but there are different opinions as to the relationship between a phenomena in the mind and its cause, a noumena in the world.

I would guess that half of the Forum are Direct Realists and as such have no regard for the CPR, whilst the other half are Indirect Realists, for whom the CPR might be relevant.

The Direct Realist, such as Austin and Searle, holds the position that if they perceive a red postbox there is a red postbox in the world, ie, in perceiving a phenomena in the mind they are also perceiving the noumena in the world.

The Indirect Realist such as Kant, holds the position that what we perceive might not be the same thing that caused our perception, in that although we perceive the colour red we might be looking at a wavelength of 700nm. IE, the phenomena perceived in the mind is not of necessity the same as what caused this perception.

Colour is a phenomena in the mind, but colour can also be used to enable a metaphorical understanding of the relationship between phenomena and noumena. George Lakoff makes the point that the metaphor is fundamental in how humans understand complex abstract ideas.
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How do you get from the fact they are different sizes, that space is real? — Mww

If space wasn't real, how could things be of different sizes?
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If I think object, the extension of it is given. If I need not go beyond the conception of a body, I need not consider space. And because it’s an analytic judgement, true because of itself, there’s no need for the synthetic a priori judgment the pure intuition of space provides. — Mww

A proposition may be analytic or synthetic

A7/B11 - “…. when I say, “All bodies are extended,” this is an analytical judgement. For I need not go beyond the conception of body in order to find extension connected with it, but merely analyse the conception, that is, become conscious of the manifold properties which I think in that conception, in order to discover this predicate in it….”

A7/B11 - On the contrary, if I say: "All bodies are heavy," then the predicate is something entirely different from that which I think in the mere concept of a body in general. The addition of such a predicate thus yields a synthetic judgment.

It is true that a body by its very nature is extended in space, in that the word "body" means being extended in space. This is analytic, regardless of the nature of the world.

Similarly the word "unicorn" means a mythical animal typically represented as a horse with a single straight horn projecting from its forehead. This is also analytic, regardless of the nature of the world.

The fact that I can say "all bodies are extended" and "unicorns have a a single straight horn projecting from its forehead" does not presuppose that either bodies or unicorns exist in the world.

If I want to know whether "bodies" or "unicorns" exist in the world, this requires a synthetic judgement.

In Kant's Realism, he does believe that objects exist in the world

From the SEP article section 2.3 on Kant’s Transcendental Idealism, in his Prolegomena he was apoplectic that Feder and Garve had claimed that his Transcendental Idealism was just a Berkeleyan or Phenomenalist idealism, and pointed out that in the CPR bodies exist in space and that we have immediate, non-inferential knowledge of them.

For Kant, bodies exist in the world, even if we only have transcendental knowledge of them. As by definition of the word "body", such bodies are extended in space, this means that if the body is real then the space the body extends into must also be real.

In the preface CPR, Kant sounds like he is on duty to reinstate Metaphysics as the queen of all Science. — Corvus

To reinstate a scientific metaphysics in place of traditional metaphysics, from his position as Scientific Realist.

Introduction to CPR - Kant's position thus required him not only to undermine the arguments of traditional metaphysics but also to put in their place a scientific metaphysics of his own, which establishes what can be known a priori but also limits it to that which is required for ordinary experience and its extension into natural science.
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He is not talking about the space in empirical reality in CPR (it is presupposed existence). — Corvus

:up: As a thing-in-itself it cannot be talked about (like the Fight Club)

come up with a whole bunch of ideas demonstrating how space isn’t real..........From which follows necessarily, that the knowledge of things is the determinant factor for their reality, the space of them utterly irrelevant, insofar as the knowledge is remains regardless of the space of it.................If you say, space is that which is contained in an empty bucket, what have you actually said? — Mww

Space allows me to compare sizes. For example, the distance between the two sides of a garden bucket is less that the diameter of the Milky Way Galaxy.

If space wasn't real, then the garden bucket would be the same size as the Milky Way Galaxy.

Imagine how practically impossible it would be to talk about things, if it were denied from the outset such things were not, and could not, be thought as extended in space. From the perspective of the thesis itself, it was never meant to imply there actually is such a thing as space into which things extend, but only that the constitution of the human intellect can’t function without the transcendentally given objective validity granting it. — Mww

I agree that it would be impossible to talk about things if we denied they could be extended in space, but it is Kant's position that there is in fact a space into which things extend.

From the SEP article section 2.3 on Kant’s Transcendental Idealism:
Kant in the Prolegomena was apoplectic that Feder and Garve had claimed that his Transcendental Idealism was just a Berkeleyan or Phenomenalist idealism, and pointed out that in the CPR bodies exist in space and that we have immediate, non-inferential knowledge of them. He pointed out that his idealism is merely a formal idealism, and it is only the form of objects that is due to our minds not the matter of the objects, in that the matter we experience depends on a source outside of the mind.

This does not mean that the matter in space we perceive as appearance is the same as the matter in space that exists outside our perception of it. For example, thinking about the analogy of colour, we perceive the colour red when looking at a wavelength of 700nm. Our perception of the colour red has been caused by the wavelength of 700nm, yet what we perceive, the colour red, is different to what caused it, a wavelength of 700nm.

We can talk about there being the colour red in the world even though the colour red doesn't exist in the word, yet although the colour red doesn't exist in the world there was something, a wavelngth of 700nm, that caused our perception of the colour red.

For Kant as a Empirical Realist, there has to be something in the world for us to be able to perceive something, but the something we perceive doesn't of necessity have to be the same thing as the something that caused our perception in the first place.

I don't think he was denying space and time for empirical reality at all. He presupposed it. But he had to postulate space and time as pure intuition in CPR in order to give ground for necessity of a priori knowledge such as Geometry and all the Metaphysical judgments, which are supposed to be superior to the natural science based on the space and time of the empirical reality. Inevitably Kant was a dualist. — Corvus

As you say, Kant wanted to combine the two schools of rationalism and empiricism.

However, not to show that Metaphysics is superior to the Natural sciences, but rather better explain both Metaphysics and the Natural Sciences. Neither Metaphysics nor the Natural Sciences could be properly understand without first amalgamating both rationalism and empiricism.

Kant's synthetic a priori amalgamating transcendental idealism and empirical realism is necessary to better understand both Metaphysics and the Natural Sciences. He was a dualist.

Exactly. Existence of matter. Things. Objects. That which appears to human sensibility. That of which sensation is possible. That for which phenomena are given. In Kant, space and time are none of those. — Mww

I agree that matter and space and time are different kinds of things, in that I can imagine space empty of matter, yet I cannot imagine matter not being in a space. But the fact they are different kinds of things does not mean they cannot both be real, albeit we only they are real transcendentally.

This doesn't answer Guyer's and Woods statement in the Introduction to the CPR that for Kant, space and time are empirically real.
Kant's thesis that space and time are pure forms of intuition leads him to the paradoxical conclusion that although space and time are empirically real, they are transcendentally ideal, and so are the objects given in them.

If we all accept that for Kant matter is empirically real, then how could it be the case that matter is empirically real yet the space and time that this matter is existing within is not empirically real?

What does it mean that the matter is real yet the space and time it exists within is not real?

Th only conclusion is that if matter is empirically real, then the space and time that it is existing within must also be empirically real.

Despite the direct textual references refuting that opinion, you both continue the misunderstanding — Mww

Is it the case that for Kant, space and time are empirically real?

In the Introduction to CPR by Paul Guyer and Allen W. Wood is the statement that, for Kant, space and time are empirically real.

Kant's thesis that space and time are pure forms of intuition leads him to the paradoxical conclusion that although space and time are empirically real, they are transcendentally ideal, and so are the objects given in them.

Kant writes that a transcendental idealist can be an empirical realist

A370 - The transcendental idealist, on the contrary, can be an empirical realist, hence, as he is called, a dualist, i.e., he can concede the existence of matter without going beyond mere self-consciousness and assuming something more than the certainty of representations in me, hence the cogito, ergo sum.

The SEP article on Kant's Transcendental Idealism writes that Kant was an Empirical Realist:
This provides a further sense in which Kant is an “empirical realist”

I would say that the above is some evidence that for Kant, as an Empirical Realist, space and time are empirically real.

If Kant were to think space and time inhere or subsist in themselves, and thereby they represent empirical reality, hence can be properties of things, he contradicts the tenets of his own epistemological metaphysics, not to mention it beggars the imagination as to why he would, on the one hand contradict itself, and on the other spent ten years constructing a philosophy in which it is proved they don’t. — Mww

I'm still interested in Critique of Pure Reason.

For Kant, as an Empirical Realist, space and time and the matter within it are empirically real. However, this can only be established by synthetic a priori judgements, empirically through the sensible intuitions of phenomena and appearance and transcendentally through the non-sensible intuitions and understanding.

Introduction to CPR - Kant's thesis that space and time are pure forms of intuition leads him to the paradoxical conclusion that although space and time are empirically real, they are transcendentally ideal, and so are the objects given in them.