In your first question, "a person who can speak English" is a description, not an object. — Metaphysician Undercover

Can there be a description without an object being described?

Isn't "a person who can speak English" a description of the object (a person who can speak English)?
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It is not a true representation of how we use numbers, to think of a number as itself an object. — Metaphysician Undercover

The word "object" has different meanings. In mathematics, a mathematical object is an abstract concept (Wikipedia – Mathematical Object). In natural language, it can be something material perceived by the senses (Merriam Webster - Object).

For example, we can think of the number ${\sqrt{2}}$, the number ${2 * 10^{100}}$ and ${\infty}$ as abstract mathematical objects but cannot think of them as natural concrete objects.

However we can think of the numbers 1. 6 and 10 as not only abstract mathematical objects but also as natural concrete objects.

That raises the question as to how we are able to think of something that is abstract, disassociated from any specific instance (Merriam Webster – Abstract). For example, independence, beauty, love, anger, Monday, ${\infty}$, ${\sqrt{2}}$ and the number 6.

George Lakoff and Mark Johnson in their book Metaphors We Live By propose that we can only understand abstract concepts metaphorically, in that we understand the concept of gravity by thinking about a heavy ball on a rubber sheet.

Thereby, we understand the concept of independence by remembering the feeling of leaving a job we didn't like. We understand the concept of beauty by looking at a Monet painting of water-lilies. We understand the concept of infinity by thinking about continually adding to an existing set of objects. We understand the concept of ${\sqrt{2}}$ by thinking about the number 1.414 etc etc. We understand the concept of 6 by picturing 6 apples.

IE, we can only understand an abstract concept metaphorically, whereby a word or phrase literally denoting one kind of object or idea is used in place of another to suggest a likeness or analogy between them (Merriam Webster – Metaphor).

If that is true, then even more reason why one would then consider the question in regard to mathematics. If it's meaningless in context C but defined in another context D, then it wouldn't make sense to say that then it is inapposite to context D. — TonesInDeepFreeze

That raises the interesting question that if an expression such as "infinite infinities" has no meaning in a natural language, the everyday spoken and written language used to describe the world around us, but does have meaning in the formal language of set theory, then what exactly is the relationship between a formal language such as set theory and the world around us?

The principal problem with set theory..............is that set theory is derived from a faulty Platonist premise, which assumes "mathematical objects" — Metaphysician Undercover

In a random web site is set a problem that can be solved by set theory:

In a group of 100 persons, 72 people can speak English and 43 can speak French. How many can speak English only? How many can speak French only and how many can speak both English and French?

Doesn't this problem, soluble by set theory, assume "objects", such as the object "a person who can speak English"?

If the number "1" does not refer to an object, what does it refer to?

along with its fantastic representation of "infinite" — Metaphysician Undercover

I would say that "infinite number" does not refer to an object, because unknowable by a finite mind, but does refer to a process along the lines of addition, which is knowable by a finite mind.

There are infinite sets that have sizes different from one another. — TonesInDeepFreeze

I take the OP as asking the question "are there an infinite number of infinities?"

The answer would depend on whether looked at from set theory or natural language.

Set Theory is a specific field of knowledge with its own rules, and as the Scientific American noted: As German mathematician Georg Cantor demonstrated in the late 19th century, there exists a variety of infinities—and some are simply larger than others.

However the terms infinity and infinite sets are also used in everyday language outside of set theory, such as "I have an infinity of problems" and "I have an infinite set of problems".

As the OP doesn't refer to the very specific field of "set theory", having its own particular rules, I think the OP should be considered as a problem of natural language.

Within natural language, the question "are there an infinite number of infinities" is meaningless, as not only is "an infinite number" unknowable, it follows that whether there is one or more infinite numbers must also be unknowable.

On the assumption that the OP refers to a problem in natural language, otherwise it would have specifically referred to "set theory", as it refers to that which is unknowable, although syntactically correct is semantically meaningless.

That reminds me of intuitionists or at the very least of psychologists in the ontology of mathematics, where the number 2^100 does not exist until it is thought up. — Lionino

But then again, the number 2 does not exist until it is thought up.

The whole confusion resulted from the wrong premise that infinite numbers do exist. No they don't exist at all. So it is an illusion. — Corvus

:up: :up: :up:

Of course, but I'm saying that in context of sets in mathematics, 'infinity' as a noun invites misunderstanding, especially as it suggests there is an object named 'infinity' that has different sizes. — TonesInDeepFreeze

In the Merriam Webster dictionary infinity is classed as a noun, and within mathematics is the infinity symbol ∞. But as you say, this is problematic as it suggests that infinity is an object, such as a mountain or a table, which can be thought about. But in one sense this is impossible, as it impossible for a finite mind to know something infinite, where infinity is an unknowable Kantian "ding an sich" ("thing in itslef").

So what does the word "infinity" refer to, if not a noun inferring an object?

As the Wikipedia article on Infinity writes: Infinity is a mathematical concept, and infinite mathematical objects can be studied, manipulated, and used just like any other mathematical object.

As Literature as a noun refers to the study of books, perhaps Infinity as a noun refers to the study of infinite sets. Both Literature and Infinity are nouns, but refer to a process, not the intended conclusion of the process. This makes sense, as processes are comprehensible to finite minds. A finite mind can comprehend the process of adding to an existing set, even if not able to comprehend the eventual conclusion of continually adding to an existing set .

IE, "infinity" is a noun and refers to a process rather than any conclusion of that process.

'infinity' is not an adjective. — TonesInDeepFreeze

True, infinite is an adjective and infinity is a noun

But it can get complicated.
Music fills the infinite between the two souls - Rabindranath Tagore
Infinity pencil with eraser - Amazon

If that is the case, then it seems barmy to talk about different size of the infinite sets. — Corvus

There cannot be different sizes of infinite sets

As you say: "Infinity is a property of motion or action..............Infinite number means that you keep adding (or counting whatever) what you have been adding (or counting) to the existing number"

What does "infinite set" refer to?

It cannot refer to an object, an infinite set, as comprehending an infinite set is beyond the ability of a finite mind. It can only refer to the process of being able to add to an existing set.

In other words, "infinite set" refers to "a set that can be added to", where "that can be added to" qualifies the object "a set".

As a "set" is an object it can have a size, and therefore there can be different sizes of sets.

However, as the qualifier "that can be added to" is not an aspect of the size of the set, whilst the expression "different sizes of sets" is grammatical, the expression "different sizes of infinite sets" is ungrammatical.

What is infinity

On the one hand we have the concept of infinity within the symbol ∞, but on the other hand a finite mind cannot comprehend an object of infinite size. So what does our concept of infinity refer to?

As the Wikipedia article Extended Real Number Line notes, the infinities are "treated" as actual numbers, not that the infinities are actual numbers.

As our concept of infinity cannot refer to an object, as comprehending an infinite number of things is beyond the ability of a finite mind, it can only refer to the process of adding to an existing number of things until it is not possible to add any more, which can be comprehended by a finite mind.

IE, "infinity" refers to a process not an object.

Infinity is a property of motion or action — Corvus

I agree. "Infinite" is a property attached to an object, such as "large house" or "infinite number".

As "large" doesn't exist as an object, "infinite" doesn't exist as an object.

As I wrote before: ""infinity" as an adjective means something along the lines "any known set of real numbers can be added to"".

The fact that you can stack a property onto a substance to make an object does not mean that that object is instantiated in real life, — Lionino

Yes, for example as in "infinite number" where "infinite" is a property of "number".

Can there be infinite infinities?

Can there be an infinite set of (infinite set of numbers)?

The word "infinite" is not a noun but an adjective qualifying the noun "set".

Therefore, there can be infinite infinities because the word "infinity" is an adjective.

does that mean that there are infinitely infinite infinitely infinite infinitely infinite infinitely infinite infinitely… (etc.) infinities? — an-salad

Hopefully this doesn't contradict what @TonesInDeepFreeze has said. It seems that if the word "infinity" was being used as a noun, then yes, there would be an infinite number of infinities. However, the word "infinity" is not being used as a noun, but rather is being used as an adjective, in which case there is only one infinity. IE, "infinity" as an adjective means something along the lines "any known set of real numbers can be added to".

But he is not denying the outside empirical world where you see all the daily objects and interact with them. — Corvus

There are several things in your posts that I don't agree with, but as I am off on holiday, I won't be able to tackle them.

However, I think you are misusing the term "Empirical World".

The IEP article Immanuel Kant: Metaphysics differentiates between an "empirical world" in the mind and a "mind-independent world" outside the mind

Kant responded to his predecessors by arguing against the Empiricists that the mind is not a blank slate that is written upon by the empirical world, and by rejecting the Rationalists’ notion that pure, a priori knowledge of a mind-independent world was possible. Reason itself is structured with forms of experience and categories that give a phenomenal and logical structure to any possible object of empirical experience. These categories cannot be circumvented to get at a mind-independent world, but they are necessary for experience of spatio-temporal objects with their causal behaviour and logical properties. These two theses constitute Kant’s famous transcendental idealism and empirical realism.

IE, the "Empirical World" is the world as perceived via the senses. That we may perceive tables and chairs in this "Empirical World" does not of necessity mean that tables and chairs exist in a "Mind-Independent World".

So the indirect realist believes that what we can't see is what is real? — Wayfarer

Not necessarily. Just because I cannot see a unicorn doesn't mean that I think unicorns are real.

From Wikipedia Direct and Indirect Realism

Indirect realism is broadly equivalent to the scientific view of perception that subjects do not experience the external world as it really is, but perceive it through the lens of a conceptual framework.
Direct realism postulates that conscious subjects view the world directly, treating concepts as a 1:1 correspondence.

I see the colour red, yet the colour red doesn't exist outside my perception of it. I do have, however, the fundamental belief that there is something in the world that caused me to perceive the colour red.

My seeing the colour red is a real experience, and I believe that there is also a real something in the world that caused my seeing the colour red.

For example, you may feel a sharp pain in your hand caused by a bee sting. I don't think anyone would argue that the pain and the bee sting are the same thing and thereby interchangeable. Both are real, yet different things. One is the effect and the other is the cause.

Isn't it fairly simple that our perceptual abilities, and also our intellectual abilities, are limited in some ways, so that what the world is outside of those bounds can't be known by us? — Wayfarer

Exactly. This is the point that Kant is making in the CPR, and as an Indirect Realist, something I totally agree with.

However, I don't think that the Direct Realist would agree with you.

How many external worlds do you have, and which one is the real world? Why do you need more than one world? — Corvus

There are many uses for the word "world". There is the world of dance, the world of science, the world of literature, the world inside our minds, the world outside our minds, etc.

One word having several uses is in the nature of language.

What is real? Is the thought of a mountain any less real than the mountain itself?
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What is the unknowable Things in themselves that exist outside you exactly mean? What are they? — Corvus

Kant wrote in Prolegomena section 32:

"And we indeed, rightly considering objects of sense as mere appearances, confess thereby that they are based upon a thing in itself, though we know not this thing as it is in itself, but only know its appearances, viz., the way in which our senses are affected by this unknown something."

We perceive appearances, phenomena, in our senses. We may see the colour red, feel a sharp pain, taste something sweet, smell something acrid or hear a grating noise.

We have the fundamental belief that something caused these phenomena. But we don't perceive what caused these phenomena, we only perceive the phenomena.

The cause of the phenomena is irrelevant in our experience of the phenomena, in that whether the sharp pain was caused by a bee sting, a sewing needle or a thistle plays no part in the nature of our experience of a sharp pain.

The cause of the sharp pain can be called a Thing in Itself, and even if unknowable, has no bearing on the nature of the actual experience of a sharp pain. Even if we knew what the cause was, this would not change the phenomena that we had perceived.
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So Things-in-themselves exist outside you, but it also exists in your mind? Are they the same Things-in-themselves? Or are they different entities? Are they visible or audible to you? Can you touch them? If they are not perceptible, then how do you know they actually even exist? — Corvus

My belief is that Things in Themselves have an ontological existence outside us even if a particular Thing in Itself is unknowable.

Kant uses Transcendental Reasoning on what we do know, appearances, to conclude that Things in Themselves must exist outside us.

Therefore, "Things in Themselves" have an ontological existence outside us, and they exist as thoughts inside us.

There are many things outside us that are not directly perceptible through the senses yet we reason exist. For example, gravity.

Now the question goes back to Thing-in-itself. Is the Thing-in-itself something in the mind or does it exist outside of the mind? If outside, then would it be in the external world, or some other world totally separate from the external world? — Corvus

It depends what you mean by "external world". There is the external world that I perceive as Appearance, and there is the external world outside me that I cannot perceive that is causing these Appearances.

Kant wrote in B276:

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

Kant wrote in Prolegomena section 32:

"And we indeed, rightly considering objects of sense as mere appearances, confess thereby that they are based upon a thing in itself, though we know not this thing as it is in itself, but only know its appearances, viz., the way in which our senses are affected by this unknown something."

To my understanding of Kant, Appearances are affected by unknowable Things in Themselves that exist outside me.

However, as we can also think in general terms about Things in Themselves using Transcendental Reasoning on Appearances, thoughts about Things in Themselves exist in the mind.

I do believe in only one world i.e. the physical world. I was asking about the external world in the Refutation for the Idealist you quoted. — Corvus

In B276 Kant refers to objects existing outside any human observer: "The mere, but empirically determined, consciousness of my own existence proves the existence of objects in space outside me."

You say that you see only one world, it is empirical, it is physical, it is external, it is not internal and it is not Mind-Dependent.

Are you:

An Indirect Realist who believes that the objects they see are only a representation of different objects that exist outside the observer in a non-mental world?

A Direct Realist who believes that the objects they see are the same objects that exist outside the observer in a non-mental world?

A Berkelian Idealist who believes that the objects they see are the same objects that exist outside the observer in a mind?

A Solipsist who believes that the objects they see only exist inside their own mind?

How does one know one's own existence "determined in time" without yet being sure of the external world? — Corvus

I assume you know your own existence within time, yet you don't seem to believe in an external world.

As you wrote:

I don't see it anywhere. Even with binoculars, telescope and magnifying glasses and microscopes, there is no such a thing as a Mind-independent world. There is just the empirical world with the daily objects I see, and interact with. That is the only world I see around me. Nothing else. — Corvus

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Should the indirect realist not check the argument of the Refutation for the Idealism for any logical obscurity before accepting it? — Corvus

I'm sure they do. I know I have.
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It would be likely to be a biased opinion. It is better to look at the original work first, and then various other commentaries rather than just relying on one 3rd party commentary source. — Corvus

As Kant's philosophy is extremely complex and notoriously difficult to understand, I think the sensible approach is first to read various commentaries and then look at the original material.

You cannot prove the existence of the objects in space outside of you by simply saying you are conscious of your own existence. — Corvus

In B276, Kant starts his proof with "I am conscious of my existence as determined in time."

He doesn't start his proof with "I am conscious of my existence".
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Not contradictory, but not making sense either. — Corvus

Kant's Transcendental Idealism and Refutation of Idealism B276 make sense to an Indirect Realist but perhaps not to a Direct Realist.
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Do you have the CPR reference for backing that points up? No Wiki or SEP, but CPR. — Corvus

For posts on the Forum, the SEP as source information is more than adequate.

Welcome to the Stanford Encyclopedia of Philosophy (SEP), which as of Summer 2023, has nearly 1800 entries online. From its inception, the SEP was designed so that each entry is maintained and kept up-to-date by an expert or group of experts in the field. All entries and substantive updates are refereed by the members of a distinguished Editorial Board before they are made public. Consequently, our dynamic reference work maintains academic standards while evolving and adapting in response to new research. — https://plato.stanford.edu/about.html

You seem to think a world is some logically reasoned object. — Corvus

The Empirical World inside us we know through our sensibilities. The Mind-Independent World outside us we know through Transcendental Reasoning about the Empirical World inside us.

A photograph is to show visual image, not the form of reason. It is nonsense to say that a photo can only show the form of reason. — Corvus

The Mind-Independent world can only be known using transcendental reason.

Reasoning is a logical connection between several strands of an argument, for example, the syllogism. A syllogism has the same form, in which a conclusion is drawn from two premises, regardless of its content.

For example, i) all men are mortal, Socrates is a man, therefore, Socrates is mortal ii) all dogs are animals, all animals have four legs, therefore all dogs have four legs.

As a syllogism can only have content when its form is complete, reason can only have content when its logical form is complete.

A single photograph as a single premise is only one part of a logical sequence within a reasoned argument, and as its logical form is incomplete, it cannot be said to have content.

This is why a single photograph cannot show a Mind-Independent World, as knowledge about a Mind-Independent World requires Transcendental Reason, and reason in order to have content requires a complete logical form. A single photograph as a single premise cannot have the necessary content for a Transcendental Reason as it is an incomplete logical form.
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In that case, would it be the case that you have been mistaken Kant's refutation of Idealism as Kant's TI? — Corvus

No.

From the Wikipedia article Transcendental Idealism

Transcendental idealism is a philosophical system founded by German philosopher Immanuel Kant in the 18th century. Kant's epistemological program is found throughout his Critique of Pure Reason (1781). By transcendental, Kant means that his philosophical approach to knowledge transcends mere consideration of sensory evidence and requires an understanding of the mind's innate modes of processing that sensory evidence.

In his Refutation of Idealism is his Theorem "The mere, but empirically determined, consciousness of my own existence proves the existence of objects in space outside me" B276.

These are not contradictory positions.
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In that case, should it not be a representation of the empirical world in your mind, rather than an internal world inside you? — Corvus

Of course, that's why in our internal world is a representation of the external world.
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As an aside, the Thing in Itself has nothing to do with God, the soul or freedom.

There is only one world called the empirical world, and it is outside the mind. Appearance is from the empirical world....................When I see a book in front of me, it is via the appearance or phenomenon from the object (the book) in the empirical world (outside of the mind).................. The physical objects in the empirical world also continue to exist through time.................There is no such thing as an internal world. In your mind, there are only perceptions. — Corvus

I wrote that there are different "Worlds". One exists within the mind, an "Empirical World", and the other exists outside the mind, a "Mind Independent World"

From the Merriam Webster Dictionary, "empirical" means i) originating in or based on observation or experience, ii) relying on experience or observation alone often without due regard for system and theory.

"Empiricism" means i) the practice of relying on observation and experiment especially in the natural sciences ii) a tenet arrived at empirically.

So far, the word "empirical" refers to what exists in the mind rather than what exists outside the mind, inferring that an "Empirical World" also refers to what exists in the mind rather than what exists outside the mind,

The SEP article on Rationalism vs Empiricism also distinguishes between an external world and an internal world

The dispute between rationalism and empiricism takes place primarily within epistemology, the branch of philosophy devoted to studying the nature, sources, and limits of knowledge. Knowledge itself can be of many different things and is usually divided among three main categories: knowledge of the external world, knowledge of the internal world or self-knowledge, and knowledge of moral and/or aesthetical values.

You say that there is only "one world", and in this "one world" physical objects continue to exist through time. IE, whether one million years ago or one million years into the future. But we know that one million years ago there were no humans, meaning that in this "one world" you are referring to, humans are not a necessary part.

So how can this "one world" be an "empirical world" if humans are not necessarily there to observe it?

I am not sure if a philosophical topic which is totally severed from the Empirical world has a meaning. Are you? — Corvus

The Empirical World is the world of Phenomena, and the Mind-Independent World is the world of Things in Themselves.

I am sure that the Mind-Independent World is of philosophical interest.

Whether Kant intended the (negative) noumena as part of the Empirical world or the Mind-Independent World is ambiguous. Sometimes he treats the noumenon as a part of the Empirical World, and sometimes he treats the noumenon as part of the Mind-Independent World. In classical philosophy, Plato etc, the noumenon is part of the Empirical World.

From Wikipedia Noumenon

In Kantian philosophy, the noumenon is often associated with the unknowable "thing-in-itself" (German: Ding an sich). However, the nature of the relationship between the two is not made explicit in Kant's work, and remains a subject of debate among Kant scholars as a result.

As regards tables and chairs, we perceive them in our Sensibilities as Phenomena. If they exist as Things in Themselves in a Mind Independent Word then they are unknowable, meaning that we can never know whether they do or do not exist. But we do know about tables and chairs, meaning that our knowledge about them must have come from our Empirical World, as Ideas or Forms, ie as Noumena.

We can only know about Things in Themselves in general in a Mind Independent World using transcendental reasoning, in the same way as used by Kant in his Refutation of Idealism in B275.

If you can see it, can you take a photo of a Mind-independent world, and upload here? — Corvus

As a Mind-Independent World can only be known by transcendental reason, and as a single photograph can only show the form of reason and not its content, a single photograph can never show a Mind-independent World.
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This thread is for reading Kant's CPR. Why try to show Berkeley's Idealism is incorrect? — Corvus

Kant refers to Berkelian Idealism in B275, which is part of his purpose in the Refutation of Idealism.

Idealism (I mean material idealism) is the theory that declares the existence of objects in space outside us to be either merely doubtful and indemonstrable, or else false and impossible; the former is the problematic idealism of Descartes, who declares only one empirical assertion (assertio), namely I am, to be indubitable; the latter is the dogmatic Idealism of Berkeley, who declares space, together with all the things to which it is attached as an inseparable condition, to be something that is impossible in itself, and who therefore also declares things in space to be merely imaginary.

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In summary how did you manage to cram in the whole universe into inside your mind? — Corvus

Because a "mountain" as a representation in the Empirical World within the mind is different in kind to a "mountain" weighing one billion tonnes in a Mind-Independent World outside the mind.

Even with a binoculars, telescope and magnifying glasses and microscopes, there is no such a thing as a Mind-independent world.............If you can see it, can you take a photo of a Mind-independent world, and upload here? — Corvus

Even if I uploaded a photo of a Mind-Independent World, the Solipsist wouldn't believe it.

Where is a Mind-independent world? — Corvus

All around us. It existed before us and will exist after us.
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Again what is the point even talking about something which is unknowable? — Corvus

To show that Berkelian Idealism is incorrect.

In fact, for the day to day survival of humans, there is no necessity to know more than what is perceived in our Empirical World of Phenomena. Any transcendental thought about a Mind-Independent World is out of philosophical interest only.
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If it was unknowable, then how did you know it was unknowable? — Corvus

Kant wrote that Appearances are based on Things in Themselves, even though Things in Themselves are unknown.

And we indeed, rightly considering objects of sense as mere appearances, confess thereby that they are based upon a thing in itself, though we know not this thing as it is in itself, but only know its appearances, viz., the way in which our senses are affected by this unknown something. — Prolegomena, § 32 — https://en.wikipedia.org/wiki/Thing-in-itself

Kant uses a Transcendental Argument in the Refutation of Idealism to prove his Theorem that Things in Themselves exist, even though what they are is unknown.

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

No one was claiming Kant said the Thing-in-itself, something that is knowable. — Corvus

When I see the book in front of me, I know the book. I know it is in blue colured cover, it is a paperback book, the title of the book is "CPR" by Kant. I cannot be wrong on that. It is the truths I know about the book in front of me. I don't need to worry anything about Thing-in-itself book of CPR. There is no such thing as Thing-in-itself CPR book, but there is a CPR book in front of me. — Corvus

All this is true, in that you see the book in your Empirical World, the world that exists as Appearance in your Sensibilities. The world as Phenomena.

However, what you are not seeing is any world outside these Phenomena.

In a world outside these Phenomena are Things in Themselves, which are unknowable, and as unknowable, cannot even be thought about.

Even if books existed in a Mind-Independent world, as Things in Themselves they would be unknowable, and being unknowable, we couldn't even know whether they existed or not.

In Kant's Refutation of Idealism, he proposes the Theorem in B276: "The mere, but empirically determined, consciousness of my own existence proves the existence of objects in space outside me."

Yes, Kant as a believer in Realism does believe that a Mind-Independent World exists outside us, and within this Mind-Independent World are objects in space, but we only know that there are objects as a generality, we don't know what these objects are in particular

B279 – Here it had to be proved only that inner experience in general is possible only through outer experience in general.

We may know in general that Things in Themselves exist in a Mind-Independent World, otherwise we couldn't be discussing them, but that does not mean we can know individual Things in Themselves.

We may know the book in front of me in my Empirical Word, but we cannot know if there is a Book in a Mind-Independent World, as that would be a Thing in Itself.

Meaning of "Empirical World"

Does the Empirical World exist within Appearances or does it exist the other side of these Appearances, whatever is causing these Appearances?

There are different "Worlds". One exists within the mind and the other exists outside the mind, independent of the mind.

There are two meanings of the word "empirical", i) a person's subjective experience and ii) exterior, objective data (Psychology Today – Gregg Henriques)

"Empirical Realism" is a term coined by Kant in the CPR. On the one hand "Empirical" because it gives the mind an active role in the cognition of empirical objects, an aspect of epistemology in establishing a subjective empirical reality. On the other hand, "Realism", endorsing the view that there is a world that exists outside and independent of the human mind. (Paul Abela Empirical Realism).

In his Theorem for the Refutation of Idealism in B276, Kant argues that objects exist in space outside the mind

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

The IEP article Immanuel Kant: Metaphysics differentiates between an "Empirical World" in the mind and a "Mind-independent World" outside the mind

Kant responded to his predecessors by arguing against the Empiricists that the mind is not a blank slate that is written upon by the empirical world, and by rejecting the Rationalists’ notion that pure, a priori knowledge of a mind-independent world was possible. Reason itself is structured with forms of experience and categories that give a phenomenal and logical structure to any possible object of empirical experience. These categories cannot be circumvented to get at a mind-independent world, but they are necessary for experience of spatio-temporal objects with their causal behaviour and logical properties. These two theses constitute Kant’s famous transcendental idealism and empirical realism.

In summary, there is an "Empirical World" inside the mind, within Phenomena, within Appearances, within the Sensibilities and within the Senses and there is also a "Mind-independent World" outside the mind.

There are different interpretations on this point. — Corvus

Kant wrote that we cannot have knowledge of a Thing in Itself. From Wikipedia Thing-in-itself

And we indeed, rightly considering objects of sense as mere appearances, confess thereby that they are based upon a thing in itself, though we know not this thing as it is in itself, but only know its appearances, viz., the way in which our senses are affected by this unknown something.— Prolegomena, § 32

Do you have a reference that says that Kant believes that it is possible to have knowledge of Things in Themselves?
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Things-in-themselves are for the objects we have concepts, but not the matching physical objects in the empirical world. We can think about it via concepts, but we don't see them in the phenomena. They belong to Thing-in-itself. — Corvus

You are referring to (negative) noumena, not Things in Themselves.
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If you believe in the existence of invisible particles and forces in space and time, then why do you deny the existence of the physical objects such as the bent stick in the empirical world?
If you had a single particle of the bent stick, would you say that is a part of the bent stick, and it is a stick?
In the absence of humans, sounds a condition that you must clarify before progressing further.
Where does "if something cannot be judged" come from? — Corvus

The discussion goes back to the question of whether, when we perceive a stick in our sensibilities, are we also perceiving the same object external to us in the world. This is something that the Direct Realist would argue is the case. Kant's position is not that of the Direct Realist.

You are still seeing an object external to you when you see the bend stick in the water jug. — Corvus

Do objects such as "sticks" exist in the empirical world?

In the empirical world are simples.

In the presence of humans, humans may name one particular set of simples "stick". This creates the object "stick", meaning that objects such as "sticks" do exist in the empirical world, but they only begin to exist after being named.

In the absence of humans, as naming is not possible, objects such as "sticks" cannot be created, meaning that objects such as "sticks" cannot exist.

I understand Kant's Thing-in-itself, is not everything outside us in the world. If that was the case, Kant would be an extreme sceptic, who professes everything outside us is unknowable. That would render all our knowledge of external world impossible. In that case, Kant would have been rejected for being an extreme scpetic, and nobody would take him as a serious epistemologist or philosopher. To even suggest that would be a gross misunderstanding of Kant and his philosophy. — Corvus

On the one hand, Kant held that we can never know about Things in Themselves, we can never have knowledge of Things in Themselves. Things in Themselves include everything outside us in the world, meaning that there are not some Things in Themselves that we do have knowledge of whilst there are other Things in Themselves that we cannot have knowledge of.

In philosophy, scepticism is the theory that certain knowledge is impossible.

On the other hand, I agree that Kant was not a sceptic.

To explain why Kant was not a sceptic is the subject of many articles

As a start, the fact that we cannot have knowledge about Things in Themselves does not presuppose that we cannot have knowledge about the world.
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Isn't your perception of the sticks enough evidence they exist? — Corvus

Yes, my perception of a stick is evidence that it exists – evidence that it exists in my mind.

In the same way, my perception of pain is evidence that it exists – in my mind.
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Even when no humans exist, all the material things must exist as they have been...............................Where humans don't exist, of course, there is no perception, no thoughts. But we can still make logical inference (from the human world), that things keep exist as they have done. — Corvus

My belief is in Neutral Monism, in that what exists in the absence of humans are fundamental particles and fundamental forces in space and time.

If the fundamental particles are thought of as "material things", then I agree that "material things" exist in the absence of humans.

However, I don't agree that "sticks" if thought of as a material thing exists in the absence of humans. I agree that a human can judge whether or not something is a "stick", but in the absence of humans, who or what judges that something is or is not a "stick"?

And if something cannot be judged to be either a stick or a branch, then how is it possible to be either a stick or a branch?

What Kant would have said is, that even if your sensibility sees a bent stick in the water jug, your category of concepts and understanding (followed by reading the scientific explanation on why the stick looks bent), would come to a proper reasoning on the experience, and judge the stick is straight in actuality, even if it looks bent. — Corvus

For Kant, a stick in the world outside us is a Thing-in-Itself and therefore unknowable. Being unknowable, it is impossible to judge whether bent or straight.

From the Wikipedia article on Thing-in-Itself.

In his doctrine of transcendental idealism, Kant argued the sum of all objects, the empirical world, is a complex of appearances whose existence and connection occur only in our representations.

Kant introduces the thing-in-itself as follows: And we indeed, rightly considering objects of sense as mere appearances, confess thereby that they are based upon a thing in itself, though we know not this thing as it is in itself, but only know its appearances, viz., the way in which our senses are affected by this unknown something.  Prolegomena, § 32

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What you have been calling as your internal world is nothing more than a figment of representation of the world in your mind via your sensibility from the external world. — Corvus

:100:
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What else do you need for proof that bent sticks exist in the world? — Corvus

First it has to be proved that sticks exist in the world.

There is the world inside the mind and there is the world outside the mind. The word "world" refers to two very different things

We know "sticks" exist in the mind as concepts, as we are discussing them

The question is, do "sticks" exist outside the mind and independently of any mind

Humans can judge when something is a stick and when something is no longer a stick, but in the absence of humans, in the absence of any definition of stick, in the absence of anyone to judge when something is a stick or no longer a stick, what determines when something in the world outside us is a stick or no longer a stick. A god or nature itself?

How can you prove that "sticks" exist in the absence of human thought without using human thought?

By virtue of drawing meaningful correlations between different things, some of which are not "internal to your mind". — creativesoul

There is a world outside the mind, and there is a world inside the mind, of streets with cars and building. The same word "world" is being used to refer to two very different things. The world inside the mind can only be a representation of the world outside the mind.

Kant in his Realism believed that there is a world outside the senses, and information from this world can only get into the mind through the senses, meaning that our only knowledge about an outside world comes through our senses.

The problem is, how can we correlate our thoughts about an outside world with the outside world, when we only know about an outside world by what has been given to us by our senses.

Our knowledge of an outside world stops at our senses. We may perceive the colour red through our senses, but it doesn't necessarily follow that the colour red actually exists in an outside world.

It is like saying that you used your camera, and took a photo of the mountain across the field in your town, and then the camera thinks that it has a mountain in its memory card, because it cannot understand why the mountain is out there outside the camera. — Corvus

A mountain could weigh a billion tonnes, so it is hardly surprising that the camera doesn't think it has a mountain in its memory card.

Even people only have a representation of a mountain in the minds, not the real thing. That really would be a load on their mind.

If X doesn't exist outside of RussellA, then X must exist inside of RussellA.
This sounds logically unsound. Groundless premise, and unsound conclusion. — Corvus

True. There is no reason to think that if something doesn't exist outside me then it must exist inside me.
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If X doesn't exist outside of RA? Under what ground do you claim that premise? — Corvus

An expression starting with "if" is not a premise. The expressions "X does exist outside me" or "X doesn't exist outside me" have the form of a premise.
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What do you mean by "X exist"? — Corvus

I see a bent stick. Seeing a bent stick is not proof that bent sticks exist in the world. The bent stick exists as an object in appearance whether or not a bent stick exists as an object in the world.

Similarly, I may see two things. Seeing two things is not proof that there are two things existing in the world.

Similarly, I may see a statue. Seeing a statue is not proof that there is a statue existing in the world.

Kant proposed that we have pure concepts of understanding prior to any possible experience. It would follow that it is the a priori Categories acting on the sensibilities that determine what we experience rather than our sensibilities alone determining what we experience.

For Kant, the experience of seeing a bent stick, the number two or a statue has been determined by the a priori categories acting on the sensibilities rather than by the sensibilities alone.

You have a mental space which is total darkness without your visual perception — Corvus

The light reflected from the stick in the water, passes through the water with the refraction, so it looks like double or bent in the water of the jug. — Corvus

For Kant, the pure intuition of space and time and the pure concepts of the understanding provide the possibility of experience, they don't provide the experience. As you say "You have a mental space which is total darkness without your visual perception".

For example, I may have the innate ability to perceive the colour red, but I cannot imagine the colour red in the absence of any faculty of sensibility, ie, the faculty of getting information through our senses about the world outside us.

You are correct to say that the stick that looks bent does not exist in any world outside me, but as I see a bent stick as clear as day, this means that if the bent stick doesn't exist in any world outside me, it must exist as a representation of a world that only exists inside me.

I agree that I cannot imagine any internal world in the absence of any faculty of sensibility, but because I do have the faculty of sensibility and do get information through my senses about the world outside me, the world I perceive is not directly of any world outside me but is a representation of any world outside me.

As the world I perceive is only a representation of any world outside me, the world I perceive is an internal world that is not necessarily the same as any world outside me.

I agree we cannot imagine a world in the absence of our faculty of sensibility. However, when we do perceive a world because of our faculty of sensibility, as it can only be a representation of any world outside us, the world we perceive cannot be directly of any world outside us, but can only be an internal world that is a representation of any world outside us.

They are external. You can think about it, because you have the concepts in your mind. — Corvus

Yes, this is what Kant is saying, that the pure concepts of understanding is a prior condition for experience.

IE, without these pure concepts of understanding I wouldn't be able to have the experience at all. For example, humans don't have a concept for the colour infrared as they don't have the innate ability to see infrared in the first place.

The street we see in our senses cannot be external to our senses, because the empirical concept of street is no more than the combination of pure concepts that are prior to any experience, and it is these pure concepts that determine the empirical concept of street, rather than anything external to the senses.
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How do you know your pain is real? What if it were just itchy skin, and you might have mistaken the itch sensation for pain? — Corvus

True, I may have misnamed my private sensation.

However, assuming I have correctly named my private sensation, my private sensation is real, even though it only exists in my mind.
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Close your both eyes totally and decidedly for 10 minutes, you will see nothing, but a total darkness. — Corvus

I agree that there must be something the other side of our senses, something that causes the sensations in our senses, because as you say, otherwise "we would see nothing".

I agree that we have the concept of street in our minds, because as you say "You can think about it, because you have the concepts in your mind."

The question is, what exactly is on the other side of our senses.

The Neutral Monist argues that on the other side of our senses there are no streets but only fundamental particles and fundamental forces in space and time.

The Direct Realist argues that on the other side of our senses are streets, cars and buildings.

What reasons are there to believe that the Direct Realist is right and the Neutral Monist wrong?

Just because you have a concept of something in your senses does not mean that the something you have a concept of exists on the other side of your senses. For example, when you see a stick bent in water, are you saying that on the other side of your senses there must be a bent stick in water?

How do you know you have a world internal to your mind? — Corvus

When you look at a world containing a street with cars and buildings, if this world was not internal to your mind, how would you be able to think about it?
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Is it a real world? — Corvus

Pain is real yet only exists in the mind, so why cannot your thought of a street with cars and buildings be real even though the thought only exists in your mind?
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How do you know it is the real world or just a imagination? — Corvus

Exactly, how do you know whether the street with cars and building only exists as a thought in your mind or exists outside the mind, when you only know about it through the senses?

Possible worlds, and worlds in your imagination and memories exist in your mind, but they don't cause your perception for the external world. — Corvus

How can you step outside of your concept or intuition? — Corvus

But that is what Kant is saying in the CPR, that the a priori intuitions of space and time and a priori pure concepts of the Understanding, ie the Categories, are conditions for the possibility of experience. Kant is saying that we cannot "step outside of your concept or intuition".

We perceive a world through our senses. You are assuming that there is one world in your mind and a different word that is external to your mind.

How do you know that the world you perceive in your senses has been caused by the world external to your mind rather than the world internal to your mind?

For example, when you perceive in your senses the colour red in the world, how do you know that the colour red exists in a world external to your mind rather than in the world internal to your mind?

Can you justify, for example, that the colour red exists in a world independent of any mind?
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Kant's first premise in the refutation is that he is conscious in time. Some might ask to prove how does he know he is conscious in time? What if he was dreaming, or hallucinating? — Corvus

I would agree with "I am conscious of my existence". The problem is, am I conscious of my existence at this one moment in time, or am I conscious of my existence through time.

If the latter, then I must be existing at two moments in time in order to be conscious of the passage of time. But such a possibility is beyond my powers of comprehension.

I don't think Kant's proof in the Refutation of Idealism is the best.