I raised a similar point about this same issue here: https://thephilosophyforum.com/discussion/11642/the-critique-of-pure-reason-discussion-and-reading-group

I raised a similar point about this same issue here: https://thephilosophyforum.com/discussion/11642/the-critique-of-pure-reason-discussion-and-reading-group — darthbarracuda

Oh, I didn't know that. I'll check it out soon, thanks.

In the morning I take an empty coffee cup from the cupboard. It appears empty, but is actually filled with the earth’s atmosphere, which my coffee will displace. If I take my coffee cup beyond earth’s atmosphere, into the vacuum of empty space, my cup will truly be empty. I don’t see any problem in imagining the empty space in my coffee cup.
Empty space is defined and given context by the things which exist within it. If there were no things in empty space, then empty space itself, would not exist. It’s harder to imagine the absence of empty space, then it is to imagine the absence of things.

I don’t see any problem in imagining the empty space in my coffee cup. — Present awareness

But according to Kant there is only one space. Can you imagine (visualize) there being only one empty space?

If there were no things in empty space, then empty space itself, would not exist. — Present awareness

But didn't you say earlier that you could imagine the empty space of a coffee cup in a vacuum? How can you imagine what would not exist?

Yes, I believe there is only one space and ALL things exist WITHIN it.
The coffee cup itself, gives definition to the empty space within the cup and also the empty space around it. Something needs to be there, in order to see that which is not there.

So, I'm hoping someone more knowledgeable in Kant, like Mww, can help me out here (though of course anyone else is free to help) with the question in the title. — Amalac

I guarantee I'm not who you had in mind. I get the feeling that Kant was good at coming up with ideas people can chew on without ever really tasting. It seems like Russell was suggesting that perhaps it's time to spit out the gum and get onto something that can be right or wrong or otherwise progressed. We gave it a hundred years; the morality bit was good, but time to move on. At times I wonder how much was window dressing just so the church can feel like he wasn't a threat.

Kant's right hand glove thought experiment is meant to show the symmetry between left and right. In an empty a right-hand glove is introduced. Is this the same as a left-hand one? Had God a preference? Is He right-handed? It appears nowadays He indeed is (if only looking at our universe).

But what does Kant mean by empty space? (Einstein thinks globally empty space can't exist according to his equations) Can we imagine empty space? Is it just blakness? Are there coordinate axes? A flat metric? Can you imagine "the nothing", even no space? Space is not a thing. Is space subjective? Of course. If I dream I experience space. I could have dreamed 5 minutes, according to someone watching me sleep and dream (REM), while I have experienced hours days or even years.

So space, empty or filled, is a subjective thing, but it refers to objects and shows us how these objects interact. Empty space, empty ad infinitum, is timeless (see Feynman's one electron universe). There are no categories in this space. You can imagine introducing them but that takes away its emptiness. It must be completely dark in there. Try to imagine you float inter galactically.... Imagine...

I should emphatically deny that we can imagine space with nothing in it.

Russell wrote "I should emphatically deny that we can imagine space with nothing in it"

However, in the space above the table in front of me there is no apple.

In order for me to know that there is no apple in this space, I must also know that there is a space in which there is no apple.

If Russell was correct in saying that we cannot imagine space with nothing in it, then it would necessarily follow that it would not be possible to imagine that there is no apple within this space.

And yet, I know that there is no apple in the space above the table in front of me.

If I can imagine that there is no apple in the space above the table, then it necessarily follows that I must also be able to imagine the space in which there is nothing.

IE, Russell was wrong in saying that we cannot imagine space with nothing inside it.

However, in the space above the table in front of me there is no apple. — RussellA

But according to Kant there is only one space, so the space in which the apple is must be the same as the space in which the table is. So if you imagine there being nothing in the table, then space would still not be empty, since the table would be in space, unless you can imagine just that table, not being in space, and nothing else.

So the question is, can you imagine how Kant's unique space would look like when completely empty?

It must be completely dark in there. — SoftEdgedWonder

But can you actually visualize, in your mind's eye, there just being darkness? When I try to do that, I can't help but also imagine space as having edges of another color.

And why shouldn't we consider that the color of space is also in space?

Space has no color.

What color has space?

But can you actually visualize, in your mind's eye, there just being darkness? When I try to do that, I can't help but also imagine space as having edges of another color. — Amalac

That's because your eyes have edges. Space can be closed, finite, and without edges.

What color has space? — SoftEdgedWonder

Well, you said it would look like darkness, so wouldn't it be black?

That's because your eyes have edges. Space can be closed, finite, and without edges. — SoftEdgedWonder

Right, and therefore I can't imagine that space that's pure darkness according to you, and I can't imagine (visualize) a space without edges.

Also, according to Kant space is an “infinite given magnitude”. If the space in my mind's eye is finite, then I can't imagine (visualize) a space with an infinite magnitude, right?

Therefore, if this infinite space is the same as the empty space to which Kant is refering, then I can't imagine it being empty, in fact I can't even imagine it not being empty.

Therefore, if this infinite space is the same as the empty space to which Kant is refering, then I can't imagine it being empty, in fact I can't even imagine it not being empty. — Amalac

This is Einstein's view, more or less. Dark is not the same as black though. Black is the color of an object (or the it). It refers to an object. Space is no object.

Black is the color of an object (or the it). It refers to an object. Space is no object. — SoftEdgedWonder

Then in that space of pure darkness, there's a black object, and therefore that space is not empty, right?

Then in that space of pure darkness, there's a black object, and therefore that space is not empty, right? — Amalac

Wrong. The objects have no color. Only when connected to our minds they have color. Later I'll expand on this. We must go to the vet now. Puppy dog has a thing with her right hind leg. Maybe it's comedy, maybe not. I couldn't find anything and yesterday she started crying when I paid attention to another dog... :smile:

The objects have no color. Only when connected to our minds they have color. — SoftEdgedWonder

I agree, but I'm talking about an imagined object; if it looks like darkness in one's mind's eye, then it looks black, right? And therefore that space of darkness that I'm visualizing in my mind's eye is not empty.

If the imagined object finds itself in a dark space then the space imagined looks all black. No light coming out. The object is black too in the sense that no light comes from it. So there is only darkness in your imagination. But there is an object in it. And there is no difference between an imagined empty space and one with an object in it. What's the difference? You can feel no objects bumping into or hitting you in an empty space, while a space filled with black objects will become clear if you touch these objects.

By empty space, Kant refers to only that space which would bound the extension of a possible object.

“....We never can imagine or make a representation to ourselves of the non-existence of space, though we may easily enough think that no objects are found in it....”

Regarding Russell, who correctly denies the possibility of imagining space with nothing in it, for to do so is to imagine the non-existence of that which contains the subject thinking space as empty of all things, a contradiction, Kant stipulates that by objects space is thought to be empty of, are those external to he who is thinking, from which is derived the principle that space is no more than the necessary condition by which objects relate to each other as such, or, relate to us as mere phenomena.

“...in order that certain sensations may relate to something without me (that is, to something which occupies a different part of space from that in which I am); in like manner, in order that I may represent them not merely as without, of, and near to each other, but also in separate places, the representation of space must already exist as a foundation....”
————-

Kant's space is absolute, like Newton's, and not merely a system of relations.

Kant doesn’t call out space as absolute, and it certainly was nothing but a system of relations, but Russell invokes that representation, perhaps mistakenly, from this:

“....For, in the first place, we can only represent to ourselves one space, and, when we talk of divers spaces, we mean only parts of one and the same space. Moreover, these parts cannot antecede this one all-embracing space, as the component parts from which the aggregate can be made up, but can be cogitated only as existing in it. Space is essentially one, and multiplicity in it, consequently the general notion of spaces, of this or that space, depends solely upon limitations....”

In fact, in “The Metaphysical Principles in the Foundations of Natural Science”, Kant refutes Newton’s iteration of both absolute time and space, which ironically enough, predates Einstein by a century, and even though Einstein had precious little appreciation of Kant, at least in some respects.

Anyway....hope this helps.

By empty space, Kant refers to only that space which would bound the extension of a possible object — Mww

Tthe extention of possible objects?

So if you imagine there being nothing in the table, then space would still not be empty — Amalac

Continuing Russells' " The second metaphysical argument maintains that it is possible to imagine nothing in space, but impossible to imagine no space".

Possible to imagine nothing in space
It is true that the space above the table is bounded by the table, but being able to imagine the space above the table having nothing in it means that I can imagine "a space" with nothing in it.
So, if I can imagine "a space" of 1m size with nothing in it, there is no reason why I cannot imagine "a space" of 1km size with nothing in it, or "a space" of 1 light year size with nothing inside it. In fact, there is no reason why I cannot imagine "a space" of any size with nothing in it.

In this sense - "it is possible to imagine nothing in space"

Impossible to imagine no space
"Red" exists in two ways. There is the "red" that exists as 650nm independently and externally of the mind and there is our subjective concept of "red".
In the same way "space" exists in two ways. There is the "space" that exists independently and externally of the mind and there is our subjective concept of "space"
As we know that our subjective experience of "red" is different in kind to the physical nature of "red" outside our mind, we should expect that our subjective experience of "space" to be different in kind to the physical nature of "space" outside our mind.

As we are born with an innate concept of "red", we are born with an innate concept of "space", ie, we don't need to learn either of them.
As Kant wrote: "Space is a necessary a priori representation that underlies all other intuitions"

Being born with an innate concept of "space", our concept of "space" is subjective.
As Kant wrote: "Space is not something objective and real, nor a substance, nor an accident, nor a relation; instead, it is subjective and ideal, and originates from the mind’s nature in accord with a stable law as a scheme, as it were, for coordinating everything sensed externally". Inaugural Dissertation Ak 2: 403

Kant is not saying that we don't observe the world (as he uses the words "sensed externally" and "intuition"), but he is saying that what we think we observe is determined by the innate nature of our brain.
Kant wrote: "Space and time are merely the forms of our sensible intuition of objects. They are not beings that exist independently of our intuition (things in themselves), nor are they properties of, nor relations among, such beings.

Regardless of the degree of correspondence with any "space" existing independently of us, as we are born with an innate concept of "space", it would be impossible for the brain to ignore something that was a part of it's own structure.

In this sense, it is "impossible to imagine no space"

Tthe extention of possible objects? — Nummereen

Yes. Possible for us. Has nothing to do with the possibility of objects in themselves.

Everything Kantian has to do with us, without exception.

Yes. Possible for us. Has nothing to do with the possibility of objects in themselves. — Mww

What are possible extentions? Interactions with us? Our perceptions os space immersed, saucaged, objects? What's the difference between a dreamt space and a perceived space while waking?

Sorry....don’t know the best way to respond to those questions.

So, if I can imagine "a space" of 1m size with nothing in it, there is no reason why I cannot imagine "a space" of 1km size with nothing in it, or "a space" of 1 light year size with nothing inside it. In fact, there is no reason why I cannot imagine "a space" of any size with nothing in it. — RussellA

There is a reason, namely the limited space in your mind's eye. Unless you mean merely that we can conceive of such a space.

Kant isn't saying that we can imagine a space with nothing in it but rather that we can imagine the single, unique space with nothing in it. And that space must not itself be an object, since otherwise we would run into one of Aristotle's paradoxes: that space would need to be contained in another space, and this last space would have to be contained by yet another space, and so on in infinitum.

I doubt whether this is really impossible as Aristotle and (I think?) Kant contend, but for the moment I want to focus on whether this is consistent with the rest of Kant's philosophy.

So, to say that a cup is empty does not imply that the cup is a space, since the cup is an object, and therefore not the space to which Kant refers.

And if the empty space to which you refer in that example is not the cup itself, then it is not something that can be visualized.

And so, if you cannot in fact visualize it, that proves that absolute empty space cannot be visualized (imagined) by us in the actual world, even if there were some possible world in which we could imagine a single, absolute empty space.

Also, one can't do away with boundaries, which presuppose a space with something in it, and is therefore not empty. Unless we were to claim that the space in our mind's eye is infinite, which seems strange, since surely its size must be about the same as that of our visual field, which is bounded (though it is difficult to point out where exactly it ends).

I know Wittgenstein said that our visual field is in some sense endless, but I'm not sure what he meant by that.

As we are born with an innate concept of "red" — RussellA

I disagree with this, surely an impression of at least one red thing is needed to apprehend the notion of red, and so a man born blind has no ideas of colors (not without special training anyway, I'm thinking of creating a thread about this other subject some day). I don't see why, in principle, the same could not be true about space.

Kant is not saying that we don't observe the world (as he uses the words "sensed externally" and "intuition"), but he is saying that what we think we observe is determined by the innate nature of our brain.
Kant wrote: "Space and time are merely the forms of our sensible intuition of objects. They are not beings that exist independently of our intuition (things in themselves), nor are they properties of, nor relations among, such beings. Critique of Pure Reason (A26, A33) — RussellA

Ok.

Regardless of the degree of correspondence with any "space" existing independently of us, as we are born with an innate concept of "space", it would be impossible for the brain to ignore something that was a part of it's own structure.

In this sense, it is "impossible to imagine no space" — RussellA

I don't disagree with that last claim, I only doubt that we can imagine (that is: visualize in the mind's eye) space with nothing in it.

Regarding Russell, who correctly denies the possibility of imagining space with nothing in it, for to do so is to imagine the non-existence of that which contains the subject thinking space as empty of all things, a contradiction, Kant stipulates that by objects space is thought to be empty of, are those external to he who is thinking, from which is derived the principle that space is no more than the necessary condition by which objects relate to each other as such, or, relate to us as mere phenomena. — Mww

But if Russell is correct in pointing out that we can't imagine space with nothing in it, wouldn't that refute Kant's argument that we can imagine nothing in space, but not that there should be no space? Since that is the basis of the argument.

Or did Russell misinterpret what Kant meant by “imagine”?

in order that certain sensations may relate to something without me (that is, to something which occupies a different part of space from that in which I am); in like manner, in order that I may represent them not merely as without, of, and near to each other, but also in separate places, the representation of space must already exist as a foundation....” — Mww

Russell had a different counterargument against this other argument, but that would take us away from the question guiding this thread, I think.

In fact, in “The Metaphysical Principles in the Foundations of Natural Science”, Kant refutes Newton’s iteration of both absolute time and space, which ironically enough, predates Einstein by a century, and even though Einstein had precious little appreciation of Kant, at least in some respects. — Mww

I admit I haven't read that work, so I'll have to look into that.

Anyway....hope this helps. — Mww

It sure did, thanks.

But if Russell is correct in pointing out that we can't imagine space with nothing in it, — Amalac

He is not correct. If I imagine an empty fish bowl in intergalactic space I imagine an empty space.

space with nothing in it — Amalac

Is Kant referring to the whole of space or only a part of space

Kant wrote "One can never forge a representation of the absence of space, though one can quite well think that no things are to be met within it."

I agree with Mww, who wrote "By empty space, Kant refers to only that space which would bound the extension of a possible object."

However, whether Kant is referring to the whole of space or only a part of space is irrelevant to the point that he is making.

Kant's position is important because it is at odds with Leibniz and the relationist claim that the idea of space existing independently of objects is incoherent.

IE, Kant is making the point that space can exist independently of there being any object within it, regardless of whether this is the whole of space or just a part of space.

Can one imagine a space with nothing in it

(Defining space as a continuous area or expanse which is free, available, or unoccupied rather than everything beyond the Karman Line.)

Russell wrote: "I should emphatically deny that we can imagine space with nothing in it"

If Russell is correct in saying that we cannot imagine a space with nothing in it, as space has by definition nothing in it, then it follows that Russell was saying that we cannot imagine space.

Because, if Russell is correct in that we cannot imagine space, then it would follow that when we observe the world we would observe all objects touching each other.

However, this is clearly not the case

IE, when we observe that in the world that there is space between objects, then it follows that we must be able to imagine a space that has nothing in it.

wouldn't that refute Kant's argument that we can imagine nothing in space — Amalac

It’s a fine line between your imagine nothing in space, and Kant’s “think space with no objects in it”. If it is true that to think space with nothing at all in it, is self-contradictory, it is safe to assume that is not what Kant meant by thinking space with no objects. One should then allow himself to understand, within the context of the section in which Kant’s statement is found, he meant that we must grant the necessity of space as an intuition even if there are no objects contained in it. This in contradistinction to the absolute impossibility of intuiting an object if it is not contained in a space.

Or did Russell misinterpret what Kant meant by “imagine”? — Amalac

It is reasonable to suppose Russell was familiar with Kant’s productive/reproductive double-sense of the faculty of imagination. I don’t see any need of this confusion, when self-contradiction serves to negate the notion of space completely empty of all objects.

In addition, regardless of imagination. there is also the question of whether Russell took space as a conception, which in itself doesn’t include objects** indicating that space could be conceived as completely empty, or, as an intuition, which only manifests because no object whatsoever can be a phenomenon for us without it, which indicates either space cannot be completely empty, or, we never intuit phenomena. The latter being utterly absurd serves to justify the former.
(**Nod to )