That's technically true, yes, but it doesn't affect my main point.

That's technically true, yes, but it doesn't affect my main point. — Thorongil

Yes it does, because lines not being material objects don't show up in your experience a posteriori at all. They are possible solely because of the nature of space that is given in your intuition. Thus geometry studies space as given in the intuition. Lines apply to material objects only as limiting conditions - they determine the spatial relations possible among material objects. But lines, by virtue of having no thickness for example, are constructs of your spatial intuition - they literarily are nothing except a spatial relation.

The noumenal just becomes unnecessary if the categories aren't ideal. Experience is no longer representation. — Agustino

Firstly, what exactly do you mean by "if the categories are not ideal"?

It doesn't work for Kant either, just for corrections of Kant. Kant certainly didn't allow for it. Space is ideal for Kant through and through. Non-Euclideanism disproves unaltered Kant as well. — Agustino

Kant thinks exactly this as well, are you kidding me? This is quotes from Kant in the OP — Agustino

Kant is a very subtle thinker, and there is no general consensus among scholars as to exactly what his stance on the kind of transcendental empirical realism I have been recommending would be. There are scholars who actually interpret Kant as a transcendental realist despite Kant's own self-identification as a Transcendental Idealist. I mean, the empirical must contain, independently of our actual experience properties of its own which we may later discover, or maybe never discover, right? So space could be real in this kind of sense that its properties are not exhausted by what is intuitive self-evident to the human mind.

And that is what I meant by asking whether it is, exhaustively, a function of the human mind; the human mind considered here in terms of what is intuitively obvious to us. It's hard to see how Kant could deny that the empirical world consists in countless things of which the human mind, in terms of the totally of human experience up till now, has not been, is not, or will not ever be aware. I think that Kant's meaning in saying that space is a function of the human mind, is to say that it is a function of the transcendental ego, the totality of which we cannot be intuitively aware. So, what conditions human experience might be thought as ideal, and yet still independent of any and all human experience and intuition.

Seems like Kant has become quite relevant to this thread, after all.
8-)

No problem.
:)

No, my main point was that space has no properties. I was thinking of physics when I said material objects. Geometry, you are right, deals with mental objects like lines and triangles. But these are imagined as being in space, just as material objects are perceived to be in space. So in both cases, space is being presupposed.

Firstly, what exactly do you mean by "if the categories are not ideal"? — John

The categories are provided by the mind, by the understanding, they are pure concepts and therefore they are ideal... In addition to these I include space and time which are also ideal and are forms of cognition provided by the mind.

I mean, the empirical must contain, independently of our actual experience properties of its own which we may later discover, or maybe never discover, right? So space could be real in this kind of sense that its properties are not exhausted by what is intuitive self-evident to the human mind. — John

The empirical is NOT space, but what is found within space. Kant makes this very clear in the paragraphs I have quoted to you - there is no doubt that for him space is transcendentally ideal fully and completely. He makes it very clear - he says space is not empirical.

I think that Kant's meaning in saying that space is a function of the human mind, is to say that it is a function of the transcendental ego, the totality of which we cannot be intuitively aware. — John

This is not Kant's meaning at all. If it was, Kant would not have thought that the propositions of geometry are synthetic a prioris and hence certain. It seems to me that your love for Kant is getting in the way of your quest for truth. Kant makes it very clear that space is not empirical. That space is not empirical means that there cannot be empirical truths about the nature of space, that much is certain.

So space could be real in this kind of sense that its properties are not exhausted by what is intuitive self-evident to the human mind. — John

Not according to Kant.

No, my main point was that space has no properties. I was thinking of physics when I said material objects. Geometry, you are right, deals with mental objects like lines and triangles. But these are imagined as being in space, just as material objects are perceived to be in space. — Thorongil

You misunderstand - those geometric objects aren't objects at all - they are pure spatial relations. Geometry is the study of possible spatial relations.

I mean this nonsense:

On the other hand something like this seems that it might work if we allow a triune noumenon (God) Who is both immanent and transcendent and drop the notion of absolute monism. We should also drop the idea of the noumenal as blind (Schopenhauer) or deterministic or necessitous (Spinoza). — John — Agustino

This is the predominant Christian idea of God: Father, Son and Holy Spirit, three-in-one. I'm puzzled that you would say it is nonsense, since I have been under the impression that you considered yourself to be a Christian.
:s

No, my main point was that space has no properties. — Thorongil

If space has no properties, then how come lines are possible in it? How come circles are possible? How come any geometric figure is possible in it? What governs what is possible in space if not its properties? What governs what space is, if not its properties?

they are pure spatial relations — Agustino

And what, pray tell, is a "pure spatial relation?" For what it's worth, Wikipedia disagrees with you.

This is the predominant Christian idea of God: Father, Son and Holy Spirit, three-in-one. I'm puzzled that you would say it is nonsense, since I have been under the impression that you considered yourself to be a Christian.
:s — John

I do but I'm not big on the Trinity at all. I still consider One God to be more significant than the Trinity - the Trinity is a secondary development if you want out of that. Like one substance with multiple attributes.

And what, pray tell, is a "pure spatial relation?" For what it's worth, Wikipedia disagrees with you. — Thorongil

They are possibilities which are determined to exist by the nature of space itself - by the properties of space. If space is 1 dimensional, there can be no relationships which we identify as triangles. That space simply doesn't allow them. So space determines, by its properties, what relationships are possible in it (hence what geometrical figures are possible, and what their properties must be).

For example, space being non-Euclidean determines that the angles in a triangle can add up to something different than 180 degrees, and inversely - space being Euclidean determines that the angles in a triangle necessarily add up to 180 degrees. The properties of geometric objects are the properties of space itself

I think that passage has the genesis for "saving" Schopenhauer's approach in a way, though it may more of a clarification of term that sort of breaks from the original intent. What exactly is space? Or time? Or casualty? Not any particular state we have observed. Each is "a priori," a truth no matter what the world might be doing at any moment. I think our investigation much begin here.

You stared with the challenge that an empirical space, time and causality poses to a priori nature claimed by Schopenhauer. My question is: does this challenge even make sense? Is Schopenhauer actually talking about seeing the curvature of space-time or the states which make-up the world?

No doubt this empirical space, time and causality is true, but that means nothing if Schopenhauer is talking about something else entirely. I think a priori space, time and causality are different things to the empirical forms we encounter. Unlike what we observe, a priori space, time and causality do not say anything about the world. They are entirely in the logical realm by their definition. Not a state of the world at all, but rather a particular logical expression of the world: the logic of empirical states belonging to space,time and causality.

Seems to me the ideality of space, time and causality only becomes an issue if it confused with empirical space, time and causality,

The empirical is NOT space, but what is found within space. Kant makes this very clear in the paragraphs I have quoted to you - there is no doubt that for him space is transcendentally ideal fully and completely. He makes it very clear - he says space is not empirical. — Agustino

Again this is an interpretive subtlety I would say. Space is not an empirical object, but the empirical is spatial. If there are parts of the empirical that currently lie beyond human experience, which I think Kant would certainly have agreed with, then they must be spatial right? It is in that sense that spatiality is not dependent on any or all individual human perceptions or intuitions. IT is not dependent on the mind in this sense. It is the presence of ambiguities like this in Kant , that are due to the enormous conceptual difficulties of the subject matter, that have allowed for the controversies in Kant scholarship about what it is that he actually meant; 'was he actually a kind of transcendental realist?' and so on.

Right but what is a priori space? A priori space doesn't say anything about the world, but it certainly says something about the possibilities that exist in the world, and this is precisely the problem. Since Kant and Schopenhauer identify a priori space with the Euclidean space given in our intuitions, what is possible in such a space, turns out to be more limited than what is actually possible in space as we encounter it.

So Christ was not actually God Incarnate, but just a man, according to you?

If there are parts of the empirical that currently lie beyond human experience, which I think Kant would certainly have agreed with, then they must be spatial right? — John

No, since space is a form of knowledge - that which makes knowledge and experience possible - there cannot be any spatial knowledge to be gained by experience (hence why geometry is necessarily synthetic a priori and never synthetic a posteriori - Kant was very clear about this). If knowledge of space is gained by experience then that which was supposed to make experience possible in the first place was not known by the very mind which structured experience according to it - that's a contradiction.

It is the presence of ambiguities like this in Kant , that are due to the enormous conceptual difficulties of the subject matter, that have allowed for the controversies in Kant scholarship about what it is that he actually meant; was he actually a kind of transcendental realist and so on. — John

I think if we are loyal to Kant things are much more clear. If we try to see how good that Kantian approach is or can be, that is an entirely different question, and then you can take your interpretations, however unlikely and impossible they actually are for Kant himself, and use them. Indeed that's what pretty much all people who still call themselves Kantian have done.

Christianity falls apart without trinitarian theology.

Kant and Schopenhauer both make the mistake of thinking that what we can perceive is all that can exist, and if we can't perceive it, it can't exist. The curvature of space we can't perceive directly - we only notice its effects.

So Christ was not actually God Incarnate, but just a man, according to you? — John

I personally believe that Jesus is God in Spirit, and Man in flesh. But I wouldn't personally be very aghast at a Tolstoy re-reading of the Gospel as he does it in Gospel in Brief if you know it, where Jesus is just a man, given birth by a woman with an unknown father in the flesh. As I have said however, I believe Jesus is God in Spirit and Man in flesh but fuck if I know what that is supposed to actually mean. I'm a theist ignostic on this point.

fuck if I know what that is supposed to actually mean. — Agustino

>:O >:O >:O

Christianity falls apart without trinitarian theology. — Heister Eggcart

Why do you think so? Have you read Tolstoy's Gospel in Brief? It was one of Wittgenstein's favorite books

>:O >:O >:O — Heister Eggcart

Why are you laughing it's true mate! >:O I'm just being honest

You sound like John trying to talk about the thing-in-itself. A priori space is... a priori space: the logical expression of space itself. It doesn't tell us anything about the world and it's not meant to. All it deals is the logic of space.

In the case of Euclidean space, one has the logic of Euclidean space. The question of what's possible in the space doesn't make sense. Logic of Euclidean space doesn't apply outside itself and it doesn't need to. Many other things are possible of course, different logics which are true and may be used, but that doesn't affect Euclidean logic. It just means sometimes we need a different logic to talk about what we want to.

You sound like John trying to talk about the thing-in-itself. A priori space is... a priori space: the logical expression of space itself. It doesn't tell us anything about the world and it's not meant to. All it deals is the logic of space.

In the case of Euclidean space, one has the logic of Euclidean space. The question of what's possible in the space doesn't make sense. Logic of Euclidean space doesn't apply outside itself and it doesn't need to. Many other things are possible of course, different logics which are true and may be used, but that doesn't affect Euclidean logic. It just means sometimes we need a different logic to talk about what we want to. — TheWillowOfDarkness

Okay but now you've evacuated the whole Kantian concept of a priori space of its meaning as it was given by Kant and Schopenhauer. Space being ideal for them guaranteed the truths of geometry - it made them synthetic a prioris. They applied to any and all experiences simply because the mind structured all experiences within Euclidean space. And it didn't guarantee the truths within the reference frame of Euclidean geometry only, it guaranteed them it terms of their applicability to the empirical world, precisely because the empirical world is structured to be, by the mind, in Euclidean space.

If space has no properties, then how come lines are possible in it? How come circles are possible? How come any geometric figure is possible in it? What governs what is possible in space if not its properties? What governs what space is, if not its properties? — Agustino

I'm not sure what you're asking here. Your last question seems to commit the category mistake I listed above. Nothing can "govern" space.

They are possibilities which are determined to exist by the nature of space itself — Agustino

A possibility is a thing that may happen or be the case, so you're saying that a line is a thing, which is what I said. It is an object, albeit a mental object.

space being non-Euclidean determines that the angles in a triangle can add up to something different than 180 degrees, and inversely - space being Euclidean determines that the angles in a triangle necessarily add up to 180 degrees — Agustino

No. Non/Euclidean geometry's axioms determine such things. Not space.

I haven't read that Tolstoy work. If you believe Christ was "God in spirit, Man in flesh" in a sense that other humans are not, then i can't see how that would not be to believe in the trinity. You say you don't know what your belief means, but what is the problem with that? People believe in the Trinity, or less ambitiously, the noumenal, or monistic substance or mind-independent physical reality or whatever; and I'm quite sure they don't really know what those really mean either.

No. Non/Euclidean geometry's axioms determine such things. Not space. — Thorongil

What allows those axioms to be possible if not space?

I'm not sure what you're asking here. Your last question seems to commit the category mistake I listed above. Nothing can "govern" space. — Thorongil

Why does space allow triangles to exist? Why isn't the nature of space such that triangles are impossible?

A possibility is a thing that may happen or be the case, so you're saying that a line is a thing, which is what I said. It is a object, albeit a mental object. — Thorongil

Or a relationship.

No. Non/Euclidean geometry's axioms determine such things. Not space. — Thorongil

And what determines the possibility of non-euclidean axioms (and Kant and Schopenhauer have both critiqued the notion of axiom actually) if not the nature of space itself? When we postulate axioms, don't we actually refer to a specific kind of space?

For sure, but that alludes to the deeper problem with their approach. "Cannot perceive" is an incoherence. Perception is always an actual state, the presence of an experience of something.

To try to say one cannot perceive it to think that one's idea of the world must necessarily happened, that somehow the thing is question is predetermined never to be perceived. It is to ignore the necessity of possibility.

I haven't read that Tolstoy work. If you believe Christ was "God in spirit, Man in flesh" in a sense that other humans are not, then i can't see how that would not be to believe in the trinity. You say you don't know what your belief means, but what is the problem with that? People believe in the Trinity, or less ambitiously, the noumenal, or monistic substance or mind-independent physical reality or whatever; and I'm quite sure they don't really know what those really mean either. — John

I think they should stop believing in them then. I believe it simply based on the authority of the Scripture, and recognise that I can't understand it.