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.That's technically true, yes, but it doesn't affect my main point. — Thorongil
The noumenal just becomes unnecessary if the categories aren't ideal. Experience is no longer representation. — Agustino
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
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.Firstly, what exactly do you mean by "if the categories are not ideal"? — 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 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
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.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
Not according to Kant.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
You misunderstand - those geometric objects aren't objects at all - they are pure spatial relations. Geometry is the study of possible spatial relations.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
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
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?No, my main point was that space has no properties. — Thorongil
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.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
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).And what, pray tell, is a "pure spatial relation?" For what it's worth, Wikipedia disagrees with you. — Thorongil
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
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.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
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.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 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.So Christ was not actually God Incarnate, but just a man, according to you? — John
Why do you think so? Have you read Tolstoy's Gospel in Brief? It was one of Wittgenstein's favorite booksChristianity falls apart without trinitarian theology. — Heister Eggcart
Why are you laughing it's true mate! >:O I'm just being honest>:O >:O >:O — Heister Eggcart
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.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
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
They are possibilities which are determined to exist by the nature of space itself — Agustino
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
What allows those axioms to be possible if not space?No. Non/Euclidean geometry's axioms determine such things. Not space. — Thorongil
Why does space allow triangles to exist? Why isn't the nature of space such that triangles are impossible?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
Or a relationship.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
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?No. Non/Euclidean geometry's axioms determine such things. Not space. — Thorongil
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.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
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