That's hardly relevant; it is well known that there are still armies of Kant scholars arguing over how to interpret his ideas.

But regardless, if you're not such a Kantian, then yes, if NE geometry refutes S it would also refute K. And it quite simply does as far as I see at the moment - if the cognitive faculties provide a priori the forms in which experience is given, then no experience can contradict those forms - because by default they are provided on an a priori basis, and since experiences are constructed in those forms, they cannot but share those forms. If no experience can contradict those forms, and intuition gives us, on an a priori basis, an Euclidean space, then experience does contradict those forms - as seen in physics. Thus we must reject the premise that the forms are a priori, or we must reject the premise that our pure intuition is of an Euclidean space. Take your pick.

Your only other escape is to run away "Ahh but Kant is talking just about our perception" but again we do perceive non-Euclideanness in the world. So where is that non-Euclideanness coming from? From the things-in-themselves? Then good luck with your noumenal space ;)

This is what I was referring to when I said Kant derives the a priori of space and time from empirical observation.

For Kant, the logically necessary is a means of explaining representations. For the computer in front of me to exist and be observed, for example, it needs a place in space and time, and the thing-in-itself to be represented, else I couldn't exist observing my computer. Under Kant, the a priori is drawn out of a perceived need to account for empirical observations.

For Schopenhauer, the a priori doesn't work in this way. Rather than an account explaining empirical observations, a priori truths (e.g. space, time, causality, the thing-in-itself) are their own logical objects.

Any "vendetta" is a product of your own imagination. — John

Yes, but as Schopenhauer told you, it takes a genius to imagine from the very imperfect information one has, to what is actually the case X-)

The Will is closer to thing-in-itself than Representation as it's only conditioned by one of the categories, time, and not the other ones. However, later Schopenhauer disavows and walks back on the identification of Will as Thing-in-itself and returns to the thing-in-itself being unknown - an unknown which is nevertheless non-dual.

And there is no quadruple aspect theory. Will is the ground of the phenomenon. Platonic Ideas are encounters with and glimpses of the thing-in-itself through art, or mystical experiences. The thing-in-itself is the unknown ground or source of the Platonic Ideas and of the Will. So it's still double aspect - Phenomenon composed hirearchically of Will and then the other Representations, and Thing-in-itself. — Agustino

If the thing in itself is the noumenal and Will is not it, but rather merely "close to it", then is Will phenomenal? Obviously it cannot be part of the noumenal according to Schopenhauer, because the noumenal cannot have parts (according to both Schopenhauer and Kant).

It must be part of the phenomenal if it is "conditioned" by "only one of the categories", or even one of the categories, because the categories, although they are themselves transcendental "condition" only the phenomenal, not the noumenal.

And what about the platonic ideas? are they noumenal? If they are then how can there be more than one idea. And if all four the noumenal (timeless) the ideas ( timeless) the Will ( temporal only) and the phenomenal ( temporal and spatial) are different form one another, then how are there not four ontological categories?

Unless you can give cogent answers to these questions you should be beginning to see why Schopenhauer's ontology is a hopeless mess that doesn't need to be refuted by any geometry; it refutes itself.

But you have not shown that any experience, as opposed to merely inferences from mathematical models and observations, does refute Euclidean geometry. We infer that space is curved; we do not experience it as curved.

If the thing in itself is the noumenal and Will is not it, but rather merely "close to it", then is Will phenomenal? — John

Ultimately yes, hence why you experience it in time.

It must be part of the phenomenal if it is "conditioned" by "only one of the categories", or even one of the categories, because the categories, although they are themselves transcendental "condition" only the phenomenal, not the noumenal. — John

Yes, your brain is working well in logical deductions.

And what about the platonic ideas? are they noumenal? If they are then how can there be more than one idea. — John

They are glimpses of the noumenon, they are obviously still individuated, hence why they are not thing-in-itself. The thing-in-itself qua thing-in-itself is not experienced as an empirical state. The Platonic ideas can be experienced, but not as phenomenon (the subject-object distinction breaks off during such experiences - they are merely the grades of the objectification of the thing-in-itself).

And if all four the noumenal (timeless) the ideas ( timeless) the Will ( temporal only) and the phenomenal ( temporal and spatial) are different form one another, then how are there not four ontological categories? — John

They are different in degree of objectification/individuation of the thing-in-itself. One substance

Unless you can give cogent answers to these questions you should be beginning to see why Schopenhauer's ontology is a hopeless mess that doesn't need to be refuted by any geometry; it refutes itself. — John

That was a quick job. I'm waiting for another one.

I already know you think you are a genius. If only you could demonstrate it. :-}

But you have not shown that any experience, as opposed to merely inferences from mathematical models and observations, does refute Euclidean geometry. We infer that space is curved; we do not experience it as curved. — John

Yes you do experience its effects. And if space isn't curved, and space is an a priori form provided by the mind, where the hell are those curved effects coming from? Unless you can answer this question you can say bye bye to your Kantianism.

Get a room you two. Preferably one where I can still watch.

delete - was off topic >:O

You haven't given any cogent account at all of how something completely timeless and undifferentiated can manifest itself in either individual spatio-temporal forms, or in timeless forms or in a temporal Will or in temporal wills. This is why I reject any form of monism as incoherent. The Christian idea of God as Trinity is far more coherent. In that conception God is both immanent and transcendent. This is also the basis of my criticism of Spinoza's philosophy, insofar as it wants to say that God is natura naturans but not natura naturata, because the latter is immanent and the former (as something like the laws of nature) is transcendental.

You haven't given any cogent account at all of how something completely timeless and undifferentiated can manifest itself in either individual spatio-temporal forms, or in timeless forms or in a temporal Will or in temporal wills — John

Hegel regurgitation!

I have given a means for how it does so. It does so via the forms of space, time and causality.

I'd go one further. Sometimes we do perceive it outright. We draw examples of it all the time. It's even possible someone could see it out in the world. All it would take in an aura of plane, lines, etc. in the right places of someone's visual experience-- much like seeing any other part of the world.

We experience effects, which we (perhaps incorrectly) infer to be due to curvature of space. All inferences are fallibilistic. We do not experience space as curved.

I'd go one further. Sometimes we do perceive it outright. We draw examples of it all the time. It's even possible someone could see it out in the world. All it would take in an aura of plane, lines, etc. in the right places of someone's visual experience-- much like seeing any other part of the world. — TheWillowOfDarkness

Yes we can. Have a look here ;) it's called a convex mirror

We experience effects, which we (perhaps incorrectly) infer to be due to curvature of space. All inferences are fallibilistic. We do not experience space as curved. — John

Right so if they're not due to the curvature of space, what the fuck are they due to?! :s

But where in an utterly undifferentiated timeless unity do those forms come from? This is the perennial Parmenidean problem with monistic conceptions of reality.

But where in an utterly undifferentiated timeless unity do those forms come from. This is the perennial Parmenidean problem with monistic conceptions of reality. — John

You're trying to ask what causes the thing-in-itself to be so and so - that's stupid, nothing causes it, because causality applies only for the objectification of the thing-in-itself (the empirical states) not for the thing-in-itself qua thing-in-itself.

How would I know? Perhaps God put them there to confuse us...or perhaps the science is simply wrong and will be corrected in the future, when we have more information (if the species can manage to survive that long).

You haven't given any cogent account at all of how something completely timeless and undifferentiated can manifest itself in either individual spatio-temporal forms, or in timeless forms or in a temporal Will or in temporal wills. This is why I reject any form of monism as incoherent. — John

The monism itself is the answer. In being timeless and undifferentiated,all of the many changes in the world have no impact on how it is expressed. If individual spatio-temporal forms affected it, it would be differentiated and no longer by timeless.

But where in an utterly undifferentiated timeless unity do those forms come from. — John

It cannot come for anywhere. If it were, it would be a differentiated state coming out of another differentiated state. The timeless monism, Substance, the-thing-in-itself, does not come from anywhere. It always so, no matter change or time-- that's why it's timeless.

How would I know? Perhaps God put them there to confuse us...or perhaps the science is simply wrong and will be corrected in the future, when we have more information (if the species can manage to survive that long). — John

The old trope - there's no explanation but I'll go on believing it >:O

The monism itself is the answer. In being timeless and undifferentiated,all of the many changes in the world have no impact on how it is expressed. If individual spatio-temporal forms affected it, it would be differentiated and no longer by timeless. — TheWillowOfDarkness

John has forgotten that the principle of causality which he presupposes in asking the question applies only to the phenomenon (empirical reality) not to the thing-in-itself.

delete - was off topic — Agustino

Too late, I already voyeur'd what you originally wrote. It got me uncontrollably hard, too, goddamn it.

Now you are saying that we cannot know anything at all about the thing in itself, a position that you were earlier criticizing Kant for upholding. This is where faith steps in, and reason bows out. The conceptions we have of the thing in itself must all be inadequate, but some may seem more satisfying to reason than others.

Just the opposite-- he saying we can know the thing-in-itself. It just doesn't have an empirical form, so any attempt to describe in such terms fails (which Kant understands) and that any question asking for its empirical form is incoherent (which the Kantians do not understand).

I haven't anywhere stated that I think the thing in itself is or is not timeless. It might be both temporal and eternal (immanent and transcendent) which I think would be a more satisfying and explanatory view. Causality has nothing to do with the issue. Either the thing in itself gives rise to the world we experience or it is utterly disconnected from it; which would make it irrelevant to us. Or it doesn't exist at all, in which case we are left with phenomenalism.

Of course, in a sense if there is a thing in itself then we do know it in all our experience, since all our experience arises from it. That is uncontroversial. But we do not know the nature of it; we do not know what we know of it, in other words.

In case you hadn't noticed I'm ignoring any ad hominems directed at me and trying not to get drawn into exchanging personal insults. I'm really only interested in critiquing the ideas.