Schopenhauer's Transcendental Idealism

Agustino

I've been discussing this privately until now (@Heister Eggcart will now know what all this space talk is for >:O ), but I'm interested to get more ideas on the subject, so I'm coming out with it. As is known Schopenhauer borrows and adapts Kant's Transcendental Idealism, reducing the categories to (1) space, (2) time and (3) causality. Both Schopenhauer and Kant take space to be an a priori form of representation, applied by the cognitive faculties to the senses. They understand this to mean that the propositions of geometry are synthetic a priori judgements, and are therefore apodeictic - certain.

Space is not an empirical concept which has been derived from outer experiences. For in order that certain sensations be referred to something outside me (that is, to something in another region of space from that in which I find myself), and similarly in order that I may be able to represent them as outside and alongside one another, and accordingly as not only different but as in different places, the representation of space must already underlie them. Therefore, the representation of space cannot be obtained through experience from the relations of outer appearance; this outer experience is itself possible at all only through that representation — Kant

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 — Kant

Space is a necessary a priori representation that underlies all outer intuitions. 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. It must therefore be regarded as the condition of the possibility of appearances, and not as a determination dependent upon them, and it is an a priori representation that necessarily underlies outer appearances. — Kant

Space is not a discursive, or as one says, general concept of relations of things in general, but a pure intuition. For, firstly, one can represent only one space, and if one speaks of many spaces, one thereby understands only parts of one and the same unique space. These parts cannot precede the one all-embracing space as being, as it were, constituents out of which it can be composed, but can only be thought as in it. It is essentially one; the manifold in it, and therefore also the general concept of spaces, depends solely on limitations. It follows from this that an a priori intuition (which is not empirical) underlies all concepts of space. Similarly, geometrical propositions, that, for instance, in a triangle two sides together are greater than the third, can never be derived from the general concepts of line and triangle, but only from intuition and indeed a priori with apodeictic certainty — Kant

Schopenhauer follows Kant in conceiving of space (and geometry - the study of space) as transcendentally ideal:

"Perception, partly pure a priori, as establishing mathematics, partly empirical a posteriori as establishing all the other sciences [...] We demand the reduction of every logical proof to one of perception. Mathematics, on the contrary, is at great pains deliberately to reject the evidence of perception peculiar to it and everywhere at hand, in order to substitute for it logical evidence. We must look upon this as being like a man who cuts off his legs in order to walk on crutches [...] Whoever denies the necessity, intuitively presented, of the space-relations expressed in any proposition, can with equal right deny the axioms, the following of the conclusion from the premises, or even the principle of contradiction itself, for all these relations are equally indemonstrable, immediately evident, and knowable a priori" - Schopenhauer WWR Vol I §14-15

Now Schopenhauer's ontological idealism (and I refer here to the phenomenon/noumenon distinction largely) critically requires that the stage on which experience occurs be transcendentally ideal, for this stage being transcendentally ideal is what enables experience to be called the veil of Maya - appearance - and hence necessitates the noumenon, the thing-in-itself. Without space, time and causality (which constitute the stage in/on which experience occurs) being transcendentally ideal, the distinction between noumenon/phenomenon is in danger, as is idealism - for if at least part of the stage on which experience occurs is real, then Schopenhauer's ontological idealism is false.

Schopenhauer laughed at mathematicians trying to prove Euclid's Fifth Postulate, thinking that it is known from pure perception a priori:

"In fact, it seems to me that the logical method is in this way reduced to an absurdity. But it is precisely through the controversies over this, together with the futile attempts to demonstrate the directly certain as merely indirectly certain, that the independence and clearness of intuitive evidence appear in contrast with the uselessness and difficulty of logical proof, a contrast as instructive as it is amusing. The direct certainty will not be admitted here, just because it is no merely logical certainty following from the concept, and thus resting solely on the relation of predicate to subject, according to the principle of contradiction. But that eleventh axiom [11th axiom is equivalent in the context of Euclidean geometry with Euclid's Fifth Postulate] regarding parallel lines is a synthetic proposition a priori, and as such has the guarantee of pure, not empirical, perception; this perception is just as immediate and certain as is the principle of contradiction itself, from which all proofs originally derive their certainty. At bottom this holds good of every geometrical theorem" - Schopenhauer WWR Vol II §8

Non-Euclidean geometry came along, and it turns out that we have empirical proof that Euclid's Fifth Postulate is actually false, with regards to space as investigated by physics. Now the curvature of space cannot be perceived - we perceive objects in space - things in space curve - but how can space itself curve - that is anathema to our perception. What does this mean for Schopenhauer? Well for one, Euclid's Fifth Postulate isn't apodeictic, and neither is it a priori - contrary to what Schopenhauer thought. So Schopenhauer was wrong at least about this one truth of mathematics, and if he was wrong about this one, why should the other mathematical propositions that he was certain of be anymore certain than this? Indeed, it is his method that is wrong. Grounding mathematical propositions in a priori perception without appeal to experience is wrong. As Einstein said:

As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality

More importantly, there is one feature of space - its non-Euclideanness which is NOT a synthetic a priori, but rather a synthetic a posteriori, and therefore not transcendentally ideal, but empirically real - for it takes experience (physical experiments) for us to know of it. This means that at least part of the stage on which experiences occur isn't imposed on reality as a structure by our cognitive faculties, but rather is empirically real. If part of the stage is empirically real, then Schopenhauer's ontological idealism falls apart.

Can Schopenhauer's transcendental idealism and ontological idealism, along with the phenomenon/noumenon distinction be saved? Please note discussions of Kant's Transcendental Idealism with regards to non-Euclidean geometry isn't under question here - just Schopenhauer's.

Wayfarer

Now Schopenhauer's ontological idealism (and I refer here to the phenomenon/noumenon distinction largely) critically requires that the stage on which experience occurs be transcendentally ideal, for this stage being transcendentally ideal is what enables experience to be called the veil of Maya - appearance - and hence necessitates the noumenon, the thing-in-itself. — Agustino

I had the idea that Schopenhauer disagreed with Kant's usage of 'noumenon':

it was just this distinction between abstract knowledge and knowledge of perception, entirely overlooked by Kant, which the ancient philosophers denoted by noumena and phenomena. (See Sextus Empiricus, Outlines of Pyrrhonism, Book I, Chapter 13, ' What is thought (noumena) is opposed to what appears or is perceived (phenomena).' ) This contrast and utter disproportion greatly occupied these philosophers in the philosophemes of the Eleatics, in Plato's doctrine of the Ideas, in the dialectic of the Megarics, and later the scholastics in the dispute between nominalism and realism, whose seed, so late in developing, was already contained in the opposite mental tendencies of Plato and Aristotle. But Kant who, in an unwarrantable manner, entirely neglected the thing for the expression of which those words 'phenomena' and 'noumena' had already been taken, now takes possession of the words, as if they were still unclaimed, in order to denote by them his things-in-themselves and his phenomena.

The World as Will and Representation(vol. 1, Dover edition 1966, ISBN 0-486-21761-2 p. 476-477)

I would also question the metaphor of the intuition of space as a 'stage' on which 'things occur'.

Agustino

I would also question the metaphor of the intuition of space as a 'stage' on which 'things occur'. — Wayfarer

The metaphor isn't central. Space, time and causality form the framework in which representation necessarily occurs, according to Schopenhauer. This framework is provided by the cognitive faculty, and is not empirically real.

Janus

I had the idea that Schopenhauer disagreed with Kant's usage of 'noumenon': — Wayfarer

As I remember it his disagreement is with the notion of 'noumena' (plurality). For Schopenhauer it it should be understood as noumenon (singular=the Will). However, in relation to this in another thread Mongrel writes:

"He did want to say that the thing-in-itself is the Will, but he later backed off of that and agreed with Kant that it's unknowable."

I have no doubt that Mongrel is more familiar with Schopenhauer's philosophy than I am.

I would also question the metaphor of the intuition of space as a 'stage' on which 'things occur'. — Wayfarer

I agree. I think the OP is off-target with the idea that non-Euclidean geometries have any bearing on the validity of human a priori intuitions about the nature of space. The latter are certainly valid when it comes to perceptual space. We can describe non-Euclidean spaces mathematically and, obviously, geometrically, but we cannot visualize, for example, curvature of 3D space, and understand the idea non-mathematically, only in terms of analogies to curvature of 2D surfaces.

What the ontological significance of the existence of non-Euclidean geometries might be is not itself an uncontroversial matter.

Agustino

I think the OP is off-target with the idea that non-Euclidean geometries have any bearing on the validity of human a priori intuitions about the nature of space. — John

So it seems you see no problem with a priori intuitions being false. In trying to save Schopenhauer, you're already on the run - re-treating to saying something merely about human perception and not reality - which is what Schopenhauer and Kant have been attempting to do all along.

Did Schopenhauer mean that the truths of geometry are true only in-so-far as our perception goes? Or did he hold that, since our cognitive faculties structure the world via space, time and causality - these form the very structure of the world, and hence are apodeictic, and cannot be wrong or disproven empirically? Indeed it is this which makes them synthetic a priori judgements - their truth doesn't depend on experience.

Janus

I should add that for Kant, at least (I cannot speak for Schopenhauer) time, space and the twelve categories apply only to the empirical world (the world of perception). Mathematics and geometry thus would also apply only to the empirical world. If there is an anomaly between how we understand time and space intuitively and how empirical observations seem to suggest it 'really is': the question we are left with is What can that "how it really is" be independent of our perceptions and judgements?". Can it be anything for us? Can it be anything in itself? Can it be anything in itself, beyond what we might think it is in itself? It must always remain a speculative hypothesis, I would say.

Agustino

I should add that for Kant, at least (I cannot speak for Schopenhauer) time, space and the twelve categories apply only to the empirical world (the world of perception). Mathematics and geometry thus would also apply only to the empirical world. If there is an anomaly between how we understand time and space intuitively and how empirical observations seem to suggest it 'really is': the question we are left with is What can that "how it really is" be independent of our perceptions and judgements?". Can it be anything for us? Can it be anything in itself? Can it be anything in itself, beyond what we might think it is in itself? It must always remain a speculative hypothesis, I would say. — John

This is not a thread for discussing Kant's transcendental idealism - that should have been clear. You do perceive non-Euclidean space. Not directly. But you perceive its effects. If space is shaped as a sphere, you could drop an egg here, walk in a straight line, and return to the egg. That is perceiving space to be non-Euclidean. What you mean is that you cannot see space itself curving. But that is obvious - you'd need 4D eyes to see your 3D space curving. All that tells us is that our perception is limited and we have blind spots.

Agustino

Are there so few people fluent in Schopenhauer on these boards? :s So far no one with any knowledge whatsoever of Schopenhauer has replied in this thread. This kind of annoys me, because I want to solve this problem. Please reply only if you have read at least one volume of World as Will and Representation, otherwise it seems that it's impossible to have sufficient knowledge.

Agustino

I think the OP is off-target with the idea that non-Euclidean geometries have any bearing on the validity of human a priori intuitions about the nature of space. The latter are certainly valid when it comes to perceptual space. — John

I should add that for Kant, at least (I cannot speak for Schopenhauer) time, space and the twelve categories apply only to the empirical world (the world of perception). — John

I hate dealing with such misrepresentations as these - how is space as given in perception even Euclidean to begin with? Parallel lines in perception do meet at the horizon - just like parallel lines meet at the vanishing point in a painting. So perceptual space isn't even Euclidean to begin with. Our intuition of space - which isn't the same thing as perceptual space - is Euclidean.

Shawn

I believe Schopenhauer wouldn't disagree about curved space; but, would rather say that humans don't have the capacity to conceptualize it.

This is obviously a false assumption to make.

Agustino

This is obviously a false assumption to make. — Question

Which one?

Shawn

↪Agustino

That humans can't conceptualize curved space.

Buxtebuddha

Are there so few people fluent in Schopenhauer on these boards? — Agustino

Thoronkill, Schopenpower1, darthbarrasputum to name a few, I think.

Michael

That humans can't conceptualize curved space. — Question

I know I certainly can't. Maybe I'm lacking something.

Shawn

↪Michael

Maybe I should add "normal humans". Then there are the John Von Neumann's...

Mongrel

That humans can't conceptualize curved space. — Question

Curved relative to what?

Shawn

↪Mongrel

You tell me. I suspect curved relative to distant objects occupying the space-time continuum.

Mongrel

I suspect curved relative to distant objects occupying the space-time continuum. — Question

This is a curve. What are we using the x-y axes for?

Agustino

Thoronkill — Heister Eggcart

Yes that is true, but I've already been discussing with him. He is indeed the only one I'm aware of who is highly knowledgeable in the metaphysics of Schopenhauer

Schopenpower1, darthbarrasputum — Heister Eggcart

These two may be knowledgeable in Schopenhauer, but they are more pessimists, than they are transcendental idealists :P

Agustino

That humans can't conceptualize curved space. — Question

But we can conceptualise it very easily. We can't imagine it perceptually, but that's another story.

Agustino

This is a curve. What are we using the x-y axes for? — Mongrel

Y is time and X is space :-O - but what happens if the x, y, z axis are space, and time is the m axis ;) ? Can you see that? A system with four axes.

Agustino

Curved relative to what? — Mongrel

Curved in a 4th dimension, obviously.

Agustino

Thoronkill, Schopenpower1, darthbarrasputum to name a few, I think. — Heister Eggcart

In addition to those three, @The Great Whatever also deserves a mention. While he has moved beyond Schopenhauer, he has read him and has good understanding.

Buxtebuddha

↪Agustino

I bet you that my Eckhart knowledge trumps yours! :D

Agustino

↪Heister Eggcart

Eckhart Tolle? O:) >:O

Or Eckhart Meister? >:O In either case, I have no doubt about that lol - I never read either one.

Shawn

↪Mongrel

Sorry, my math skills ended at Calc III and so with it my hopes of becoming an engineer. Wish I got to do the fun stuff, like linear algebra...

Janus

↪Agustino

This is nonsense. We know via perception that parallel lines never really meet. Think of railway lines; they never meet and it would be disastrous if they did. You are conflating the idea that due to perspective effects parallel lines are perceived to appear to meet at the horizon, with the very different and erroneous idea that they are actually perceived to meet.

Agustino

This is nonsense. We know via perception that parallel lines never really meet. Think of railway lines; they never meet and it would be disastrous if they did. You are conflating the idea that due to perspective effects parallel lines are perceived to appear to meet at the horizon, with the very different and erroneous idea that they are actually perceived to meet. — John

Okay, then I seemingly misunderstand the way you are using perception. Would you like to define it more clearly, so that I can make future arguments based on it? Is perception what appears in my visual/sensory fields? If not, then what is perception in the way you use it?

Janus

↪Heister Eggcart

What about Maggotsino and Shyster Eggfart? If you don't have a good understanding of Schopenhauer yourself how could you possibly tell whether others do or not? :s

Janus

↪Agustino

Perception encompasses all the sensory modalities, including the somato-sensory and proprioception; it is not restricted to the merely visual, obviously.

Agustino

Perception encompasses all the sensory modalities, including the somato-sensory and proprioception; it is not restricted to the merely visual, obviously. — John

Is perception what appears in my visual/sensory fields? — Agustino

Yes, hence visual/sensory fields

The reason behind this thread is that Schopenhauer makes it clear in WWR that space, time and causality cannot apply to the thing-in-itself - indeed space time and causality apply only to the phenomenon/representation which is constituted through the principium individuationis. This for me is the only interesting transcendental idealism - Kant's is too shy, because Kant allows for a noumenal space, Schopenhauer doesn't. But if non-Euclidean geometry is the case, then there appears to be something to space that is not given directly in perception a priori - there appears that there is a noumenal space - this is catastrophic for Schopenhauer.

Schopenhauer's Transcendental Idealism

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