Kant is thoroughly confused and muddled up. Schopenhauer clarifies and redeems Kant for the most part, while also in some way maybe also critically deforming the Kantian project. In either case, Schopenhauer is encyclopaedic in the way K will never hope to be. — Agustino

How is Kant "confused and muddled up" ? How does Schopenhauer "clarify and redeem Kant"? It's one thing to make such sweeping claims, but they are completely vacuous unless you can provide some detail and explanation of the purported grounds upon which you make them.

This thread isn't about how Schopenhauer applies a corrective to Kant and it would entail quite a long and off-topic discussion to explain. I don't see why my statements irk you so much. You could read the Appendix to WWR Volume I though if you are interested for a critique of Kant, the categories, and Kant's own misunderstanding of the thing-in-itself (for example Kant didn't understand the nature of the thing-in-itself - he didn't identify that noumena is nonsense - only noumenon makes sense (thing-in-itself CANNOT be plural) - Kant didn't understand what he was talking about, that's why even today Kantians talk about shit like noumenal space, or space in-itself.....................)

The thing-in-itself may remain unknown to Schopenhauer - unknown philosophically, but not mystically. Many occurrences reveal the thing-in-itself - romantic love being one of them - but these experiences resist conceptualisation, and hence remain forever out of the grasp of philosophy.

The first passage, as far as I can tell, basically just says that a person earns the right to own property by work. I'm pretty sure that idea was expounded by Locke, and I'm not sure he was the first either. Perhpas you can poiint to what you ( presumably) think I have missed in this passage.

The second passage reads like an unjustified romantic paean to the potent powers of genius. I'm not seeing anything great or even insightful in these passages, They only confirm my previous opinion that Schopenhauer was somewhat of a philosophical hack (although nonetheless a very good writer and encyclopedic mind) who basically repeated Kant's philosophy with a few changes (like subsuming the twelve categories to Causality) and threw in some Upanishadic mysticism and Buddhistic pessimism. I haven't bothered reading Schopenhauer much beyond his Wisdom of Life and Counsels, a couple of secondary works (one by McGee which I found fairly superficial and romanticised) and some of WWR which I could never really sink my teeth into, because it seemed to lack any of the kinds of cogent insights of Kant and Hegel.So my impression has long been that Kant and Hegel are philosophers of far greater stature than Schopenhauer, and nothing you have quoted here has done anything to change that opinion.

At least Spinoza presented a more or less cohesive system (although not without its inconsistencies). A glaring problem with Schopenhauer's system, so far as I understand it, is that although he proposes a dualistic ontology of Will and Representation, he also tries to incorporate Platonic Ideas as something like universal forms governing the process of individuation from undifferentiated will to differentiated representation, but he seems to give no account of whether they are part of Will (noumenon) or part of Representation (phenomenon). It seems that, as intermediaries, they cannot be fitted to either category, which seems to leave a massive elephant in the room of his very speculative ontology.

I don't see why my statements irk you so much. — Agustino

Did I say your statements "irked" me? I just can't see the point in making statements if you are not prepared to back them up, however cursorily.

I am already familiar with Schopenhauer's critiques of Kant's purportedly plural notion of noumena; I have very recently referred to that very issue myself either in this thread or in Mongrel's 'Nietzsche' thread (or perhaps both, I can't be bothered checking). This point shows Schopenhauer's misunderstanding of Kant's nuanced conception of noumena, of the 'things in themselves'. Kant sees them not as substantive things (only phenomena are substantive things) but as placeholders for the unknowable X that appears to us as individuated empirical things. Kant does not wish to reify the noumenal, that would be to fall into the tendency of the human mind that is conditioned by experience of and judgements about, the empirical. It is actually Schopenhauer who reifies the noumenal by identifying it with an idea adapted from Spinoza's notion of 'conatus',. So, I would say he actually reintroduces a kind of backwards looking objectivism with the idea of a deterministic striving as being the ontological ground of reality. So, I have long thought his critique of Kant on this point is rather naive, even simplistic.

Before I proceed, I want to distinguish mathematical from geometrical. I think that this is important, and the importance may become evident when we bring time in relation to space. So far we've discussed spatial geometry independently of time, in an abstract way. When you say "the shortest distance from a line to a point is the perpendicular", this is not a mathematical truth, but a geometrical truth. That this is true, is proven with measurement, and when we measure we apply mathematics. Geometrical principles are proven with mathematics.

The problem is that this process of proving, measuring, is an empirical process. One could state any random geometrical principles, and the truth, falsity, or certainty of them is only revealed through the empirical proof. Because of this, geometrical truths are not really a priori. They might be in principle a priori, but that the shortest distance from a line to a point is the perpendicular, rather than some other angle, is true, is a posteriori.

So let's take the basic principle, the shortest distance between two points is a straight line. That there is a separation between two points assumes that there is something between them. This we call space. So even to demonstrate that there is separation between two points requires an empirical process, so all geometrical concepts are fundamentally a posteriori.

What Kant/Schopenhauer do, is that they go further and claim that, instead of being a posteriori to experience, they are a priori - hence why they are certain. — Agustino

I think that this is a mistaken principle then. These geometrical principles are a posteriori, and therefore they are not certain. This is due to the nature of the empirical proof, and it is well demonstrated by Einstein's relativity theory. The problem is that when we assume a separation between point A and point B, we assume space between them. To measure this separation, something such as a beam of light must traverse the space between point A and point B. This requires time. Due to this passing of time, the shortest distance between two points is no longer considered to be a straight line. That's the curvature of space-time. So even the most fundamental geometrical principle, that the shortest distance between two points is a straight line is not certain. It has been proven uncertain by the empirical process which is required to demonstrate its truth.

Yes, but put yourself in Schopenhauer's shoes. Euclidean geometry is capable to perfectly represent your reality in spatial terms. How is that possible? It's because the form that our mind imposes on experience (space) ensures that this is so. There is nothing to wonder about - they are certain because they are of subjective origin - they are forms through which experience itself is possible. In fact, remove those forms, and our experience itself becomes impossible. The world as representation is impossible if there is no space, time and causality. Why? Because any representation is a representation by virtue of being situated in space, time and causality. And these three are ideal - they are the structures of the mind - the forms provided by the mind. — Agustino

So I believe this is all backward. Euclidian geometry is not capable of perfectly representing spatial reality. It is deficient because it does not take into account the way that time is related to space. When we bring time and space into relationship, which is necessary in order to understand spatial reality, Euclidian geometry fails us. So instead of what you say, ("It's because the form that our mind imposes on experience (space) ensures that this is so"), the reality of space imposes itself onto the forms which our minds produce, forcing us to change what we may have previously considered to be a certainty.
And as I explained in the case of space, all three of these, space, time, and causation, are concepts which we are forced to produce in order to account for our experience. We produce a concept of space to account for our experience of separation

Some parts of mathematics evolve - BUT, not all. — Agustino

Now, that we have separated geometry from mathematics, and I think that this was necessary because it is evident that all aspects of geometry are uncertain, and are evolving, we can ask whether there are aspects of mathematics which are certain, and cannot evolve. I believe that there is, and that this is to be found in a number of aspects. First, there is a necessary equality of units, and second there is a necessary order. Each of these may be an a priori certainty.

Yeah well said... which is tragic. It makes reality unintelligible. There is no controlling factor at all. — Agustino

Why would you say this? Surely there is a controlling factor, that is the passing of time. What do you have in mind as a "controlling factor"?

The first passage, as far as I can tell, basically just says that a person earns the right to own property by work. I'm pretty sure that idea was expounded by Locke, and I'm not sure he was the first either. Perhpas you can poiint to what you ( presumably) think I have missed in this passage. — John

No that's not the point. The point is WHY he earns the right to property by work, which is the most significant point, otherwise it would be just a meagre assertion.

The second passage reads like an unjustified romantic paean to the potent powers of genius. I'm not seeing anything great or even insightful in these passages, — John

Sureeeeee... except that it tells exactly how the imagination functions and how it aids the genius to reach a truth that others cannot even see...

So my impression has long been that Kant and Hegel are philosophers of far greater stature than Schopenhauer, and nothing you have quoted here has done anything to change that opinion. — John

Yes, especially Hegel X-)

dualistic ontology — John

Nope. One substance ontology involving double aspect theory

he also tries to incorporate Platonic Ideas as something like universal forms governing the process of individuation from undifferentiated will to differentiated representation, but he seems to give no account of whether they are part of Will (noumenon) or part of Representation (phenomenon) — John

Thing-in-itself
Platonic Idea (out of time)
Will (in time, but out of space and causality)
Representation

This is roughly the hirearchy, your account shows merely a shallow misreading of Schopenhauer.

Did I say your statements "irked" me? I just can't see the point in making statements if you are not prepared to back them up, however cursorily. — John

It's merely sharing what I think. I don't have to back up everything I say, especially when it's totally unrelated to the topic and a quick reply about a side conversation

'things in themselves' — John

Things in themselves are incoherent. If space/time/causality are what individuates things, then there cannot be individual things apart from space, time and causality.

So, according to you, the thing in itself is not identified as Will by Schopenhauer? It's "one substance" involving quadruple aspect theory, then?

It's merely sharing what I think. I don't have to back up everything I say, especially when it's totally unrelated to the topic and a quick reply about a side conversation — Agustino

You don't have to do anything you don't want to do. Your failure to do it just makes it look like you cannot do it, though.

Things in themselves are incoherent. If space/time/causality are what individuates things, then there cannot be individual things apart from space, time and causality. — Agustino

You didn't read what I wrote about Kant's attitude to things in themselves, and simply quote a phrase out of context. So, you are repeating the same mistake as Schopenhauer by imputing a claim, that things in themselves exist, to Kant that he quite explicitly disavowed.

So, according to you, the thing in itself is not identified as Will by Schopenhauer? It's "one substance" involving quadruple aspect theory, then? — John

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.

I don't see why my statements irk you so much. — Agustino

I think I do: Schopenhauer doesn't treat the thing-in-itself like an empirical state. He steps towards recognising as logical, rather than a thing we would grasp through observation. Sure he says it's "mysterious" like Kantians do, but it "mysterious" on it's own terms, rather than by a failure to appear empirically. It's to take out the common Kantian approach of "unknown" to the thing-in-itself. We might say that Schopenhauer says we know the-thing-itself, that it is a "mystery" we conceive and recognise (as opposed to Kant, who suggests "we know nothing" ).

You didn't read what I wrote about Kant's attitude to things in themselves, and simply quote a phrase out of context. So, you are repeating the same mistake as Schopenhauer by imputing a claim, that things in themselves exist, to Kant that he quite explicitly disavowed. — John

Right, things-in-themselves don't exist then >:O How about you cite me some of Hegel's insights, as a shallow reader of Hegel I'd be more interested in that, than hearing about your shallow reading of Schopenhauer.

If you want to avoid discussing the relationship between Kant's and Schopenhauer's conception of noumena and phenomena, which is very pertinent to the OP, in my view, then bringing Hegel into the discussion is the perfect way. No one's forcing you to discuss anything

We might say that Schopenhauer says we know the-thing-itself, that it is a "mystery" we conceive and recognise — TheWillowOfDarkness

Yes.

I think I do: Schopenhauer doesn't treat the thing-in-itself like an empirical state — TheWillowOfDarkness

It seems to me that John is merely carrying out his personal vendetta though, with little interest to the underlying philosophy. As you can see, the statements that irk him is that I consider Schopenhauer more correct than Kant - as if my personal judgement on the relative correctness of Schopenhauer in comparison with Kant actually mattered in a discussion of Schopenhauer's transcendental idealism with reference to non-euclidean geometry :s

If you want to avoid discussing the relationship between Kant's and Schopenhauer's conception of noumena and phenomena, which is very pertinent to the OP — John

How is it pertinent to the OP? The OP is "can S's transcendental idealism survive the challenge posed to it by non-euclidean geometry?" And in fact, we're not one inch closer to answering this than we were before all this mumbo-jumbo. That means that our discussions have failed.

hat this is true, is proven with measurement, and when we measure we apply mathematics. Geometrical principles are proven with mathematics.

The problem is that this process of proving, measuring, is an empirical process. — Metaphysician Undercover

I disagree with this. There can be no situation where measurement would indicate that the perpendicular from a line to a point isn't the shortest distance from the line to the point. If you think there can be, please conceive of and give me such an example.

So let's take the basic principle, the shortest distance between two points is a straight line. That there is a separation between two points assumes that there is something between them. This we call space. So even to demonstrate that there is separation between two points requires an empirical process, so all geometrical concepts are fundamentally a posteriori. — Metaphysician Undercover

Not if space is a form that the mind supplies a priori...

To measure this separation, something such as a beam of light must traverse the space between point A and point B. This requires time. Due to this passing of time, the shortest distance between two points is no longer considered to be a straight line. — Metaphysician Undercover

Not necessarily, I could theoretically build a ruler long enough and measure it. And even if it did take sending a light beam, I fail to see how this disproves that the perpendicular is the shortest distance... Perhaps if you could explain this in more detail or give an illustration via youtube or somehow.

reality of space imposes itself onto the forms which our minds produce, forcing us to change what we may have previously considered to be a certainty. — Metaphysician Undercover

Right, so then you're a transcendental realist

First, there is a necessary equality of units, and second there is a necessary order. Each of these may be an a priori certainty. — Metaphysician Undercover

Where is this a priori certainty coming from?

What do you have in mind as a "controlling factor"? — Metaphysician Undercover

The thing-in-itself is ultimately real, while the phenomenon is only real qua phenomenon and not as thing-in-itself.

I would say this context of discussion relies on dismissing Kant's understanding of noumena. To conceive S's transcendental idealism, one has to accept noumena is something we understand. Space, time and causality have to understood as logical-- things known without reference to empirical observation.

To even address the question you are asking, one has to accept Kant's account is mistaken. John isn't willing to do that, even in imagination.

I would say this context if discussion relies on dismissing Kant's understanding of noumena. — TheWillowOfDarkness

Well it presupposes bracketing it, to say the least, as it's not what is under discussion.

To even address the question you are asking, one has to accept Kant's account is mistaken. John isn't willing to do that, even in imagination. — TheWillowOfDarkness

Yes, I agree, so this discussion isn't for him, he's free to open another to discuss the differences between Kant and Schopenhauer's conception of noumenon if that's what he's interested in. I selected Schopenhauer's transcendental idealism for this discussion because that's the only one I find philosophically interesting - he obviously doesn't.

Well your shallow reading of Schopenhauer and comparison with Kant is just as offtopic as your reciting to me some of Hegel's insights, however, I might actually gain something from the latter, while I definitely won't gain anything from the former. Both of them will be a waste of time considering the purpose of this discussion, but at least one has the potential of being interesting.

.

I think I do: Schopenhauer doesn't treat the thing-in-itself like an empirical state. He steps towards recognising as logical, rather than a thing we would grasp through observation. Sure he says it's "mysterious" like Kantians do, but it "mysterious" on it's own terms, rather than by a failure to appear empirically. It's to take out the common Kantian approach of "unknown" to the thing-in-itself. We might say that Schopenhauer says we know the-thing-itself, that it is a "mystery" we conceive and recognise (as opposes to Kant who suggests "we know nothing" ). — TheWillowOfDarkness

Kant certainly does not treat the thing in itself "like an empirical state". Kant conceived it as a purely formal notion, not at all as something we could "grasp through observation". It was Kant who first clearly defined what can be grasped through observation as the empirical, so I have no idea what point you are attempting to make here. Also, for Kant the noumenal is mysterious precisely on its own terms; it is the 'in itself', after all. Of course, it is also true that it is mysterious for us; who else could it be mysterious for? So of course it is, as much for Kant as for Schopenhauer, 'a "mystery" we conceive and recognize".

So of course it is, as much for Kant as for Schopenhauer, 'a "mystery" we conceive and recognize". — John

This just isn't true. You don't recognise the thing-in-itself at all for Kant. It's just a big X with no understanding of it at all. No understanding even what that X is meant to be, or what it stands for... That's why many of the Kantians who came after, even today, are seriously seriously deluded... you have Kantians speaking of space in-itself >:O

I think it goes deeper than that. Kant more or less derives the a priori nature of space and time from empirical observations-- he more or less says space and time are necessary because he thinks they are needed to have empirical states. But I'm swinging widely off-topic now, so I'll leave it there.

This is so misconceived there seems to be little hope that addressing it will make any difference. Space and time are for Kant the 'pure forms of intuition' they are explicitly conceived by a priori synthetic reasoning (pure reason or logic) not via observation. Space and time are not observed, they are the conditions for any observation, they are thus a priori. They are synthetic though, insofar as they can only explicitly conceived subsequent to experience; they are in that sense reliant on experience.

That approach is the very one I'm talking about. For Kant, the thing-in-itself is a "mystery" because it doesn't have an empirical appearance. We don't have any idea about because it doesn't appear in the terms we can know something (the empirical).

Schopenhauer treats it differently. For him it not a "mystery" because it doesn't appear empirically. Rather the thing, the thing-in-itself, is mystery-- a logical object not defined by what we don't know (a presence beyond our empirical observation), but rather by what we do know, the logical object of thing-in-itself.

How is it pertinent to the OP? The OP is "can S's transcendental idealism survive the challenge posed to it by non-euclidean geometry?" And in fact, we're not one inch closer to answering this than we were before all this mumbo-jumbo. That means that our discussions have failed. — Agustino

Well, I would say that first we must ascertain exactly what his transcendental idealism consists in before we can discover whether it is threatened by non-Euclidean geometry. To do that it will certainly be helpful to bring Kant in, since Schopenhauer's TI is an adaptation of Kant's. I would also say that if non-Euclidean geometry turns out to refute Schopenhauer's TI, then it will necessarily also refute Kant's.

Well, I would say that first we must ascertain exactly what his transcendental idealism consists in before we can discover whether it is threatened by non-Euclidean geometry — John

That was outlined in the OP largely and in subsequent posts

To do that it will certainly be helpful to bring Kant in, since Schopenhauer's TI is an adaptation of Kant's — John

That is not needed, as S's transcendental idealism can clearly be treated as independent of Kant's, given their ultimately strong disagreements.

I would also say that if non-Euclidean geometry turns out to refute Schopenhauer's TI, then it will necessarily also refute Kant's. — John

No this doesn't follow, because Kant allows for space in-itself

Nonsense, for Kant the thing in itself is recognized as being logically necessary. He says that for there to be representation it follows logically that there must be something that is represented. It is thought by Kant as noumenal only in the sense that it utterly escapes, by its very definition, empirical investigation.

Kant does not ever refer to "space in itself" as far as I am aware or can remember. Can you cite a reference for this?

Kant does not ever refer to "space in itself" as far as I am aware or can remember. Can you cite a reference for this? — John

No he doesn't, but future Kantians do ;)

It seems to me that John is merely carrying out his personal vendetta — Agustino

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