- The thing-in-itself, which is completely unknowable.
- The will as the thing-in-itself when the latter becomes conscious of itself, which is knowable in time as distinct acts of will identical to the movements of the body.
- The Platonic Ideas as the different grades of the will's objectifying itself, that is, the different degrees of what the will wills, which is life/existence, and knowable in aesthetic contemplation when willing has temporarily abated, wherein one is conscious solely of the Idea and not the movements of one's body or of individual objects in space and time.
- Individual objects as the Platonic Ideas come under and known in space, time, and causal relation to each other. — Thorongil

I agree with (1) and (4), but (2) and (3) should be reversed. First, the will is given under time - we know of the will in time. The Platonic Ideas are known outside of space, time and causality, and hence must be higher than the will in the hirearchy. I might disagree that Platonic Ideas still presuppose subject/object, rather I'd say that in the case of experiencing the Platonic Ideas the subject and the object become one - thus there is a quieting of the will, temporarily - one knows a Platonic Idea by being it. But the Platonic Idea is a relic of the thing-in-itself so to speak - only a glimpse. So it is still individuated.

As I have said a million times, Non-Euclidean geometry does not refute the axiom that the shortest distance is the perpendicular - among many other axioms that aren't refuted. So you have to explain to me where does this axiom get its certainty from, because it seems that regardless how our space is, it can't be refuted. — Agustino

I'm confused about exactly what you want to argue. But it seems reasonable to derive the least action principle from empirical experience of the world. If a geometry appears to offer many paths, it is rational to suggest one will involve the least effort of all the alternatives. So once energy is included in our picture of physical reality, non-Euclidean geometry should pop out.

If we fire off two objects into empty space on parallel tracks, we can then observe whether they diverge, converge, or stay the same distance apart. The behaviour can then be interpreted either in terms of interactive forces or geometric curvature. And both would be complementary views of a world understood to be organised in terms of the deeper synthetic a priori of the least action principle?

So if the question is does non-Euclidean geometry change anything about our ability to grasp the essence of existence through a leap to rational generality, then it seems not. We just needed to drill down another level beyond Newtonian physics to a view where space, time and energy are combined in the form of the idea of a path in which the least energy gets expended (or equivalently, a space that is globally expanding or shrinking at a non-accelerating rate).

I would say part of the principle of individuation because time for example also individuates. — Agustino

Sure.

the Will is closer to an idea or a subject than to matter. — Agustino

This is still a bizarre claim to me. It's equally distant from both ideas and matter in terms of what it is.

Kant/Schopenhauer, because remember all knowledge must be ultimately reducible to some perception — Agustino

No! This is profoundly antithetical to transcendental idealism. Rationalists thought we had knowledge of things not derived from experience, or a priori knowledge. Empiricists thought all knowledge was grounded in experience, or a posteriori knowledge. Transcendental idealism says that we do have knowledge a priori, but that this is limited to the forms of knowledge itself. In other words, we have immediate knowledge of the conditions of knowledge, while all other knowledge is mediated by those very conditions, and so is a posteriori.

If space is inseparable from our cognition, and non-Euclideanness is not perceivable in perception a priori, that means that non-Euclidean geometry cannot be knowledge, since it has no perceptual referent. — Agustino

It's interesting to note here the semantic shift from "non-Euclidean space," a phrase you have used up until now, to "non-Euclideanness." Just what is "non-Euclideanness?" The properties of certain points, lines, etc derived from non-Euclidean geometry? I don't see anything else it could be, but if so, then, as I said, the points, lines, etc are themselves in space. It's one thing to say, "lines and shapes can be measured a certain way, a way different from what Euclid taught in some cases," which is what non-Euclidean geometry says, and quite another to say, "this describes space itself." Simply put, geometry, whatever model one uses, measures the properties of things, but space is not a thing, therefore it says nothing about what space is in itself. If it were an object, then it would be perceived as such. But we don't perceive it as such. We rather perceive objects that are already in space.

I don't mean that by stage. I mean space, time and causality by stage. — Agustino

Well, what I said is what I believe Schopenhauer means by that term. The stage is the unity of what I am presently conscious of.

In other words, we have immediate knowledge of the conditions of knowledge, while all other knowledge is mediated by those very conditions, and so is a posteriori. — Thorongil

Why then are geometrical judgements synthetic a prioris? They are synthetic because they are reducible to a perception a priori. And they are a priori because one doesn't need experience to have such a perception. Such a perception is achievable a priori.

It's one thing to say, "lines and shapes can be measured a certain way, a way different from what Euclid taught in some cases," which is what non-Euclidean geometry says, and quite another to say, "this describes space itself. — Thorongil

But the relationships between geometric figures is what space itself is. I mean I ask you again, what else could space be? You say a form of our cognitive faculties... well, to be more exact, what is that?

Well, what I said is what I believe Schopenhauer means by that term. The stage is the unity of what I am presently conscious of. — Thorongil

I don't actually remember Schopenhauer using the term stage, but it may be possible. It's been awhile since I read WWR in full.

The Platonic Ideas are known outside of space, time and causality, and hence must be higher than the will in the hirearchy — Agustino

No, not according to Schopenhauer. The Platonic Ideas are dependent on the will, as the adequate objectification thereof.

That being said, as I have told you before, I myself sometimes think Schopenhauer ought to have reversed this order. But I was only trying to explain what Schopenhauer says on this point, instead of criticizing him.

I might disagree that Platonic Ideas still presuppose subject/object — Agustino

You can disagree if you like, but again, Schopenhauer still explicitly says they do.

The Platonic Ideas are known outside of space, time and causality, and hence must be higher than the will in the hirearchy. — Agustino

So, to return to an earlier question I asked you: are the Platonic Ideas noumenal or phenomenal? It seems odd to say they are noumenal if they are multiple. If they are not multiple then there would only be the Platonic Idea. But even then the noumenal would consist in two aspects, which again seems wrong. This is just why I have been saying that I don't think Schopenhauer's ontology is well thought out. 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).

Thorongil raises a good point that we don't directly perceive space and so we do not directly perceive it as either curved or flat. But apokrisis also makes the good point that at the scale of our perception, given our ability to build structures that consist of parallel members that can be shown not to converge, that we naturally conceive space as flat. If you accept, though, that gravitational warping of space points to a real phenomenon which is independent of our perceptions, then you are inevitably moving towards transcendental realism. Personally, I am more in favor of transcendental realism (only when it comes to the phenomenal, however the phenomenal in this context is not conceived as being exhausted by our perceptual experience). So, I think there is both a transcendental aspect of the phenomenal, and beyond that a transcendental noumenal. Of the latter I don't believe it could be appropriate to refer to it as either ideal (in the sense of being a function of our minds) or real (in any empirical sense as a phenomenal existent).

We can approach the latter with intellectual or mystic intution, but any attempt to reduce it to a monistic substance objectifies it. The triune conception is not completely intelligible to us, which is as it should be; it is the best we can do with out limited intellectual capacities. That's my take anyway.

No, not according to Schopenhauer. The Platonic Ideas are dependent on the will, as the adequate objectification thereof. — Thorongil

Personally I would disagree, and I would say they're dependent on the thing-in-itself. Their objectification as representation - that is dependent on the will, since they are objectified further down into the representation through the means of the will

You can disagree if you like, but again, Schopenhauer still explicitly says they do. — Thorongil

Yes, that is true. But I think the version I outline is stronger and more internally coherent than the one outlined by Schopenhauer, hence why I dared :P

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. — John

........ :-}

Thorongil raises a good point that we don't directly perceive space and so we do not directly perceive it as either curved or flat. But apokrisis also makes the good point that at the scale of our perception, given our ability to build structures that consist of parallel members that can be shown not to converge, that we naturally conceive space as flat. If you accept, though, that gravitational warping of space points to a real phenomenon which is independent of our perceptions, then you are inevitably moving towards transcendental realism. Personally, I am more in favor of transcendental realism (only when it comes to the phenomenal, however the phenomenal in this context is not conceived as being exhausted by our perceptual experience). So, I think there is both a transcendental aspect of the phenomenal, and beyond that a transcendental noumenal. Of the latter I don't believe it could be appropriate to refer to it as either ideal (in the sense of being a function of our minds) or real (in any empirical sense as a phenomenal existent). — John

Okay, I have no problem with that position in-so-far as this thread is concerned. I told you that moving towards transcendental realism is the only way to save Kant. But it won't work for Schopenhauer.

So, to return to an earlier question I asked you: are the Platonic Ideas noumenal or phenomenal? It seems odd to say they are noumenal if they are multiple. If they are not multiple then there would only be the Platonic Idea. But even then the noumenal would consist in two aspects, which again seems wrong. This is just why I have been saying that I don't think Schopenhauer's ontology is well thought out. — John

Schopenhauer's system is indeed a bit muddy, but these are hardly serious difficulties that are unresolvable based on Schopenhauer's own system. The Platonic Ideas are glimpses - partial glimpses - of the noumenon - hence why they are still individuated, or they appear individuated (this is my interpretation to make this clear). The noumenal doesn't consist in two aspects at all, except that we never encounter it as it is in-itself, we just encounter glimpses of it.

So, I think there is both a transcendental aspect of the phenomenal, and beyond that a transcendental noumenal. Of the latter I don't believe it could be appropriate to refer to it as either ideal (in the sense of being a function of our minds) or real (in any empirical sense as a phenomenal existent). — John

This is all pretty compatible with my triune metaphysics which would call the noumenal a vagueness - a naked unformed potentiality. The noumenal would thus have no character apart from that which develops via phenomenology - that is, shaped up into intelligible divisions by a (perceiving and willing) mind.

So beneath the jargon, there looks to be a lot of compatibility. All metaphysics of any interest tends towards a triadic or hierarchically organised view - the only kind of metaphysics that can do justice to the three things of observers, observables, and their shared developmental or causal history.

We can approach the latter with intellectual or mystic intution, but any attempt to reduce it to a monistic substance objectifies it. The triune conception is not completely intelligible to us, which is as it should be; it is the best we can do with out limited intellectual capacities. That's my take anyway. — John

I find the world qua Spirit to be quite insipid personally.

Why then are geometrical judgements synthetic a prioris? — Agustino

Are you asking me this? Because if you are, I think I quite clearly implied above (and in my PMs) that I am not necessarily committed to defending this claim. I am only trying to defend the a priori nature of space itself, not the alleged a priori nature of geometrical judgments.

But the relationships between geometric figures is what space itself is. — Agustino

Saying this doesn't make it so.

I mean I ask you again, what else could space be? You say a form of our cognitive faculties... well, to be more exact, what is that? — Agustino

I thought I answered this in a whole paragraph above. I don't know what more you want.

I don't actually remember Schopenhauer using the term stage, but it may be possible. It's been awhile since I read WWR in full. — Agustino

I seem to recall him using it.

Man this guy just loves promoting his own philosophy... >:O

are the Platonic Ideas noumenal or phenomenal? — John

For Schopenhauer, they are phenomenal.

Agustino wonders what space is if not its properties, Euclidean or otherwise. There are several ways to answer this question. First, I think we can say that space is the principle of individuation, i.e. it is that part of my cognition that makes what I perceive a plurality of distinct objects. However, because space is inseparable from our cognition generally, the question is technically based on a category mistake, because it's asking for knowledge of that which conditions all knowledge. Space can no more be known in itself than the eye can see itself or digestion can digest itself. It can still be known and perceived, but not in the way that the question assumes. Lastly, geometry tries to determine the properties of points, lines, surfaces, and so on, so it's technically not correct to say that it determines the properties of space itself, since points, lines, and surfaces are themselves in space. Any attempt to know what space is through experience, that is, a posteriori, necessarily presupposes it. — Thorongil

I did see this paragraph but I don't see how it answers the point. By means of what is space the principle of individuation if not by the relationships it creates amongst geometric figures?

No lines aren't themselves in space - rather they emerge from the properties of space itself. It is the properties of space that make lines possible to begin with. These properties are what geometry studies.

I told you that moving towards transcendental realism is the only way to save Kant. — Agustino

Any transcendental realism in Kant can really only a be a kind of transcendental empirical realism, though; and that is what I have been trying to get you to see. The noumenal is still, for Kant, unknowable. The move to realism may well not work for Schopenhauer's system but I think that only goes to show that he has not corrected, extended, or improved upon Kant at all, but rather muddled him up.

What do mean by "world as spirit"; who promotes that idea?

Any transcendental realism in Kant can really only a be a kind of transcendental empirical realism, though; and that is what I have been trying to get you to see. The noumenal is still, for Kant, unknowable. — John

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

The move to realism may well not work for Schopenhauer's system but I think that only goes to show that he has not corrected, extended, or improved upon Kant at all, but rather muddled him up. — John

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.

What do mean by "world as spirit"; who promotes that idea? — John

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

Time to go back to Berkeley, and Leibniz, and Spinoza and those guys... if that doesn't work... we can all become Skeptics, nothing to worry about >:O (joking lol)

Does Schopenhauer think space. time and causality are, exhaustively, functions of the human mind, such that they can have no existence or properties beyond, or contradictory to, how we directly experience and intuitively conceive them?

Does Schopenhauer think space. time and causality are, exhaustively, functions of the human mind, such that they can have no existence or properties beyond, or contradictory to, how we directly experience and intuitively conceive them? — John

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

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 — Agustino

But that passage says nothing at all about the world. :s

But that passage says nothing at all about the world. :s — John

You asked me what I meant by that expression. I didn't mean something very technical by "world" in that context, so my apologies for not being more clear.

By means of what is space the principle of individuation if not by the relationships it creates amongst geometric figures? — Agustino

It doesn't create whatever relationships you might be referring to. It creates your ability to say "figures," plural.

No lines aren't themselves in space — Agustino

Rubbish. Try thinking of or drawing a line that is not located in space. It's impossible.

rather they emerge from the properties of space itself — Agustino

This is sheer incoherence. I have no idea what you're talking about here.

Does Schopenhauer think space. time and causality are, exhaustively, functions of the human mind, such that they can have no existence or properties beyond, or contradictory to, how we directly experience and intuitively conceive them? — John

Yeah, I think so.

It doesn't create whatever relationships you might be referring to. It creates your ability to say "figures," plural. — Thorongil

Which is a property of space governed by geometry... the fact that two objects can't be in the same place at once is a statement of geometry. This is what individuates as you say... Why do you think Kant and Schopenhauer thought that geometry is synthetic a priori? Because geometry is the study of space qua space. Spatial relations and what they entail - that's what geometry studies. It's those relationships which individuate things.

Rubbish. Try thinking of or drawing a line that is not located in space. It's impossible. — Thorongil

You perceive lines in space, but they are possible only because of the properties of space itself.

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 — Agustino

Kant said this - does everyone see it? Space - if it is to be a form of our intuition, must condition and determine all possible spatial relationships that can exist within it.

Which is a property of space governed by geometry — Agustino

No it isn't. Space has no properties. Only material objects in space have properties and these properties are what geometry studies.

Only material objects in space have properties and these properties are what geometry studies. — Thorongil

Geometry does not study material objects... A line is not a material object at all. Neither is a triangle for that matter. Remember that a line has no thickness for example. Show me a line in the world that has no thickness....