believing in the potential for something to be true? — Heister Eggcart

You're still believing that something's true here, namely, you believe it is true that something else could potentially be true.

Not sure one is claiming that the potential is true, either.

No such thing exists. You're just referencing a mathematical model. That model, whether it's accurate or not, is not and cannot be identical to that which it is a model of, otherwise it would be the thing and not a model. I don't know how many times I need to say this.

If you possess mediate knowledge of something called "Euclidean space," or any other kind of space, that's great, perhaps you possess an extra special kind of cognition. But I don't. — Thorongil

But you also presuppose a model of space which individuates. That model of space isn't the space itself... And as space is ideal (as opposed to empirically real), how can something ideal be other than of the same kind a model is?

I'm pretty sure doubting the Trinity is a big no-no for them. — Thorongil

Well I don't doubt the Trinity, because I said I believe it. I just don't understand what that means.

Not sure one is claiming that the potential is true, either. — Heister Eggcart

But that is what you're doing.

Your only option really, is to think with John of a Big Mind which provides the forms of space, time and causality - back to Berkeley.

In Kant/Schopenhauer, knowledge necessarily involves perceptual and conceptual content (since they join both rationalism and empiricism). Geometrical judgements involve a spatial perception a priori (not an empirical perception) structured by the form of space itself. As you yourself note, lines are not material objects. So they can't be perceived empirically. How are they perceived? They are perceived a priori, through the form of space itself. Thus, if they are perceived a priori through the form of space itself, a form in which experience is then given, that means that no unperceivable feature of space can be found in experience, because if it is found, then it should have existed in the intuition to begin with.

So to structure it as an argument:
1. For something to be knowledge, it must contain both perceptual and conceptual content.
2. Geometrical objects and their properties are not empirical objects
3. Only empirical objects are perceived empirically
4. From (2) and (3) it follows that geometrical objects and their properties cannot be perceived empirically.
5. Geometrical objects and their properties are constructed and perceived a priori in the form of space provided by the cognitive faculties
6. Non-Euclideanness is a geometrical property that isn't / can't be perceived a priori in the form of space provided by the cognitive faculties
7. From (6), (5), (4) and (1) it follows that non-Euclideanness isn't a known geometrical property of any geometrical object since it only has conceptual content without any attending perception (rationalism without any empiricism) (it would contradict [1] if it was known) - it is neither perceived a priori (by [6]) neither can it be perceived a posteriori since it is a geometrical object/property (would contradict [5] or it just wouldn't be a geometrical object or a property of one (by [4]).
8. (7) is false
9. Therefore one of the premises is wrong.

Possibly (1), (2), (5), or maybe even (6) - I've seen people arguing that non-Euclideanness can be intuited but that's very rare. (2) can't be attacked since lines can nowhere in nature be perceived. (1) could be attacked, but bye bye to Kant and Schopenhauer's synthesis of rationalism/empiricism. (5) is the only possibility remaining granting (1) and (4), so can't really be attacked. An attack on (6) would just not be granted by most - few would say non-Euclideanness can be perceived a priori.

But you also presuppose a model of space which individuates. — Agustino

No I haven't. Not a mathematical model at any rate.

how can something ideal be other than of the same kind a model is? — Agustino

What you term "Euclidean space" is a phantasm, something created by the model itself. It has no real, independent existence and has nothing to do with what space may be in itself (which is unknowable and unthinkable).

lines are not material objects. So they can't be perceived empirically. — Agustino

Yes, but they are derived empirically, and this is where I part company with K/S. This also negates premise 4 in your argument, since points and lines are abstractions from the world of perception. So all geometry is ultimately based on empirical observation, but what we observe empirically isn't space but objects that are in space, which is to say, objects that are mediated, in part, by space. The two simply can't be separated out, as Tesla says. And here's Berkeley: "Extension, figure, and motion, abstracted from all other qualities, are inconceivable." A "matter-less space," such as "Euclidean space" would have to be, is a contradiction in terms. That being said, it is still true that we perceive and therefore know space, but this perception and knowledge is a priori. What I mean by a priori is not "based on reason alone," but "logically prior to experience." What this means is that space cannot be caused to exist by a Divine Mind, and so I part company with Berkeley, because it is an inseparable ingredient in causality itself, which is the union of space and time.

Meister Eggfart,

Become a Schopenhauer fan, you know it's good for you.

Is it?

Meister Eggfart,

Become a Schopenhauer fan, you know it's good for you.

Is it? — Question

I'm not sure.

I'm not sure. — Heister Eggcart

I think Schopenhauer has this magical ability to convince anyone he is true and right. I feel in love with him after reading his aphorisms.

More people tend to disagree with him than agree with him, in my experience. I'm the only person I know who actually agrees with his philosophical system in the main.

Dunno about that. I think the quality of his prose keeps a lot of people away.

Ahh, but on what grounds have these disagreements arisen? I feel as if it were a matter of taste and feelings, eh? Not everyone buys into his pessimism, although the pessimist can never be more wrong than wrong.

I feel as if it were a matter of taste and feelings, eh? — Question

Yeah, and a lot of people like to reject him by making ad hominems. Some in the secondary literature try to offer actual arguments against his positions, of course, but I've never been very persuaded by them.

Yes, but they are derived empirically, and this is where I part company with K/S — Thorongil

So it seems you are denying premise (3) [you can't deny 4, that is a conclusion]. So you think non-empirical objects are perceived empirically. I'd say this is just false. Or alternatively, you think that there can be purely conceptual knowledge, void of any perception, such as the geometric objects which are abstracted from perception a posteriori (this is a denial of [1]). If you deny (1), then you have negated S/K's foundations.

what we observe empirically isn't space but objects that are in space, which is to say, objects that are mediated, in part, by space — Thorongil

What does being mediated by space entail?

That being said, it is still true that we perceive and therefore know space, but this perception and knowledge is a priori. What I mean by a priori is not "based on reason alone," but "logically prior to experience." — Thorongil

If you know space a priori, in what does this knowledge and perception consist?

you think that there can be purely conceptual knowledge, void of any perception, such as the geometric objects which are abstracted from perception a posteriori (this is a denial of [1]). If you deny (1), then you have negated S/K's foundations. — Agustino

This is the closest to my view, but I would say that conceptual knowledge, such as what mathematics reveals, is not "void" of any perception, since it is abstracted from perception.

What does being mediated by space entail? — Agustino

That we perceive a plurality of objects, which, along with their being in time, are in causal relation to each other.

If you know space a priori, in what does this knowledge and perception consist? — Agustino

Once again, this question is technically unanswerable, because to do so would commit the category mistake I talked about. Space cannot be separated from the whole of cognition. That is, it cannot be thought of apart from time and matter.

Do not mistake the objects of our experience for objects existing independently of experience. No object can exist independently of experience, for all objects presuppose a subject. So there can be no space as an object that exists independently of experience, which you seem to think. Can there be space as an object that exists within experience? No, because I experience no such object. If you think we do, I would simply ask you to point it out to me. Can there be a physical space based on geometrical and physical models? Yes, and this, I suppose, would the be 4D space-time of modern physics, but these models are themselves based on experience, which, again, does not contain space as a distinct object within it. We don't experience 4D space-time, as you have noted before, which means it cannot be said to have any independent existence; it's just something that drops out of the model. That it agrees with our experience does not mean it is our experience or that it must be posited as existing outside of experience. If you think it must be, then tell me why. So where does that leave us? I say it leaves us positing that space is a priori. It's not something found in experience and can't exist independently of experience. It's an essential ingredient in our ability to experience at all.

This is the closest to my view, but I would say that conceptual knowledge, such as what mathematics reveals, is not "void" of any perception, since it is abstracted from perception. — Thorongil

An abstraction is not a perception though. Lines are nowhere to be found in your experience. In fact Berkeley did the right thing and denied the existence of abstractions independently of any perception.

"It is agreed on all hands, that the qualities or modes of things do never really exist each of them apart by it self, and separated from all others, but are mixed, as it were, and blended together, several in the same object. But we are told, the mind being able to consider each quality singly, or abstracted from those other qualities with which it is united, does by that means frame to it self abstract ideas. … Not that it is possible for colour or motion to exist without extension: but only that the mind can frame to it self by abstraction the idea of colour exclusive of extension, and of motion exclusive of both colour and extension"

You have to do the same to be consistent.

Do not mistake the objects of our experience for objects existing independently of experience. No object can exist independently of experience, for all objects presuppose a subject. So there can be no space as an object that exists independently of experience, which you seem to think. Can there be space as an object that exists in experience? No, because I experience no such object. Can there be a physical space based on geometrical and physical models? Yes, and this, I suppose, would the be 4D space-time of modern physics, but these models are themselves based on experience, which, again, does not contain space as a distinct object within it. We don't experience any such 4D space either, as you have noted before, which means it cannot be said to have any independent existence; it's just something that drops out of the model. That it agrees with our experience does not mean it is our experience or that it must be posited as existing outside of experience. So where does that leave us? I say it leaves us positing that space is a priori. It's not something found in experience and can't exist independently of experience. It's an essential ingredient in our ability to experience at all. — Thorongil

Okay fine that works, but this is no longer Schopenhauer's/Kant's position. Your new position has to reformulate what knowledge consists in, in a framework that is separate from S/K, such that there can be purely conceptual knowledge, or simply denying that mathematics consists in knowledge , or re-conceptualising mathematics along different EMPIRICAL lines (like Berkeley - §122 in Principles), and hence denying that mathematics of any kind as is most often interpreted consists in knowledge.

In fact Berkeley did the right thing and denied the existence of abstractions independently of any perception. — Agustino

But this is basically what I did just say: "it is abstracted from perception." Obviously the abstraction is not empirically perceived, but your use of the word "void" was unclear, for I took it to mean "not derived from perception."

Okay fine that works, but this is no longer Schopenhauer's/Kant's position. — Agustino

With respect to this one issue, yes. But I still don't think it affects much of the rest of Schopenhauer's system.

or simply denying that mathematics consists in knowledge — Agustino

I would lean toward this.

much of the rest of Schopenhauer's system. — Thorongil

What do you mean much of the rest? It certainly affects the overall structure of it, in quite a significant way. That it doesn't affect a lot of the insights Schopenhauer had, sure.

What do you mean much of the rest? It certainly affects the overall structure of it, in quite a significant way. That it doesn't affect a lot of the insights Schopenhauer had, sure. — Agustino

I think this conversation is somewhat tedious, unimportant, and one-sided, for we are really just confronting the problems with assuming that the world as presentation is the world entire. If we stop short at the presentation, or the first book of the WWP, then we face insoluble problems, including the one we have been discussing. In one sense, Schopenhauer accepts realism, in that we can posit a mind independent world of matter, space, and time as the necessary condition for, and in which arose, knowing beings. However, such a world is not even thinkable without presupposing a subject and so cannot be said to exist with certainty. I was born, acquired ever more control over my faculties, and through them surmised that I am a product of a world that existed before my birth. At the same time, I could never know this world absent said faculties, and thus in another sense I appear as though I came from nothing

Schopenhauer is a materialist, in part, and a Berkeleyan idealist, in part. He affirms both. "But they are mutually incompatible," you will say. Correct. Schopenhauer calls this an antinomy of knowledge. How does one solve the antinomy? Not by picking a side. One must find the common essence of mind and matter, and that essence is the will, which is neither a mind nor a material thing. I have always read Schopenhauer in this way, as a neutral monist. So this explains my incredulity at times concerning your objection and the cautiousness of my replies, e.g. "I lean toward," "I could grant," etc. It makes little difference, from this new perspective, whether space is an a priori concept, an a posteriori object, or both. The will has manifested itself as a world in space regardless. How it has done so is an ancillary and much less interesting question to me. The mere fact that it has solves the fundamental problem in philosophy. It also doesn't negate the bedrock claim of Schopenhauer's that there can be no object without a subject and no subject without an object. These are correlates. They stand and fall together. Take the subject away and there is no objective world. Take the object away and there is nothing to be conscious of.

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. — Agustino

So, you believe on the basis of authority and not on the basis of your own intuitions? I cannot relate this; it is not how I operate at all. I lean towards the trinity, for example (of which you have, somewhat confusingly said both that you are "not big on it" and that you "believe it") because it makes the most intuitive sense to me, more than absolute monism does.

This is not to say that I thoroughly understand it; I don't think anyone can thoroughly understand it (or absolute monism for that matter). This should be no surprise, I have no doubt that even on the mundane level we routinely believe many many things we do not thoroughly understand.

It doesn't negate the bedrock claim of Schopenhauer's that there can be no object without a subject and no subject without an object. These are correlates. They stand and fall together. Take the subject away and there is no objective world. Take the object away and there is nothing to be conscious of. — Thorongil

Yes, I also agree in fact with this insight. My personal view on metaphysics is probably still closest to Spinoza - one substance with two parallel attributes, thought (idea) and extension (matter). The one substance is the thing-in-itself, and the attributes are the two ways of looking at this same substance. I think this insight is still at its freshest and purest in Spinoza.

neutral monist — Thorongil

This reminded me of this video (note I don't agree with everything there):

However, such a world is not even thinkable without presupposing a subject and so cannot be said to exist with certainty. — Thorongil

Yes, you'd need this more Berkeleyan route into it, rather than the Kantian.

So, you believe on the basis of authority and not on the basis of your own intuitions? — John

Yes, because my intuitions don't tell me anything to be honest with you

of which you have, somewhat confusingly said both that you are "not big on it" and that you "believe it" — John

Yes it's not essential for me - doesn't have much practical import - but I believe it, without knowing what it really means.

because it makes the most intuitive sense to me — John

How come it makes sense? I don't really understand what "intuitive sense" means... You either understand something or you don't...

But anyway transcendental idealism seems to fall apart in the way put forward by Kant - it's only in the sense of "subject correlated with object and object correlated with subject" that transcendental idealism survives. This transcendental idealism is, well, transcendental. Only from the point of view of the thing-in-itself are subject and object and the entire world qua representation "ideal".

How come it makes sense? I don't really understand what "intuitive sense" means... You either understand something or you don't... — Agustino

It means that intuitively it feels right. If we are made in God's image why should we not be able to know the nature of and truth about ourselves by what Zen refers to as direct knowing, otherwise known as gnosis, or more mundanely, 'what feels right'? Surely you don't believe that the truth about us can be discovered by empirical investigation or logic, do you? All the great religions have asserted, in different ways and with different emphases, the superiority of this 'inner' way of knowing over the 'outer' objectifying, rational discursive intellect. Where do you think the scriptures come from in the first place?

Only from the point of view of the thing-in-itself are subject and object and the entire world qua representation "ideal". — Agustino

Can the thing in itself have a point of view?

Surely you don't believe that the truth about us can be discovered by empirical investigation or logic, do you? — John

Why not? I don't see how "what feels right" is anymore likely to be correct than empirical and rational investigation, in fact quite the contrary. According to "what feels right" everyone has a different opinion, and there is no way to decide what is right. For example, look at us two. For you it is intuitively obvious that the Trinity feels right. For me it isn't. Who is right and how can this be determined? Certainly not by appealing to what feels right, because that's different for both of us, and therefore we cannot determine according to it. We must determine according to what we have in common - reason and empirical investigation.

All the great religions have asserted, in different ways and with different emphases, the superiority of this way of knowing over the rational discursive intellect — John

Maybe, but then this doesn't make much sense to me. You always see me around here complaining, especially against Wayfarer, with regards to this mental masturbatory mysticism.

Where do you think the scriptures come from in the first place? — John

Insight gained by the natural light of reason.

Can the thing in itself have a point of view? — John

No, I meant point of view as a logical criteria indicating that the thing-in-itself is more fundamental than subject and object, and therefore subject and object are both ideal - not real. Only Substance exists and is divine - the modes and the empirical world are illusory.

My personal view on metaphysics is probably still closest to Spinoza - one substance with two parallel attributes, thought (idea) and extension (matter). The one substance is the thing-in-itself, and the attributes are the two ways of looking at this same substance. I think this insight is still at its freshest and purest in Spinoza. — Agustino

Yes, I view Spinoza as a neutral monist. For a very long time, I counted myself a Spinozist because I thought he offered a solution to the mind/body problem of Descartes. But while he provides the blue print for how to solve it, his actual solution I was never fully convinced of. Kant merely states the same problem in different terms. When reading Schopenhauer, however, I thought, and still think, his notion of the will is the best solution.

This reminded me of this video (note I don't agree with everything there): — Agustino

Oh god, I hate that video. The voice, special effects, and music are way too pretentious. I actually think I was banned by the original maker of the video for pointing this out too.

The distinction really doesn't make sense though, for every rational of "outer" thought makes use of the intuitive. All our observations and reasoning are intuited in the first instance. Before I can pick out an object in the world, I need to understand what it is, else I won't spot it even when it right in front of me.

Rather than an opposition of "inner" (intuited) and "rational" (observation and logically derived"), there is only the "inner," logic and meanings understood, from which "rational" understandings are born. Any instance of knowledge amounts to "what feels right."

When reading Schopenhauer, however, I thought, and still think, his notion of the will is the best solution. — Thorongil

Yes but even Schop. abandons it for thing-in-itself ultimately. And don't forget that Spinoza does have the equivalent of will - it is called the conatus, which is our essence. I think Schopenhauer also anthropomorphises the Will to a certain degree - Spinoza does no such thing, that's why his system remains in my eyes pure.

Oh god, I hate that video. The voice, special effects, and music are way too pretentious. I actually think I was banned by the original maker of the video for pointing this out too. — Thorongil

>:O LOOOL! I never comment on youtube, but I agree with you on those points. He does point out the central bit regarding neutral monism though, hence why I was reminded of it. And its extravagance makes it memorable :-O >:O

Only from the point of view of the thing-in-itself are subject and object and the entire world qua representation "ideal". — Agustino

Exactly!