I've determined that Agustino is much more heretical than he appears.

I've determined that Agustino is much more heretical than he appears. — Thorongil

>:O meaning?

Geometry is the study of possible spatial relations. — Agustino

But only as conceived in terms of relata like points and lines. Or at a deeper level - one that includes the reality of material being. - in terms of least actions and the global symmetries they break.

So geometry certainly started out as a maths of space (thus excluding time/energy). But that turned out to be an incomplete view of spatiotemporal reality.

I think I have performed a Copernican revolution actually to tell you the truth, and replaced the question "what must I know to be religious?" with "how can I still be religious in the absence of knowledge?" O:) :-O

No, since space is a form of knowledge - that which makes knowledge and experience possible - there cannot be any spatial knowledge to be gained by experience (hence why geometry is necessarily synthetic a priori and never synthetic a posteriori - Kant was very clear about this). If knowledge of space is gained by experience then that which was supposed to make experience possible in the first place was not known by the very mind which structured experience according to it - that's a contradiction. — Agustino

I think Kant scholars would all agree on one thing; that Kant was not very clear about anything. I think you're still not getting the point that the mind that intuitively conceives space, time and causality is not exhaustively) the same mind that structure experience. I mean we are not intuitively aware of the minds activity of structuring experience are we? So how can we presuppose that we can know all things about how space structure empirical experience?

When it comes to time, which also is considered synthetic a priori there is not even any consensus about its intuited nature. Does it flow, or does it stand still and objects and events move within it, and so on, Such things are not to be empirically discovered, but only intuitively considered and yet we do not fully understand time; so the nature of time is not immediately self-evident to the mind from which it purportedly originates. This problem may be resolved if one thinks that time, space and causality originate in a Greater Mind and that their characteristics are only partially obvious to us.

Why do you think so? Have you read Tolstoy's Gospel in Brief? It was one of Wittgenstein's favorite books — Agustino

Your fascination with Tolstoy is...(N)

Why are you laughing it's true — Agustino

I'm laughing because, if I don't understand something, I do not believe it to be true.

That's why I say my argument goes against their intention. The ideal can be saved, but only by turning into its own thing, where is is no longer a ground or defined by correlation. In doing so, their understanding of the logic of the empirical is lost. The world may do more and may express different logics than they thought. Sometimes Euclidean geometry is not expressed by the world (as you noted in challenges).

It's the relationship of logic to the empirical that Kant gets wrong. Euclidean geometry is a synthetic a priori (and so is the logic of space). It's just that the world doesn't always express those rules (despite the rules of Euclidean geometry always being true) and the logic of space is an expression rather than a ground.

The logical conclusion of that is that you should believe in nothing that is not either empirically given or given by scriptural authority. In which case, forget all (or at least most) of philosophy.

All this is resolved if one thinks that time, space and causality originate in a Greater Mind and that there characteristics are only partially obvious to us. — John

Yes, as I said, back to Berkeley you go

So how can we presuppose that we can know all things about how space structure empirical experience? — John

Because space is an a priori form of our KNOWLEDGE. We know through space, hence space conditions our knowledge.

The logical conclusion of that is that you should believe in nothing that is not either empirically given or given by scriptural authority. In which case, forget all (or at least most) of philosophy. — John

But for example I believe in one substance because all other conceptions are incoherent. So it's not only empirical truths that I believe or those given by scriptural authority. I also believe in rational truths.

I'm laughing because, if I don't understand something, I do not believe it to be true. — Heister Eggcart

Well you can be mistaken in both believing or not believing but you have to choose one.

Belief doesn't require a truth claim.

Because space is an a priori form of our KNOWLEDGE. We know through space, hence space conditions our knowledge. — Agustino

To be coherent, the latter must be reversed. Space is a condition of our knowledge. Our instance of knowledge is inseparable from the logic of space. Rather than a ground which acts causally (i.e. without space, you could not be caused to exist), space is an expression of this instance of knowledge (as a state, you express space). Without our knowledge, this expression of space (our knowledge expressing space) would not be.

This means knowledge has a wider context than just space. Space may be expressed by it, but that logic is no needed for any instance of knowledge. Logically, we may know of things beyond or without space.

Belief doesn't require a truth claim. — Heister Eggcart

What do you mean? Belief in itself is a truth claim isn't it? To believe something is to think it true.

Why does space allow triangles to exist? Why isn't the nature of space such that triangles are impossible? — Agustino

There is a sense in which triangles are indeed impossible, for we don't perceive perfect triangles in nature, while the triangles we can imagine are based on the imperfect shapes that we perceive. So space only determines that things are numerically distinct, not what they are. What determines what they are, i.e. what their essence is? The will. What determines what the will is? Nothing, for the will is groundless. So your question is nonsensical.

There's a quote from Nikola Tesla I like and feel like quoting here, as he says much the same thing I do:

I hold that space cannot be curved, for the simple reason that it can have no properties. It might as well be said that God has properties. He has not, but only attributes and these are of our own making. Of properties we can only speak when dealing with matter filling the space. To say that in the presence of large bodies space becomes curved is equivalent to stating that something can act upon nothing. I, for one, refuse to subscribe to such a view.

-

And what determines the possibility of non-euclidean axioms (and Kant and Schopenhauer have both critiqued the notion of axiom actually) if not the nature of space itself? When we postulate axioms, don't we actually refer to a specific kind of space? — Agustino

Your answer has been "experience," which I need not dispute to maintain my position. A model of experience is not the experience itself.

>:O meaning? — Agustino

That people ought to take your declarations of being an orthodox Christian with a grain of salt.

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 never said that one refutes the other, remember, I said we establish compatibility between the two. The heliocentric model of the solar system does not refute the claim that the sun rises in the morning. It just allows us to see this in a different way.

As I said before, your axiom gets its certainty from empirical verification, measurement. Without measurement you could state any random axiom such as "the shortest distance from a line to a point is at an 80 degree angle to the line". How is your axiom of the perpendicular more certain than this axiom of the 80 degree angle, without measurement? The only reason why your axiom cannot be refuted is because it can be demonstrated empirically, measurement. Therefore it does derive its certainty from "how our space is".

If you want to look for principles which do not derive there certainty from empirical verification, true a priori principles, you should look to mathematics. I already suggested two possibilities, the equality between units, and the order. I'm starting to think that order may not be truly independent of experience, because it may be derived from the experience of temporal order. So let's look at the equality of units.

How is it that we know, with a very high degree of certainty, that there is an equal difference between one and two, two and three, three and four, etc.? Where do we derive this idea of equality? It seems that in all empirical observations we see no examples of such absolute equality. However, we seem to know with absolute certainty that there is an absolute equality with respect to the difference between the integers.

So space only determines that things are numerically distinct, not what they are — Thorongil

I'm sure it also determines how they appear...

What determines what they are, i.e. what the essence of things is? The will. What determines what the will is? Nothing, for the will is groundless. — Thorongil

Yep, never disagreed on this.

I hold that space cannot be curved, for the simple reason that it can have no properties. It might as well be said that God has properties. He has not, but only attributes and these are of our own making. Of properties we can only speak when dealing with matter filling the space. To say that in the presence of large bodies space becomes curved is equivalent to stating that something can act upon nothing. I, for one, refuse to subscribe to such a view.

Well Tesla certainly didn't like Non-Euclidean geometry :P - but regardless, whether you call them attributes of space, or properties of space, it's the same thing really.

That people ought to take your declarations of being an orthodox Christian with a grain of salt. — Thorongil

But amongst philosophers Orthodox Christians can be very different from each other. It's one thing to read Tolstoy, and a different thing to read, for example, Berdyaev. You'd claim that these two are also more heretical than they seem at first, and yet they are both Orthodox Christians.

How is it that we know, with a very high degree of certainty, that there is an equal difference between one and two, two and three, three and four, etc.? Where do we derive this idea of equality? It seems that in all empirical observations we see no examples of such absolute equality. However, we seem to know with absolute certainty that there is an absolute equality with respect to the difference between the integers. — Metaphysician Undercover

Another thread!! :P

I'm sure it also determines how they appear... — Agustino

Only if by "how" we mean that it determines that things appear in the plural.

But amongst philosophers Orthodox Christians can be very different from each other. It's one thing to read Tolstoy, and a different thing to read, for example, Berdyaev. You'd claim that these two are also more heretical than they seem at first, and yet they are both Orthodox Christians. — Agustino

Ah, but I said "orthodox," lower case. Perhaps it's true that one can be an unorthodox Orthodox Christian. Perhaps that's what you are, but you appear unorthodox in either case.

What do you mean? Belief in itself is a truth claim isn't it? To believe something is to think it true. — Agustino

One can believe something without claiming it to be the truth.

Only if by "how" we mean that it determines that things appear in the plural. — Thorongil

Why stop there? The fact that 3D Euclidean space allows for a plurality of objects is true, but Euclidean 1D space doesn't for example. So clearly the individuation and the extent to which it is possible is governed by the geometrical properties of the space in question. So why stop with just those properties that ensure individuation? In fact, you necessarily bring about all the others if you try to do that.

Perhaps it's true that one can be an unorthodox Orthodox Christian — Thorongil

O:)

One can believe something without claiming it to be the truth. — Heister Eggcart

One can believe something without knowing it is true, but I think it's just definitional that to believe something is to regard it as true.

One can believe something without claiming it to be the truth. — Heister Eggcart

How would you define believing something then?

The thing though is that a lot of what you'd see as unorthodox wouldn't be perceived as unorthodox by other orthodox Orthodox Christians :P

Isn't it worth distinguishing between believing something to be true, and believing in the potential for something to be true?

Isn't it worth distinguishing between believing something to be true, and believing in the potential for something to be true? — Heister Eggcart

The latter is really just a degree of certainty or if not then it's just pure logical plausibility.

Why stop there? — Agustino

Because I have to. That's where my knowledge stops.

3D Euclidean space — Agustino

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.

The thing though is that a lot of what you'd see as unorthodox wouldn't be perceived as unorthodox by other orthodox Orthodox Christians :P — Agustino

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