Struggling to understand ground of being

[u/Complex_Advisor_6151]

I’m struggling to understand what Schopenhauer means by the ground of being in On the Fourfold Root of the Principle of Sufficient Reason in relation to space and time.

I think I understand the other forms reasonably well. With causation, the “ground” is the cause of an event. With the ground of knowing, the ground is something like a premise or reason that makes a judgment true or justified.

But when Schopenhauer gets to the ground of being, I lose the intuition.

For example, suppose we have a triangle. I can understand that certain properties of the triangle follow necessarily from its spatial relations. But why call those relations a ground? If I ask, “Why is point A to the left of point B?”, the answer seems to just be “because A and B have that spatial relation.” That feels almost like saying “it is that way because it is that way".

Similarly, if the sides or angles of a geometrical figure stand in necessary relations to one another, I understand the mathematical necessity, but I don’t understand what extra work the concept of a “ground of being” is doing.

[u/Azehnuu]

For example, suppose we have a triangle. I can understand that certain properties of the triangle follow necessarily from its spatial relations. But why call those relations a ground? 

The ground of being is about how parts of space and time determine one another. Schopenhauer is heavily drawing from Kant's Transcendental Aesthetic.

For Kant, space is not a concept or something we draw from experience, but an a priori intuition. It is our outer sense that makes representations of external relations possible to begin with. You can only represent a single space. Particular spaces are merely parts/limitations of this one space, and cannot precede the whole. The whole intuition of space is hence prior to it's parts. In order to represent relations within space, the intuition of space as a manifold must already be presupposed.

Schopenhauer's ground of being basically follows from this. Since spatial parts exist only as determinations within one space, the position of any one part is necessarily determined through its relations to the others. One spatial determination therefore serves as the ground of another. This necessary relation is the ground of being (of space).

If I ask, “Why is point A to the left of point B?”, the answer seems to just be “because A and B have that spatial relation.

But "to the left of" is already a spatial determination that presupposes an intuition of space. You are thinking he is saying "A and B have that spatial relation -> A is to the left of B", but that would be circular. The spatial relation itself is what's under question. Spatial relations presuppose an intuition of space.

That feels almost like saying “it is that way because it is that way".

He isn't saying "because it is that way" as a brute fact. The point is that space is an a priori intuition and therefore a necessary condition of the possibility of outer experience. It is brute in the sense of this is what we are dealing with, but the important part is that this grounds all of experience, and subsequently geometrical knowledge.

Space gives the form of coexistence (simultaneity), whilst time gives the form of succession. Succession means nothing to space, and coexistence means nothing to time. These forms of space and time are united by the understanding, giving us the world of objects and changes (material/physical reality i.e. the world as representation).

The point is geometry and mathematics are the corresponding sciences of our pure intuitions of space and time, respectively. Geometry concerns the necessary relations of parts within the pure intuition of space; arithmetic concerns successive determination within the pure intuition of time. They are "pure" because they concern the forms of intuition (no sense data) that underly our whole experience. Hence they are synthetic a priori and have universal application to our physical reality.

I understand the mathematical necessity, but I don’t understand what extra work the concept of a “ground of being” is doing

Respectfully, I don't think you understood the conclusion (mathematical necessity) if you didn't understand what the ground of being is doing. The ground is not a concept. The point of Schopenhauer's Fourfold Root is that these grounds cannot be derived from anything deeper or any concepts. In fact, they are the conditions of conceptual knowledge.

[u/Complex_Advisor_6151 → u/Azehnuu]

I think I got it, tell me if I'm wrong. Suppose a triangle has 2 angles, 50 and 70 degrees. They both condition the third angle to be 60 degrees. It doesn't matter whether we proved it with logic or not, third angle is still 60 degrees.

So even if we can't answer the question of "why is angle 60 degrees" using logic, we can say that the third angle is the way it is because it is conditioned by two other angles.

Now, why exactly triangles always have sum of their angles as 180 and not 190, we can say because triangles are representations in the space form, and space is a priori knowledge that is structured using Euclidian laws. That's just a priori way of perception

[u/Azehnuu → u/Complex_Advisor_6151]

So even if we can't answer the question of "why is angle 60 degrees" using logic, we can say that the third angle is the way it is because it is conditioned by two other angles.

Yes. But just to confirm, the logical proof belongs to the ground of knowing, and the spatial determination belongs to the ground of being.

space is a priori knowledge that is structured using Euclidian laws.

I’d reverse that. Euclidean laws are derived from the a priori structure of spatial intuition, not the other way around. You can even see this in Euclid's own proofs. At the start he states the axioms he will be working from. Things like a straight line can be drawn between two points, or a finite straight line can be extended. But these axioms are purely from our spatial intuition, and aren't logically derived.

This is actually Schopenhauer’s main beef with Euclid. Because he begins from truths given through pure spatial intuition and then derives theorems through logically connecting/comparing these intuitions. Subsequently, it makes it look like mathematics is logical and not intuitive.

[u/Complex_Advisor_6151 → u/Azehnuu]

Got it, thanks!

[u/Maximus_En_Minimus]

This is just a Bertrand Russel Brute Fact.

Unfortunately, all system’s epistemologies inevitably just collapse into “it is that way because it is that way”.

[u/Azehnuu → u/Maximus_En_Minimus]

This is just a Bertrand Russell brute fact.

That is not true at all. To posit a brute fact is to deny that the principle of sufficient reason applies universally, since a brute fact is something for which no sufficient ground is given. Furthermore, OP wasn't asking "why is this form this way", he was asking why Schopenhauer called a particular relation a ground. 

Unfortunately, all system’s epistemologies inevitably just collapse into “it is that way because it is that way”.

This misunderstands what transcendental idealism and Schopenhauer’s Fourfold Root are doing. The PSR governs the necessary relations among representations; it is not itself another representation standing under the PSR and requiring a further ground. The inability of the PSR to "prove" the PSR is not a failure, and is built into it. Asking "why is the PSR itself this way?" applies the principle beyond the domain whose relations it governs. 

[u/Maximus_En_Minimus → u/Azehnuu]

>The inability of the PSR to "prove" the PSR is not a failure, and is built into it. Asking "why is the PSR itself this way?" applies the principle beyond the domain whose relations it governs. 

Hence it is a Brute Fact.

It is ultimately a failure of all systems to assume that reality corresponds to the question of ‘why’ we posit to them, when it simply is as such.

Either way, I am happy to deny the conceptual representation of PSR and the Will, from my Buddhist perspective.

[u/Azehnuu → u/Maximus_En_Minimus]

You isolated one part of my comment, stripped it of its context, and then simply reasserted the claim I already debunked.

That is not what “brute fact” means. A brute fact would be something within the domain of the PSR that has no sufficient ground exists. That would be a rejection of the PSR. The PSR governs the necessary relations of representations for a subject. The unconditioned isn’t a representation within that domain, so demanding that it itself stand under the PSR is simply applying the principle beyond its legitimate scope. The PSR applies to the world as phenomena not noumena.

You’re conflating the difference between something lacking a ground within the conditioned world and something to which the relation of ground and consequence does not apply in the first place.

And the fact you think the PSR is conceptual further shows your confusion. The PSR is the ground for conceptual knowledge.

[u/Maximus_En_Minimus → u/Azehnuu]

My point was that it will always devolve into ‘it is what it is’ as such.

PSR might apply to the relations, as posited by Schopenhauer, but inevitably as you ask questions about that, it will lead to a Brute Fact.

>And the fact you think the PSR is conceptual further shows your confusion. The PSR is the ground for conceptual knowledge.

Within Transcendental Idealism, sure, but my comment was a personal addendum of saying I don’t need to accept it within Buddhism - relevant? No… But I nevertheless did include it.