Assuming that you must exist in order to argue, is not 'begging anything' and is not 'bias'. It's a simple statement of fact and not a matter for debate.

It seems the position is a form of “Ontological Relativism” or possibly “Relational Realism”. I want to explore this view, but can find little if any references to how I envision it. — noAxioms

There is already a Relational Realism at least discussed by Jonathan Cohen, and its terms are completely incompatible with your radical nihilism, being declined as "x is P for S in C".

Things exist only in relation to something (anything) else. There is no objective existence of anything, thus solving the problem of why existence exists. — noAxioms

How can a relation stand between things which do not exist? If the relation grants existence to the things, then the relation cannot follow from the things.

I don't know what you mean by this, "based only on relations". I think a relation requires things that are related, and the recognition of the things is prior to the recognition of the relations. In other words we must acknowledge that there are things, before we can acknowledge that there are relations. Therefore it is impossible that there is only relations. So I would argue the exact opposite of what you are saying. Evidence that there are relations is based on the premise "there are things". Therefore the conclusion "there are only relations" is invalid because "relations" requires necessarily, that there are things which are related. — Metaphysician Undercover

This.

Assuming that you must exist in order to argue, is not 'begging anything' and is not 'bias'. It's a simple statement of fact and not a matter for debate. — Wayfarer

And this.

If things need other things to exist and those things are defined by their relationships with other things, why would relationships themselves be excempt from this rule? Wouldn't relationships need the existence of non-relationships to exist as relationships?
— Harry Hindu

They don't need other things to exist since they don't exist. The structure simply has these relations, and those relations are independent of the existence of the structure. — noAxioms

Wat?

and the recognition of the things is prior to the recognition of the relations — Metaphysician Undercover

Is not he "recognition of things" entirely relational .. An aware subject in relation to phenomenal objects?

I think I'm also saying that existence of things is not necessary for the experience of those things. Only a relationship between the experiencer and the experienced. — noAxioms

This is confusing. Are you sure you mean what you just said? How can the experience be of those things, if those things don't exist? If no unicorns exist, then I can't have an experience of a unicorn. I can experience something resembling a unicorn, but I can't experience a unicorn. How could I ever encounter one?

Pretty much agree. That the universe is a mathematical structure (and is not merely modeled by one) is not new. The latter half seems to be what I've been exploring, and one which I have not necessarily seen litterature, let alone even a name for the stance.

The giant object is nearly equivalent to the class of objects. Membership in the class is given by the ability to denote the member. If you restrict this even bigger 'set of all things' style object to the set of relations of arbitrary arity with arbitrary related terms, you get essentially the one I tried to construct above. Pegasus is as much a member as rocks rolling down hills, the rocks and the hills, and that 'my feet are positioned below my knees relative to my body' considered as a conceptual object.

I'm indifferent to the claim that the universe has a mathematical structure. Insofar as 'mathematical structure' means 'exhibits patterns which are analysed well through mathematics', I agree. Further ontological commitments - like reality itself being fundamentally like something essential to mathematics - I don't want to go that far, nor to discuss this here.

When I say I don't think it's the time to discuss that, I'm gesturing to that I think your OP is different problem from the alleged mathematical nature of reality. Subordinating being to to relation; to be is to be part of a (chain of) relation (s); what it is is how it is; is something that can be done regardless of whether you believe the real existence of the related terms. Put another way, if all this was 'merely a fiction' it would still be the same except insofar as 'is a fiction' makes a difference.

Aggregating everything together into one of these giant objects whose implanted structures are then identified as the rules governing particulars in the object (rather than terms which are standing in for them...) isn't without its problems... Another irrelevant thread.

Even if you grant that this agglomerative operation is justified before adjoining 'is a fiction' or 'is real in the usual sense' to its product, it doesn't make much of a difference to the OP's argument. What I really wanted to take to task was this:

This is a key concept, demonstrating why objective ontology (or lack of it) makes no difference in the relations between different parts of the same structure.

relates a very impoverished understanding of what an ontology is. Loosely, an ontology really is an account of the relations between different parts of a structure, where 'parts' are understood in a exceptionally loose sense. (eg an ontology can look for how things came to be and develop a conceptual apparatus surrounding that, things coming to 'parthood' is also within ontology's subject matter). Picking which structures to designate as primordial, which as derivative, privileging none.... etc and to provide a conceptual apparatus circumscribing the most general ways in which things are is exactly what an ontology does.

Picking out a structure from the giant object because it in some sense mirrors our world leaves an account of the mirror; and the explication of the chosen structural symmetries. In the OP, nothing is lost by refusing the question because it sets out a picture of ontological accounts in which nothing can be gained from them.

Most of what's in the giant object is totally alien to us, so we're situated in a way to ask questions and question those questions. The existence of the giant object isn't particularly consoling in this manner. It functions as an already presumed terminus of ontological questioning despite those questioners, us, not knowing the full extent of what's in it and what obtains in it.

Again I thank everybody for their contributions. I am attempting to keep up.

Those are all relational observations.
— noAxioms
Even if they are, why does that matter? — Sapientia

It matters because empirical observation cannot be different, and therefore cannot be evidence one way or the other. This is an interpretation of observations, and like any interpretation, suggests no falsification test. If there is one, then it is science and the matter can be settled by running the test.

The nonexistent structure would still have those relations. There is something to see.
— noAxioms

That doesn't make any sense. You're committing the reification fallacy by talking about a nonexistent structure as if it exists. There would be no structure whatsoever, and nothing to relate to.

That's right. There is no structure to relate to, but its components still relate to each other. A square's opposite sides are still parallel despite no explicit existence of the square. The structure still has those internal relations, and our empirical experience is nothing more than such internal relations of the structure of our universe of which we are a part, whether that structure exists or not.

There wouldn't be anything, there would be nothing. If there is something to see, then it can't be nothing. So what are you talking about? Something or nothing?

I am talking about the structure, whether it exists or not. It only needs to exist to relate to something outside the structure, and then only in relation to that outside thing. The reification fallacy concerns relating two things with different ontology (map and territory, horse and unicorn), not denial of the relation that the opposite sides of a square are parallel. The unicorn exists in my imagination, so that's a mental relation, but not in the same way I relate to a horse. So the unicorn doesn't exist in relation to the horse.

Well, I'm a foundationalist, because I think that being a foundationalist leads to a picture which can best reflect reality. Starting from a foundation, I can demonstrate a thing or two.

I guess I'm building from a different foundation here, experimentally perhaps. I don't really identify with any particular <something>ist, even if I have a particular distrust of anthropocentrism, or views where we're special.

A concept is not the same as an instantiation. What do you want to talk about?

My simple example has been squares, not the concept of squares. I have examples of little universes like chess, Conway Game of Life. The chess one is interesting because it has entropy and the beginnings of quantum mechanics, but it has limited use in illustrating the point being pushed in this thread. The square seems to serve quite well for now.

The concept of nothing, which I have no problem granting has relations, or nothing, for which there would be nothing to relate to anything, as there would only be nothing. There could only be nothing.

I'm just being logical here.

So squares must exist (in concept or other form) in order to have properties? My definition of a square doesn't include that requirement. The requirement seems only necessary for our knowledge of those properties, and I've really tried to emphasize that the stance is not an epistemological one.

What could I have possibly done wrong to deserve this? Now the next point the premise "that there is something" supports the cosmological argument. You still agree? — Metaphysician Undercover

Yes, I feel it does support it. But then the argument falls apart by not solving the problem. It just adds one more turtle under the current unexplained turtle pile, and violates the spirit of the argument by asserting that no more turtles are needed. If that is a valid option, no new turtle is needed. You just declare the bottom one not to need anything to stand on just like you did with the God turtle.

So I did away with all the turtles. There doesn't need to be anything. There is nothing in need of rationalization on this front.

Assuming that you must exist in order to argue, is not 'begging anything' and is not 'bias'. It's a simple statement of fact, so if you wish to take issue with facts, you will no doubt find others willing to oblige. — Wayfarer

I must have absolute existence to produce an argument that has absolute existence, but my arguments are all relative to the structure of which I am a part. Nobody addresses the square. Why must it exist for its opposite sides to have the relation of being parallel? It is perhaps a valid premise to assume, but it is still just a different premise than the one being proposed here.

It is a different premise, not a statement of fact.

It matters because empirical observation cannot be different, and therefore cannot be evidence one way or the other. — noAxioms

Different to what? Evidence of what? What you're saying here suffers from a lack of clarity, and, as a result, your meaning is lost on me.

Not a good start.

This is an interpretation of observations, and like any interpretation, suggests no falsification test. If there is one, then it is science and the matter can be settled by running the test. — noAxioms

It's the most plausible interpretation, and it can be tested by way of explanatory power. The alternatives can be reasonably rejected by reductions to absurdity. If you and I do not exist, then how are we having this conversation? If no other objects exist, then, again, how are we having this conversation? And if the world doesn't exist, then - you guessed it - how are we having this conversation?

That's right. There is no structure to relate to, but its components still relate to each other. — noAxioms

No, no components either. Nothing means nothing, so no components. Nothing at all. There wouldn't be anything to relate to anything else. There can be no exceptions, so it's amusing, in light of the futility of trying, that you nevertheless keep attempting to find a way around the impossible.

A square's opposite sides are still parallel despite no explicit existence of the square. — noAxioms

That can be better put logically, as folows: if there exists a square, then it is such that its opposite sides are parallel.

That can then be used to determine whether or not squares exist.

The structure still has those internal relations, and our empirical experience is nothing more than such internal relations of the structure of our universe of which we are a part, whether that structure exists or not. — noAxioms

Do you not realise that it makes no sense to, on the one hand, talk of us as being part of the structure of the universe, and on the other, question whether that structure exists? You are tacitly contradicting yourself. If we are part of the structure of the universe, then the structure of the universe exists, as do we.

You've got yourself in a right tangle, methinks.

I am talking about the structure, whether it exists or not. — noAxioms

Right, let's get a few things straight, shall we?

1. If you're talking about the structure, then you're talking about something, not nothing.

2. If you can't say whether or not it exists, then, to be clear, you shouldn't be talking about, "the structure", as though it exists. You should instead be talking about its possibility. Or, alternatively, you could talk about the imaginary or presumed structure.

It only needs to exist to relate to something outside the structure, and then only in relation to that outside thing. — noAxioms

That's confusing. What are you actually talking about? What does it mean? "The structure only needs to exist to relate to something outside of the structure, and then only in relation to that outside thing." What is this structure of which you talk? Why are you speaking in such vague abstract terminology. If you want to talk about the universe in a meaningful way, then you should talk about the stuff and things of the universe, as well as their relations. Sorry, but I think I've had enough of your peculiar manner of talking.

This is why philosophy gets a bad reputation.

Is not he "recognition of things" entirely relational .. An aware subject in relation to phenomenal objects? — snowleopard

No, I don't agree. You are simply assigning to the "recognition of things", a relational existence. You are simply assuming, falsely concluding, or something along those lines, that a recognition of things is necessarily a subject in relation to objects, but this need not be the case. The recognition of oneself, as a thing, is not a relation. If you posit the recognition of oneself as a relation, then oneself is not an identified thing, but a relation between two distinct things. But that's contradictory to say oneself is two distinct things And if oneself is one identified thing, then it is one and the same thing, and this is not a relation, it is the simple recognition of a thing.

Yes, I feel it does support it. But then the argument falls apart by not solving the problem. It just adds one more turtle under the current unexplained turtle pile, and violates the spirit of the argument by asserting that no more turtles are needed. If that is a valid option, no new turtle is needed. You just declare the bottom one not to need anything to stand on just like you did with the God turtle. — noAxioms

I don't see what you mean by "not solving the problem". Nor do I get the turtle reference. The assumption is "that there is something". The cosmological argument demonstrates that from this assumption it is impossible that there ever was nothing. Therefore the question, why is there something rather than nothing, is solved, it is because it is impossible that there is nothing. But this raises the question of why is it not "possible" that there is nothing

So we can proceed, and replace "nothing" with "the potential for something", or the simple possibility for something. This appears to be a more rational question because we observe that prior to the existence of anything there is the potential, or possibility, for that thing. So to avoid an infinite regress (perhaps this is the turtle reference), we might assume a time when there was the potential for things, but no actual things. This is what the cosmological argument denies. If at one time, there was the potential for things, with no actual things, no actual things could ever come into existence from that potential because any potential requires something actual to actualize it. This is what is referred to as the necessary actuality which is prior to all contingent things.

And if oneself is one identified thing, then it is one and the same thing, and this is not a relation, it is the simple recognition of a thing. — Metaphysician Undercover

No, what I am is not a thing at all. There's awareness ... There's the contents of awareness ... but there's no actual boundary and no 'out there.' So it does seem that any relation is dependent upon an apparent duality. Could this be what the mystics refer to as the spell of maya, for the sake of the compelling dream of relational experience? The One is the many ... The many are the One ... Quite amazing!

<These:> Wat? — Sapientia

I am going to fall back to my square again. I seem to be on my own. The view must be faulty if nobody seems to grasp what I'm trying to describe.

I think a relation requires things that are related, and the recognition of the things is prior to the recognition of the relations. — Metaphysician Undercover

The sides of a square are parallel, a relation. That relation does not make the square exist. I'm not claiming relation prior to existence. But one side of a square exists (existential quantification, not a designation of ontology) in relation to the other sides and to the angles. This doesn't mean any of it has objective existence.

Assuming that you must exist in order to argue, is not 'begging anything' and is not 'bias'. It's a simple statement of fact and not a matter for debate. — Wayfarer

A different premise, not fact.

If things need other things to exist and those things are defined by their relationships with other things, why would relationships themselves be excempt from this rule? Wouldn't relationships need the existence of non-relationships to exist as relationships?
— — Harry Hindu

They don't need other things to exist since they don't exist. The structure simply has these relations, and those relations are independent of the existence of the structure. — noAxioms

Well, the wording there wasn't my best effort. I'm not claiming ontological existence of anything, or of the relations. The opposite sides of a square have a relation of being parallel. That doesn't make the square exist or the relation exist. It means that squares have that property. If only existent squares have that property, then either platonic existence is necessarily true, or the opposite sides of squares are not parallel because there are no actual squares, only abstractions/concepts, and concepts don't have sides that can be said to be parallel.

Similar, the moon and I stand in relation to each other, and so I say it exists in relation to me, but that is not a declaration of absolute ontology. Yes, the view is a form of ontological nihilism, but I've read up on nihilism, and it is something else.

Similar, the moon and I stand in relation to each other, and so I say it exists in relation to me, but that is not a declaration of absolute ontology. Yes, the view is a form of ontological nihilism, but I've read up on nihilism, and it is something else. — noAxioms

I think I'm also saying that existence of things is not necessary for the experience of those things. Only a relationship between the experiencer and the experienced.
— noAxioms

This is confusing. Are you sure you mean what you just said? How can the experience be of those things, if those things don't exist? If a unicorn doesn't exist, then I can't experience it. I can experience something resembling a unicorn, but I can't experience a unicorn. — Sapientia

I just quoted what I just posted above. I am not being careful with my wording. I say the moon exists, but formally I say it exists only in relation to me. We're part of the same structure.

So as to what I said in the bit you quote there, I'm saying the absolute (objective) existence of things is not necessary for the experience of those things. But my experience depends on there being a relation between me and the thing, meaning both need to be part of the same structure. So one side of a square could experience its neighbor if it was the sort of thing with enough complexity to experience something, which it isn't. A square isn't even a temporal structure, and I cannot imagine experience in a structure without process.

So I relate to a horse because we're both parts of the structure, with sufficient interaction for there to be experience. The unicorn is an imagination, and that imagination is part of the physical process that is part of the same structure as me. So I relate to my imaginations. The imaginations exist to me, and the unicorn is one of them. Different relation than the one I have with the horse where the interaction is through external senses. Yes, you said it. You experience something resembling a unicorn, but it is an imagination, not a physical object like the horse.
I can speak of a horse or unicorn interchangeably. You can interpret that as speaking of the concept of either of these things, or of an actual horse or unicorn, despite the lack of relation of "empirically observable" between people and the unicorn.

"why is there something instead of nothing"
What an amazing question. I really used to ponder over it. The great presocratic Parminedes answers it. There can be no such thing as nothingness. There's only beingness. Once we realize 'why something exists instead of something' .next step is to analyze is the nature of nothingness and existence. Nothingness cannot be. Because what is not IS . That is a contradiction. Neither can nothingness can be a predicate. Unicorn don't exist. Is a contradiction. Because even by uttering the word 'unicorn' we ascribe a certain ontological status to it .even if it is in our minds. It has certain properties . A certain form. So when we say unicorns don't exist.So logically what we are saying is. "a unicorn(a horse with wings) is not a horse with wings." Because it is not. Whole Eleatic philosophy is based on rejection of nothingness. Which results in a logical necessity for things to just exist.

That can be better put logically, as folows: if there exists a square, then it is such that its opposite sides are parallel. — Sapientia

It not worded that way in the relational view, and I've never seen in worded that way anywhere. It seems weak, since there are no actual squares (since there are no actual line segments or planar objects for that matter. There can be no truth to the statement above, lacking anything real to give any weight to the right side of the statement. I might have well said that if there exists a square, then it is round. That isn't false since there are no squares outside of platonism. Hence my comment that platonism would be necessarily true, but nobody uses this line of reasoning to prove platonism.

For purposes of this discussion, the relational stance says that opposite sides of squares are parallel, an ontology-independent property of parallelograms, and squares are parallelograms.

Well, the wording there wasn't my best effort. I'm not claiming ontological existence of anything, or of the relations. The opposite sides of a square have a relation of being parallel. That doesn't make the square exist or the relation exist. It means that squares have that property. If only existent squares have that property, then either platonic existence is necessarily true, or the opposite sides of squares are not parallel because there are no actual squares, only abstractions/concepts, and concepts don't have sides that can be said to be parallel.

Similar, the moon and I stand in relation to each other, and so I say it exists in relation to me, but that is not a declaration of absolute ontology. Yes, the view is a form of ontological nihilism, but I've read up on nihilism, and it is something else. — noAxioms

If you are not claiming the ontological existence of anything, then what are you actually saying? You are not saying anything interesting or meaningful.
Are you describing a state-of-affairs that exists, or no? Are we actually having this conversation or no?

Similar, the moon and I stand in relation to each other, and so I say it exists in relation to me — noAxioms

Really, when it comes down to it, all of these conscious machinations are doing nothing to address the 'hard problem' -- i.e. what is consciousness? What is the aware 'I'-ness which is aware of the moon, whatever the moon may be in essence, Platonic forms, mathematical structures, or otherwise? Absent any explanation, why should one adopt this metaphysical stance over physicalism? Physicalism at least has a theory of consciousness, however incomplete or inadequate it may currently be.

How can the experience be of those things, if those things don't exist? If no unicorns exist, then I can't have an experience of a unicorn. I can experience something resembling a unicorn, but I can't experience a unicorn. How could I ever encounter one? — Sapientia

I see a white and gold dress. You see a black and blue dress. But we're both looking at the same thing. One can say that the object of perception is determined by the quality of the experience and not by the external stimulus.

Just as a painting is of a unicorn, even though there isn't a unicorn, the experience is of a unicorn, even though there isn't a unicorn.

No, what I am is not a thing at all. There's awareness ... There's the contents of awareness ... but there's no actual boundary and no 'out there.' So it does seem that any relation is dependent upon an apparent duality. — snowleopard

So you have relations without boundaries, how?

The sides of a square are parallel, a relation. That relation does not make the square exist. I'm not claiming relation prior to existence. But one side of a square exists (existential quantification, not a designation of ontology) in relation to the other sides and to the angles. This doesn't mean any of it has objective existence. — noAxioms

OK, I'll see if I can make sense of this. You are assuming "a square", that is your premise. Now you are talking about the sides of that square. It is all in your mind, the square and the sides, so you say that it has no objective existence. How do you get to the point of talking about things outside of the mind?

Similar, the moon and I stand in relation to each other, and so I say it exists in relation to me, but that is not a declaration of absolute ontology. Yes, the view is a form of ontological nihilism, but I've read up on nihilism, and it is something else. — noAxioms

Now you are talking about the moon. Aren't you assuming that the moon has some sort of existence, before you can talk about a relation between you and the moon?

just quoted what I just posted above. I am not being careful with my wording. I say the moon exists, but formally I say it exists only in relation to me. We're part of the same structure. — noAxioms

Aren't you assuming the existence of this thing, the "structure", in order to make this claim of relations? I still don't see how you get to the point of saying that any of this is outside your mind. The "structure", the "relations", the "moon", they are all just in your mind. How would you give reality to this "structure" if you do not assume that it is a thing outside your mind?

So you have relations without boundaries, how? — Metaphysician Undercover

You seem to have overlooked the word 'apparent' -- which I did italicize for a reason, but perhaps the 'bold' will help too -- or I should have said 'seeming.' You also seem to have overlooked the part about "the compelling dream of relational experience." ... In other words an apparency.

I see a white and gold dress. You see a black and blue dress. But we're both looking at the same thing. One can say that the object of perception is determined by the quality of the experience and not by the external stimulus. — Michael

One could also say that the state of the sensory organs and the brain, along with the state of the object being perceived by said sensory organs, help determine what is experienced.

I don't get you. You said "there's no actual boundary". You're clearly not talking about apparent boundaries, you're talking about actual boundaries.

If you are not claiming the ontological existence of anything, then what are you actually saying? You are not saying anything interesting or meaningful.
Are you describing a state-of-affairs that exists, or no? Are we actually having this conversation or no? — Harry Hindu

We are having this conversation since we stand in relation to each other, through this forum as well as other means. That is what ontology is in the relational view. The question is not "does A exist?", but rather "does A exist to B". You among others are reaching for non-relational assumptions. So the universe exists to me and you, and that means we can have this conversation.

Really, when it comes down to it, all of these conscious machinations are doing nothing to address the 'hard problem' -- i.e. what is consciousness? — snowleopard

Not a consciousness thing. The moon stands in relation to my mailbox, so each exists to the other, despite neither having awareness of each other.

Well actually I referred to an apparent or seeming duality. In any case, how is saying 'there is no actual boundary' different from saying that any boundary is an apparency, or a seeming boundary? In other words it is not what it appears to be. Perhaps we're running into some issue of semantics here.

OK, I'll see if I can make sense of this. You are assuming "a square", that is your premise. Now you are talking about the sides of that square. It is all in your mind, the square and the sides, so you say that it has no objective existence — Metaphysician Undercover

Not talking about a square in my mind. Talking about any square, the mathematical form itself, and not merely the concept of it, which would require a relation with a conceiver.

The moon stands in relation to my mailbox, so each exists to the other, despite neither having awareness of each other. — noAxioms

Again, this offers no explanation or theory of conscious awareness/experience whatsoever, so isn't of much interest to me -- and indeed does feel quite nihilistic. But since it is of interest to you, then carry on. :)

Perhaps we're running into some issue of semantics here. — snowleopard

No we're going around in circles. You claimed that the recognition of things is entirely relational. I claimed that the recognition of myself as a thing is not relational. You said boundaries are unreal, so I asked how do you have relations without boundaries. Now you seem to be claiming that both of these, things, and relations, are unreal. Is that your point?

Not talking about a square in my mind. Talking about any square, the mathematical form itself, and not merely the concept of it, which would require a relation with a conceiver. — noAxioms

Wait a minute, what are you talking about, "a square" or "any square". The former is a particular square, the latter is a general idea allowing for the possibility of a particular. Am I correct that you are assuming a Platonic Form, "the mathematical form itself"? Doesn't this mathematical form exist as an eternal object?

But each of us existed prior to our conversation. In order for our relationship to exist, we must exist prior to our conversation. Our conversation is a relationship, but not one that is necessary for each of our existence.

The universe existed prior to any relationship. If not then, it needs a relationship with a non-universe to exist. Again what keeps you from falling into the bottomless pit of an infinite regress? Why does the universe not need something else in relation to it to say that it exists?