Sure, but it doesn't mean that tails is twice as likely to occur as heads, — Michael

It is twice as likely to occur to miss Beauty. Tails happens twice, and heads only once.

So, I ran 100,000 games and gave 1 point for successfully guessing heads and 0.5 points for successfully guessing tails (because you get two opportunities). It doesn't matter if you always select heads, always select tails, select tails 1/2 the time, or select tails 2/3 of the time. The average score is 0.5 in every case. — Michael

Ouch... Does miss Beauty know that she's getting fewer points on some of the bets. In that case the outcome is certain and she can win every bet. If not, she's not the one doing the gambling.

This whole betting thing demonstrates the correct answer. It only needs to be done twice, not 100000 times, because there are only two unique cases occurring in equal probability.
I wake up and am expecting to bet a coin with even odds. I bet tails and win 2 coins (one each day) if it is tails, and lose one coin on Monday if it is heads. Sounds like a winning bet to me.

If the stakes depend on the coin toss, then I bet tails if the stakes are 0.5 coins per bet, and heads if the stakes are 1 coin in the bet. I win every time in that case.

I noticed a discrepancy.
The description of the problem does not make it clear that sleeping beauty knows the procedure. If she doesn't, then she has no knowledge of anything other than their asking about what is a random coin toss. The odds would be 50% then.
The 33% comes from the sleeper knowing that there will not be a waking on Tuesday if the result is heads, but there will be a waking on the other three scenarios. In this case, new information is gained (it is not Tuesday/heads), and the odds are not 50/50

Another simple way to compute this, objective, but without knowledge:
There are four equal probabiltiy states (each equally has 50% chance of being visited eventually, all depending on the coin toss. Monday and Tuesday are eventual certainties):
A Monday Heads
B Monday Tails
C Tuesday Heads
D Tuesday Tails

The sleeper wakes up and knows not which of the four it is, but she has the additional knowledge (new information) that it is not C, so 33% chance of each of the other choices, and only one of those is heads. Odds are 33%

Slow reply, I know. Been away.

This one is begging a different answer. From Sleeper's perspective, this has not been established.
— noAxioms

She already knows that it was a fair coin toss and that a fair coin toss has a 50% chance of landing heads. Nothing can change that. — Michael

Information about the toss can very much change that. If she is able to actually see the result of the toss, the odds become a certainty one way or another, not 50/50. So information does change the odds, and she has information beyond the simple fact that a coin was tossed.

To assert 50/50 odds here is to use a perspective other than that of the sleeper.

I don't know what you mean by adding up to 33%.

P(Heads) = 50% — Michael

This one is begging a different answer. From Sleeper's perspective, this has not been established.

But one of those awakenings is twice as likely as each of the other two, which is why the halfer answer is correct. — Michael

Yes, the Monday awakening is twice as likely as the Tuesday one. It doubles the weight of that awakening. So it adds up to 33% since there is a 50/50 shot on the heavier awakening, and a 0% shot on the Tuesday one.

So we have:

H: A, S
T: A, A

So since there are three possible awakenings and only one is when the coin comes up heads, then won't that mean she has a 33% chance of it being heads? — Jeremiah

I hate to say there is no conundrum about this one. I've not read most of the posts past this point in the thread.
Jeremiah's answer here seems correct to me. The 50/50 answer is from one who has no additional data and knows only that there is a coin flip. Sleeper here has additional data: I am awake, which reduces the case to which of the three awakenings above is this one.

Before you are born is the period I am referring to. If I start to exist there is the question of how I start to exist as that person. — Andrew4Handel

Well as I said, I think I am the wrong person to give answers to questions about a view that I do not hold.

When does combustion start to exist as a specific flame? Strange way to word it...

You could not be anyone else now but you could have been someone else and been born in another body or era or gender. — Andrew4Handel

Yes, that's the second guy I'm referring to. I say it doesn't exist. There is nothing that could have been somebody else until being born in this specific body. Mind you (pun intended), I am not asserting this. I'm just saying that the question you pose goes away with my answer. If this dualistic view is one you prefer, fine. As I said, religion has a lot of answers to how you got to be the fourth of six siblings, or how you got to be human at all for that matter.

I am one of 6 children I am conscious of being the fourth child but why not the first or sixth?

My answer is that it would seem absurd for the 4th child to be conscious of being the second child. That's what monism says. I think a lot of people that claim to be monists actually don't understand it and cannot accept that simple answer. It sure took me a long time.

That's why my first post dove into that 'objective' rant. The whole thing is easier to grasp from the outside in. Don't propose reasons P why I experience such and such. Ask instead that if proposal P is true, what would be the experience of person X? Same question, but more in 3rd person, and it yields different answers given the different assumptions built into the different perspective.

Never said I wasn't a person. I said I'm not two of them.

There is no realistic way of taking the "I" out of any theory because that raises the question of who is talking and what they are talking about. — Andrew4Handel

Fine. I have never heard of anybody that was somebody else. Why am I me? Well, who else could I be?

More your wording:

inhabit this conscious location of having experiences of a reality and how this subjective location arises — Andrew4Handel

'Inhabit'. OK, I see the path you want. Never mind at all what I say then. Religion has better answers to this one than I do.

But concerning location, I've also never know a person to be conscious at a different location than where they were. Both questions seem absurd to me, because there is only me, not two things paired by an 'inhabit' relationship.

The question already has biases built in, so you're on your own answering it. I struggled for quite some time figuring out this one until I identified the bias and the source of it. I found myself to be an improbable thing to be since there are so many other things (a bird, a stick, the duration of a flame), but here I am a well-off member of the species at the top of the food chain during the 2nd gilded age, pretty much the perfect thing to be. Baffling until I removed that bias.
So instead, don't assume that there is an 'I' that got to be 'me', or got to be 'here', and the problem vanishes.

As Thomas Nagel says "Objectivity is a view from nowhere" — Andrew4Handel

Well, an objective viewpoint is a view from nowhere and thus not really a viewpoint, but an objective description need not be precluded, and it often yields answers that elude a subjective description. You're going to need it for answers like this one.

I cannot render a 'view' (a drawing say) of a car without choosing a perspective, but I can describe one in full detail without the necessity of selection of a perspective.

Well this is not my paradox, I didn't invent it. It is a well known paradox, and widely recognized as such. Also the mathematical proof is posted in the OP. — Jeremiah

So you don't think is a paradox, OK fine, I don't really care. — Jeremiah

Fair enough. The relevant definition of paradox that pops up says this:

a : a statement that is seemingly contradictory or opposed to common sense and yet is perhaps true
b : a self-contradictory statement that at first seems true
c : an argument that apparently derives self-contradictory conclusions by valid deduction from acceptable premises — Webster

The funny cone seems to fall under definition 'a' since it seems opposed to common sense to many people. So yes, it makes sense to 'resolve' such paradoxes by showing that the seeming contradiction is something that is actually the case. The mathematics (a computation of the area and volume) is linked in the OP, but not sure what part of that is a 'proof' of something.

'b' seems to be the opposite of 'a': something that seems true at first but false on closer inspection.

I guess my idea of a paradox falls under 'c', the most basic example being "This statement is false". Any truth value assigned to that seems to be incorrect. I've seen it resolved in law-of-form using an imaginary truth value (square root of false) just like imaginary numbers solve square root of -1. There is application for such logic in quantum computing.

Saying there is no mathematical basis for this just tells me you can't read the math, as it is posted right there for you to review.

I never contested the mathematics, which simply shows that the object indeed has infinite area but finite volume. I can think of more trivial objects that are finite in one way but infinite in another, and your cone did not strike me as a connundrum. But I retract my assertion that it is not a paradox. The definition above speaks.

You can say, well it is not in the real world — Jeremiah

Indeed, it is only a mathematical object. A real one could not be implemented, growing too thin to insert ice cream particles after a while.

Interestingly, a liter of physical paint contains insufficient paint to actually cover a square meter of surface. There is a finite quantity of fundamental particles making up the volume of paint, and no fundamental particle has ever been found that occupies actual volume. So the paint is all empty space with effectively dimensionless objects which are incapable of being arranged to cover a given area without gaps. Instead, paint atoms work by deflecting light and water and such using its EM properties, not by actually covering a surface without gaps. Point is that this particular mathematical object has little relevance to even a hypothetical physical object.

Any container or solid object that has an endless surface area, but a finite volume is paradoxical, abstractly or otherwise.

Volume is the amount of space it takes up, so if it has endless surface area it should have endless volume. — Jeremiah

This assertion is exactly that: just an assertion, and a false one at that. There is no mathematical basis for this. The paradox apparently comes from your assumption of this nonexistent law.

The horn both converges and diverges, so it fits your personal take on what is needed for a paradox. — Jeremiah

A paradox is usually of the form of "If A is true, then A can be shown to be false". Your original 25 25 50 60 thingy would have been paradoxical had the 60 entry read 0%. What you seem to be reaching for here is not a paradox, but rather a violation of the law of non-contradiction, that a thing cannot be both X and not-X at the same time in the same way. I don't see the violation due to the 'in the same way' part.

So you are suggesting a finite amount of paint that goes on forever.

that paints an infinite surface. 'goes on forever' is not what I said, and seems a sort of undefined wording.
The alternative is that there is some points along your surface that do not enclose volume and are thus not painted.

So in your suggestion the volume of the paint both converges and diverges?

No, the volume is finite. You said that. There is finite (convergent as you put it) volume of ice cream, which could be paint.

I think you just can't admit that you were wrong. — Jeremiah

That is not philosophy, not by a long shot and if that is the standard that passes on these forums, then I have to question if I belong here at all. — Jeremiah

Because my arumgent is sound, besides I hate it when everyone sits around agreeing with each other, it is incredibly unproductive. — Jeremiah

This popped up this morning:
https://www.gocomics.com/fminus/2018/05/23

Thought it expressed my takeaway on this topic.

This one is a bit trickier and as far as I know it has not been resolved. — Jeremiah

In what way is this in need of 'resolution'? You haven't stated a problem with this scenario.
Is there some law somewhere being broken, like infinite surfaces must enclose infinite space? There is obviously no such law, as demonstrated by this example.

So you are suggesting if it was filled with paint, you could use a finite amount of paint to paint an endless surface.

It seems to me, that you'd run out of paint, and even if you could stretch the paint infinitely thinner, that still does not resolve the paradox. As abstractly what you have is a cone with a converging volume and a diverging surface area. — Jeremiah

Clearly the paint would not run out, as it hasn't in your example. It covers the entire surface, and doesn't even need to be spread out to do so, since it has finite thickness (all the way to the center line) at any point being painted.

I see no paradox in need of resolution. The volume converges and something different (the area) does not. It is only paradoxical if the same thing both converges and diverges.

So what would constitute a proof that your first assertion is wrong, what kind of proof would we need to present, and what standards would be assessing that proof by to see if it held? — Pseudonym

A simple example to the contrary suffices in proving wrong an assertion that all A is B, or in this case, the only valid interpretation (A) is one of a sample space of 4 (B). Many of us have produced that alternate interpretation of a sample space of three (~B).
That leaves it up to Jerimiah to demonstrate that either this sample space is not 3 in number, or that one has no way of randomly selecting from this sample space. The latter would be the case if the answers were hidden, but the OP concerned an open multiple choice question, not drawing of hidden names from a bag.

33% is not a valid answer no matter how you slice it. It completely ingores the distribution. — Jeremiah

Not so. You just refuse to slice it the way some others are.

The people saying 33% are demonstrating a fundamental misunderstanding of basic probability. — Jeremiah

This misunderstanding comes from an imprecisely wording of the problem, and you're assuming everybody interprets the problem the way you are.

So back to the red, yellow, and two blue balls example. I have one of those colors in mind, and I ask the odds of you guessing correctly. The odds are 25%, 33%, or 50% depending on the choice and the interpretation. 25 and 50 come from blindly reaching into the bag and selecting a ball. 33% comes from looking at the available colors, randomly selecting one of the valid options, and then choosing a ball that matches that choice.

Similarly, your original problem had three unique answers to choose from, and there is a 33% chance of each of those if I choose from them randomly. But there is a 25% of each of A,B,C,D and I don't need to look at the answers to choose those randomly.

Am I choosing randomly from the 4 bullets, or from the three unique answers? Never mind that in both interpretations, all the answers provided are wrong.

There is only one purposed chance event. It does not loop back on itself, it is not a circle and, as long as you don't say C), then you are not wrong until after the chance event, only then can you be wrong. — Jeremiah

????

You're wrong no matter what you choose. There is thus zero percent chance of choosing correctly, which is what the question asks. That the thing is self-referential doesn't seem to change that. It's not a paradox as written.

The problem as I see is that the outcome changes the solution and I not sure if I would consider that truly circular. — Jeremiah

Of course it is circular. Perhaps there is a paradox that is not, but I cannot think of one offhand.

The question concerns the answer to the question. That's a circle, or more formally, self-referential.

You ask about the odds of correctly guessing the answer giving the correct odds of correctly guessing the answer giving the correct odds of correctly guessing the answer giving the correct odds of correctly guessing the answer ....

0% is not a possible outcome, which means there is a 0% chance of it being 0%. — Jeremiah

If none of the choices is correct, then the correct answer is simply not among the choices. 0% is the answer since it cannot be chosen. This itself is not paradoxical. Hence my comment that (C) should have been 0%, not 60. That forces the paradox.

It is not necessarily invalid for a question to be circular.

How many letters does the correct answer have?

• two
• three
• four
• five

Sorry. See edit

Guessing what correctly though? — StreetlightX

of correctly guessing the answer giving the correct odds.
Yes, circular, but that doesn't mean there's no actual question.

Heh
Thought of a variation of the original one:

If you choose an answer to this question at random, what is the chance you will be correct?

A) 25%
B) 50%
C) 100%
D) 50%

Each answer is correct (not necessarily in the same way), so are any of them really?

There's no criterion for correctness, so there's no possible answer. — StreetlightX

But there is. It asks about the odds of guessing correctly.

Therefore, the correct answer is 0% which is correct because it is not a choice on offer. — unenlightened

I agree, and the consistency of this makes it not a paradox. Choice C should probably have been 0% instead of 60%. Then it would be a paradox I think.

Is your existence dependent upon the existence of our conversation? — Harry Hindu

Non-relational use of 'existence', so no . We can converse partly because of our existence in relation to each other. That is not a sufficient condition. It also requires the relation of 'can interact'. I have only the former relation with Napoleon, and thus cannot converse with him. I have questionable existence in relation to Napoleon. I was presuming (as I stated many posts back) a mono-world deterministic interpretation of QM. If not, even that relation goes away.

What is the difference between the relationship of the Moon and a mailbox and the moon and yourself? Doesn't the differences lie in the attributes that make up the objects of those relationships?

Not much difference. There is the additional relationship of 'can experience' that I have with the moon.

And you keep cherry-picking my post, ignoring the point I keep making about the universal structure itself needing a relationship with something else in order for it to exist. How do you prevent yourself from falling into an infinite regress?

Yes, it would need a relationship with something else in order for it to exist, and then only in relation to said other thing, degrading the 'no-longer-universe' to a component within a larger structure. For example, for there to be a way for a non-deterministic interpretation of QM to work, there would need to be a relationship between the physical sub-structure and whatever is rolling the dice for it.
But I never claimed the structure exists or needs to. That would be the different premise that I am rejecting. There is no infinite regress because there is no unqualified existence in the view.

..or a multiverse.

I am using 'universe' as 'the whole structure'. Multiverse is another term for this, with multiple universes. I would alternatively call the complete structure 'the universe' with multiple worlds. The difference is just choice of terminology. For example, distant (say 30BLY away) stars do not exist in relation to our solar system. There is no direct relation between us. So the natural QM fit is the relational interpretation where the state of one thing is defined strictly in terms of specific other states. Such and such is true in relation to Alice, but a different state of affairs is the case for Bob or Bob a minute hence or the cat in the box. Other worlds do not exist in relation to any of them.

It must have a name and maybe an article somewhere.
— noAxioms

Process philosophy?

https://www.youtube.com/watch?v=-Q6cDp0C-I8

"The universe is a set of relationships between relationships, between relationships - all of which change over time. None of these relationships is ever static."

Haven't watched it yet. The summary you give seems true of realism as well, so not sure if it is what I'm seeking.

The law simply says "in the same way". Time is simply one of the ways that might not be the same.
It is daytime, and it is not daytime can both be true if they are truths about different times of day. The two statements are not 'in the same way', so there is no violation of the law.

Relatvity allows one to say that event A happens before event B in one frame, but in another frame B happens before A. A precedes B and B precedes A, but in different frames, so they're not 'in the same way'. Again, no violation of the law of non-contradiction.

I used the word, "object", as you did. I said nothing of physical objects. — Sapientia

Ah yes, so I did. And we're not using the word to mean physical objects.

You said that you want to explore this point about objects needing to be real for them to have properties and relations, and, in relation to this, you seemed to be taking the Mandelbrot set as an example of an object. You are also calling it a mathematical structure. But, is the latter what you're saying it is specifically, or is it what you're saying it is instead of an object?

I admit that the word has connotations of being a member of something bigger. Earth is an object, but the universe isn't really thought of that way, unless in context of something larger like a god and his creation-object that he puts on the shelf next to his five other ones. So I suppose it was careless language use since those connotations are not intended. A side of a square is an object of sorts more than is the structure that is the square that is not in a larger context like a coordinate system.

Anyway, what I'm interested in, is what the consequences of committing to the alternative stance would be. That is, if objects don't need to be real to have properties and relations, then what does that entail? Anything of significance?

Well the OP mentioned that it removes the perplexing question of how existence comes to exist. I can't say how it was created since that puts existence inside the larger context of time, reducing it to an 'object'. Objects in our universe get created. The concept is confined to the rules here.

So committing to the alternative stance eliminates the designation of 'is real', which only serves its own purpose. If the universe is real, the stuff in it is also real, but if it doesn't need to be real, then we don't either. It's like presentism's assertion of a real slice of spacetime (events not on that slice are not real) that changes position over a different sort of time than what clocks and other physical processes measure. While intuitive, it is completely undetectable and explains nothing, and there is no way to measure the pace of it. Seems superfluous. So around a century ago when all this was realized, they proposed that it could be eliminated without empirical difference, and eternalism was the result. I'm trying to see if that can be done with 'is real' in general since it seems to serve only its own purpose but doesn't really add anything.

On the face of it, it seems to be right to say, for example, that a property of a unicorn is that it has a horn, or that a property of the Mandelbrot set is that it is complex or contains numbers. But you ask how it is that things like unicorns, which are not real, can have properties. That's a good question. There does seem to be something counterintuitive about that. I'm going to give this encyclopaedia entry on nonexistent objects a read, as I think that it relates.

Well thank you for giving it fair consideration. Most of the responses have been knee-jerk protests based on assumptions of realist views. And hey, I identified as a realist for some time, but I'm learning not to identify as anything, because that just closes you off to further exploration. There are few stances I've not given fair consideration. I don't think idealism is incompatible with physicalism. Both are relational views, but relative to different things. Mine is sort of a generalization, but minus a fundamental core of reality.
So it is a bit nihilist I guess, but not the usual sort. I don't think there are no morals or that life is meaningless, but those are what pops up under nihilism.

Surely I'm not the first to consider all this. It must have a name and maybe an article somewhere.

Well, it seems to me that it would make sense to start by questioning what kind of thing the mandelbrot set is. You seem to suggest above that it's an object. But is it? What makes it an object, rather than anything else? — Sapientia

Not a physical object. I didn't use the word. It is a mathematical structure, one that can be referenced but not really instantiated. Again, I'm not talking about our awareness of the structure (it's concept), but about the structure. Only the latter has that property of being connected. The concept only has an awareness of that property.

I can draw a crude depiction of the set the same way I can draw a crude square. Neither of them has the properties we've been discussing, but it's all the instantiation either is likely to have.

The wording ("there exists", "such that") is associated with first-order logic — Sapientia

That is exactly what 'existential quantification' means. It is not an assertion of the realism of the thing in question. But in the relational view, perhaps that is all there is.

Anyway, I want to explore this point about objects needing to be real for them to have properties and relations. Take the mandelbrot set. That set cannot be instantiated by any means known. We can sample it a bit and print pretty pictures of the result of that, but it is just a sampling, not the set itself. So how can it be said that it has properties like being everywhere connected?

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. — Harry Hindu

Not following this. Are you talking about temporal existence? For that, the conversation requires sufficient proximity and simultaneous overlap of existence in spacetime to allow interaction. The square isn't a temporal structure, so I don't think this is what you mean.
But the relational view has no un-relational existence, so nothing can depend on that in order for there to be relations within the structure.

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? — Metaphysician Undercover

Going to need more time with this one. I think the question is important, but most of Platonic views are ones of realism, not relativism. Nothing exists as an external object, so no 'is real', but only 'is real to...'.

Squares are not just that. There is pure mathematical square, which has fewer properties than unit-square, or square in a coordinate system. There is the square cross section of a tetrahedron. All these make the square a part of a larger structure, and thus not the structure itself.
I don't think a square is necessarily a particular, but the cross section is is a particular cross section of the tetrahedron. So 'particular' itself seem to be a relation. The overall structure seems not to be a particular since there is nothing with which it has that relationship.

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.

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.

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.

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.

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.

<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.