I agree that a unicorn here on our world is not consistent with our particular universe of discourse, but I didn't ask if it existed in our universe of discourse, I asked if it exists (the general property form, not the relation with our concrete world), and it being in our particular universe of discourse is not a requirement for its logical consistency. — noAxioms

If there is a logically consistent definition of unicorn in a particular universe of discourse then the unicorn exists (in that particular universe of discourse and thus also in reality as a whole). I just meant to point out that although it may seem that the definition of a unicorn existing on our planet is consistent, it is in fact not consistent, and so there is no unicorn on our planet. This is a perhaps somewhat surprising point about logical consistency: reality cannot be different than it is because then it would be what it is not and thus would be inconsistent.

You really don't seem to like your own definition, litewave. You said 'exists' means 'logically consistent', not 'logically consistent with the universe of discourse ('UoD', which unfortunately conjures an image of a birth control device) consisting of what I see'. The latter is not a property.

If there is a logically consistent definition of unicorn in a particular universe of discourse then the unicorn exists (in that particular universe of discourse and thus also in reality as a whole). — litewave

Every time you say 'exists', you qualify it with a relation to a UoD.
This isn't the property definition you gave. I asked if the unicorn exists, not if it exists in a particular realm. You seem to not disagree with this. You say the unicorn is consistent with its own particular UoD, so how then is the unicorn not logically consistent?
You also introduce 'reality as a whole' here, which, absent a different definition, I presume to mean 'all things that exist' (no specified relation), which means all that is logically consistent.
If by 'reality' you mean 'consistent with what you personally observe', then we're back to an epistemological version of my relational definition.

I just meant to point out that although it may seem that the definition of a unicorn existing on our planet is consistent

I never asked if it exists on our planet, but I did mention a common evolutionary ancestor which at least eliminates unicorns on distant star systems. Under say MWI, Earth with unicorns on it is as likely (probably more likely) than an Earth with humans on it. It's a possible world, and thus it exists (say in the UoD of all the evolved coherent states of the Earth's wavefunction 150M years ago) as much as this world does. There's nothing logically inconsistent about that.

Your demonstration of inconsistency assumes an empirical definition. You don't see them, so you say they don't exist here. Well, the unicorns don't see you, so by the same token, you don't exist to them by that definition.

This is a perhaps somewhat surprising point about logical consistency: reality cannot be different than it is because then it would be what it is not and thus would be inconsistent.

There's the term 'reality' again. Is this a separate property than that of 'existence'? What possible evidence have you that unicorns (logically consistent ones) are not also a part of reality?

You said 'exists' means 'logically consistent', not 'logically consistent with the universe of discourse — noAxioms

But 'logically consistent' means 'logically consistent with everything'. Everything must be logically consistent; there can be no inconsistency in reality.

You say the unicorn is consistent with its own particular UoD, so how then is the unicorn not logically consistent? — noAxioms

It is, but only as a part of that UoD. It would not be consistent as a part of a different UoD in which no unicorns exist. Like a triangle is consistent as a member of the set of all triangles but inconsistent as a member of the set of all circles.

You also introduce 'reality as a whole' here, which, absent a different definition, I presume to mean 'all things that exist' (no specified relation), which means all that is logically consistent. — noAxioms

Yes.

Under say MWI, Earth with unicorns on it is as likely (probably more likely) than an Earth with humans on it. It's a possible world, and thus it exists (say in the UoD of all the evolved coherent states of the Earth's wavefunction 150M years ago) as much as this world does. There's nothing logically inconsistent about that. — noAxioms

I guess that's right although if you don't know all the details you can't be sure about the consistency.

Your demonstration of inconsistency assumes an empirical definition. You don't see them, so you say they don't exist here. — noAxioms

Well, I took it for granted that it was included in the definition of 'unicorn' that if a unicorn was standing right now in front of my house I would see it. And so since I don't see it I conclude that there is indeed no unicorn standing in front of my house right now. And if there is no unicorn standing in front of my house right now, it would be logically inconsistent if a unicorn was standing in front of my house right now - because it would be standing where it is not standing.

But 'logically consistent' means 'logically consistent with everything'. — litewave

That makes no sense. You're not logically consistent with a UoD of a two-spatial dimension universe, so since there's something with which you're not consistent, you don't exist?
You probably don't mean that, but then I cannot make any sense out of this new changed definition.

It is, but only as a part of that UoD. It would not be consistent as a part of a different UoD in which no unicorns exist.

Likewise, you're not consistent with a different UoD in which no litewave exists.

I'm trying to drive this to a distinction. Some reason that you have the property of existence and the unicorn does not. So far all I have is that they're in different worlds.

Like a triangle is consistent as a member of the set of all triangles but inconsistent as a member of the set of all circles.

So by your' 'with everything' definition just above, there are no triangles because they're not also circles. They're not logically consistent with everything.

I guess that's right although if you don't know all the details you can't be sure about the consistency.

Being sure about consistency is just an epistemological problem.

Well, I took it for granted that it was included in the definition of 'unicorn' that if a unicorn was standing right now in front of my house I would see it. And so since I don't see it I conclude that there is indeed no unicorn standing in front of my house right now.

Right. So it's not in your personal UoD. By your original definition, your ability to see something has nothing to do with its property of existing. My definition did (sort of). I would never have used the word 'see'.

And if there is no unicorn standing in front of my house right now, it would be logically inconsistent if a unicorn was standing in front of my house right now

Right, but nobody asserted it was standing in front of your house right now. It's in its own UoD. It's logically consistent with that UoD. Therefore (until you changed the definition above), it exists.

I'm just trying to point out the implications of your definition.
I say it doesn't exist, but again, I'm using a different definition.

"But 'logically consistent' means 'logically consistent with everything'." — litewave

That makes no sense. You're not logically consistent with a UoD of a two-spatial dimension universe, so since there's something with which you're not consistent, you don't exist? — noAxioms

No, every object is logically consistent with every other object in every universe of discourse. Do you think that a flat space is inconsistent with a curved space? They are perfectly consistent with each other, each space is a particular object, a particular kind of set and both sets exist in the universe of sets. An inconsistency would arise if you tried to claim that a flat space is curved.

Likewise, you're not consistent with a different UoD in which no litewave exists. — noAxioms

The UoD in which I exist is a particular set. Another UoD is a different set. Both sets exist in the universe of sets. No inconsistency. But it would be inconsistent to claim that I exist in a UoD in which I don't exist.

Right, but nobody asserted it was standing in front of your house right now. It's in its own UoD. It's logically consistent with that UoD. Therefore (until you changed the definition above), it exists. — noAxioms

The unicorn is also logically consistent with all other universes of discourse but only as a part of a UoD in which it exists. It would be logically inconsistent if it existed in a UoD in which it doesn't exist, for example in front of my house.

Your last replies didn’t really engage with any particular argument I was making.

To recap, you started out with the question of why anything would actually exist in a fashion that mathematics could now describe it. And also you seemed to want to clarify something about the role of time in all this.

My reply was that Hawking’s question could be flipped by ontic structural realism. The cosmos exists as it does not because nothingness was impossible but because quantum "everythingness" was self-limiting. Nothing could prevent symmetry breaking and the expression of the least action principle as an act of cosmic Darwinism. Gauge invariance had to emerge locally, Lorentz invariance globally.

So that is the structuralist view. But structuralism still suffers from needing a model of the raw action - the initial everythingness - that can breath fire into the equations. There is still a "first cause" issue in some form. But the big step forward is that it is as little of a "material something" as could be imagined. It is just a quantum foam of possibility as yet to be structured by an emergent topological order.

So ontic structural realism, or the condensed matter view of a cosmos shaped by the principles of topological order, is the part of reality that is the most "mathematical" and thus what the maths of fundamental physics seems to be "all about". The maths is the natural way to capture the organising limits of nature – its emergent gauge symmetry in particular.

But also we need a theory of the stuff – the material cause that complements the formal cause – that "breathes fire into the equations" in the sense of giving the symmetries something to limit. And this is where we need some kind of model of the quantum foam, or vague Apeiron, too.

I wasn’t aware of this. Can you expand or provide a link about this issue? — noAxioms

On the problems with Bohmian mechanics, that Adlam reference is useful as a general overview – given you seem to want to incorporate retrocausality or temporal nonlocality into whatever QM interpretation you wind up with.

Moreoever, most mainstream interpretations of quantum mechanics, including the Everett interpretation, spontaneous collapse models and the de Broglie Bohm approach, are prima facie temporally local.

But SR of course already tells us that the idea of a present moment and tidy temporal order is problematic. And this then is a reason why Bohmian mechanics and its pilot wave fails to be relativised.

https://doi.org/10.3390/e20010041

But in general, BM doesn't relativise because where QFT path integral demands that particles take all possible paths, including the non-classical, BM's pilot waves just take classical trajectories.

Goldstein has tried to use backwards causality to fix this – https://arxiv.org/pdf/quant-ph/0105040.pdf

But what else is meant by the "breathes fire", "makes a universe", "should be a universe", and "bother of existing"?
If my interpretation of those words is a bit overzealous, then what did Hawking actually mean by them?What for instance, other than the ontological property itself, would distinguish two sets of rules and equations, one which exists, has fire breathed into it, and the other doesn't exist, no fire, etc. Suppose they're even the same empirical thing. — noAxioms

That mathematical models of the universe is just that -- no actual "reality" was harmed in the making of a model. No fire of life can be felt within a mathematical model. We cannot answer the normative questions such as "why is there a universe?"

MDR (model-dependent realism) is what Hawking is known for. Which makes him a hypocrite by saying philosophy is dead. (This is actually annoying to hear from a well-respected physicist). It tells me he did not understand Philosophy -- it becomes cumbersome to read through passages of philosophical concepts when you have a photographic memory of mathematical equations).

You can test this yourself by just using algebra or calculus, for example. The brain would have a hard time switching with ease between mathematical equation and an exposition of philosophical theory. The brain becomes impatient. You start to doubt whether philosophy is keeping pace with the developments happening in the "universe" -- developments which could be written in a neat bundle of axioms and theorems. ("mechanical" should be the monster we're after here). The slow, meticulous philosophical inquiry and scrutiny of concepts about our claims regarding reality doesn't look like a knight in shining armour. It is the sage, whose secrets are given to those who wait -- and if the wait is forever, so be it.

Little wonder that some of the best writers of philosophy are mathematicians who turned against the mechanical mind of a math purist. They wrote of the power of the lowly, much maligned empirical observations. They went to see the sage. Of course, they're heroes to me because admitting this would be tantamount to a child yelling "the emperor has no clothes!"

So, back to the basics -- because this is as close as we could get to the claim that we've touched "reality" out there.

Thanks again all for your comments and patience with my slow replies.

And also you seemed to want to clarify something about the role of time in all this. — apokrisis

The role of time has to do with my selection of an alternate definition of existence based on causality, something not defined the same way for non-temporal structures. Still, my definition only seems to work for local interpretations of our physics. The primary definition of existence is the sort spelled out in the OP with the prime number example. There’s a term for that sort of existence, but it escapes me for the moment.

The cosmos exists as it does not because nothingness was impossible but because quantum "everythingness" was self-limiting.

This is already a relation since it seems only related to a structure following QM rules. Yes, there’s an everythingness about it, but how to explain the quantum structure in the first place? That seems to be what Hawking is asking.

But structuralism still suffers from needing a model of the raw action - the initial everythingness - that can breath fire into the equations.

This sound like what I’m attempting to resolve with this topic. It seems to be an issue with any form of realism.

There is still a "first cause" issue in some form.

I’d call it an initial state. Relativity theory seems to have no problem with initial and final states, but a unified theory would probably be needed before we can actually assert that.

But the big step forward is that it is as little of a "material something" as could be imagined. It is just a quantum foam of possibility as yet to be structured by an emergent topological order.

If that little material something needs fire breathed into it, then it matters not that it’s minimal. The problem is still there. I eliminate the problem at the start by not suggesting the need for it. But it acts against a strong bias and nobody else seems to be able to accept that.

I don’t know what emergent gauge symmetry means, sorry.

given you seem to want to incorporate retrocausality or temporal nonlocality into whatever QM interpretation you wind up with.

I don’t actually. I’m a locality kind of guy, but I’m aware of other interpretations that have these things.

Moreoever, most mainstream interpretations of quantum mechanics, including the Everett interpretation, spontaneous collapse models and the de Broglie Bohm approach, are prima facie temporally local.

Again, I don’t know what that term means.

But SR of course already tells us that the idea of a present moment and tidy temporal order is problematic. And this then is a reason why Bohmian mechanics and its pilot wave fails to be relativised.

Pilot waves require a preferred ordering of events? I was unaware of that, but such a preferred ordering has never been disproven either, despite even my attempts to do so.

But in general, BM doesn't relativise because where QFT path integral demands that particles take all possible paths, including the non-classical, BM's pilot waves just take classical trajectories.

How do the BM people respond to this criticism? I wasn’t even sure if they still clung to the pilot wave model since the physical wave tanks failed if baffles were put in.

No fire of life can be felt within a mathematical model. — L'éléphant

But I’m not talking about a model, which is an epistemological tool. I’m talking about mathematics itself, that our universe (and others) is, at the most fundamental level, a mathematical structure. Life can very much be felt within such a thing, and my addition to this premise is the lack of need of the fire to feel that. The mathematics is no different with or without the fire, so it isn’t necessary.

We cannot answer the normative questions such as "why is there a universe?"

Maybe, but in finding the question unanswerable, I suggest instead that it is the wrong question.

MDR (model-dependent realism) is what Hawking is known for. Which makes him a hypocrite by saying philosophy is dead.[/quote]Agree with the hypocrisy accusation. All the quotes I’ve seen of him in this topic (and an entire book, despite it no doubt containing science) is philosophy.

The UoD in which I exist is a particular set. Another UoD is a different set. — litewave

Fine. The unicorn is part of that other UoD, so at the objective level, it exists (per your definition, not mine) as much as do you since both are members of this universe of sets.
Is that acceptable? You’ve seemed very resistant to the unicorn having the same ontology as you.

Both sets exist in the universe of sets. No inconsistency. But it would be inconsistent to claim that I exist in a UoD in which I don't exist.

Fine. The unicorn is part of that other UoD, so at the objective level, it exists (per your definition, not mine) as much as do you since both are members of this universe of sets.
Is that acceptable? — noAxioms

Yes.

If that little material something needs fire breathed into it, then it matters not that it’s minimal. The problem is still there. I eliminate the problem at the start by not suggesting the need for it. But it acts against a strong bias and nobody else seems to be able to accept that. — noAxioms

Minimising our notion of material cause by maximising our understanding of formal cause is still progress. It is answering the question of cosmic existence in causal terms.

So we can breathe fire into the equations by understanding them to be describing formal causal necessity. We can see why the symmetries of nature are not just some random choice but a mathematical necessity. Existence couldn't be otherwise.

And at the same time, the material cause – which is what folk conventionally think of as the bit needing to be supplied as the animating fire – is revealed to be the most accidental or incidental kind of cause. It has to be there as a cause in some minimal sense, but ends up being hardly anything at all.

This is the message of spontaneous symmetry breaking. The ball on the top of the dome has to roll off. The situation is so poised that absolutely any and every nudge will tip it. Therefore the actual nudge that tips the situation is as unspecial and "immaterial" as it gets. You couldn't really say it caused anything as such. One fluctuation would has been as good as any other. All you need is the impossibility of ruling out fluctuations.

And structuralism lets you argue that fluctuations can't be ruled out until in fact structure starts emerging to produce its suppressive constraints. A fluctuation ain't even a fluctuation except retrospectively to the context it then revealed.

How do the BM people respond to this criticism? — noAxioms

As I said, folk like Goldstein agree it is an issue and hope to solve it. But what is the point of just catching up to QFT with an inherently clunky QM interpretation when the goal is already to find a way forward to a full QG theory?

Minimising our notion of material cause by maximising our understanding of formal cause is still progress. It is answering the question of cosmic existence in causal terms. — apokrisis

It isn't answering the question at all. Do you at all understand what I'm getting at? Any cause (material, formal, whatever) is still only related to a created thing, and the universe cannot be such a thing. That's the category error I was talking about. You're treating a causal structure like a caused structure. This is intuitive, yes, but only because language treats it so. It's still wrong.

And at the same time, the material cause – which is what folk conventionally think of as the bit needing to be supplied as the animating fire

No, a material cause cannot do that. The material in question has to already exist, so the 'fire' is already there (unexplained). A material cause (or any cause) is something explaining a caused thing, which is a different category.

The ball on the top of the dome has to roll off.

Again, wrong category, but great example. Yes, I say a ball on a dome must roll off on some random side at a random time with computable probability even. But the question asked by the topic is, does there need to be an existing ball on a dome for this to occur, or will just a ball on a dome suffice? None of your causal discussion seems to be relevant to that question.

It isn't answering the question at all. Do you at all understand what I'm getting at? Any cause (material, formal, whatever) is still only related to a created thing, and the universe cannot be such a thing. That's the category error I was talking about. You're treating a causal structure like a caused structure. This is intuitive, yes, but only because language treats it so. It's still wrong. — noAxioms

I thought I was clearly arguing against a "first cause" position. Emergence and development are different from "acts of creation".

So I would say you don't follow what I've actually said. You don't yet get the subtlety of the structuralist or systems perspective.

But the question asked by the topic is, does there need to be an existing ball on a dome for this to occur, or will just a ball on a dome suffice? — noAxioms

You were meant to pay attention to the mathematical structure of that example, not the substantial being that is some literal ball on some literal dome.

Again, my argument is that we start by following Aristotle in dissecting substantial being into its formal and material causes. And what we find is that we wind up where we do in mathematical physics. We have a tale of Platonic-strength structural necessity – the inevitability of the invariances due to symmetries – coupled to the most nebulous sense of "materiality" possible. QFT winds up talking about excitations in fields due to inherent uncertainty or instability.

So the fields must fluctuate due to a fundamental indeterminacy. And that is all that is required by way of material cause to breath fire into the equations of the Standard Model.

But if you can't shake a more concrete conception of Nature from your imagination – the one based on a metaphysics of "medium sized dry goods" – then yes, this won't compute.

The causes of substantial being have to be dissected. Once that is done, formal cause gives the reason for why structure has to be what it is – under the further finality supplied by a least action principle.

And then material cause is reduced until it is virtually equivalent to a nothing – a quantum foam of possibility or Apeiron of random fluctuation.

Structure supplies the determination. Fluctuation supplies the indeterminacy. Chance encounters constraint and an evolutionary cosmic process is unleashed.

Simple. :grin:

I thought I was clearly arguing against a "first cause" position. Emergence and development are different from "acts of creation".
So I would say you don't follow what I've actually said. — apokrisis

But I'm arguing against any act of creation, so yes, at least one of us is not following what the other is saying. I'm hardly an expert in the views you're referencing, so it's more likely to be me not following, but the language of creation seems entirely inappropriate to address the problem to which I'm seeing. Structuralism, while something I may indeed not fully understand, seems to not address the issue at all.
I'm not asking how the world we see emerges from the quantum foam. I'm questioning the objective existence of the quantum foam or any other structure or system, temporal or not.

You were meant to pay attention to the mathematical structure of that example, not the substantial being that is some literal ball on some literal dome.

But the substantial being (your term, not mine, so maybe I'm using it wrong) of the ball and dome is what the topic is about, so you were very much meant to pay attention to that. The mathematics says the ball rolls off after a while, uncaused if you will. It actually takes infinite time to do so, but they had a mathematical model of one that doesn't take infinite time. I cannot find a reference on short notice. All besides the point. The point is that the 'substantial being of the ball and dome' (its objective existence) isn't relevant to what happens to the ball. The ball/dome system doesn't behave differently depending on its ontology.
It's kind of an anti-platonic view. Plato says abstract things exist (that the existence property is meaningful, and that such abstract things have it). I say the property is meaningless, and that a triangle not being a circle is not a function of its ontology.

Again, my argument is that we start by following Aristotle in dissecting substantial being into its formal and material causes. And what we find is that we wind up where we do in mathematical physics. We have a tale of Platonic-strength structural necessity – the inevitability of the invariances due to symmetries – coupled to the most nebulous sense of "materiality" possible. QFT winds up talking about excitations in fields due to inherent uncertainty or instability.

Either I am massively misunderstanding most of your post, or you're wildly off topic.
Can you explain to me what you think the topic is about?

I'm not asking how the world we see emerges from the quantum foam. I'm questioning the objective existence of the quantum foam or any other structure or system, temporal or not. — noAxioms

OK. So how would you objectively measure the quantum foam? In what sense does it exist as a measurable stuff?

If you properly follow that question, you can perhaps start to see how a substance ontology – one that says "show me the fundamental substance, and then tell me why it exists" – is just an inadequate way of framing the ontological issues.

You keep looking for the "stuff" that breathes fire into the equations. Hawking was too. Pretty much everyone frames its as the hunt for the fundamental substance, that then brings with it it's own "well, why that?" question.

So my position is based on trying to get around that whole frame of thought. I follow the line taken by Anaximander, Aristotle and Peirce in particular. And this then leads to the kind of structuralism which explains the success of the mathematical equations, coupled to the "material potential" of Peirce's logic of vagueness, Aristotle's prime matter, and Anaximander's apeiron.

Or, as here, Wheeler's quantum foam.

But the substantial being (your term, not mine, so maybe I'm using it wrong) of the ball and dome is what the topic is about, so you were very much meant to pay attention to that. — noAxioms

I was doing so in arguing for Aristotle's hylomorphic view of substantial being. I was pointing out that you are taking substance for granted in a way that Ancient Greek metaphysics already shows is unwarranted.

Have you studied hylomorphism? That seems to be the sticking point.

It's kind of an anti-platonic view. Plato says abstract things exist (that the existence property is meaningful, and that such abstract things have it). — noAxioms

And have you studied the Timaeus closely enough to see that Plato also needed to breathe fire into his equations by positing a chora or receptacle to take the imprint of his forms?

Both Plato and Aristotle were wrestling with the same metaphysics when it came to an explanation of substantial being. Neither had the perfect answer. But they point the conversation in its right direction.

Can you explain to me what you think the topic is about? — noAxioms

I agree that Hawking is scratching at the right itch. But say he - like you, and indeed most – still make the mistake of thing of material cause in terms of actually formed stuff. Substantial being. Something that can be measured in some basic way, even if it is a bland stuff like some kind of clay.

Remember that what breathed fire into Newtonian mechanics was the idea of objects with mass. These bounced about in an empty space and time void.

But then mass became confined energy under relativity. Energy in turn became an entropy gradient, and even information. Physics has kept moving its understanding of the animating fire into a more and more structural definition.

And this ain't wrong. It is correct. But it then leaves us asking what we mean by the stuff that breathes fire into all the maths? What is it that is being informed by all the form?

This is where we have to stop and be ready to give up on thinking of material cause as something fundamental rather than as something itself emergent. Material cause is something that structural necessity itself makes manifest.

That's a whole new metaphysical ballgame. Or in fact, one as old as Anaximander, the first real metaphysician.

*sigh* I give up on this thread. It seems that the misunderstanding is rampant here. :roll:

@noAxioms, when you say this.....

But I’m not talking about a model, which is an epistemological tool. I’m talking about mathematics itself, that our universe (and others) is, at the most fundamental level, a mathematical structure. — noAxioms

you are, in fact, exhibiting Hawking's MDR. That's what it means by model-dependent: you have in mind a universe that has a mathematical structure. And the question you should be asking yourself is -- how do I know this? How did I come to think this way? MDR posits that it is inescapable. We, by default, think in terms of a model.

OK. So how would you objectively measure the quantum foam? — apokrisis

By definition, measurement isn't objective. I suppose that point can be argued.

If you properly follow that question, you can perhaps start to see how a substance ontology – one that says "show me the fundamental substance, and then tell me why it exists" – is just an inadequate way of framing the ontological issues.

Agree, which is why I point out in the OP that "tell me why it exists' is the wrong question. It presumes it exists. A better question is to first ask if it exists, or if its existence can be meaningful. 'No' seems a better answer to both questions, so the question of why vanishes.

You keep looking for the "stuff" that breathes fire into the equations.

But I'm not. I'm saying its a mistake to presume it. The 'God did it' answer doesn't work for the reason you give: "well, why that?".

But the substantial being (your term, not mine, so maybe I'm using it wrong) of the ball and dome is what the topic is about, so you were very much meant to pay attention to that.
— noAxioms

I was doing so in arguing for Aristotle's hylomorphic view of substantial being.

Aristotle starts with primary matter. Well, why that? If you start with something, it is just a discussion of how it evolves from that start. Off topic.

Have you studied hylomorphism? That seems to be the sticking point.

Seems off-topic since it starts with the presumption of potential. Why is there that potential at all?
No, I’ve not studied most of the things you’re bringing up, but I am looking at each one enough to see if any of it is actually addressing my point. Either I have poor reading skills or none of it does. I don’t have any formal philosophy background in the ancient works.

And have you studied the Timaeus closely enough to see that Plato also needed to breathe fire into his equations by positing a chora or receptacle to take the imprint of his forms?

No, but this one actually seems to have a potential for being relevant. I cannot seem to find a good reference discussing it. The receptacle seems to be a thing with presumed existence, which would make it off-topic. I could not find a decent description of what ‘chora’ is, distinct from that.

Can you explain to me what you think the topic is about?
— noAxioms
I agree that Hawking is scratching at the right itch. But say he - like you, and indeed most – still make the mistake of thing of material cause in terms of actually formed stuff.

This seems to be a statement of what you’re talking about, not the subject for which I opened this topic.

Substantial being. Something that can be measured in some basic way, even if it is a bland stuff like some kind of clay.

Again, not sure what you mean by ‘substantial being’, but the kind of being that I’m talking about should not be measurable at all, hence it being meaningless.

But then mass became confined energy under relativity. Energy in turn became an entropy gradient, and even information. Physics has kept moving its understanding of the animating fire into a more and more structural definition.

All this seems to be about what keeps it going, and not at all about why it is in the first place.

I am apparently not conveying my point at all. Nobody seems to get it, even if to just disagree with it. You’re all discussing other things.
Forget our physics and materials and quantum foam and such. Start with the simple examples like the triangle and such where talk of ‘cause’ and such doesn’t come into the picture.

you are, in fact, exhibiting Hawking's MDR. — L'éléphant

Of course I am, but despite my usage of this tool, the tool isn’t what the topic is about.

That's what it means by model-dependent: you have in mind a universe that has a mathematical structure.

As one possibility, yes. Hard to think of a different one. It being a mathematical structure is a MUH topic, and this topic is an ontological one.

And the question you should be asking yourself is -- how do I know this?

I don’t claim to know this at all. I’m claiming a solution to the problem naively worded as: “why is there something instead of nothing?”. I’m not claiming that things cannot be otherwise.

How did I come to think this way? MDR posits that it is inescapable. We, by default, think in terms of a model.

Right, but the topic isn’t about how we think. The disclaimer in the OP says it isn’t about epistemology.

You keep looking for the "stuff" that breathes fire into the equations.

But I'm not. I'm saying its a mistake to presume it. — noAxioms

Yes, I agree. The mistake is to assume the universe was created to raise human emotions.

Yes, I agree. The mistake is to assume the universe was created to raise human emotions. — jgill

lol. Where did this come from? Are you just thinking out loud to yourself? Who in this thread is talking about human emotions?

Breathe fire :cool:

By definition, measurement isn't objective. — noAxioms

We were talking about the problem of substantial existence - ontology rather than epistemology. So this is off the point.

A better question is to first ask if it exists, or if its existence can be meaningful. 'No' seems a better answer to both questions, so the question of why vanishes. — noAxioms

Pfft. My argument is that this is about modalities of existence. We can have potential existence or actual existence. We can have accidental existence or necessary existence. We can have vague existence or definite existence.

You can give up on "existence" if you like. But my argument is all about more careful definitions of its modality. And I've pointed you towards the long history of metaphysical discussion on that.

I am apparently not conveying my point at all. Nobody seems to get it, even if to just disagree with it. You’re all discussing other things.

Forget our physics and materials and quantum foam and such. Start with the simple examples like the triangle and such where talk of ‘cause’ and such doesn’t come into the picture. — noAxioms

Where did you lay out a triangle argument? You mean why a triangle is not a circle? You mean triangles as eternal Platonic forms?

If you checked out the Timeaus you would see that triangles become a good example of how Plato tried to breath animating fire into his ideal forms.

The Timaeus is Plato’s only cosmological dialogue where one of the most difficult questions
of his doctrine is considered in some detail: the so-called ‘participation’ of ‘sensible world’ in
the intelligible world, or the Forms or Ideas.

The khôra is not only the place where perpetual changes of the sensible bodies occur, but also the unqualified and unchanging ‘genus’ required to explain these perpetual changes; it is the dynamical whole, consisting of these bodies in perpetual change, their ‘nurse’, their nourisher and their ‘mother’.

First, Timaeus claims that anything that is born must have a body. Thus, to be corporeal, the
universe needs to be both ‘tangible and visible’. For the former attribute to hold true, earth is
needed, fire for the latter. However, Timaeus claims immediately that the unity of the world
needs both elements to be strongly bound, and that the ‘most beautiful’ bound, is the
‘proportion’ between four terms: a/b = c/d.

https://arxiv.org/pdf/2008.11947.pdf

And so we arrive at a Pythagorean triangle - divided in two – as the primal form from which nature could be atomistically constructed. The "two triangle universe" that hinges on the orthogonality of the right angle and the minimal number of sides that could bound an object in such a Euclidean notion of space.

It is like the ancient world's version of string theory. :razz:

But the point is even Plato was wrestling with the issue that I take Hawking as pointing towards.

Yes you can reduce reality to geometric or symmetry principles. Talking about the necessities of form really does seem to capture most of what needs to be said in modelling the world. And that is what equations do.

But you still need a khôra to supply whatever then breaths the animating fire into the structural forms. That is the bit of the puzzle which really demands breaking out of the mould of concrete thought. The question about the material cause of being is where the hard work has to be done.

Peirce said we needed a new logical category. And Peirce after all pretty much invented modern logic, even if Frege got the credit for his simpler – more reductionist – version.

By definition, measurement isn't objective.
— noAxioms
We were talking about the problem of substantial existence - ontology rather than epistemology. So this is off the point. — apokrisis

You the one who asked how one would objectively measure the quantum foam, so if it was epistemic measurement you were talking about, then it is you that is off topic.
I presumed a physics definition of measurement, not an epistemic one, so my statement stands: Measurement is meaningful between two systems, and thus is a relation between them. There is no objective measurement, at least not in the sense of the physics of our universe.
I really hate to keep pointing you to my disclaimer in the OP, but here I'm doing it again.

A rock measures the temperature (physics definition), but doesn't know that it's cold out (epistemic definition). But it being cold out at a particular location is true in this world and not others, so it isn't an objective measurement.

My argument is that this is about modalities of existence.

This is closer to being on topic. I spent quite some time failing to find a decent article on modality of existence. The modality page on SEP is quite careful to use the term existence only in a relational sense, and seems to not discuss objective existence at all, which, if nothing else, seems to lend weight to what I'm saying. They're not committing the category error that I pointed out above.
So sure, I can see why a planet in our solar system cannot be square, but I cannot see why the quantum foam must be.

We can have potential existence or actual existence. We can have accidental existence or necessary existence. We can have vague existence or definite existence.

All depends on the definition of existence again. As a property, I don't see how anything has necessary existence. Given a 'member of' definition, sure, all those things are relevant. The SEP article only seemed to use the relational definition. Apo exists in this world, and not in others. Apo does not exist in the set of integers. Apo has potential existence in the quantum foam. All relations. The article seemed not to delve into 'Apo exists' at all, but it's a long thing and maybe I missed it.

You can give up on "existence" if you like. But my argument is all about more careful definitions of its modality. And I've pointed you towards the long history of metaphysical discussion on that.

Where did you lay out a triangle argument?

Let's go with the question "does a triangle have three corners?". I'm talking about a geometric triangle, not a physical triangular shaped thing. We can confine it for now to Euclidean geometry if you like. If the answer is 'no' or 'maybe', then elaborate. If 'yes', then my point has been illustrated.

You mean why a triangle is not a circle? You mean triangles as eternal Platonic forms?

I reworded it as a positive question (corners) instead of the negative one (round) which just made it confusing. As for forms, I suppose yes. I had no specific triangle in mind except a typical one (no weird edge cases where one angle is 180° or something). As for it being Platonic, I said my position was sort of anti-platonic, so probably not. Eternal? Planar geometry doesn't require a triangle to be contained temporally, so it is eternal (timeless) by that definition.

If you checked out the Timeaus you would see that triangles become a good example of how Plato tried to breath animating fire into his ideal forms.

But what if I don't see the necessity to attempt that? Said ideal forms are no less forms without fire breathed into them.

Not sure what part of it is relevant. Per the wiki page, Timeaus says "Timaeus suggests that since nothing "becomes or changes" without cause, then the cause of the universe must be a demiurge or a god, a figure Timaeus refers to as the father and maker of the universe." which says the universe must be a caused thing, the usual 'God explanation' which just shifts the problem to explaining the being of this God.
Plato seems to just record all this and doesn't contribute. Maybe he does. The god explanation doesn't solve the problem. Spell it out for me, because I'm probably not going to take seriously a work by somebody who sees teleology in the universe.

You seem to not be able to describe my point in your own words, and you seem to be steering me to works that address a different point.
Hence my reaching to simple examples like the triangle. Once we analyze that (a simple question above), one can apply the conclusion to something complex like ourselves.

But the point is even Plato was wrestling with the issue that I take Hawking as pointing towards.

And perhaps making the same mistakes, except I don't actually see Plato contributing to the dialog.

But you still need a khôra to supply whatever then breaths the animating fire into the structural forms.

I don't need that since I'm not positing the necessity of this fire breathing. The form is enough.

Measurement is meaningful between two systems, and thus is a relation between them. — noAxioms

Frankly I tire of these weak arguments. There is no problem measuring different states of the one system at different stages of its development.

The problem with vagueness becomes that it’s measurement is in fact defined by becoming unable to make a measurement. It marks the point where the determined tips into indeterminacy.

That is what I asked you to think about to get a clear idea of what vaguess logically means. It is the point where counterfactuality ceases, where the PNC no longer can obtain.

The quantum foam is that kind of “stuff”. Uncertainty maximised. And yet we still want to call it a something in that it is now a complete certain lack of certainty. We can still treat it as a modal category that gets us over the familiar difficulties when it comes to metaphysical-strength inquiry.

A rock measures the temperature (physics definition), but doesn't know that it's cold out (epistemic definition). But it being cold out at a particular location is true in this world and not others, so it isn't an objective measurement. — noAxioms

You’re pissing around with quibbles because you haven’t understood what I’ve said.

My epistemology is founded on an ontology of relations. Structuralism is simply that. But I “agree” that seems to leave the problem of the relata. Something must always anchor the two ends of a relation it would seem.

That is why you need to take the next step to a triadic metaphysics that can give you the threeness of relata in relations. And a developmental triadic metaphysics at that. You want to have a general logic of how relata in relations could arise out of a foundation of logical vagueness.

I realise this is a difficult idea. But this is a philosophy site.

Let's go with the question "does a triangle have three corners?". — noAxioms

Does a polygon have three corners? Did you notice that one corner of the triangle is very slightly dented so we could argue it has four corners. Etc.

We are always working within an ontology where formal descriptions and material measurements go hand in hand.

The necessary form of a triangle is in its structural definition. The substantial existence of a triangle is dependent on that form being actually actualised. The potential to actualise particular forms is where the material principle comes in.

The query would be more interesting if you asked the general question of is there a minimal polygon. The triangle could then emerge as a development of an inquiry seeking its maximal simplicity. It’s limit condition.

But you just want to talk in particulars and bypass the reality of universals. Even when you mean to speak about universals.

Plato’s Timaeus arrives at triangles as the basic form of actualised reality - the kind that lives in time and thus fixes an energy - by applying a least action principle. And modern particle physics does its own similar sum over histories in arriving at the gauge symmetries that explain the Standard Model.

But what if I don't see the necessity to attempt that? Said ideal forms are no less forms without fire breathed into them. — noAxioms

If even Plato couldn’t actually go that far with Platonism, why do you think there is no problem at all for you?

Plato seems to just record all this and doesn't contribute — noAxioms

Is the Platonic dialogue an unfamiliar format to you?

https://en.wikipedia.org/wiki/Timaeus_of_Locri

You seem to not be able to describe my point in your own words, — noAxioms

I would say you didn’t have a thought clear enough to articulate. And no progress is being made on that score.

There is no problem measuring different states of the one system at different stages of its development. — apokrisis

Measurement isn't even defined objectively. It only seems relevant to certain kinds of structures like the one we live in. You asked about objective measurement. I don't see how that is meaningful. I'm not making an argument here, I'm just trying to answer your question.

Measurement is seemingly undefined for our triangle, therefore measurement is probably outside the scope of this topic. I'm keeping the example simple and abstract in an effort to sidestep the biases associated with our own particular universe.

OK, in your posts I can see that you're trying to show how the Greeks explained the fire breathing. There's a point to what you've been pushing. I don't get it since I cannot follow what is being said, and when I do, it all looks like invocation of magic. Apologies for my lack of formal education in ancient philosophy.

I would appreciate a decent modern article on modality of existence (where existence is a property, not a member-of relation).

You’re pissing around with quibbles because you haven’t understood what I’ve said.

Probably so, but what you're saying is mostly addressing the wrong point.

Something must always anchor the two ends of a relation it would seem.

I suspect such an anchor is unnecessary. 5 is less than 7 (right??). That's a relation, neither especially anchored. Maybe you cannot accept that without an asterisk.

That is why you need to take the next step to a triadic metaphysics that can give you the threeness of relata in relations. And a developmental triadic metaphysics at that. You want to have a general logic of how relata in relations could arise out of a foundation of logical vagueness.

Example please. So much clarity can be added with examples. Most of the ideas I've actually researched seem to not address my concern.

Let's go with the question "does a triangle have three corners?".
— noAxioms
Does a polygon have three corners? Did you notice that one corner of the triangle is very slightly dented so we could argue it has four corners. Etc.

Not all polygons have as few as three corners. A dented triangle isn't a triangle. This initial reply isn't an answer.

We are always working within an ontology where formal descriptions and material measurements go hand in hand.
...
The potential to actualise particular forms is where the material principle comes in.

This is the first mention of 'material principle' which seems to have religious connotations when I google it, but perhaps it implies that the actualized triangle needs to be made of something (like three line segments). Does it count if the line segments themselves are not further actualized into say a set of points? Is there a more fundamental material for geometric points? I mean, our triangle isn't even assigned a coordinate system.

The necessary form of a triangle is in its structural definition.

Isn't that enough to give it 3 corners?

The substantial existence of a triangle is dependent on that form being actually actualised.

OK. I didn't specify an actualized triangle, since the point of this whole topic is that the triangle doesn't seem to need to be actualized in order to have 3 corners. The form is enough, although it will need to be a less general form if it's to be a right triangle or not.

The query would be more interesting if you asked the general question of is there a minimal polygon.

That seems to be the wrong question though, similar to asking if 221 is prime.

The triangle could then emerge as a development of an inquiry seeking its maximal simplicity. It’s limit condition.

This doesn't tell me if the triangle gets actualized in the process of this emergence. I don't see why it should any more than 221 gets actualized because it divides by 13.

But you just want to talk in particulars and bypass the reality of universals.

Kind of the opposite. No particulars, and no reality of universals. Everything could be a universal, some more minimal than others, but none to the point of the actualization required for it to be designated a particular.

Plato’s Timaeus arrives at triangles as the basic form of actualised reality - the kind that lives in time and thus fixes an energy - by applying a least action principle.

I'm probably not interested in Timaeus then since I'm not talking about an approximately triangular shaped object in our universe. It seems that Timaeus defines actual things as those that are in this universe, meaning only our universe is preferred. Maybe I'm wrong about that, but it's how you're framing it. It doesn't explain why our universe is actualized, and not say the universe of Euclidean geometry. It's using a relational definition, which is fine, but no fire breathing is needed for that. It seems to require a god to do the actualization.

But what if I don't see the necessity to attempt that? Said ideal forms are no less forms without fire breathed into them.
— noAxioms
If even Plato couldn’t actually go that far with Platonism, why do you think there is no problem at all for you?

I've not had the problem pointed out, so I see no problem.

Plato seems to just record all this and doesn't contribute
— noAxioms
Is the Platonic dialogue an unfamiliar format to you?

Seems so. OK, It's a conversation between fictional characters taking different sides of a debate. Again, I've not taken any classes in ancient philosophy. Plato requires a god to do the magic parts. I'm hoping for something a little more modern than that.

You asked about objective measurement. I don't see how that is meaningful. I'm not making an argument here, I'm just trying to answer your question. — noAxioms

Just stop. You know that my epistemology is semiotic and pragmatic. The subjectivity and informality of acts of measurement are what it is all about, I only used “objective” in the conventional sense so as not to add yet another level of confusion to this thread.

OK. I didn't specify an actualized triangle, since the point of this whole topic is that the triangle doesn't seem to need to be actualized in order to have 3 corners. The form is enough, although it will need to be a less general form if it's to be a right triangle or not. — noAxioms

Will you ever clarify your point then?

In what sense does your triangle exist? Where in nature does the abstraction reside? Does a count of corners say everything that could be said about triangularity? How many different kinds of measurements distinguish triangles from one another yet are also differences that don’t make a difference to you proclaiming you see a triangle … in your mind or somewhere?

You seem to want to claim a triangle as a Platonic form, yet have no proper theory of what that means. How are you imagining triangularity in terms of its measured essentials, and thus able to disregard differences that you consider accidental, or only essential now to some subclass of triangles.

Even if you go full Platonic idealism, you will find the same logic of vagueness coming into view. You will just be taking a different route.

Naming distinctions that break symmetries is how it works. It is counterfactuality all the way down until … finally, in the limit, it isn’t. And we need a larger logic, a deeper sense of modality, to handle such a cut-off in our descriptions of nature.

This doesn't tell me if the triangle gets actualized in the process of this emergence. I don't see why it should any more than 221 gets actualized because it divides by 13. — noAxioms

Your simple notion of a triangle as a three corner object arises in the limit of the sum of all the differences in triangularity that don’t make a difference.

So you adopt the position that the three corners don’t have all have the same angle, they only have to add up to 180 degrees. But someone else might insist that only an equilateral triangle is a true triangle. Someone else might point out that even your 180 degrees is a suspect definition as there are also hyperbolic and hyperspheric triangles.

What you claim to be simple and obvious just isn’t that at all. Your replies seem to say you are either confused or insensitive to that fact.

Everything could be a universal, some more minimal than others, but none to the point of the actualization required for it to be designated a particular. — noAxioms

Fine. You can make a hierarchy of distinctions and claim it is counterfactuals all the way down. Everything rests on its stack of turtles.

But what you have forgotten is that every counterfactual step describes some act of measurement. It specifies a way to separate what is formally necessary from what is materially accidental.

So in moving from some emergent notion of completely abstract triangleness to every acceptably nameable grade of triangularity - from a topological definition to increasing constrained geometric ones - you keep squeezing out the accidental features. But where do you finally exhaust this process and find the bottom of this chain of measurement? You can show me the last concrete distinction.

Or do you instead simply subdivide your general notion of triangularity to the limit of what seems pragmatically useful and interesting to you, and then declare any further differencing as merely accidents and not necessities. Noise not signal. And as the next step, conveniently forget that it was these accidents that were necessary to the formal counterfactualising all the way down to your chosen limit of interest.

Well this is the Platonic issue. This is the problem that exists even in Platonia. The accidental must exist for the necessary to claim its existence. It is the same metaphysical argument by which we say that formal cause must be matched by material cause in a theory of substantial or actual being.

That is why we can reduce the notion of material cause to “accidents that don’t matter” - as in a quantum foam of virtual excitations or fluctuations. The material principle can be both as little as imagined, yet still absolutely necessary to breath fire into those damn equations.

Again, I've not taken any classes in ancient philosophy. Plato requires a god to do the magic parts. I'm hoping for something a little more modern than that. — noAxioms

Listen to yourself. You admit your understanding is superficial. You demonstrate your understanding is superficial. Then you give yourself an excuse not to address that superficiality in your understanding.

If you want something more modern, read Peirce. But you are even less prepared than you realise.

Hi Apo,

I will be on the road for a couple weeks will little enough web access to make long replies. They’ll come less frequently than one a day. Got a wedding to go to and we’re taking the scenic route.

In what sense does your triangle exist? — apokrisis

It is a polygon, thus it exists as a member of the set of polygons, among other things.
It’s why I brought up the prime number thing in the OP. 221 is not prime because there exist factors (13 & 17) that divide it. The triangle exists in the same sense as that usage of the word.

OK. I didn't specify an actualized triangle, since the point of this whole topic is that the triangle doesn't seem to need to be actualized in order to have 3 corners.
— noAxioms
Will you ever clarify your point then?

That’s the point right there, as clear as I can make it. Your extra questions all seem to drive away from this point. Further details about a generic triangle are irrelevant to how many corners it has.

Where in nature does the abstraction reside?

It's a triangle, not a triangle in nature. There's no nature in geometry, despite there being geometry in nature. Despite your choice of epistemic/semiotic philosophy, I happen to be talking about the triangle itself and not a mental abstraction of it. I use symbols and a mental abstraction to refer to it, but I’m not talking about how we consider it. I’m talking about the triangle itself. It is not very particular. I’ve only specified that it is a triangle.

Does a count of corners say everything that could be said about triangularity?

Of course not, but said count is all we need to answer the question asked.

How many different kinds of measurements distinguish triangles from one another yet are also differences that don’t make a difference to you proclaiming you see a triangle … in your mind or somewhere?

Measurement doesn’t seem to be part of geometry. It only seems applicable to applied geometry in a universe where measurement is meaningful. You seem very reluctant to concede that it has 3 corners, or 3 sides for that matter. Something measuring it would be a very complicated addition. Trying to keep it simple.

You seem to want to claim a triangle as a Platonic form, yet have no proper theory of what that means.

I don’t know Plato’s terminology. From what I’ve read, ‘form’ seems to fit. So does ‘universal’, but that’s probably different than form.

How are you imagining triangularity in terms of its measured essentials, and thus able to disregard differences that you consider accidental, or only essential now to some subclass of triangles.

Don’t follow this, probably because you’re still talking about our abstraction, measuring, and not the triangle itself. A system of multiple triangles sharing a plane is no longer a polygon. It’s a more complex thing, a collection of polygons say.

Even if you go full Platonic idealism

Not sure what that is, but idealism suggests to me that mind is fundamental, which is exactly the opposite of what I’m trying to convey, per the disclaimer.

Naming distinctions that break symmetries is how it works.

Then illustrate it with the triangle, and without introducing an observer/measurer.

Your simple notion of a triangle as a three corner object arises in the limit of the sum of all the differences in triangularity that don’t make a difference.

That sounds pretty correct. The question only asked the number of corners. The point of the topic was about a denial of the assertion that only actual triangles have three corners, and having 3 corners is not a property of triangles that are not actual.

Fine. You can make a hierarchy of distinctions and claim it is counterfactuals all the way down. Everything rests on its stack of turtles.

I’m actually denying the hierarchy. I said I disagreed with Plato, and I think the hierarchy comes from him. How are you using the term counterfactuals? Being in denial of any meaningful objective actuality, mathematics (or maybe law of form) is fundamental and its turtles all the way up from there. Actuality wouldn’t emerge somewhere along the way.

But where do you finally exhaust this process and find the bottom of this chain of measurement?

I don’t see how measurement can be meaningful in geometry. It’s only meaningful to something like us utilizing geometry.

Or do you instead simply subdivide your general notion of triangularity to the limit of what seems pragmatically useful and interesting to you

What I’m doing to my concept of the triangle is irrelevant. I don’t think you can conceive of the triangle itself. Sure, the other features are essential to geometry, but they’re irrelevant to the trivial question asked.

Well this is the Platonic issue. This is the problem that exists even in Platonia. The accidental must exist for the necessary to claim its existence. It is the same metaphysical argument by which we say that formal cause must be matched by material cause in a theory of substantial or actual being.

It must be, but it also cannot be. There is no material cause accounted for, hence my proposal to leave out the requirement of actuality, resolving this contradiction.
Maybe I’m still not getting what you’re saying. I don’t really understand what you mean by accidents. You’re incredibly thin on examples. I know about accidents in quantum fluctuations, but this already begs the actuality of a quantum structure in order to give rise to the actual being of say a mug. This is why I went with the triangle example, to bypass your biases about quantum and even temporal rules. They don’t apply to geometry. Once you accept that, the same conclusions can be applied to our universe.

Listen to yourself. You admit your understanding is superficial.

That’s right. It’s why I opened this topic, to explore and learn. But I didn’t do so to hear an ancient rationalization. I mentioned Plato only because he pondered the reality of things (like our triangle) that are not part of our universe. What I want in this topic is to know why my proposal is wrong, not why some different rationalization might work. But you seem to be stuck in one idea and seem incapable of actually considering a different one long enough to critique it on its own terms.

You’re the only one left still engaging.

I’m talking about the triangle itself. It is not very particular. I’ve only specified that it is a triangle. — noAxioms

So a triangle as something free of all possible ontological commitments?

That is itself another ontological commitment even if you believe you have safely placed yourself beyond ontological questions.

I mean I can’t stop you picking such a position. There just ain’t nothing to engage on if that is the case.

You declare equations need no animating fire and that’s it. We can all go home. Nothing to see here, folks.

It is a polygon, thus it exists as a member of the set of polygons, among other things. It’s why I brought up the prime number thing in the OP. 221 is not prime because there exist factors (13 & 17) that divide it. The triangle exists in the same sense as that usage of the word. — noAxioms

I was going to leave it there but then thought worth dealing with this from the epistemological angle that speaks to the need for ontological commitments in anyone's view.

My epistemology is semiotic and pragmatist. Peircean. And so what I would point out is how "triangle" is a word that functions as a sign – a symbol – that anchors a modelling relation between mind and world.

If I say "triangle", you will be put in mind of some suitable way to act. You will come at the world equipped with a certain communal habit of interpretation.

Is this a triangle....



Is this a triangle....



Is this a triangle....



Is this a triangle....



So the point is that the word is a sign by which we navigate reality via some habit of interpretation. We have a working sense of what it would mean for nature to be triangular in form in a materially instantiated fashion.

The meaning of the word "triangle" is the sum of all the possible ways we could stretch and yet not break the sense of what is essential. And essential in the sense of being a particular kind of formal constraint imposed on material being.

So in language, a sign is what we use to coordinate our behaviour. We are a community of speakers who learn the same habits of interpretation and so standardise our behaviour in regards to the worlds in which we must exist.

Maths then takes speech to the next level in terms of semiotic abstraction. The signs become even simpler. A triangle can be represented as three connected points. You mention three corners. More exactly, it is three edges with three vertexes.

Yet still, the drawing of a triangle – its icon – is just a much a sign as the word "triangle". As a community of thinkers, it is meant to put us in mind of a certain standard way of imposing form on the material world. It coordinates our actions. The sum of what the mathematical symbol means is the sum of all the specific set of acts it makes possible – in the sense of stretching and yet not breaking the "essential" meaning.

So this should make it clearer what I mean about breathing fire into equations. An equation is just some set of squiggles on a page. But as a habit of interpretance, we can read it to impose formal order on material disorder. We can share a mental attitude as to how to organise our environments.

What breathes fire is the fact that there are minds making use of some set of symbols to make change in the world. The triangle doesn't exist in its sign – a word or a picture or an equation. It exists as a modelling relation between a self and its world.

The symbol is a bit of technology or mechanism to anchor the two sides of the relation. And a triangle then exists to the degree that it makes to act "triangularly" in the world.

So you seem to be saying that a sign like "triangle" just exists, floating free of any ontological ground. Semiotics says a triangle is a sign that constrains action in some habitual or lawful way.

Any action is potentially possible in a material sense. But a structure of constraint then acts to restrict it in a concrete fashion in the formal sense.

And it is this fact – the embedding of the sign in a system of meaning – that allows an equation to be animated. Engineers can really do something with an equation that "knows the mind of God", or however Hawking put it.

So a triangle as something free of all possible ontological commitments? — apokrisis

Free of all meaningful ontological commitments perhaps. I've never seen a geometry book talk about the difference between a triangle and an actualized triangle. If relations (like 'is a member of' or 'is larger than') count as ontological commitments, then we're not free of them, and we very much use the word 'exists' to mean such relations, such as my prime number example.

That is itself another ontological commitment even if you believe you have safely placed yourself beyond ontological questions.

I'm not saying it doesn't exist (which would be an ontological commitment). I'm saying there's no distinction between the two objects differing only in this actualization property. Given that, the statement of 'no need for ontology' is an ontological statement, but maybe you should elaborate in what way you see it to be a commitment.

I mean I can’t stop you picking such a position. There just ain’t nothing to engage on if that is the case.

Exactly! It solves the problem of why anything is actualized in the first place, all without the need to invoke magic. And since there's nothing further to engage on (no contradictions result), the question of 'why there is something and not nothing' goes away. All that remains is relations. The moon exists to me. It doesn't exist to the triangle. But to suggest that either 'is' or 'is not' becomes meaningless as does the something/nothing conundrum.

I was going to leave it there but then thought worth dealing with this from the epistemological angle that speaks to the need for ontological commitments in anyone's view. — apokrisis

I think it does, but it becomes a relation then. I can measure this. A rock can equally measure it since I don't define measurement as a conscious act. As for the view of a conscious being, I can knowingly interact with X. I can abstract Y. So X and Y exist as those relations. A unicorn (not the abstraction) cannot be measured by you or the rock in your presence, but it can be measured by the rock in the unicorn's presence. So the unicorn exists to the latter rock and you don't. Most people don't think that far and only worry about what they can see in order to sort things into exists (moon) and not-exists (unicorn) The list never changes for them, so it's natural to assume it's a property, but it becomes a bias, preventing open-mindedness to an alternate view, that this division into exists/not-exists is all just relations, not actuality. The property view seems unable to answer how this property comes about without invoking magic.

And so what I would point out is how "triangle" is a word that functions as a sign – a symbol – that anchors a modelling relation between mind and world.

That it is. No argument. But I'm not talking about the word, the symbol, or the abstraction. I can't interact with geometry without those things (words, concepts, symbols) either, but I can talk about the triangle itself just like I can talk about a proton despite never having seen one, my only interactions being through words, symbols, concepts and abstractions.

Is this a triangle....

None of them are triangles of course. I like the pictures. Technically, not even the clean triangle draws with a straight edge is a triangle since it has lines of finite width and is composed of matter which doesn't even have an exact location. That nit aside, all of your pictures probably invoke the concept of triangularness in people. The rock is more triangular than the typical rock. The Wankel part has three corners but like the first three, still isn't a polygon. Neither physical object is planar. A triangle cannot be part of our world.
The 4th picture invokes three triangles and three more concave polygons. They're actually just collections of pixels that represent/approximate these polygons, which is why I use the word 'invokes'. As I said, we have no access to a geometric world and hence no physical access to one. But our physical approximate triangles are close enough that we can observe and use their properties. Triangles are essential to sturdy bridges for instance.

A question came up though. A circle is a closed curved line, all points being equidistant from the center. Contrast this with a disk which is a circle filled in and contains all points <= radius from center. I attempted that distinction with a line triangle typically depicted and could not find a separate term for the filled-in version such as the one in your 4th image. They're both just referred to as triangles.

So the point is that the word is a sign by which we navigate reality via some habit of interpretation. We have a working sense of what it would mean for nature to be triangular in form in a materially instantiated fashion.

No argument. I just wasn't talking about our nature world with my question. I was deliberately avoiding it in fact.

The meaning of the word "triangle" is the sum of all the possible ways we could stretch and yet not break the sense of what is essential.

Which is why I qualified my description with more words than just the one. I was quite explicit about it being a triangle as defined by planar geometry and not a physical one. I don't deny that the concept of triangle is invoked by each of your pictures, but I wasn't talking about the concept. I was talking about the triangle, just like I talk about the integer itself and not the symbol ('scribble' as H-H would put it) or the mental abstraction that we use to represent/manipulate it.

I know you think in semiotics, but when pondering the fundamentals of the the universe, one must be able to step outside that philosophy unless you want to suggest that the semiotics are fundamental, which is a form of idealism. Sure, they're fundamental to our interactions with other things, but this isn't a topic about how we interact with things.

More exactly, it is three edges with three vertexes.

I think you finally answered my question.

What breathes fire is the fact that there are minds making use of some set of symbols to make change in the world.

This defines actuality in terms of minds and symbols, which is a form of idealism, and it doesn't explain the actuality of the fundamental minds. Per my disclaimer, I'm not looking for such anthropocentric views. I don't question what's real to me, I question what's real, and conclude the meaningless of that phrasing of the question.

So you seem to be saying that a sign like "triangle" just exists,

No!
1) I'm not talking about a sign at all. Your philosophy seemingly bars your from discussing anything except the symbols, preventing discussion of the referent. Your inability to do this doesn't mean I have such an inability.
2) I don't find distinction between something existing and not existing (being actual or not being actual), so I find any statement of something existing to be meaningless.

As I said, we have no access to a geometric world and hence no physical access to one. — noAxioms

So there is a world where geometry exist and another where physics exists?

There is no material access but there is a relation?

but I wasn't talking about the concept. I was talking about the triangle, — noAxioms

You mean you were talking about the mathematician’s concept and not the physicalist’s concept?

I know you think in semiotics, but when pondering the fundamentals of the the universe, one must be able to step outside that philosophy unless you want to suggest that the semiotics are fundamental, which is a form of idealism. — noAxioms

Well Peirce called it objective idealism. And I like it because it is indeed epistemology become ontology. Pansemiosis would be the position that the Cosmos develops into being as a rational structure. The logic of structure itself causes the Universe to come to have a necessary existence.

Your philosophy seemingly bars your from discussing anything except the symbols, preventing discussion of the referent. Your inability to do this doesn't mean I have such an inability. — noAxioms

It ain’t about talking. It is about acting in the world as a community of mind. It I say draw a “triangle”, I doubt I will find myself protesting, but you’ve drawn a circle. Or a canoe. Or anything else.

I don't find distinction between something existing and not existing (being actual or not being actual), so I find any statement of something existing to be meaningless. — noAxioms

So you say. But that is an eliminative assertion which you betray every time you in practice sit down without looking backwards to check the “chair” is still “there”.

So there is a world where geometry exist and another where physics exists? — apokrisis

There's are mathematical structures where geometry is valid. There are mathematical structures where our physics is valid. There is a world where a unicorn exists (same structure, different world).

There is no material access but there is a relation?

I don't know how the relation of '
access' might be meaningful between different mathematical structures. They're both mathematical structures, so they relate in that manner.

You mean you were talking about the mathematician’s concept and not the physicalist’s concept?

Talking about the mathematical triangle yes, but the concept no.

Well Peirce called it objective idealism. And I like it because it is indeed epistemology become ontology. Pansemiosis would be the position that the Cosmos develops into being as a rational structure. The logic of structure itself causes the Universe to come to have a necessary existence.

I don't disagree with this, but it doesn't explain the actuality of the rational thing causing the necessity of the rest of the universe.

But that is an eliminative assertion which you betray every time you in practice sit down without looking backwards to check the “chair” is still “there”.

First of all, the chair being there is a relation with me, not a property of the chair.
Secondly, I do very much indeed hold pragmatic beliefs, or at least the part of me that makes the decisions in my daily life. The thing is, that part isn't very rational. It simply has a rational advisor that is occasionally allowed to make suggestions, but the rational beliefs held by that advisor are for the most part ignored by the first part that presumes the chair has the property of existing.