Whence are these informational models? — schopenhauer1

Genes, neurons, words, numbers. The basis of a symbolic modelling relation aren’t a secret.

Sharing of valence electrons, attraction based on forces, sharing of chemical molecules, etc. — schopenhauer1

So what goal is served such that it “works”? In what sense is causality closed such that it is a “system”?

You are not really saying anything about a process yet.

First though, are you familiar with the second law of thermodynamics? — Metaphysician Undercover

You mean that obscure theory about all the many ways to arrange some system that are differences that don’t make a difference? When a system arrives at equilibrium, changes no longer result in a change?

but your claim is that nature only produces differences which make a difference. — Metaphysician Undercover

Wrong.

They were not created by human beings, so they were created by nature. — Metaphysician Undercover

I don't know what "nature fails to limit those differences" could even mean. — Metaphysician Undercover

Hmm. Nature creating seems to pose no issue for you. Yet nature failing to prevent accidents does.

Backwards as usual.

So, the onus is on you to demonstrate why nature would create differences which do not make a difference, when it doesn't care about such differences. — Metaphysician Undercover

But my claim is that nature fails to limit those differences - they are simply accidents that don't change anything - while your claim is that nature creates them, and thus somehow they must exist for some (still undefined by you) reason.

So the onus is on you to support your crazy theories about nature.

Physically interacting in a way that they work together in a system. — schopenhauer1

What is it about the physical interacting that meets a definition of working and a definition of system?

And when do you start talking about processes that are informational models and processes that are material flows?

What do you mean by integrated? In what manner exactly?

All these words/phrases bolded, can you please provide a definition of each — schopenhauer1

Maybe. If you can define "process".

(mind as substrate) — Anthony

Make up your mind then. Did you intend to defend a substance ontology or a process one in talking about this "substrate" you call "mind".

If "nature' was as you say, so that it didn't care about such differences, then why does nature make each individual unique? — Metaphysician Undercover

Because it doesn't care enough about preventing differences.

I see that you have things backward. — Metaphysician Undercover

Of course you do. If you learnt to stand the right way round, everything might look the right way up for a change.

But ontologically, every individual is different and unique despite the fact that we classify them as the same. — Metaphysician Undercover

Show that nature cares to prevent what it appears to permit.

The agency is automatically confounded. — Anthony

No it bloody isn't. The psychological process produces the difference between a "self" and a "world". That is the function. To become an agent by gaining prediction-based control over the material flows the world that is "not us" can offer.

Isn't it interesting how the most important meters, physiological processes and biochemical pathways keeping us alive are autonomic/automatic? See, this is where I'd say we must stretch the definition of cognition to include perfect absence of automation. — Anthony

Sure. You start with the simple and then build up the complexity.

But the mistake you are making is to presume that the goal would be to escape from unthinking automaticity. Cognition is all about building up so many layers of practiced habit that you can get by with thinking as little as possible to achieve whatever goals you could reasonably have.

So yes, we need attentional level processes to work out what to do when things go wrong - when we get caught out by a prediction failure. But the general goal being instantiated is always to be able to predict the world with the least cognitive effort.

So the ideal situation would be the kind of "flow" celebrated in psychology where you can do everything with effortless ease. There would be an absence of attentional effort and hesitation, not the perfect absence of automation.

If you're careful in your definitions, you'll notice that there's only one act of cognition/every moment, picosecond, whatever. After this, we have a re-cognition, a re-presentation of what once was. — Anthony

I am happy to be careful about psychological science. So if you wanted to talk "frame rates", then it takes about half a second to complete some attentional act, and only about a fifth of a second to make a skilled automatic decision. Habit shortcuts things so we can fire and forget.

Then when it comes to reportable awareness - the re-presentation of states - that gets us into another whole conversation about the role language plays in structuring human cognition and self awareness. That is a further level of sociocultural regulation, a further level of human habit, that we all have to learn.

Nonetheless, there can be no cloning of a mental impression, let alone the mind itself. A mental impression would be the concept of functionalism, like an algorithm with a goal. Whereas, a mental impression has no goal. — Anthony

A perception is an act of measurement. A conception is the theory being tested. The whole of this would constitute the psychological function that is the one of modelling the world in a way that minimises its capacity to confound our agential intentions.

So again, you are not being clear about what point you mean to make. But the mental impression is the evidence whether the functional goal is getting met. It is not the goal but the signal. That would be why it "doesn't have a goal", and the function is what does.

This sounds like Gregory Bateson. — Anthony

It is Bateson. Cybernetics was biosemiotics back in the 1950s.

But not the same place and time...so there IS always a difference, fundamentally. — Anthony

But a difference that matters fundamentally or a difference that is instead fundamentally accidental?

There's a big leap from the difference that makes a difference to a function. — Anthony

Not really. A function is a semiotic process. It needs signals - feedback - to tell it if it is doing wrong or right.

So a difference making a difference - to some point of view - is definitional of a function. At the very least, it distinguishes a purposeful function from a mere material tendency when it comes to an ontology of processes.

The mind doesn't function at anything at all. — Anthony

Uh huh.

When you're identifying an individual every difference makes a difference. — Metaphysician Undercover

Sure. If you care. But that is epistemology. My claims about process philosophy are ontological. So now it is about the process that is individuation. And nature only seems to care about differences that make a difference in some practical sense. Nature is essentially statistical.

"What" is being emerged from the process? — schopenhauer1

The "mind". Whatever that is best understood to be.

(Remembering that there is no reason to think that it wouldn't feel like something to be in a modelling relation with the world - especially when that modelling relationship it is as complex and agential as the one instantiated by a socialised human brain.)

A claim that there is a mind isn't perspectivally related to panpsychism. — Anthony

The issue is how we view a "mind". And the contrast here is between viewing it as some kind of process or instead as some kind of property. Is "substantial being" merely emergent, or is it brutely fundamental? And panpsychism usually winds up on the non-process side of the issue when you get down to it.

You participate with the cosmos through your thought-forms, through a storehouse of memories you take as your self and the order you identify with, all at once. — Anthony

Here you appear to be siding with my own biosemiotic approach.

By what definition. Not functionalism, first of all, because every object is truly different from every other, as they do not and cannot occupy the same space-time. — Anthony

I disagree as the same function can be realised at many different places and times. New minds are being born constantly. So sure, every organism is an individual. But also every organism is an expression of some common set of functions. As processes, there is a shared history informing what they are.

Every bottle of my Michelob isn't exactly the same as the next even though it appears that way. — Anthony

But the differences can be insignificant. So that is not an issue.

Does the beer drinker care? Only to the extent it makes a difference in terms of their purpose.

If you agree on a definition of mind, then you have to talk about local and nonlocal causality involving mind. Gravity, as a plausible place to start, is action at a distance. Does gravity affect the mind? If gravity can effect the mind at a distance, is there anything else that impels the mind from a distance? — Anthony

Again, are these differences that make a difference to the mind in question? Your response is all over the shop.

What you want to say isn't very clear. But I guess it boils down to a panpsychic claim that there is such a thing as "the mind" and our minds participate in the greater mind that is the Cosmos, or existence, or God's mind, or something.

Or alternatively, you could be just making the apophatic argument that whatever reality is, however we should conceive of it, it definitely ain't the kind of simple objective material reality of classical ontology. In some sense, the holism of a process view must be the way to think about things.

Panpsychism can be dismissed as it is not a process view. Instead it is claiming that mind is a substantial property of substantial being. Consciousness "just is" a brute fact of reality. It does not emerge as the result of some particular form of process we might hope to describe.

But if we are talking about a holistic view of nature - and one that accounts for observers along with observables - then I would say a key point is that the separability of the observer is the crucial thing. The mind, as a natural process, is about semiosis or points of view. It is about being able to step back from the general physical flow of events to then be able to impose some "personal" level of constraint or regulation on that flow. So mindfulness is all about organismic agency. The disconnection - even if it can't be absolute - is how a different kind of connection, one imposing its own wants and needs, could arise.

Now all this is pretty standard from a scientific perspective if you are a systems type of thinker. The flow of nature is the thermodynamic flow of the Big Bang on its way to its Heat Death. It is the flow of entropy production. And then that driving gradient becomes something life and mind participate in as negentropic dissipative structure - the complex informational organisation that arises to break down any local blockages in that generalised flow.

Life and mind are then "what it is like" to have that modelling relation with the world. It is how it feels to be an organismic agent with intentions and regulative possibilities.

So in a general sense, life and mind are not about simply participating in nature. They are about standing aside from that material entropic flow in such a fashion that the flow can be informationally regulated from a "point of view" that transcends it.

So a process philosophy view - beyond the usual woo - would be anchored in an understanding of the Cosmos as a dissipative structure, a vast entropic flow, and then an understanding of life and mind as a second kind of parasitic process. The cosmic entropic gradient suffers local blockages. They become the food source for more complex structure with the necessary agency and organismic design. Thus life and mind as a process would then have its own more specific description. Biosemiotic is the scientific term I would favour.

Life and mind can only live in the material world. They colonise its flow. But life and mind must stand apart from that flow so as to live off it. They must be able to form their own information or memory based point of view from whence to plan and act.

They're status of facthood. — Posty McPostface

If facts are definite things, then they would have to obtain by being judged in terms of some metaphysical strength dichotomy. We would need an essential distinction - along the lines of claiming some hard and sure contrast between facts of the mind and facts of the world.

Heraclitus, who likened the structure of reality to the element of fire, as change is reality and stability is illusion. — schopenhauer1

Yes. Metaphysically what matters is that process thinking sees instability as fundamental, and atomistic thinking sees stability as fundamental.

So both views can see that concrete reality is based on substance. But the process view would see that substantial state as emergent. It would be the result of the stabilisation of instability - the constraint on uncertainty and fluctuation. While the atomist or materialist view would be that stable substance just brutely exists, and then "real change" becomes an illusion. At a fundamental level, all change is merely a rearrangement or recombination.

What is it like to actually "be" a process? — schopenhauer1

Did you mean some specific kind of process - like a brain's modelling relation with the world? Or a generic kind of physical process - a dissipative structure like a river?

Process philosophy itself has been pretty much hijacked as a term by theist philosophers. So that shifts you into a different kind of distinction. You wouldn't be seeking a better description of physical nature but talking about what it is like to be participating in the divine cosmic mind. :grin:

The argument relies on the acknowledgement that the manner in which we sort out the wheat (fruitful mathematical theories) from the chaff (unprincipled and uninteresting sets of axioms) reflects contingent features of our specific form of life. — Pierre-Normand

Good post. I agree it is about finding the (pragmatist) middle path.

So in my simple-minded way, the debate is about the interaction between the formal and the material in a hylomorphic conception of nature. Maths stands for a notion of all the forms that are possible. And as such, it is unconstrained by material considerations. Practical considerations of energy and matter - whatever it is that instantiates a form as something actually physical - are left out of the story.

And that disconnection is where all the confusion arises. It in fact is the same confusion that leads to mind~body dualism. It is only once psychology is understood as something embodied and function serving that we can see why physics acts to produce the kind of "information processing" nervous system that we see.

So the maths that matters is the maths of purpose-serving structures. They do reflect the features of a form of life. But the features need not be contingent, nor the way of life just ours. Instead, we could find our centre ground in the standard structuralist claim that there are generically necessary "forms of life". For actualised substance to be the case, there has to be a systematic organisation - that interaction between downward constraining forms and upward constructing material degrees of freedom.

So tracking the genericity of structures leads you towards a thermodynamic, probabilistic, and indeed semiotic, metaphysics. Life is certainly a form of thermodynamics - a semiotic elaboration on a dissipative structure. And even the Cosmos is a "form of life" in being a dissipative structure at a universal level.

In the grand scheme then, we would seek to unite the formal and the material in the substantial. That hylomorphism must be the thread that connects existence at its every level, its every stage of complexity. So substantial reality can be said to have a general interest in the formal structures that work - the structures that can harness material flows or entropy to achieve the goal of wresting stablility from impermanence. A "way of life" boils down to just that. And the maths that matters most, the maths that has true reality, is that which describes the kinds of forms or structures which subserve that fundamental purpose.

So if the mathematical realm is some vast landscape of possible algorithms, then only a limited number would be highly effective at doing the job of harnessing material instabilities. The "good" maths would be that which has the emergent property of producing finitude or constraint. Junk maths just wanders off forever in open-ended fashion. Good maths - like symmetry maths or fractal maths - speaks of nature because it speaks of self-organising limitation and closure.

Of course, mathematicians are free to explore the "junk". They could just play with open-ended patterns as a matter of contingent human choice. The constructed view of maths could be true as part of the socially-accepted "mathematician's way of life". :)

But still, humans have historically valued the maths that could speak to natural structure. And natural structure is hylomorphic. What matters is how constraints can organise freedoms to produce substantial actuality.

We can kick around Plato as if he were some kind of ancient mystical fool. But from my own readings, what strikes me is how dimly we appreciate the systems-based revolution that was Greek metaphysics - especially in the writings of Anaximander and Aristotle. It was how science was born. And then the systems view got obscured because causal reductionism took over. Nominalism made formal/final cause appear mystic and uncool. And we have been living with that metaphysical confusion ever since.

The further point is that the fact ( if it is a fact) that a perception must be (to at least some minimal degree) conceptually mediated, does not entail that a perceptual experience is a concept. Similarly then, an experience of material concreteness is not a concept of material concreteness. — Janus

My argument is that conception and perception would be the two extremes of the one process. To speak of one versus the other is merely to highlight the grounding generality vs the focally individuated particular. You actually have nothing without having both together striking an appropriate balance. So you need three things. The limits of the conceived, the limits of the perceived, and the outcome of that which is then "the experiential state".

That is a holistic description of experiencing as a general psychological process. And that would apply to the business of modelling the world whether it was neurological, linguistic, or mathematical.

But then you introduce the further issue of how the different levels of semiosis might relate - given that they do seem differentiable in principle, but also again are always in action together in any brain trained to understand its world in a "modern" way.

So you want to argue something familiar - the biology does the perception, the sociology does the conception. And there is a rough truth to that. But I am saying it becomes an unacceptably rough description if we want to be thorough-going metaphysical holists. It wants to make absolute a distinction which can't absolutely exist.

My original response was a result of you both accusing me of misplaced concreteness and then refusing to recognise that you yourself were doing just that with your own talk of "materiality" or "tangible objects".

Science is always talking about matter. But it long ago dropped most of what most folk think "matter" means from their everyday linguistic talk about the kind of neurobiological perceptions they experience. Science is now talking about matter as fields, and fields as information. It is galloping along because it doesn't restrict itself to ordinary language descriptions of neurobiological conceptions.

I was pointing out how your own use of the term was still overly concrete in taking the meaning of "material" as just something one could simply point at the world and exclaim: "See, right there before your eyes, just as it looks and feels." To avoid the charge of naive realism, or simple epistemic confusion (they are usually the same thing), you would have to show how you were meaning something more sophisticated.

But where is any connection to Hoffman's computational idealism?

Then as to algebra and geometry, I don't buy evolutionary contingency as the explanation. Rather it would be the necessity of such a structural conception of nature. The two ways of seeing the world are formally complementary. For instance, as Atiyah argues....

Algebra is concerned with manipulation in time and geometry is concerned with space. These are two orthogonal aspects of the world, and they represent two different points of view in mathematics.

So first up, evolutionary biology did not make us mathematical creatures. Although it did leave us - as the smartest animals, our brains already being reshaped by our language and tool-use - with highly lateralised neurobiology. Large brain animals already have that "algebra vs geometry" dichotomy wired in as a division between object recognition processing and spatial relations processing. Things vs their relations. And then humans continued on to have a strong left vs right brain dichotomy in terms of attentional style - the left specialised for focal differentiation and the right specialised for global integration (both always working together to produce the third thing of a task-appropriate balance).

So in a general way, biological evolution structured the animal brain with the kind of Gestalt figure~ground logic that would be needed to see the world "as it is". The world could be experienced as an intelligible whole because it was always being analysed in terms of its fundamental structuring dichotomies.

But then a mathematical turn of mind - one which actually see the world in terms of mechanistic construction, acts of counting and measuring - was a cultural evolutionary step. Ordinary language got it going. Then mathematical language crystalised the practice as an actual machinery, a teachable syntax.

So yes, a mechanistic conception of nature was of evolutionary value. But that couldn't become apparent until after language was developed.

And on the other hand, our neurobiological legacy was not absolutely devoid of logical structure. But it was the much more organic logic of dichotomisation and symmetry breaking. This is the logic that reflects the deepest structural reality of the Cosmos.

And then it is no surprise that both geometry and algebra developed hand in hand. They are simply the two complementary ways that structure itself breaks down. One is ground, the other is figure. One is global, the other local. We can choose either as the starting point from which to work back towards the other.

...but its ultimate concern is not utilitarian in nature. — Wayfarer

So who is defending a reductionist notion of utilitarianism? I was arguing in favour of the irreducible holism of pragmatism.

My view is that materialism kind of hijacked the Western tradition from within, although the times they are a'changing. — Wayfarer

Sure. Atomism reigns. But it can't be defeated by transcendent dualism. It must find its way to the immanence of holism. And that has a triadic logic at its heart.

Everything is, after all, a function of biological adaption; we have the kinds of maths we have, because of the kinds of creatures we are. — Wayfarer

Sure, things start there. All animals with large brains can count - at least they can count 1, 2, er many.

Linguistic humans then add on a level of social conceptualisation. And eventually a level of mathematical semiosis too. It became useful to count sheep so as not to be cheated at the market, or measure flat ground so buildings started off upright.

But I don't see the connection to Hoffman. Rovelli is not arguing idealism, only social constructionism surely.

Would you say the experience of animals conceptually structured? — Janus

Of course. Animals don't have a linguistically-structured conception of the world - so one that reflects a higher level social organisation. But they do have one that is structured by its ecologically useful generalisations, or habits of interpretance.

Surely the point about the axioms of arithmetic etc is that they're true for no further reason, they are apodictic, not dependent on some other truth. — Wayfarer

They are formed apophatically. They arise as the opposed choices of some dichotomy. And then they are proved "true" retrospectively because the system of thought that follows turns out to be useful. Even "unreasonably effective".

So the discrete and the continuous arise as an obvious opposition. We can take one as axiomatic, the other as its emergent construction. In maths, a line could be built up as an infinite succession of points, so close together as to leave no gaps. Or we could just as well choose the opposite story that a line can be infinitely divided until it is just a bunch of discrete points - continuous intervals with no actual length.

So axioms might seem to be basic truths too self-evident to deny. But history usually shows that a dichotomising discussion first took place. And that resulted in a pair of contrasting limits. Which in turn offered two complementary descriptions of nature. We could have picked either one - as the "fundamental" from which its "other" was the mechanically emergent construction - and arrived at a useful description of the actual world.

But reason itself is strictly the relationship between ideas. It doesn't need to be validated with respect to any particular state of affairs - that is why it is associated with a priori truths. — Wayfarer

But what do you mean by reason?

Mathematical reasoning is pure logical deduction. It is mechanistic. And so it is both powerful, but also only exists as the limit case. It invents its own reality - one where constraints rule absolutely. So we know it is only a powerful fiction. To the extent that it locks reality down to a picture of efficient causation, it is "othering" the very finality that you so want to be part of your reasonable world.

So you ought to be much more comfortable with a full Peircean model of reason - one that is based on the irreducible triad of abduction, deduction and inductive confirmation. But that is then the scientific story on reason. You have to accept the validation by empirical particulars along with the "inspired leap" of the hypothesis/axiom forming, and the logical deduction of some formal description or mathematically-articulated theory.

So you put yourself in a weird position by celebrating the inspiration and the logic - seeing in them a transcendent step from the mind to the divine - and then rejecting the third leg of this triad, the empiricism that roots reasoning back in the world with which it engages.

You pick transcendence when reason actually functions - in a way we see all the time - as a pragmatic and immanent activity.

To connect back to the OP, Rovelli's paper illustrates the logical junk that can be generated if we imagine "reason" becoming just every possible output state of every possible bit of machinery or algorithm. It is just another sad multiverse tale.

But a Peircean understanding of reasoning - the scientific model you want to reject - book-ends that ultimately irrational fecundity with rational constraints. First, hypotheses are meant to be reasonable too. Inferentially, we can see why they would be a jump in the right direction. They feel like the right kind of grounding generalisation. And then second, the correctness of those inferential guesses is validated by their empirical outcomes. Judgement of truth is passed pragmatically. Certain mathematical models would be considered Platonically true because they worked. They wound up limiting unwanted surprises.

So we don't even start on generating maths unless we have a good reason to expect successful outcomes. And we don't take much notice of that maths unless it empirically delivers such an outcome.

Once Rovelli's infinite M has been shrunk in both fashions, then really the space of essential mathematical structures becomes very small. Some folk would claim it can all be shrunk down to set theory, or even category theory.

But anyway, modelling is triadic. Reasoning is a three-legged process. And your own defence of dualism is confused as it wants to conflate mathematical abduction with mathematical deduction - the creative spirit and its divine machinery - placing this unholy transcendental pairing in opposition to the dull inductive materiality of empirical measurement.

But an immanent metaphysics sees the circle being completed by these three elements working collectively. Nature is irreducibly hierarchical in its organisation. That view gives each element its proper place as aspect of a whole.

The textbook explanation is parasitic upon the experience of a world of tangible objects. Only a fool would deny that. — Janus

What I questioned was your notion of "experience of a world". If you accept that experience is an Umwelt - conceptually structured from the get-go, then no problems. But if you can't see that speaking of tangibility is itself an abstraction, then there is a big problem.

You love to resort to throwing around labels like "naive realist' — Janus

Like you love to throw around labels like "over-thinking".

I'm making no claim about the "ultimacy" of the material world, only about the foundational character of the experience of tangible things. — Janus

So in claiming to escape naive realism, how are you managing to escape naive idealism here?

You are asking me to go out and feel the tangible quality of material things. And somehow that proves that materiality exists - exactly as conceived!?!

My response is that tangibility is a general conception I would apply as a contrast to some useful sense of its "other" - the intangible. And indeed, given the murkiness of what would be that dialectical other, tangibility already seems rather a confused term. Air is not tangible - until the wind blows or the plane cabin depressurises. Is the magnetic field between two magnets tangible? As a kid I spent a lot of time pushing two opposing magnets together and feeling the "bubble" or resistance that wanted to form in-between.

So you are now using "tangible" as another reified way of speaking about concrete reality - a mind-independent metaphysical framing. It sounds a little better because it also has its mind-dependent meanings. It can mean palpable or tactile - acts of mind - as well as physical, real, substantial, corporeal, or solid. Facts of the world.

I just want to draw attention to how language is being used here. And what the ontological commitments might actually be. Tangibility is a tad slippery and ambiguous about the very issue that needs to be made clear.

To again restate my own position, I am arguing that "ultimately" the material principle reduces to some kind of uncertainty or fluctuation. Naked instability. This is of course a highly abstract and not very tangible notion. And then what you are talking about is really substantiality. Formed matter. Constrained instability. Tangibility would become another word for individuation that persists due to some contextual strength of constraints.

That would be a mental picture of a concrete material reality that is the polar opposite of the usual atomistic one. So the two of us - to the degree we are immersed in these contrasting umwelts - would be taking home very different views about what we just learnt by reaching out and touching a "tangible object".

That was one of the points Rovelli argued in asking what kind of maths a Jovian would arrive at.

So again, experience turns out to be conception all the way down. Nothing enters phenomenology that hasn't already been shaped by some "fundamental" conceptual dichotomies. Sensory receptors are designed with the logic of switches that are in the business of saying yes or no to a question already posed.

This is an irreducible complexity that sits at the heart of all epistemology. It fundamentally screws up any simplicity about the relation between minds and worlds.

And I still believe this is an essential difference in our outlooks. I say that this irreducible complexity is what we must eventually embrace the best way we can. You reply by calling that over-thinking. And I still say no. That triadic irreducibility is the feature and not the bug here. It is how anything could even exist. It is what stops everything collapsing back into its own entangled confusion.

I think you're confusing yourself by over-thinking this. — Janus

Naive realists are always saying that. They like to under-think the metaphysical complexities.

Try feeling some object in your vicinity right now. You can directly feel its material concreteness, its tangibility; it is from that basic experience that the idea of substantial material concreteness originates. — Janus

Oh please. I press hard on the desk with my finger. I poke my finger with no sense of resistance through the surrounding air. I then pick up the physics textbook that tells me the solid matter is really a void of excitations, while the airy space is crammed with Newtonian particles exerting a collective pressure and resistance on my being.

Sensations are one level of semiosis - a biological level of meaning making. But an Umwelt is an Umwelt. Psychological science gives us all the evidence we need on that.

So sure, I make a perceptual distinction between what is substantial, what is void. Or what is actual, what is imagined. My psychological modelling of reality is organised by a bunch of useful conceptual dichotomies.

Thus yes, the dichotomies originate in the world in some sense. A characteristic of this era in Cosmic development is that you have solids, liquids, gases and plasmas. Concrete is a term that applies to one of the four "material state" in some everyday, not very philosophical or scientific, fashion.

But when you tell me to demonstrate the reality of "material concreteness" by poking something ... solid ... not liquid, or gas, or plasma ...

In fact to say that nature is constructed from number, or some such kind of metaphysical claim, as for example Tegmark makes, is a form of reductionism; reduction of the organic to the mechanistic. — Janus

I'm trying to say something more subtle. I am saying that number - the general thing of construction or composition - is emergent rather than basic. But having emerged as a habitual possibility of nature, it then does become basic to the greater complexity that ensues. Atomism and classicality are pretty much the truth of reality so far as we living forms are concerned, at the physical scale at which we arise.

A machine has a simple causality because it is just the sum of its parts. And nature isn't a machine - but it develops structural complexity by imposing an increasingly mechanistic order on itself.

The early universe was a relativistic gas, a hot featureless bath of radiation doing nothing but cooling and expanding. It was only because constraints emerged to cause mass particles to condense out of this spreading flow that more interesting stuff could happen. You had crunchy little electrons and protons bashing about and interacting at sub-light speed. There was now a localised form of time and action. A history of concrete or discrete events could get going against a backdrop of generalised continuity. It took a while, but a machine-like order clicked into place as the new normal. A bunch of identikit parts with constructive possibilities - individuated properties - could begin to produce a more complex world.

So physical reality as we know it is not founded in the mechanistic. But it wouldn't exist as we know it if it weren't also imbued with the propensity for a mechanistic and hierarchical form of organisation.

Numbers are then a pretty good representation of this developmental view as the very possibility of a number is emergent from the notion of an identity function. If you take a general action to the limit, like addition or multiplication, then a basic unit will emerge as the difference that doesn't make a difference, so terminating the symmetry breaking with a local symmetry. One times anything is still one. Anything plus zero is still zero. So - emergently - a basic limit, an identity function, will wind up grounding some space of functions. The units you need to justify a constructive or compositional (mathematical) reality just pops out as being eventually an atomistic regularity that can't be rotated or translated out of a freely dynamical existence.

So there is a reason why we do see a deep connection between our notions of mechanical construction and reality as it exists. The organicism of symmetry breaking or dichotomisation taken to the limit results in the emergence of fundamental units of action.

So the conception of nature as fundamentally mathematical - an atomistic construction - isn't wrong. It is a pretty good description of how reality is for us as complex creatures living in an era when the Cosmos is so extremely cold and large. But also we now know that this degree of classicality is an emergent fact. It isn't actually fundamental - unless we then go the next step that a complete holism would require, which is to realise that we are still seeking to impose a strict temporal order - a classical before and after - on a process of realisation.

So the mechanistic aspect of nature can be seen as now a finality - a cause acting from an organism's own future. Reality was being called towards the structuration that then did emerge. It was always inevitable that things would arrive there. The future becomes as real as the beginning - although now neither are real in the old privileged sense we want to give them. They have to share that foundational glory rather more equally in our conceptions of nature.

Of course my notion of it is an abstraction, but material concreteness is experienced. — Janus

Same old, same old. Semiosis says what you "experience" is your Umwelt. Sure, the "world" must stand in back of that as a noumenal constraint, some kind of recalcitrant actuality that limits the freedom of your interpretation. But then you need to pay closer attention to how conceptions are actually formed as logical dichotomies.

If you rely on a distinction like concrete~abstract, then it is the pairing that is itself the whole of the conception. Again, if you rely on experience~conception as the distinction, it is the whole of that differentiation which is the conception.

So you talk about directly experiencing the substantial material concreteness of the actual real world. But that is still just a conception. The more strongly you believe in that dualised "othering", the more deeply you are actually embedded in the Umwelt you are creating.

So the irony here is that you are strengthening your conceptualised distance from the noumenal thing-in-itself by insisting on the absoluteness of this concrete other. Your belief in the "material" - as you conceive it, conceiving it as absolutely "other" - is what makes it as abstract as it could be in terms of you "experiencing the world".

Now this is not to deny that the world is not out there in recalcitrant fashion. Nor that a conceptual division into the concrete and the abstract is not a pragmatically useful way to structure our understanding of this world. Umwelts have to achieve our lived purposes.

But to say the rock is hard, sometimes painfully hard, is no more "real" than to say a rose smells sweet or the sky is blue.

Science is at least honest in this regard. Material properties become the numbers we can read off dials. The formal aspect of existence becomes a mathematically-expressed theory. The material aspect of existence becomes an appropriately matched act of measurement. Reality is then whatever this pragmatic system of conception tells us it to be.

If it weren't we would have no way of differentiating between the concrete and the abstract in the first place. — Janus

Nope. You want to apply a rigid if/then cause and effect logic to the situation. So for you, it has to be the case that one thing comes before the other thing. That is the habitual materialist Umwelt you are seeking to impose on your experiences of the world.

But I am arguing for an organicist or semiotic causality where the complementary aspects of any fundamental division must co-arise ... as each is the cause of its "other".

So before we could say our minds were divided by their abstract conceptions and their concrete perceptions, our state of experience would just have been an undifferentiated vagueness - the blooming, buzzing confusion of the newborn babe. A distinction between the concrete and the abstract is a structuring that grows. And no surprise really. As time passes, the generalities of the world will make themselves known as seperate from their specificities.

But in nature, the distinction is not some absolute or dualised difference. That is itself a further twist given to it by a modelling human mind. It becomes convenient to conceive of the world in the simplest fashion where the concrete and the abstract exists as actual absolutes, rather than merely as complementary limits to a useful metaphysical distinction.

Whereas when logical and mathematical truths are known, they are known in a way that is not possible with respect to sensibles, almost in the sense that the mind unites with the object of knowledge. — Wayfarer

Sure. That was the surprising new thing. Human thought could be organised by this new kind of logical structure. Maths cashed out a fully constrained, very mechanical, form of pattern generation. And that machine-like deductive and state-mapping approach to causality proved to be "unreasonably effective" at delivering technological control over nature.

So this was a big intellectual shock. The idea of the Machine was revolutionary. But then physical reality isn't in fact mechanical. So the "truth" of this mechanistic ontology is not the truth of the actual world.

Machinery - mathematical machinery - can be "absolutely true" because it is based on deductive proof. You assume some axiom. You derive some consequence. It seems perfectly water-tight. That is, it all degrees of freedom of rigidly suppressed. Nothing surprising can happen to derail the sequence of events. A perfect state of constraint is in effect. The only causality operating is that of linear cause and effect sequences - blind step by step deterministic construction.

So yes, this new machine mode of thinking seemed marvellous to the first logicists and mathematicians of Ancient Greece. For them, it seemed even "divine". It was thought and reason perfected. But it is ironic that you - given the way you rail against Scientism and other continuing cultural expressions of mechanical thinking - should still seem so in awe of mathematical forms. Reality ain't a computer, is it? The Cosmos is better understood as organic. Or better yet semiotic - because semiosis is the ontology which both accepts a mechanical twist to nature, but puts in its rightful place.

What I am saying is that you are still presenting an utterly confused history of the relevance of mathematics. You want it to be some kind of door to a transcendent divine aspect of existence. You respond to the reverential view taken by Pythagoreanism. And yet that exact path - that belief that maths is the royal road to Truth - is what winds up in modern technocratic reductionism. The belief that life, mind and physical reality in general can be accounted for fully and truthfully as mechanism.

...the original impetus behind the understanding was soteriological rather than utilitarian. — Wayfarer

Bullshit ontology is bullshit ontology, regardless of whether you are claiming god is a geometer or reality is a machine.

Curvature is a geometric property of spacetime and is related by Einstein's field equation to energy. Spacetime curvature and energy determine each other through Einstein's field equation. — litewave

I'm baffled by your reply. What else did you think I said? And where yet did you say anything useful about the nature of this "energy density" which you have to go off and measure?

Sure you can quantify it as an act of measurement. But that still leaves "reality" as a number being read off a dial.

So we face a big choice at that point. Either we go with the usual naive realist view - reality is whatever we think it is that we are measuring. The phenomenological is mistaken for the noumenal. Or we instead make a virtue out the very fact that pragmatism and semiotics lies at the core of all this.

The noumenal becomes the fundamentally arbitrary or vague in our metaphysical picture. We conceive of the material principle as a state of radical indeterminism - like a quantum foam. And then structure is that formal principle which can constrain this indeterminism so that it forms an emergent state of order - like a classical realm of deterministic objects.

Again, you are talking about GR. And we know from QFT that spacetime would be material enough to be populated by an infinity of gravitational self-interaction. So nothing self-stable is specified at the level of GR modelling. Einstein's field equations had to include a cosmological constant just to prevent even a homogenous spacetime from immediately shrinking out of existence due to the smallest material fluctuation.

So you have to glue together some model of global spacetime symmetries, some model of an actual material content, plus a generic material fudge factor to keep the whole fabric expanding into a future, to get to a GR description that still needs to be fixed by constraints on is material self-interactions.

It is all kind of Heath Robinson. And yet, each of these components is well-motivated in terms the general principles they express - the need to satisfy that happy triad of constraints, the principles of locality, least action and cosmology. Through the glass darkly, the maths is expressing a holistic causal structure now. We are arriving at a Platonistic view of that kind - if not the other kind, the one that wants to conceive of nature as mere mechanistic construction.

Bear in mind that I was originally talking about a train journey between two specific destinations. — Janus

Sure. Two stakes were stuck in the ground. And so suddenly the landscape had your chosen metric imposed on it.

For me the very notion of "the reality of mathematical structures" beyond their being abstractions from concrete objects and processes, seems unintelligible. — Janus

Yeah. But what I was arguing is that your notion of material concreteness is itself just a matching abstraction.

So sure, there must be a material aspect to reality. And you are now insisting to me about the reality of that abstracted notion. If the fallacy of misplaced concreteness is a thing, it would have to apply to your claims about however you picture this idea of definite local particulars.

This is why Peirce would grant reality to both the formal and material aspects of nature. As generalisations, they are each "concrete" - or just as concrete as each other in terms of both being essential aspects of the whole.

In a holistic metaphysics, substance is emergent. It becomes localise individuation. But you sound as if you want to treat emergent individuation as the concrete baseline reality of existence. You begin with a world of objects, rather than arrive at that world.

Mathematical "reality" seems to consist far more in possibility than it does in actuality, — Janus

If we wind it back, I wasn't defending some kind of spooky seperate existence of Platonic structure. I was in fact arguing that forms are always instantiated - or would have to be intelligibly instantiable. So the kinds of structures that could exist are the kinds of structures that could dovetail with some kind of logically complementary material principle. They would have to be able to yield substantial being in interaction with that material principle.

This then leads to the question of how to conceive of that material principle in properly generic form. This would lead us towards Peirce's answer - vagueness of Firstness. Or more classically, Apeiron or Chora. Or in some modern physicalist sense, chaos or fluctuation or quantum foam. That is, a potential that is lacking in limits, but capable of being limited.

So essentially my point is that the maths that is powerful and useful when it comes to the metaphysics of possible cosmologies is the kind of maths which has this particular character. It can model the constraint of freedoms, the limitation of uncertainty, the emergence of stable habit or law.

And what is exciting is that maths could model both the formal constraints - by speaking to the necessity of certain such structures - and even the material accidents, the constants of nature that then ground that structure. These constants may turn out to be shapes - like the holes in a topological sphere. As I said, global symmetry-breaking is terminated by reaching local symmetries which it can't erase. That is why you have the particle zoo of the Standard Model. A quark or electron exists as fundamental - a fundamental excitation - because they can't be broken down any further. They put a stop to the symmetry-breaking cascade and now start to ground the construction of some kind of material content in the Universe.

That is what string theory is about. Topological irreducibility. If you curl up a higher dimensional space, you can't in the end get rid of all the kinks. You are left with some countable number of holes that then become the material character grounding the Universe. They are the knots that can't be undone.

So the material principle could be reducible to ontological structuralism - becoming the local kinks that can't in the end be rotated or translated out of existence. Matter would be part of Plato's realm, but exist in it apophatically, as the topological holes or features that can't be erased. The material part of being would be the inverse of the formal part of being.

So it was this organic conception of structure - the "co-arising holism" that physics is uncovering - that I'm contrasting to the mechanical conception of pattern generation which Rovelli is using to produce a landscape of mathematical junk.

Plato was speaking to that dawning metaphysical realisation that the intelligibility of reality is about a division of the substantial into the complementary things of the formal and material principle. Aristotle might have said it much more clearly, but the dim outlines of that emergent hierarchical view can be seen in Plato - as when he talks of The Good as a finality which acts to select certain forms, and the Chora as the need for some kind of material receptacle where structure could be instantiated.

Just consider the Platonic solids. In 2D, polygons can have any number of sides, as long as they have at least three. But in 3D, suddenly that adds a huge global constraint that limits local regularity to just 3x2 possibilities - the self-dual tetrahedron (4 triangular faces), the dual cube and octahedron (swapping faces for vertices), and the dual dodecahedron and icosahedron. So place a limit on dimensionality and only a limited number of perfectly exact resonances can fit that space.

The Platonic solids are examples of how local symmetry can become physically manifest if global symmetry is explicitly broken. And of course this mathematical realisation - this intelligible fact of any possible reality - was then used to give a Platonic account of material atomism. If material fluctuation was in fact bound by formal limitation, then these had to be the shapes that would emerge at the end of the trail. Atoms would be little triangles, and so be fiery, etc. (Of course, a sphere was the other emergent perfect shape - the one that then emerges at the infinite limit of "polygonicity".)

So yes, if maths abstracts and generalises, then of course it is stepping back towards the possible, and away from the actual or substantial.

But there are then two ways of stepping back towards generality. And hylomorphism would be about following both those paths - and being able to see the unity in the fact that they are a pair of reciprocally defined paths. Each is the other's inverse. And so the metaphysical formalisation of the description of the one can apophatically stand as the formalised description of its "other". Yin and Yang. Accident and necessity. Matter and spacetime.

It is that deep structural trick that would see Platonism - as understood charitably - being cashed out by a modern physical "theory of everything". If the material constants can be shown to be the irreducible holes produced at the limit of some process of constraint, some process of symmetry breaking, then reality would "pop out" of an intelligible mathematical description.

Again, this is the big prize that Rovelli himself is pursuing. So all his paper demonstrates is the paucity of a more conventional view of mathematics (and thence reality) as the infinite noodlings of mechanistic pattern generators.

If you want to call that "Platonism", I suppose you could. But Rovelli also wrote a book on Anaximander which showed him to be rather a lightweight on Ancient Greek metaphysics. I would rate him highly for his physical speculations, poorly for his history of philosophy.

The point was just that there is no single real (as opposed to conceptual or abstract) object, 'train journey' of which all train journey are representations or instantiations, — Janus

A train journey is a substantial act. So it is hylomorphically intantiated. My point is that we can unpack this in a general fashion by abstracting away both the formal and material principle involved. We can separate the formal necessities or constraints from the material accidents or fluctuations.

Topology seems to demonstrate this metaphysical principle in action. A compact surface is the constraint placed on the most generalised system we can imagine. We get a sphere. But then as a degree of freedom or accident that can’t be suppressed, the sphere could be punctured by holes. And so you get a primal model of countability that allows you to see what is really going on in something complicated, like the idea of countable train trips.

Train trips are a bad example because they start with a human mechanical imposition of a mathematical framework on a natural landscape. We are making it the case that there are some countable set of trips by some definition we all agree.

The argument here is then over the reality of mathematical structures themselves. And to follow what that argument would be - from my own hylomorphic and constraints based view - I would want to start with a clear mental picture of what the maths might actually be claiming.

So my claim was that the abstract object in question would be this kind of topological constraint that then still results in localised definite accidents. Limits turn out to be limited in this essential fashion. You can break a symmetry, but that symmetry breaking can in turn be broken by the arrival at some new terminating symmetry.

This is the physics we have discovered. It is why we wind up with the translational and rotational symmetries which all a cosmos of countable localised actions to exist. Constrain action to some spacetime point and it can still move or spin with inertial freedom.

So maths speaks deeply to the reality we observe. I just thought that counting train journeys was a misleading example because it is in no way a fundamental, or even natural, notion of a countable object. It is an action we mechanically impose on a landscape and so depends on our willingness to be indifferent about the acts which in the end do count.

If the train stopped only halfway into the station, we would all sit around debating if that not quite completed trip should still count. We would still be arguing about accidents vs necessities. But the answers wouldn’t carry much cosmological weight.

But what would define the value of the curvature at every point? You are still left quantifying something beyond the metric that determines a number.

Energy density is a quantity (number) — litewave

Is it just that? The claim would be that it is some quantity of something. So the structuralism of the maths still leaves open the question of how to understand the material part of reality’s equation.

Maybe G can be derived from some general principles — litewave

I would expect it can. This is strongly suggested by the fact that the Planck scale is defined by a triadic system of constants. You have an irreducible triad of dimensionless constants in c, G and h. And the whole point of a theory of quantum gravity would be to unite all three in a single theory describing a single emergent geometry.

So if hierarchical organisation is the maths of existence - the Aristotelian metaphysical picture - then mathematical physics has arrived right at that very conclusion. That is the reality that a successful combination of quantum field theory and general relativity would reveal.

Again, Rovelli is right about mathematical junk. Much of maths is the result of mere syntactical complication - a mechanistic spewing that is just too simple to model a physical reality. But where maths models actual complexity - a hierarchical view of structure and development - then ontic structural realism, as the new metaphysics, is the right way to go.

So spacetime with its complex structure seems to be a specific mathematical object. — litewave

Sure. Relativity falls out of the greater symmetry that results from switching from a distance preserving metric to an interval preserving metric. We are now talking about a world of objects with both a location and duration to be specified. Euclidean space was just too simple to stand as a model of physical reality. Lorentzian spacetime becomes the least number of symmetries we can get away with.

But even then, with general relativity, things are still too simple. We must tack on a tensor field to specify some energy density at every point in this spacetime. We have to tell Lorentzian spacetime how it should actually curve. A literally material constraint must be glued to the floppy Lorentzian fabric to give it a gravitational structure. And even then, the quantum of action - how G scales the interaction between the energy density and the spatiotemporal curvature - remains to be accounted for. This constant could have a purely mathematical explanation, but that is the big question for frontier physics. It might also be in some sense a pure accident of nature.

So the way that maths applies to physics is a complicated story. Mathematical symmetries do tell you about the zoo of possible constraints on any physical freedoms. But maths - being traditionally founded in spatial conceptions - may then tend to canonise the symmetries that are just to simple to be real. Constraints, in themselves, may be of irreducible complexity. And so the maths that really counts remains hidden from the conventional gaze as a result.

This is the case with Rovelli’s mathematical junkyard. Once you completely deconstruct maths so that it becomes just a flat and infinite syntactical machine, then it is going to spit out endless meaningless patterns. As Einstein said, the trick is to be as simple as possible, but not too simple.

And here is where Peirce, Aristotle, and other systems or hierarchical thinkers have got it sussed. They accept the irreduible triadicity of nature, where what exists is due to the fundamental reality of the possible, the actual and the necessary. Or the potential, substantial and final.

Rovelli’s relational interpretation of quantum theory and emergent approach to quantum gravity in fact have just this triadic character. So as a systems thinker, that is why he would latch on to the way that the overly simple conventional view winds up producing a world of unconstrained junk.

Should the mechanical view of reality be called Platonism? I think not. But Plato wasn’t a hierarchy theorist like Aristotle. So while he was groping in that direction with his positioning of the idea of the Good as the top of the pile constraint, and also with his talk of the chora as a complementary material principle, a fully triadic story was not cashed out. Platonism did get stuck in a dualism of opposed existences rather than united by a trichotomy of emergence.

I think it is better to think of a "mathematical object" as a way of thinking or speaking, so the sameness consists in the human action. — Janus

Rather than imagining counting train journeys, what about counting holes in a sphere. There is something perfect and absolute about the distinction between a sphere and a torus. Then you can keep on adding more holes.

So sure, some objects - like train journeys - seem pretty arbitrary. But then maths does arrive at cosmically general objects when every arbitrary geometric particular has been generalised away, leaving only the necessity of a pure topological constraint.

...the limited finite world is a part of the unconstrained world of math. — litewave

But there seems to be an obvious lack of a material principle in the formal realm of maths. Maths is spatial, or at best, spatiotemporal, and doesn't speak to energy or action in any basic way. It about the logical syntax of patterns and structures, and not about whatever breathes physical fire into those equations.

So the maths of the world would be the "maths" of constraining structure. The need to be constraining - constraining of material spontaneity or uncertainty or action - would itself be the big constraint on the maths that is physically relevant.

This is why statistical maths and symmetry maths does seem more real. It speaks to the naturally emergent structures of systems of constraint. There is a source of fluctuation or accident that is being limited by a global order. So that is where maths gets closest to the reality it might want to model. It incorporates the other thing of an action to be shaped.

Rovelli's realm of mathematical junk is then all the possible syntactical forms that can be generated when the forms serve no real organising purpose. Now you could say our finite material world is merely a part of that larger unconstrained universe. But I would say that Platonism - as a metaphysical position - is about the forms of nature that can do actual causal work. So there is the constraint that the forms do constrain. They must bring finitude to action, or the material aspect of nature. They must do the ontological job of stabilising accident and spontaneity and so allow a Cosmos to exist.

A lack of limits is pathological. It is the maths of constraining structure which promises to tell us the most about reality and the reasons for its existence.

Platonism - and Aristotle - both assume an hierarchy, but it's from a top-down, not bottom up, perspective. — Wayfarer

Yep. Constraints act top-down.

But the tricky part - which the maths of hierarchy theory realises! - is that the causality has to go both ways. There is also the upward construction kind of hierarchy. So the story becomes about the synergy between parts and wholes. You have compositional hierarchies that are the bottom-up view, and subsumption hierarchies that are the top-down view. And a stable reality can only emerge when the two are reinforcing each other's existence.

This is the kind of balance of causality that is described by dissipative structure theory - such as Bejan's work on material flows and "constructal law" - https://www.forbes.com/sites/anthonykosner/2012/02/29/theres-a-new-law-in-physics-and-it-changes-everything/#33e609ee618d

For this reason, Platonism is in a sense reductivist, though not in the way that a 'bottom-up' philosophy is. It is conceptually reductivist, not materially reductivist. — Wayfarer

I agree with the quote. But of course calling it "conceptual" is dangerous as it does suggest the mental.

For me, calling it structurally reductive would be better. My goal would be to avoid lapsing into actual mind~matter dualism on this one.

This, though, opens up a new question - what is 'interesting?' Well, interest simply is in the eye of the beholder: we develop some parts of M and not others because those parts help us do stuff, alot of the time. — StreetlightX

My point was there are reasons to think the structures and relations we use math to model exist in the world independent of us, since they led to us existing. — Marchesk

Yep. The issue is that reality and maths can seem very far apart when one is being understood in terms of the physics of constraints and the other is being viewed as a free grammatical construction. So junk can spew out of a syntax freely and meaninglessly - as in the examples like Borges’ library which Rovelli uses. But then reality and maths can seem fundamentally connected - as is the case of mathematical physics, where Rovelli is one of the leading players. When some kind of intelligible constraint - a suitable selection principle - is applied to the random junk spewing, then that gets closer to making sense of the relation.

To be fair to Plato, he did suggest such a finality. He argued for the Good as an optimisation principle that revealed the truth, beauty and justice of a subsidiary realm of mathematical (and other) forms. So that was of course still rather mystical. But it was at least recognising that something higher - a global constraint - was needed to pick out the most meaningful or fundamental patterns and structures.

Several points. It should be noted that if there turn out to be multiple descriptions of the same thing, then that thing seems to be something beyond the mere descriptions. Rovelli gives several examples. The choice between Euclidean and spherical geometry. Heisenberg's matrix mechanics and Schrodinger's wave mechanics. And as Cartesian geometry showed, in general, algebraic maths and geometric maths offer dual descriptions of everything that seems of mathematical interest. So Rovelli seems to want to use this multiplicity of descriptions to argue for social construction. Yet it also argues strongly that everyone is feeling the same elephant. Like any use of language, it is being constrained by its encounters with a recalcitrant reality beyond.

Then if we consider how maths actually advances, it is largely by the relaxation of constraints. Maths moves up to a higher level by generalising and abstracting. Euclidean geometry gives way to non-Euclidean geometry. Then geometry gives way to topology. So the map of maths - M - is not some flat plane of existence, cluttered mostly with junk with a few bright spots of interest. Instead, maths is itself a hierarchical structure. We rise up out of the clutter of the particular detail by finding some key constraint we can relax. And having gained control over that parameter, we can then add back constraints to toy with different worlds.

Give up Euclid's parallel postulate and the geometry of space can be curved. That curvature can be added back as some positive, negative, or neutral number. So what makes maths interesting is where we find the constraints that are holding things in place - imposing a particular structure or form - and can then twiddle the knobs to discover the "world" the more abstracted description lives in. Keep abstracting and you go past set theory to arrive at category theory - at least according to current wisdom. There is an ur-form at the top of the mathematical hierarchy that speaks to what is Platonically the Good - a basic idea of a relation which is the most generalised possible constraint we can imagine.

So Plato was certainly on to something. Our physical world is not some random junk of accidents. It has an intelligible structure. But the problem with Platonism is the way it suggests a flat plane of forms - where the perfect triangle exists alongside the perfect turd. That problem can be addressed by the addition of a selection principle - a hierarchical story - which does then separate reality into its accidents and its necessities. And in Aristotelian fashion, this is what you get when the material realm becomes the source of accidents or fluctuations - the blind atomistic construction - and the formal realm supplies the downward-acting constraints which are a system's regularities and inevitabilities, its essentials, or universals, or necessities.

So we recognise a triangle as speaking purely of nature's necessities. A three sided polygon is going to have internal angles of pi, or 180 degrees. This is a truth of physical space - at least in a Euclidean setting. But a turd seems mostly a set of physical accidents. A very material construction. A mathematician might find the structuring formal principles that do in fact regulate the shape of any given turd - why a liquid one might behave differently from a more solid one. But Plato's realm of forms is really a space of abstractions. Maths explores the constraints that nature imposes on material accidents - and mostly seeks to abstract them away, because what is interesting is to gain control over them.

Most of the apparent physical constraints we encounter turn out to be accidents of history. The Universe seems Euclidean to us because it has grown so large, flat and cold. So we can generalise away the particular in the world as it seems structured right now, to work back towards to the way a world could possibly be - if we were to add other general material conditions, like it being as small and hot as possible.

The mathematical enterprise is thus about trying to discover the rational forms that structure some set of material accidents. And that dualism has to give way to the triadicism of a hierarchical metaphysics as that exercise gains scientific sophistication. Science speaks of global laws and material constants. Actual substantial existence is then what arises inbetween.

So the turd becomes an entity that arises in some sense because of the shaping laws of dynamical flows - a general model that would be paired to specific material parameters, like a measure of the viscosity of the turd in question. It is this triadic complexity, this hierarchical or systems story, which the debate over Platonism is so insensitive to, but which should already be evident from the Aristotelian version.

Then a final point. The usual view is that either maths is Platonic, or it is purely a social construction. Either it speaks truly of necessity, or it is merely always a cultural accident - reality as described from a basically freely creative human subjective point of view.

But I see nothing wrong with the inbetween position. What we are getting at with mathematical physics at least is the objective point of view - the one from the perspective which would be the Cosmos contemplating its own rational structure.

So that does apply a pragmatic constraint to the enterprise - a view that has an embodied interest. The realm of junk maths is being limited by a viewpoint which speaks to the basic finality of wanting to be embodied. It is maths of that type, structure that can produce that result, which is "true, just and beautiful". We can see the universality in it as we stumble across it.

The maths of symmetry and symmetry-breaking are a good example of that. Likewise statistical mechanics and dissipative structure theory. There are areas of maths that look very organic - because they marry the accidental and the necessary in a way in which global regularity must emerge from local randomness. Structure - as the stabilisation of instability - can develop.

So sure, when maths is understood as just a realm of everything that unconstrained syntax will produce - a Borges library - then it seems to bear no real relation to a reality in which limitation or finitude is apparent everywhere. But when maths is viewed organically - as a language to capture the emergent regularities of pure possibilities - then that is a strong selection principle to sift the wheat from the chaff. We arrive at the structures that matter because they are the most irresistible. Randomness can't erode them, because randomness is in fact constructing them.

Stability is fundamental and instability is fundamental. — Metaphysician Undercover

Yep. So one is the view I would be arguing for, the other would be the one I would be arguing against. Stability was not my stated premise. It was the premise which I challenged.

If the particle is perfectly balanced on top of the dome, then there it shall remain until some net force moves it. — LD Saunders

This was your original point. And note how it relies on a notion of "net force". So the Newtonian view already incorporates the kind of holism I'm talking about.

A system in balance by definition has merely zeroed the effective forces being imposed on it by its total environment. The Newtonian formalism doesn't specify an absence of imposed forces. It just says that any fluctuations present are balanced to a degree that no particular acceleration is making a difference.

So the point about a ball balanced on a dome is you can see this is an unstable situation. There is a strong accelerative force acting on the ball - gravity. The situation is very tippable. The slightest fluctuation will lead to a runaway change. Down the ball will roll.

It now matters rather a lot whether the "net force" describes a literal absence of any further environmentally imposed force, or whether it represents a state where the fluctuations are coming from all directions and somehow - pretty magically - cancel themselves out to zero ... until the end of time.

So that was my point. The conventional view of causality likes to treat reality as a void. Nominalism rules. All actions are brutely particular. But conversely, reality can be seen as a warm bath of fluctuations. And now the kind of simple causality we associate with an orderly world has to be an emergent effect. It arises to the degree that fluctuations are mostly suppressed or ignored. It relies on a system having gone to the stability of a thermodynamic equilibrium.

But if fluctuations are only being suppressed to give us our "fluctuation-free" picture of causality, then that means they still remain. That then becomes a useful physical fact to know. It becomes a way of modelling the physics of instabilities or bifurcations.

And metaphysically, it says instability is fundamental to nature, stability is emergent at best. And that flips any fundamental question. Instead of focusing on what could cause a change, deep explanations would want to focus on what could prevent a change. Change is what happens until constraints arise to prevent it.

So this is how holism becomes opposed to reductionism. It is the different way of thinking that moves us from a metaphysics of existence to a metaphysics of process.