Fair enough, I will take that on board. However, essence and substance are basic to Aristotle, even if he differed with Platonism on the reality of forms. But I do concede, I got carried away. As I often to, by my own imagination.

Interesting? Or entirely paradoxical for reductionist meaphysics? — apokrisis

Scientific and other analytic explanations tend to be reductionist, in the sense that they fit phenomena or concepts into some theoretical framework. In that they reduce, demonstrate that one thing is nothing other than another, presumably simpler or more tractable or more familiar or otherwise more theoretically attractive thing. In that sense Newtonian, Lagrangian and Hamiltonian formulations of classical mechanics are equally reductionist, and the same goes for alternate formulations of quantum mechanics.

If there is a lesson to derive from the four causes it is this pluralism of explanations - and that would be a genuine counter to reductionism. Rather than arguing for one framework as the only metaphysically correct one, the emphasis can be placed on the fact that there are these alternate frameworks that are sometimes exactly equivalent (and the interesting question to consider is how that comes about), but in any event offer different instrumental and conceptual possibilities.

Scientific and other analytic explanations tend to be reductionist, in the sense that they fit phenomena or concepts into some theoretical framework. — SophistiCat

Sure, reductionism can have this other meaning. But the discussion was about four causes holism vs atomistic materialism. So why change the subject?

And I would say it gives you more of a problem admitting the principle of least action does reduce to a holistic position which takes finality seriously as part of the fundamental workings of the Cosmos.

If there is a lesson to derive from the four causes it is this pluralism of explanations — SophistiCat

Again, I thought you were arguing against four causes modelling. And now you are championing it under the permissive banner of pluralism.

there are these alternate frameworks that are sometimes exactly equivalent — SophistiCat

So now you have even less to carp about apparently. You think there is a formal duality between reductionism and holism. And I rather agree.

There are deeper and more interesting ways to make sense of such alternate explanatory frameworks. — SophistiCat

Terrific. You will be telling us how that pans out for QM any time now.

Per Feynman in (I think) SIx Easy Pieces, or maybe QED, the light takes all the paths. — tim wood

Worth quoting Feynman probably....

In the case of light we also discussed the question: How does the particle find the right path? From the differential point of view, it is easy to understand. Every moment it gets an acceleration and knows only what to do at that instant. But all your instincts on cause and effect go haywire when you say that the particle decides to take the path that is going to give the minimum action. Does it ‘smell’ the neighboring paths to find out whether or not they have more action? In the case of light, when we put blocks in the way so that the photons could not test all the paths, we found that they couldn’t figure out which way to go, and we had the phenomenon of diffraction.

Is the same thing true in mechanics? Is it true that the particle doesn’t just ‘take the right path’ but that it looks at all the other possible trajectories? And if by having things in the way, we don’t let it look, that we will get an analog of diffraction? The miracle of it all is, of course, that it does just that. That’s what the laws of quantum mechanics say. So our principle of least action is incompletely stated. It isn’t that a particle takes the path of least action but that it smells all the paths in the neighborhood and chooses the one that has the least action by a method analogous to the one by which light chose the shortest time.

You remember that the way light chose the shortest time was this: If it went on a path that took a different amount of time, it would arrive at a different phase. And the total amplitude at some point is the sum of contributions of amplitude for all the different ways the light can arrive. All the paths that give wildly different phases don’t add up to anything. But if you can find a whole sequence of paths which have phases almost all the same, then the little contributions will add up and you get a reasonable total amplitude to arrive. The important path becomes the one for which there are many nearby paths which give the same phase.

http://www.feynmanlectures.caltech.edu/II_19.html

So all your instincts on cause and effect go haywire apparently when you say that the particle decides to take the path that is going to give the minimum action. Yes indeedy. And yet this teleological view is the one that made his name. :)

Each of these two deals with the existence of the immaterial, which is beyond the scope of modern science. So where science doesn't go, due to its limitations, we must turn to the ancient principles, to pick up where science leaves off. Nothing procrustean, science and metaphysics just have a different scope. The latter is much more inclusive of all aspects of reality. — Metaphysician Undercover

You presume, uncritically and without qualification the "existence of the immaterial," that you imply is in or an aspect of reality. You set this existent "beyond the scope of modern science,.. due to its limitations." No problems here? On its face it's incoherent.

Clearly there are Xs that lack the materiality that is the usual object of science. Equally clearly one can attempt to identify, qualify, and quantify these Xs. One can even attempt to think about them in an organized way and it's fair to call that kind of thinking "science" - on the bases of its methods, not its content. But all of this, no matter how well done and how useful - and history shows it can be well done and useful - remains a castle in the air, a fantasy, a fable, a story. By no means do I intend to undercut the value of these enterprises. I do mean to question the claim that they're anything more than what they are.

I hold you correct in this,

science and metaphysics just have a different scope. — Metaphysician Undercover

Indeed they do.

I find your position akin to the Creationist who wants for Creationism a place at the table for science, going so far as to call it creation science. The trouble, of course, is that creationism is no science at all.

Keep, then, your metaphysics. Keep it for what it is, what it's worth, and what you get out of it. I like metaphysics too, although my understanding of it differs from yours. But it's not a trump card playable outside of the confines of its own game.

Seriously? In what sense does it actually take all the routes? You are confusing the method of calculation with the metaphysics.... All the trajectories that don't happen are virtual. They exist in concrete fashion as possibilities. And so in turn, in a contextual sense. They express the holism of the constraints being imposed on the action. — apokrisis

Did you mean science instead of "metaphysics"? In what sense does it take all the routes? Do a little research on diffraction gratings. This movement of light as a wave, capable of self-interference, like water in the ocean, I accept as a fact demonstrated by experiment.

What does it mean to "exist in a concrete fashion as possibilities"? Is a concrete possibility something different from a possibility?

You mean like an excitation in a field perhaps? — apokrisis

Are you sure the excitation and the field are different things? You seem to imply they are different.

As to holism, I find this:
"the theory that parts of a whole are in intimate interconnection, such that they cannot exist independently of the whole, or cannot be understood without reference to the whole, which is thus regarded as greater than the sum of its parts."
If you accept this, then can you explain to me what "cannot exist independently of the whole," and "is thus regarded as greater than the sum of its parts" mean?
— tim wood
And from the engine. I can remove parts and put them over there. They exist independently over there, yes?
— tim wood
Surprise. You can prove existence is a machine because a machine is a machine! Beautiful logic. Shame I've used up my quota of eyerolls already. — apokrisis

Two things are clear from this: 1) whatever holism is good for, it is of no use when applied to anything as mundane as things in the world, and 2) apokrisis has apparently started a correspondence course in sarcasm but hasn't got to the part yet where they teach him that sarcasm is usually without substance, especially the eye-rolling variety. Perhaps when he gets them back around facing front, he'll reconsider the question.

The reason that anything happens, in a sense other than, "it happened as a consequence of a series of physical transformations". 'The reason why' in the sense of an overall rationale or the purpose why something exists,.. but there's a very fine and succinct one here. — Wayfarer

Sure, everything in terms of purpose. But there's a persistent mistake. Maybe an example will help me, here.

From your citation: "Consider a knife. If you wanted to describe a knife, you would talk about its size, and its shape, and what it is made out of, among other things. But Aristotle believes that you would also, as part of your description, have to say that it is made to cut things. And when you did, you would be describing its telos. The knife's purpose, or reason for existing, is to cut things."

And add to the description the idea of a knife's sharpness, certainly a relevant consideration for what a knife is for. But the purpose of the knife is not in the knife in any way. It just is a knife. Wherein lies (the) purpose, then? In the mind of the user. The problem with sharpness is when sharpness in itself is taken as a thing in itself, which of course it is not.

Telos is just a class of answers to questions usually of the form, "What for?" The thing in itself never possesses any "what for." It just is.

Amen.

Which explains nothing about it. Were early humans to have seen things like that, we would never have come down the trees. If there was no purpose for knives, no need to cut, there would be no knives. And everything in the organic world conforms to that general principle.

Which explains nothing about it. Were early humans to have seen things like that, we would never have come down the trees. If there was no purpose for knives, no need to cut, there would be no knives. And everything in the organic world conforms to that general principle. — Wayfarer

Did we slip past each other? Indeed they did see it. That's where it came from. There never was a knife from somewhere else that approached any person and said, "Hi, I'm a knife, I have a purpose and I'd like to share that with you. Here, hold on just a second, I've got it right here!"

What about livers? Did we have to know what they were for before they started secreting enzymes? Part of the definition of a thing, is the purpose it serves - that is what makes it what it is. The ‘it just is’ is the attempt to reduce the compliexity inherent in that necessity to simple and elemental facts. And it is precisely the shortcomings of that attitude that is among the factors in the revival of interest in fourfold causation.

Part of the definition of a thing, is the purpose it serves - that is what makes it what it is. The ‘it just is’ is the attempt to reduce the compliexity inherent in that necessity to simple and elemental facts. And it is precisely the shortcomings of that attitude that is among the factors in the revival of interest in fourfold causation. — Wayfarer

Yes, part of the definition. The problem here, it seems to me, is that a) you want to attribute things to things - the functioning of the liver to the liver, purposefully and teleologically, which seems ok to me, but then you want the thing attributed to the liver to be in the liver. I think that's a wrong move.

The liver is a liver. If you want it to be anything beyond that, how does that work? If on the other hand you want to say a lot of things about the liver, its functioning, its importance, its purpose - anything at all, you're free to do so, and it's probably useful for you to do so. But those are just things that you say.

Heidegger covers this in his distinction between being and the as- structure of the being. The being of the liver is just the fact of its being. Its as structure is covered in answering the question, what is the liver when it is functioning as a liver.

To use an Aristotelian objection, it would appear that you and others are confusing substance with accidents.

Whereas, the 'domain of numbers' (for only one example) doesn't exist, in that sense, yet is still real, according to Platonists (including Godel and Frege.) So - real but not existent. And that is the dividing line between Platonism and everyone else, as everyone else says that 'what exists' and 'what is real' are the same. — Wayfarer

I think you have a problem here in that you have to show how the imagined domain relates to physical reality.

It is just like our other imaginary worlds that are so easily constructed by linguistic combination. We can imagine an infinite variety of fictional beasts - unicorns, dragons, orcs, elves, gryphons. They all exist in a domain opened up by syntactical construction. We can freely assemble animals out of bits and pieces like wings, hooves, fire breathing, horns, miniaturisation, the ability to walk through walls, etc, etc. Once you establish a syntax based on unconstrained construction, you can generate an infinite variety of the unreal in modal fashion.

So the question is, how do you divide your mathematical Platonia into a part that is physically realistic (like the maths of the standard model, or the maths of quantum probability amplitudes - both extremely arcane until it was found they had this exact fit with reality) and the part which is simply an unconstrained generation of fictions?

The talk about the unreasonable effectiveness of maths is usually much too loose. And in that confusion, it becomes unclear whether maths is generally just a human construct or an actual science of patterns.

So you can't make a good case for Platonism until you can reliably tell the difference between the fictional creations of maths, and the maths that might actually be the deep structure of nature, of existence itself.

And here is where the constraints of Aristotelian immanence might come in. If we insist that worlds have to be self-organising, then that puts a bound on free construction. Already such a world is far more limited in the patterns it could generate. We can rule out the mathematical unicorns and elves on stronger grounds because the question would become, could every beast we could possibly construct, successfully co-exist.

We are now thinking holistically. We have closed our fictional world and applied a principle of natural selection to it. Would dragons have enough unicorns to keep them fed? Would fairies just wave their wands and eliminate all nasty orcs from their world?

So this is an analogy. But it shows the further Aristotelian constraint that would start to make sense of mathematical Platonism. Once you invoke hylomorphic immanence, then you close the system in holistic fashion. You add the rule that all must be able to co-exist as the one world. And that changes everything really. It creates a boundary separating the actually possible from the fictionally possible - the kind of possibility that is merely a meaningless combination of parts, not a world of possibility united by its common purpose of being able to actually exist in a holistically meaningful fashion.

So holism really counts. It creates the closure that defines the meaningful. It encodes the finality or purpose of a world - even when that purpose is understood as just the most basic thing of being able to exist.

That is why I always point to the centrality of symmetry and symmetry breaking when talking about metaphysics. That is the area above all in maths that is focused on the holism that closes a world while also speaking to the local individuation which allows the other thing of atomistic construction. Symmetry maths takes you to the heart of immanent self-organisation.

But anyway, the critical issue is that not all maths is equal. Some of it is a runaway syntax of the kind that allows us to make infinite bestiaries out of a finite collection of parts. And a core of it gets at the holism needed to unite a world under the common immanent purpose of successfully co-existing as a functioning whole. The usual developmental and evolutionary constraint that is the hallmark of any systems metaphysics or structuralist thinking.

Two things are clear from this: 1) whatever holism is good for, it is of no use when applied to anything as mundane as things in the world, and 2) apokrisis has apparently started a correspondence course in sarcasm but hasn't got to the part yet where they teach him that sarcasm is usually without substance, especially the eye-rolling variety. — tim wood

I can't make you out. You seemed smart enough to have a serious conversation. Then you so quickly degenerate into time-wasting bickering.

To deny holism in the context of quantum theory is simply Quixotic.

Sure, it is a good scientific strategy to try to interpret QM or QFT with the least amount of holism possible. We don't want to go overboard with the woo when we can still hope to assimilate aspects of quantum metaphysics to good old reductionist locality. But in the end, you do have to give up that classical picture of a completely mechanical reality. All quantum interpretations now agree on this. The experiments are in.

So I don't know if you are playing a game or seriously believe your anti-holism. Unfortunately stuff like this suggests you have a poor grasp of what QM is actually modelling when it talks about particles and waves....

Do a little research on diffraction gratings. This movement of light as a wave, capable of self-interference, like water in the ocean, I accept as a fact demonstrated by experiment. — tim wood

A wave is a classical collective phenomenon. It can be understood metaphysically as some set of discrete objects - water molecules - with elastic connections that then oscillates with a resonant frequency. The wave forms arise as a common mode that solves its boundary conditions - the various parameters imposed on a body of water like the shape of its container, any steady driving action like a wind or other external impulse.

So wave mechanics is clearly holistic. The "parts" arise to fill the available parameter space. The wave peaks are forced to fit the container in harmonic fashion. A clearer example of top down causation is hard to imagine. A continuous liquid is broken into a set of now discrete vibrations.

Of course, the metaphysical reductionist will point out that the continuous liquid is itself a collection of discrete molecules. But that is both true and missing the point.

The discrete molecules are not discrete at all. They have charges that come into play when they are collected together. They are thus constrained to act in continuous fashion - elastically connected - by that continuous force between them. The sum is already greater than the parts once it becomes necessary for us to recognise the fact that a system contains its interactions as well as its locations.

So anyway, even classical mechanics speaks directly to holism and top-down causation. Harmonics is an actual constraint forming the features in question. When we count the wave peaks or wave troughs, we are counting the locally emergent phenomena ... and treating the underlying liquid as a continuous boundary condition, parameterised by global properties like viscosity. That just is the metaphysics of the situation.

And then once we start talking about quantum waves, we are now parameterising probability spaces - the probabilities of making particular observations. Any underlying materiality has dropped right out of the picture. Talk of a wave is now pure mathematical analogy. It is talk about an organisation imposed on possible measurements.

In the loosest fashion we might talk about some wavefunction as a solution constructed by a collection of all the possible paths connecting two points. And sometimes the additions and subtractions give you a probability that looks like a trajectory carved by a material particle, and other times, a probability that looks like the kind of interference patterns you see from interacting waves.

Yet what we actually see in reality is neither moving particles, nor interfering waves, but simply some registered event - the click of a particle detector. How that empirical fact occurred remains fundamentally mysterious. QM certainly does not model the collapse of the wavefunction. The maths can only generate a probability picture that either looks more particle trajectory like, or more wave interference like.

I say all this to emphasise how far QM moves away from materialist ontological commitments.

Even Newtonian mechanics demanded all kinds of spooky "action at a distance" and "inertial motion" woo. That was the big deal - having the bravery to drop the highly materialistic ontology of "Aristotelian" impetus theories and accept a materialism ruled by global symmetries and forces like gravity which could act without any mediating medium. So even Newtonian mechanics was the big break from literal atomism. (For amusement, check out how Descartes failed to make that mental break and kept trying to make a corpuscular theory of heavenly motions work.)

And now, with QM, the rupture with simple materialism is complete. It is a calculus of the probabilities of observables, not a picture of material events.

Of course we still want to picture what that means in metaphysically intuitive fashion. But now - in the modern era - that has to mean focusing on the mathematical form or structure of nature.

And that is the Aristotelian four causes thing. We are back to wanting to take formal and final cause seriously if we want to understand the Cosmos in some properly deep way.

I think you have a problem here in that you have to show how the imagined domain relates to physical reality. — apokrisis

It 'relates', because it is used to make predictions and calculations. Isn't it revealed when mathematical analysis is used to generate new discoveries about nature?

Consider the laws of motion as paradigmatic (while fully acknowledging their limitations). Knowledge of those laws enables you to calculate trajectories of canon balls and the motion of planets, as is well-known. So you can make predictions about 'where Mars will be' or 'where the artillery shell will land'. The movement of those objects is constrained by the laws of physics, which is what enables us to predict them. That's what I had thought you meant by 'constraints' but please tell me if I'm wrong.

Wigner, as you know, who wrote the essay on the unreasonable effectiveness of mathematics, had good reason to wonder, as his Nobel prize was for the discovery of mathematical symmetries in atomic physics (wasn't it?) So in the essay, he is posing the question, why should maths be able to do that? And he really doesn't have an answer; the word 'miracle' appears twelve times in that essay. Likewise Einstein often mused that 'the most incomprehensible thing about the universe is that it is comprensible'. So, great scientists like these two, don't themselves actually have a theory about why. But the problem seems to be solvable, if you admit that the structure of reality is itself mathematical in some sense. Where that goes against the grain, is that it is against empiricist dogma that nature ought not to be so ordered; mathematics must be somehow explicable in terms of grey matter, for it to be considered real. (That is the exact discussion we have just been having with Read Parfitt; maths is a product of the brain.) So Platonism challenges that.

And also, note that 'mathematical Platonism' is not 'the philosophy of Plato', as per the SEP entry on this topic. It says:

If the view is true, it will put great pressure on the physicalist idea that reality is exhausted by the physical. For platonism entails that reality extends far beyond the physical world and includes objects which aren’t part of the causal and spatiotemporal order studied by the physical sciences. Mathematical platonism, if true, will also put great pressure on many naturalistic theories of knowledge. For there is little doubt that we possess mathematical knowledge. The truth of mathematical platonism would therefore establish that we have knowledge of abstract (and thus causally inefficacious) objects. This would be an important discovery, which many naturalistic theories of knowledge would struggle to accommodate.

What I think it means, is that mathematics is inherently a part of the structure of intelligence. So universals and logical laws are part of the fabric of our understanding, but naturalism doesn't like that, because it has already divided the world into the external object and the subject, whose intelligence has to be understood as entirely a product of the objective domain. So what I'm always trying to articulate, is that the world exists in the reality of embodied experience, which includes, and therefore transcends, the division of subject and object. So maths is not objectively real, but it's also not merely subjectively true as a social convention or human invention. Where the real conflict lies, is not between that view and physics - many physicists have strongly Platonist tendencies, whether they know it or not - but with Darwinism.

So the question is, how do you divide your mathematical Platonia into a part that is physically realistic (like the maths of the standard model, or the maths of quantum probability amplitudes - both extremely arcane until it was found they had this exact fit with reality) and the part which is simply an unconstrained generation of fictions? — apokrisis

I don't know! One way of posing the question is: mathematics, discovered or invented? But does it have to be a simple dichotomy, either one or the other? Having the ability to discover natural numbers, and mathematical systems, then we're free to create all kinds of imaginary number systems. That doesn't mean that numbers are simply invented. There was an article about a Sydney maths prodigy in last weekend's paper; it mentions that 'G.H. Hardy, an English mathematician, was immensely pleased that his work in number theory, during the early 20th century, was "completely useless". But it's used every day by people logging onto Wi-Fi or buying a coffee with their credit card.'

As Wigner says, there is something miraculous about the human ability to reason. It enables us to imagine something that has never existed before, and then manifest it. That's why the Greeks saw us as 'betwixt apes and angels'. Whereas now, we want ourselves just as apes; we forgotten the 'sapience' that we've been named after.

What I think it means, is that mathematics is inherently a part of the structure of intelligence. So universals and logical laws are part of the fabric of our understanding, but naturalism doesn't like that, because it has already divided the world into the external object and the subject, whose intelligence has to be understood as entirely a product of the objective domain. — Wayfarer

I can't see why a philosophical naturalist would have any problem thinking that nature is fundamentally structured in a mathematical way, or that intelligence (being a part of nature) is also so structured. What's the problem?

And you still haven't addressed the problem for your position that I pointed out in a previous post:

It seems to me that the problem you have is that you're determined to say something about them (universals) being somehow real independently of the world, and yet you cannot say what you want to in any way that makes any sense. — Janus

The further point is that, as you acknowledge, the only possible evidence (if it is indeed accepted as such) for the ontological provenance of mathematics is delivered in a context of empirical conjecture, experiment and observation, and only in that context; a fact which is not consistent with your rejection of both empiricism and naturalism.

You presume, uncritically and without qualification the "existence of the immaterial," that you imply is in or an aspect of reality. You set this existent "beyond the scope of modern science,.. due to its limitations." No problems here? On its face it's incoherent. — tim wood

Why is this incoherent? Isn't the relation between one material object and another material object, something immaterial? It's seems like it's only incoherent if you start with the premise that "immaterial" is nonsense. But that's ludicrous. The existence of the immaterial is extremely evident.

Clearly there are Xs that lack the materiality that is the usual object of science. Equally clearly one can attempt to identify, qualify, and quantify these Xs. One can even attempt to think about them in an organized way and it's fair to call that kind of thinking "science" - on the bases of its methods, not its content. But all of this, no matter how well done and how useful - and history shows it can be well done and useful - remains a castle in the air, a fantasy, a fable, a story. By no means do I intend to undercut the value of these enterprises. I do mean to question the claim that they're anything more than what they are. — tim wood

Scientists think, and proceed, in terms of relations, but science has no capacity to determine the ontology of "a relation". So relations, (the immaterial), are taken for granted as something real. They are what scientists use to describe things, they describe in terms of relations. If relations between material things were not real, then what scientist are doing would be meaningless. Is the relation between the sun and the earth real? In philosophy we do not take the existence of relations (the immaterial) for granted as science does. We want to validate, justify, the ontological status of what science takes for granted, the immaterial.

I find your position akin to the Creationist who wants for Creationism a place at the table for science, going so far as to call it creation science. The trouble, of course, is that creationism is no science at all. — tim wood

This is not a good analogy. I am arguing for the priority of philosophy over science, not trying to lower philosophy to the status of a science.

Keep, then, your metaphysics. Keep it for what it is, what it's worth, and what you get out of it. I like metaphysics too, although my understanding of it differs from yours. But it's not a trump card playable outside of the confines of its own game. — tim wood

Now your right back to your complaint about "scope", speaking as if metaphysics is confined by its own game, but that's not the case. What confines metaphysics is reality, and this is no game. The mind is free to go wherever it pleases, being constrained only by reality, not by itself. So metaphysics is really not confined by its own game at all, it's only confined by reality, and that's the "free" part of free will. Science though cannot play outside the confines of its own game, and that's the nature of science. It has to follow rules, and going outside those confines renders it other than science. Science is not constrained by reality, it is constrained by artificial rules. With an adequate hierarchy, metaphysics which is properly constrained by reality, will produce those rules.

It 'relates', because it is used to make predictions and calculations. Isn't it revealed when mathematical analysis is used to generate new discoveries about nature? — Wayfarer

Yes. And so now you endorse the necessity of an empirical basis to establish any connection. It just ain't a theory unless it is founded in matching acts of measurement. That is the pragmatic constraint we impose on our free speculation so that our knowledge develops in a purposeful and reasonable fashion.

So you are starting out by granting the very things you normally strongly deny. How long before you forget what you just said here?

The movement of those objects is constrained by the laws of physics, which is what enables us to predict them. That's what I had thought you meant by 'constraints' but please tell me if I'm wrong. — Wayfarer

It is exactly that.

And he really doesn't have an answer; the word 'miracle' appears twelve times in that essay. Likewise Einstein often mused that 'the most incomprehensible thing about the universe is that it is comprensible'. — Wayfarer

Sure. Newton and Galileo were equally amazed by the universalising power of mathematical physics. Everyone always has been. When you look at "God" in the face - come to understand the inescapable necessity of the structural principles of existence - one always ought to feel awe. It's a dazzling realisation.

So, great scientists like these two, don't themselves actually have a theory about why. — Wayfarer

Well actually, Einstein in particular was famous for his "unreasonable" belief that you just have to go with the structural necessity of symmetries. So he knew what to be looking for in terms of physical reality - even when he wasn't the greatest mathematician himself.

Wigner did foundational work in seeing how symmetry maths mapped onto the emerging bulk of quantum mechanics - revealing the essential mathematical-strength structures involved.

So I think you should read these kinds of comments as a wake-up call to their fellow scientists and the interested lay public. Reality is all about intelligible structure, not meaningless matter.

Maths was merely the science of pattern, a way of modelling dynamical structure. Once you took a structural view of the Cosmos, it was inevitable that it would have to map to the kind of maths which had been developed to talk about structure in this kind of constrained, symmetry-breaking, dynamical and relational fashion.

Where that goes against the grain, is that it is against empiricist dogma that nature ought not to be so ordered; mathematics must be somehow explicable in terms of grey matter, for it to be considered real. — Wayfarer

But remember that you accept the constraint that empiricism should have over our free metaphysical speculation.

Let's not revert to the Platonism of saying human minds discover transcendent truths. All we are doing is arriving at useful models of dynamically self-organising or immanent structures. And then empirical evidence shows that we can apply those models to good predictive descriptions of the Universe as a whole. There is nothing larger that needs to be said ... for as long as evidence confirms what we think.

So the empiricist dogma is still in full force. But structuralism is the approach which says nature has to be deeply ordered to exist. It is structuralist theories that are being produced and so the ones being tested.

If we spend billions searching for a Higgs boson, it is because it has been a mathematical-grade structural necessity for about 40 years.

What I think it means, is that mathematics is inherently a part of the structure of intelligence. — Wayfarer

But which comes first? If the world is inherently structured, then brains are under an evolutionary constraint to be able to master the principles of that structure. And eventually a technical language comes along - mathematics - to take that to a further explicit level of cultural discourse.

Mathematicians get to stop talking about the shape of the world like regular folk. They just sit in a huddle talking about the shape of shapes. And they are happy to be called the most intelligent people on Earth for doing so. Although quite a lot, they get called other names. :)

Where the real conflict lies, is not between that view and physics - many physicists have strongly Platonist tendencies, whether they know it or not - but with Darwinism. — Wayfarer

Bring out your bogeyman. Give the effigy another good kick.

Your animus against evolution and development is misplaced. It is Aristotelian causality at work. It is constraint treated as something physically real, structurally foundational.

As Wigner says, there is something miraculous about the human ability to reason. It enables us to imagine something that has never existed before, and then manifest it. — Wayfarer

Again, the ability to speculate freely is half the story. Yes, it is useful to conjure up fictions, as they might turn out to be truths. But then that is where empirical test comes in - the other necessity that you want to deny.

So there is no maths that anyone invented that matters a fig - except to the degree that science has now put it to good use. End of story.

Without empirical success, all that wild invention would be utterly unmiraculous in most people's view. Who could have any reason to care. At least fabled beasts have some kind of social reality. Maths that never cashed out in an experiment would be the definition of an austistic activity, like rhythmically beating your head against the wall.

So reconsider the arc of your own argument. Maths is only miraculous because it can be used to say something testable about the deep structure of physical reality.

That is the only thing that saves it from being Pythagorean lunacy in the world's eyes.

So you are starting out by granting the very things you normally strongly deny. How long before you forget what you just said here? — apokrisis

I'm not denying empiricism. I am denying the empiricist dogma of 'no innate ideas'. And I'm denying that naturalism explains mathematics (and the rest). That is why I frequently refer to the IEP article on the necessity of explaining mathematics in empirical terms - the 'indispensability argument for mathematics'. Don't you think that is ridiculous, that it has come to that? That is said to be because, and I quote, 'our best empirical theories seem to debar any knowledge of mathematical objects.' And why do 'our best theories' seem to debar that knowledge? Because 'the rationalist’s [what I'm calling Platonist] claims appear incompatible with an understanding of human beings as physical creatures whose capacities for learning are exhausted by our physical bodies.' And why? Because mathematics is real, but it's not physical; its very nature is incorporeal, and the faculty which grasps it can't be understood through the one-dimensional lens of today's empiricism. That's what empiricism must deny, a priori, because according to it, everything real is physical. Ergo, having to justify mathematics in terms that empiricists will respect. I'm sure the irony is missed on most of them, as that, too, is not physical.

When you look at "God" in the face - come to understand the inescapable necessity of the structural principles of existence - one always ought to feel awe. It's a dazzling realisation. — apokrisis

We're nowadays rather deficient in the that sense, I think. But anyway, in no way it does enable us to 'look God in the face'. That is the hubris of (some) scientists (and Al Jarreau). But not all:

We are in the position of a little child, entering a huge library whose walls are covered to the ceiling with books in many different tongues. The child knows that someone must have written those books. It does not know who or how. It does not understand the languages in which they are written. The child notes a definite plan in the arrangement of the books, a mysterious order, which it does not comprehend, but only dimly suspects. That, it seems to me, is the attitude of the human mind, even the greatest and most cultured, toward God. — Albert Einstein

Let's not revert to the Platonism of saying human minds discover transcendent truths. — apokrisis

Everything we do nowadays transcends the imaginings of even our near ancestors. (I've just been watching Quest for Fire again - strongly recommend it to anyone who hasn't seen it.)

Your animus against evolution and development is misplaced. — apokrisis

Again - no animus against evolution, but against biologism, by the view that our abilities are circumscribed by biological ends. Evolution doesn't address the gap between surviving and living - the space in which human culture emerges - and every attempt to do so, amounts to reductionism.

Maths that never cashed out in an experiment would be the definition of an austistic activity, like rhythmically beating your head against the wall. — apokrisis

Tell that to the pure mathematicians.

So you are starting out by granting the very things you normally strongly deny. How long before you forget what you just said here? — apokrisis

Yes, I made the exact same point above. :cool:

The further point is that, as you acknowledge, the only possible evidence (if it is indeed accepted as such) for the ontological provenance of mathematics is delivered in a context of empirical conjecture, experiment and observation, and only in that context; a fact which is not consistent with your rejection of both empiricism and naturalism. — Janus

I am denying the empiricist dogma of 'no innate ideas'. — Wayfarer

That is now another shift in subject. And empirically, psychology supports that particular "dogma" to a large extent. How could genes even code for innate ideas?

On the other hand, genes can code for the general constraints under which the brain develops its processing architecture. So there is a structure that is going to grow in a way that might eventually cash out in well-structured ideas.

Plato had some nonsense about the truths of mathematics being dormant understandings that a rational soul could be prodded into remembering. But was this more than just poetic licence even for Plato? Certainly, it would be the least useful of his metaphysical positions today.

That is why I frequently refer to the IEP article on the necessity of explaining mathematics in empirical terms - the 'indispensability argument for mathematics'. Don't you think that is ridiculous, that it has come to that? That is said to be because, and I quote, 'our best empirical theories seem to debar any knowledge of mathematical objects.' And why do 'our best theories' seem to debar that knowledge? Because 'the rationalist’s [what I'm calling Platonist] claims appear incompatible with an understanding of human beings as physical creatures whose capacities for learning are exhausted by our physical bodies.' And why? Because mathematics is real, but it's not physical; its very nature is incorporeal, and the faculty which grasps it can't be understood through the one-dimensional lens of today's empiricism. That's what empiricism must deny, a priori, because according to it, everything real is physical. Ergo, having to justify mathematics in terms that empiricists will respect. I'm sure the irony is missed on most of them, as that, too, is not physical. — Wayfarer

But surely, having again been caught out by a succession of posters in this very thread, you ought to be more cautious about your enthusiasm to make all the fact fit your desired conclusion?

Right from the off with this post about neo-Aristotelianism, you made the mis-step of conflating the supernatural transcendence of Platonism with the naturalistic immanence of Aristotle. You were taking something directly contradictory as evidence for what you want to believe.

So again, you are wanting to argue that mathematical structure is incorporeal. And my comment was that maths itself divides into the real and the fictional. The kind of maths that physically matters is the kind of maths that empirically works to make actual predictions about nature.

So you can't just gaily claim all maths has this unreasonable effectiveness that no one could explain.

It is only a particular kind of maths - the kind that deals with dynamical structure - which really has this "miraculous" quality. And we can see that it is not in fact a transcendent immaterial miracle but an immanent material one.

Disorder requires order even to be disorder. For entropy to be produced, there must be a dissipative structure. So cosmic structure has to self-develop to create the Cosmos as a steady-state entropic flow - a story of a Big Bang turning into a Heat Death by the end of time.

Nothing could be more corporeal than that structure which is the means by which the substantial actuality of a material being can manifest.

This is how Aristotle fixed Platonism with his immanent hylomorphism. All we have to do then is scrub out the mystical Christian re-write that followed and we are back to the future with neo-Aristotelianism.

Again - no animus against evolution, but against biologism, by the view that our abilities are circumscribed by biological ends. Evolution doesn't address the gap between surviving and living - the space in which human culture emerges - and every attempt to do so, amounts to reductionism. — Wayfarer

Science sees sociology and culture as natural phenomena too. They are part of the same evolutionary story. They are manifestations of the constraints imposed on all forms of existence by the telos of the laws of thermodynamics.

So sure, a systems science perspective - the neo-Aristotelian one - would accept that there is much about human culture and individual taste that is merely accidental. It is not constrained in a strong fashion. And in fact - as we are now talking about a highly developed state of semiosis - it positively fetishes the creative, the spontaneous, the free.

This Romanticism itself is sensible in the context of our hugely accelerated development. We want as many "mutants" and "hopeful monsters" as possible, as that is the requisite variety that evolvability demands. :)

If we want to continue accelerating exponentially into the future we are freely inventing, the name of the game is to increase the scope for contingency, and thus mistakes, and thus the learning which is the pragmatic erasure of those mistakes and the resulting honing of even better habits of action.

So thermodynamical development completely explains life and mind - including the fact that the creative and the spontaneous are a fundamental part of the deal. Developmental structuralism predicts exactly what is observed.

We even have models now. Scalefree networks, constructal theory, and other examples of freely growing natural structures, powered by randomness and yet already predestined to arrive at maximally efficient outcomes when it comes to the job of delivering ever increasing entropic flows.

I'm not denying empiricism. I am denying the empiricist dogma of 'no innate ideas'. — Wayfarer

But, we don't need 'innate ideas" (whatever 'having innate ideas' could even really mean) to explain our ability to grasp mathematical ideas; all we need is the idea of inherent ontic structure in both the physical world and the human mind. Some forms of (nominalistic) empiricism may deny even that, but there is no necessity that empiricism or naturalism must deny the idea of real structure.

You always seem to be arguing against a 'tin-pot' version of empiricism; a straw-man that can easily be knocked over, and then claiming that if this 'tin-pot' version is refuted then it must follow that Platonism is true, rather than seeing that the real philosophical situation is much more nuanced than that.

I can't make you out. You seemed smart enough to have a serious conversation. Then you so quickly degenerate into time-wasting bickering.

To deny holism in the context of quantum theory is simply Quixotic. — apokrisis

You might have read the question before mocking it. I presented an online definition of holism and asked if you accepted it. And in the case you accepted it, if you would address what seemed an absurdity. You have returned fire with QM, which I did not ask about. (I'm still interested in how you handle the apparent absurdity, if you buy the description of holism as posted, or if not, if you'll list a site that does a better job.)

If any existing idea facilitates the creation of models that assist in talking about or thinking about QM, who am I to object? My own bias in thinking about difficult subjects is that models are at best a crutch, and the use of crutches is not cost-free. That is, it's usually better to take the subject on its own terms without an admixture of wrong ideas.

But that's for folks to choose for themselves. There is also a pernicious effect that I do object to, the insistence on the model as being in some sense in the thing itself. Teleology is a good example. That some things appear to consistently do some things and that it is useful to recognize that phenomenon is so basic as to amount to pre-scientific thought. But then some folks insist that the teleology is in the thing itself. As if an acorn had in it the purpose and intention of becoming an oak, in addition to the biological machinery that in action is that by which it becomes an oak.

On Youtube is a Feynman video of him describing three differing laws of gravitation. Each both allows and constrains some aspect of interpretation. Newton's law allows for action at a distance. The other two don't. The lesson is that it's a mistake to confuse the description of the phenomena with the phenomena itself. To be sure, sometimes that confusion is not-so-easy to avoid.

Holism is useful with QM? Great! Are you going to argue that holism - whatever it says - just is QM?

You are deflecting. The issue was already the quantum one of Feynman’s path integral. I am the one arguing that it’s models all the way down. I am the one asking you how quantum mechanics can be understood other than holistically, while pointing out that even classical physics is holistic once you ask how the principle of least action could metaphysically be the case.

The idea of transcendentals 'interacting with the world" necessarily carries a commitment to "another realm" apart from the world, though. — Janus

I disagree. Only if we dogmatically assert that something must be in the world to affect the world, or something must be physical in order to affect the physical, etc. But why would we hold to such an assumption? For example, ideas aren't physical, and yet they determine a large part of what physically happens - think about the ideas that guide scientists in inventing a new technology.

For example, ideas aren't physical, and yet they determine a large part of what physically happens - think about the ideas that guide scientists in inventing a new technology. — Agustino

C'mon! This is based on a misunderstanding of and confusion about what "cause" means. Example: get yourself a piece of wood, a nail, and a hammer. Now sit with them and try to "idea" the nail into the wood. No food or water until you do! It's all right to speak indiscriminately in informal speech, when what you precisely mean isn't too important. But it's a problem when you forget to discriminate when it does matter.

And on its face, the face I troubled to show you, holism is absurd on that face. Now, address that absurdity, or dismiss that definition of holism and point me to a better one. Anything else is just "deflection"!

I am the one asking you how quantum mechanics can be understood other than holistically, — apokrisis

And you are talking about understanding without grasping that I am not. I am simply distinguishing between phenomenon and model, and only to the extent that the one is not the other.

"Models all the way down" is not a statement of fact about a phenomenon; it is a description of a mode of understanding that on its face professes not to understand - but that in the mouths of some people is represented as being the way the phenomenon is! (Never mind the implied contradiction; i.e., because we cannot/do not understand, (therefore) we understand!)

It is difficult to fathom your logic. Are you saying that reductionist locality can account for the quantum facts? My point was that no matter how absurd you might deem a non local holism, dem are the facts.

As to holism, I find this:
"the theory that parts of a whole are in intimate interconnection, such that they cannot exist independently of the whole, or cannot be understood without reference to the whole, which is thus regarded as greater than the sum of its parts."

If you accept this, then can you explain to me what "cannot exist independently of the whole," and "is thus regarded as greater than the sum of its parts" mean?

By "in intimate interconnection," I assume that means in terms of the function of the whole, if the whole has a function. The valves are "intimately interconnected" to the crankshaft in terms of the overall functioning of the engine, but they had better not ever touch!

And from the engine. I can remove parts and put them over there. They exist independently over there, yes? — tim wood

You seemed to think there was still something to address here?

Well let's talk about organisms rather than machines. Can an organ exist without a body, and a body without its organs?

Can a heart have an independent existence - one that never involved the context of being part of an organism which needed it for the purpose of pumping blood. Or is there in fact an intimate interconnection, a co-dependent relation, that speaks to the wholeness of the biological causality?

So as I said, it is nuts to talk about proving existence is a machine because you can prove a machine is a machine. A machine is a device built in the very image of reductionist modelling. It works because all the causal holism has been stripped out of the situation.

That is why machines have to be built. They can't grow. They don't get to decide their own use or design. Quite deliberately, there is a lack of any intimate immanent interconnection between their material/efficient causes of being and formal/final causes of being. Because we, as the human builders of a machine, want to supply that part of the causal equation. It is we who have the purposes and the blueprints.

And so the realm of machinery is a special reduced kind of world we create by constraining the usual holism of nature. An internal combustion engine is a controlled explosion directed at regular intervals through a system of pistons, cylinders, cranks and gears. We make sure all the parts are machined from sturdy metal, that the petrol/air mix is just right, that the timing of the explosion is precise.

In short, we do everything possible to reduce it to a mere assemblage of independent parts. And that is why the human mind - with its ideas about purposes and designs - becomes its own culturally independent thing.

As a species, as an organism, we have been transferring a large part of our being into our technology. It started just with cooking, spears and hammers. Now its iPhones and space shuttles. And in splitting off the material/efficient causes of being into a realm of machinery, that has increasingly freed us to be purely intellectual beings - organisms that are now largely devoted to supplying the other half of the causal equation, the purposes and the plans.

So there is a nice little irony there for @Wayfarer's OP. The mathematical turn in Greek thought was all about fabricating the conditions of organismic transcendence.

We could become the gods of technological creation as maths was the basis of a new epistemic cut in nature. We could split our organismic nature in half, turn to technology as the amplifier of our material/efficient causes of being, and then in matching fashion, become amplified in terms of our scope to have grand purposes and grand designs. We transcended our biology and even sociology to the degree we made it possible to dwell in a technologically-based paradise of ideas.

So we rewrote the rules of organic holism. Or at least took it to the next semiotic level by discovering the power of mathematical/logical language - a generalised syntax or grammar now completely washed clean of any intrinsic semantics.

Again note. Language itself was made mechanical - logical, computational, a composition of atomistic parts with no holistic entanglements. So no wonder that the reductionist mindset - the one that tries to view every situation as another machine - has become so ingrained it can no longer even be noticed as a mindset.

We no longer think in the social language of words - the everyday speech that still reflects the structure of intimate interconnections and interdependencies with our other tribe mates. With a standard modern education, we are trained to be as mechanical as possible in our critical thinking skills. When asked any big questions, it seems the only right way to go. Does this compute ... in the machine-like fashion that is the standard issue model of physical reality now?

So again the ironies. To the degree we have founded ourself in mechanism, we have liberated ourselves to be gods or free spirits of the world in which we live. We have achieved Cartesian dualism as an act of self-made causal division. And that then has become a standard source of philosophical angst.

Are we just enlightened machines, or souls existentially trapped inside fleshbots? Which of the two things are we really - a construction of material/efficient cause, or an expression of transcendent formal/final cause? In fact, we are just living a thoroughly divided life that has been amplifying both aspects of our organismic being exponentially. We are being stretched in opposite directions having stumbled into the means to do so - that Greek turn, the development of pure syntax, the development of a mathematical/logical point of view which can Platonically split our world.

Now that again is why we really, really need neo-Aristotelianism today. We have to accept that all four causes compose any functional system. That has to be our philosophical frame of analysis if we really want to understand "everything".

Most folk are stuck with the conflicted image of Platonic dualism. The world is an unthinking machine. We are rational souls. So metaphysics basically can't make sense of how things are. Caught in this paradox, people fall to bickering about whether everything is in fact all mechanical, or all spiritual. Every thread on this forum goes down that gurgler. It is just the way modern culture leaves people.

And that is why it would be wonderful if more people understood holism properly. It is certainly true that to be a modern human is to be divided between the material possibilities of a mechanised existence, and the intellectual possibilities of a free imagined existence. We have made our lives as Cartesian as possible. But that is really weird when you think about it. Holism would be the way to turn that around and see the further possibilities for a psychic integration of that divided self.

Well, let's not exaggerate. Most people have zero interest in philosophy and do live rather unanalysed lives. They are social organisms, responding to their immediate cultural contexts, and probably all the happier for it. The contradictions are not felt because they just don't believe that other people are merely machines, nor in fact transcendent beings. They are simply other people and the ordinary embodied games of language apply. No need to introduce any mathematical abstractions into this equation and thus set up some further metaphysical drama.

But once you are exercised by the division that is forming our modern intellectual condition, then you ought to be pleased that there is a way to heal it - neo-Aristotelianism, or any other of the many brand-names for a holistic, four causes, understanding of metaphysics.

It settles the old differences while opening up new intellectual horizons. Human anthropology is about the most trivial and easily disposed of issue. It is how holism applies to physics and cosmology that would be cutting edge. Or to life and mind in some properly structural sense. Now we are talking about the new adventures that science has embarked upon.