Since time is not material, it does not exist in reality — val p miranda

Time is the measure of material change just as space is the measure of the lack of material change.

So yes, they are measures - the coordinate system. And you need both. One isn’t conceivable without the other, despite what Kant might say.

A lack of change can only be measured in terms of the possibility of a change. And reciprocally, the possibility of a change can only be measured in terms of the lack of a change.

Special relativity glues these coordinates together as spacetime, using the speed of light to express this reciprocal relation. Then general relativity adds in the further reciprocal deal that exists between a spacetime container and it material contents. This uses G as the constant that connects the two halves of the deal.

Quantum theory speaks to the material contents. It is the coordinate system for describing the fundamental action. And once more this is a unity of opposites related by a constant. Under QM, position and momentum are related by h. Time and energy are also a complementary pair under the reciprocality of the uncertainty relation.

Quantum field theory then shifts the point of view from point particles to spacetime-filling fields by uniting QM with special relativity. This is done by using both c and h as scaling constants.

So – as Okun's Cube of physical theories tells us – we leave the Newtonian world familiar to Kant behind by discovering the greater unity between all the parts of the Cosmos.

We have a unified theory of the spatiotemporal container in GR and a unified theory of the material contents in QFT. Next we look for a theory of Quantum Gravity that brings together all three fundamental constants - c, G and h - into a single system of reality measurement. We have a description of the Cosmos that combines the container and its contents as a reciprocal set of co-ordinates.

All the ontological elements are crisply defined in terms of their dialectical relations. Each becomes the measure of its "other" in a system of interactions.

A definition of space as a real immaterial existent that makes existence possible by providing place, in my view, is correct and realistic, not space-time with a fabric. — val p miranda

You are using terms that simply negate rather than "other". You oppose the material to the immaterial. And that is question begging when materiality itself is understood as substantial being of some kind. We know from Aristotle that substance is a hylomorphic unity of opposites – the combination of raw material potential and formal necessity.

So anything that exists in an actual or substantial way is complex. It is matter with form. To fully dematerialise it, you would have to take away both the matter and the form.

Again, modern physics accepts the irreducible complexity of the relations that could constitute a cosmos. Broadly you get to the same place – a GR container with its QFT contents. But also you preserve the unity – the symmetry – between these two sides to the story.

Spacetime tells matter how to move, matter tells spacetime how to curve. You've heard the expression of how the two are connected in a reciprocal fashion.

And a final theory – a QG theory uniting the three constants – would turn that aphorism into a concrete mathematics.

Space meets the Kantian requirements as a transcendental because it is absolute, necessary and universal. Space as a transcendental is immaterial which means that it has no fabric--it is absolutely massless. — val p miranda

Kant was dealing with Newtonian physics. It was a mistake to psychologise time. It was a mistake to talk in antimonies rather than dichotomies.

Kant was a systems thinker, but he made some basic missteps.

But the topic of having reasons that I am discussing is what it means to be a species that has reasons.. The fact that we can do things a different way.. That there is no right way for anything. — schopenhauer1

To have reasons but no purposes is incoherent.

As humans, we are constrained by meanings. Our worlds are constructed to have preferences and intentions that we can actually apply our intelligence to.

You seem to be conflating the two senses of the word "reason". One talks about our reason to aim our efforts towards some end. The other talks about how we could then rationally act towards that purpose.

So one is the final cause, the other the formal cause. They do go together in being the downward acting causes in the Aristotelean causal analysis – the complex systems approach. But this seems a sign of how your argument is all confused.

Any time you put a goal in mind, you are simply putting your "spin" on it. I called that a hypothetical imperative. Yes, if you WANT that, one way to get that is THIS. But no one has to want that by necessity nor do it in that way that is prescribed. — schopenhauer1

And so we disappear back into your confused story where all possible desires are simply arbitrary and dispensible.

We can eat only air and starve. That is "reasonable" as one could decide this is a good way to die.

If your goal is indeed death, then wouldn't it be reasonable to pick what you consider the best way out?

What would be your preferred choice? Your worldview might demand it be as horrible and messy an exit as can be imagined as that would be most in keeping with the extreme pessimist perspective on how nasty it is to be alive in any way. :smile:

Anyways, now we are just talking past each other. — schopenhauer1

That is another way of saying you were strawmanning me. :up:

The point is there is no fixed instincts anymore. — schopenhauer1

Still strawmanning.

But that would be a gross straw man to equivocate that with the types of human reasons I am discussing here. — schopenhauer1

My point is that existence is a hierarchy of constraints. And that constraints indeed define the freedoms at each stage.

You are thus not free to choose your freedoms. They emerge from the system of constraints. That is why you can complain that your choices are imposed on you and feel like a burden. Or instead, you can be grateful to have so much sophisticated choice in living a human level of life.

I did do a fuller post on how the body and brain do rely on quantum biology….

https://thephilosophyforum.com/discussion/comment/105999

The main dissentions seem based on claims like 'that's unlikely and here's why,' but nothing that convincingly proves Hameroff and Penrose wrong. — universeness

What predictions does the “theory” make that are testable? The arguments have so many free parameters that they evade specific criticism. As I say, Hameroff was quite happy to throw in microtubules using CA properties to bridge the problem of the thermal scale of quantum coherence. Speculation on top of speculation when the going got tough. It’s the game that crackpots play.

Again, the amusing thing is that this was the early 1990s and no-one thought biology had anything to do with QM. And now we can see how life really does harness decoherence and quantum tunnelling to get stuff done. That is a complete change in paradigm. Brains, being biology, depend on the same quantum mechanisms down at the nanoscale of molecular machinery. So it is neurobiology as well.

But this is actual science. It’s plausible given the constraints of quantum physics and is lab proven. The evidence exists and one happily changes one’s mind.

The idea itself is easy to debunk. My particular reason for calling Hameroff a charlatan was the transparency with which when he saw I wasn’t buying his quantum coherence in microtubules story, he then switched to his earlier speculative theory about microtubules as cellular automata computers of consciousness.

Just a make shit up kind of guy.

No, just sensitive dependence on initial conditions. — jgill

Talking of which, I was browsing this on structural chaos - https://www.researchgate.net/publication/279265558_Structural_Chaos

(Undercooked, but an interesting distinction.)

Opposites, to give a rather obvious example, like light and dark can't transform into each other (re Parmenides, what something is can't be derived from what that thing is not; ex nihilo nihil fit). — Agent Smith

Give Heraclitus a bell. Let him know the bad news. :chin:

The "Butterfly Effect" is an example of order emerging from chaos. — Gnomon

Or rather the exact opposite.

WHAT YOU BELIEVE DEPENDS ON HOW YOU FRAME THE EVIDENCE — Gnomon

Or how deeply you misunderstand it.

I prefer to follow the work of Stuart Hameroff and Roger Penrose on the question of human consciousness. — universeness

Argh! Hameroff is a charlatan. I don't say that lightly.

Neurobiology certainly is quantum in interesting ways. Science has established that. But Hameroff is peddling a different level of bullshit. Penrose gullibly is along for the ride.

But you're a fan of physics so you should appreciate that in QM the observer plays an active role converting the potential to the actual (by means of making measurements to collapse the wave function). — keystone

I'm a fan of semiotics – the modelling relation. So that is a formal theory of how observers and their realities relate by acts of measurement.

I'm working one step up. I'm speaking for those like Peirce, Rosen, Pattee, etc, who are modelling the modelling relation in a rigourous fashion. And yes that does then lead to a better metaphysical understanding of both classical and quantum physics.

A mathematical platonist would have to say infinite. I would go in a different direction. I would ask 'where?' How many numbers are 'where'? In other words, in what computer/mind are you talking about. You have to be specific about where is because there is no Platonic realm. — keystone

I am saying much the same thing. But the question is not where the numbers need to be represented or stored. It is how many decimal places do you really need for the task in hand?

What this means is that the whole business of counting becomes self-limiting. The aim of "good mathematics" is instead to represent the fewest digits you can reasonably get away with. An infinity might be available, but I would rather save time and energy for other things by only having to remember just one.

This is where we get down to binary bits of logic. The only numbers needed are 0 or 1. Or indeed, the tape head of a Turing machine that can either make or erase a mark.

But it takes the semiotic view to create this reciprocally self-limiting Nirvana – where infinite information is available, yet you can boil it all down to a simple yes/no response.

Is it a 0 or a 1? That's all I need to know to be completely certain rather than maximally uncertain. And a world that is boiled down to yes/no certainty demands hardly any time or energy to live in it.

This is what maths looks like when it does involve an intelligent observer with some actual purpose. A big enough range of possibilities to cover all eventualities. But then the complementary operation that narrows the field to a single actuality of complete certainty or counterfactual definiteness.

You believe that math itself has some fundamental limits, perhaps a frequency, a duration, or a length. — keystone

That isn't my argument. Maths can be treated as its own abstract game with its own generating axioms. That game generates a bunch of abstract nonsense, but also occasionally hits on something "unreasonably effective" so far as modelling realty is concerned.

The issue is with the abductive end of the story – the intuitions that might guide the further progress of our reality modelling as a community of philosophers, scientists and mathematicians.

If your intuitions are wedded to the concrete machinations of deductive algorithms, then you might be locking yourself into a world picture where you can't see it as instead a story of self-organising emergence with natural cut-offs.

Finitism indeed might not be the best way to extend the reach of the formalisable. But it may instead be the best way to reconnect the formalist project to the reality it left behind.

That is the debate I am focused on.

Every computer has its limits. It has a finite memory so there is a limit to the size of the numbers that it can store. — keystone

But I've already said this about computers. The abstract formalism – the Turing machine – has an infinite length of tape and infinite time to move it back and forwards through the single digital gate. However real computers live with real physical restrictions and their maximum information capacity is constrained by the Bekenstein bound. This is the point at which the computer turns into a black hole under its own gravitational pull.

So yes, we have theories about how to distinguish between the mathematical fictions and the real world realities. Time and energy become constraints on counting or cutting – as the intuitionists argued.

Mathematical objects don't exist eternally in the Platonic realm. They exist when we (computers) compute! — keystone

And yet Universal Turing Computation is a mathematical object – conceived in Platonia. This is the kind of "paradox" we are meant to be figuring out here, not simply saying one is the other as if the differences were moot.

Undefinable real numbers have no place in my view. — keystone

You reject vagueness then. That is certainly the usual thing to do. :wink:

My point is the rule not the exception. — keystone

And how do you know there is a rule unless you have ever seen some exception? How can you define a definite limit unless you actually have indeterminate challenge of the borderline cases?

A rule is meant to range as a constraint over all possible exceptions. In practice, we live by rules that simply limit exceptionality to that which doesn't matter. We reign in the differences that matter and ignore the differences that don't.

I prefer the practical approach to these things rather than the Platonic. The advantage of indeterminacy is that it then gives you something to determine. There is a reason to have been thinking deeply about what matters and thus a choice that has been made which constructs a world with some actual meaning to it.

It has not been determined whether space is discrete or continuous (LINK). I'm inclined to believe that the planck length is a limitation that is applied to measurement, not the divisibility of space itself. — keystone

But the Plank scale measures the fundamental grain of indeterminacy – quantum uncertainty or vagueness. Determination can start from that point where the symmetry is dialectically broken. We can start to say that some particle has both a limited location and a limited momentum in some strong sense.

The limit of measurement is indeed vagueness or indeterminacy – the state where the PNC finally fails to divide the world distinctly.

It sounds like you're saying that the rabbit exists even when not observed. — keystone

But the image is constructed by having the contour information split into a pair of representations which you then have to fuse bak into one by changing your depth of view. So you could only ever see the suggestive contour of whatever object has been plugged in.

If I handed you a blank white piece of paper you could argue that it is a picture of a polar bear playing in the snow but I would argue that it only contains the potential to be such a picture, and it would actually be that picture only once you cut out the bear figure with scissors. — keystone

That is a better analogy. I prefer my own still – the static on the TV screen which is both every show you could ever see, but all at once ... or else just meaningless noise.

Perhaps I'm missing your point. Do you agree that given a continuum there's infinite potential to how you cut it up? — keystone

The mathematical picture of the continuum is of something that can be unlimitedly cut. But physics tells us that the real world works with cut-offs.

That doesn't mean there is some smallest interval – a point where the line and its gaps are the same size and so you can land cleanly either, and with equal probability, on the line or the gap. It means that there is some scale where the very distinction between lines and gaps becomes vague. It ceases to be a meaningful distinction.

If you agree with a cut based approach to the continuum, then this is what lies at the end of the trail. The cuts must have some size to actually disconnect the line at a point. The more cuts you make, the more the continuous line becomes a tissue of cuts. When you get down to the scale where the line segments and the cut widths are the same, it is 50/50 whether you have one or the other. And the next cut - in a single step - then removes the line completely.

So there are some issues if you want to claim bivalence all the way down to the limit.

I agree with Max Tegmark when he said 'we should reject carbon-chauvinism'. — keystone

What does Tegmark know about carbon then?

Biologists learn that carbon chemistry is unique because of things such as that it forms 29,000 hydrogen compounds to nitrogen’s 65, oxygen’s 21, or silicon's 55. And carbon makes metastable monomer chains where silicon only makes crystals.

In other words, if the physical world wanted to do "computing" in the style of genetic codes providing the constraints to organise chemical potentials to do work, carbon was the only thing that made it a true possibility.

Rather than reject carbon-chauvinism, we ought to reject basic biological ignorance.

(1) 'finitism' has different senses. — TonesInDeepFreeze

:up:

(2) Perhaps it is not necessary to have infinite sets for an axiomatization of mathematics for the sciences. It's just that in order to evaluate a non-infinitistc axiomatization, we need to have it specified. — TonesInDeepFreeze

As I've argued, science is founded on the pragmatism of the semiotic modelling relation. That changes the view of the situation. Axiomatic deduction becomes just the middle part of a three stage process. The formality of the deductive step is matched by the informality of the initial abductive step (the inductive leap to a possible answer) and then the informality (or pragmatism) of the inductive confirmation – the act of measurement, the act of actually applying the idea of counting to the world which needn't necessarily be crisply countable.

You say the idea of the stick – as an atomistic object – gives safe ground for counting in terms of abstract objects. But are any two sticks ever alike outside your willingness to grant them the status of being "sticks" of near enough similarity in terms of size, shape, weight, etc, to ignore the differences and declare them "the same"?

So the idea of counting is different from the physical act of counting. One deals in abstract objects, the other in real objects. And all real objects full of contingency. They have any number of defects and blemishes. Indeed, the ontology of real objects – for the Peircean pragmatist – is that they are simply a state of contingency that has been constrained to some suitable degree where the differences statistically cease to matter. The set of physical objects is constructed as the range under the generator of some agreed distribution curve. Near enough becomes exact enough – in a way that is outside of deductive reason, but within grasp of the feedback loop of a hypothesis-testing pragmatism.

It is great that maths tries to make itself as robust as possible by an axiomatic approach. The methods of deductive proof. This part of the modelling relation needs to be as watertight as it can be.

But then science is equally concerned with the business of measurement. It may be informal in the logical sense, but it has to be strict in the methodological sense.

Then we must have a robust approach to abduction as well. And here things become murky. How does one bottle true creative insight of the kind that is the leap to the model that is going to work and achieve its pragmatic goals?

There are clearly ways to cultivate or train folk in abductive reasoning. But most education systems are more concerned to bash you over the head with a textbook.

Given your concern for the proliferation of cranks obsessed with offering original solutions to the biggest problems, the secrets of abductive thought should give clues to what goes wrong there.

Largely of course it is a failure to be iterative. To guess small and test. Then guess larger and larger in conjuction with broader and broader reality testing of the formal theory being constructed.

This guy has been consistently the best at analysing the frontline situation. Here he gives reasons for new concerns....

If we want for it to be provable that there does not exist an infinite set, then we need axioms to do that. — TonesInDeepFreeze

You’ve got it back to front. It has been shown there is a generator that can produce an arbitrarily large number. You’ve accepted that. Now what needs proving is that there is also this set containing an infinity of numbers.

Why do you keep shifting the burden in your posts?

Do you know of programs that cause themselves? — Gnomon

Neural networks?

I happen to think of Evolution, allegorically, as a program for creating a universe. — Gnomon

It's a constraint not an algorithm. Different thing. See neural networks.

My postulated Programmer is a metaphor, not a myth. — Gnomon

But it places the intentionality or finality outside the system. A structuralist metaphysics – such as evolutionary theory – places it inside the system as part of what has to develop by a generalised process of self-organisation.

So you are pushing a line that in fact goes against the prevailing trend in speculative physics. Holography, for example, is all about systems of constraints rather than reality constructing algorithms. The Comos evolves into determinate being by "summing over" vague everythingness. It emerges as a holographic structure of relations that reveals the path of least action.

The Universe is the evolution of a heat sink structure. Why is that happening? To give it something to fall into. It could get born in a Big Bang because it could then die in a Heat Death. The initial intention is revealed in its long run actualisation.

Do you think of the universe as a disorganized & hostile place? If so, you are missing its beautiful organization, and its ability to create living & philosophizing organisms from essentially nothing. — Gnomon

That is a very fleeting phase in the middle of the Universe's grand trajectory. Chemistry and biology are not essential to the show, just accidents of complexification that arise along the way. Life and mind do contribute something to the entropification of the Cosmos. But it isn't even a round up error in the big scheme of constructing that heat sink which in turn allows the Universe to start as a "low entropy" condition.

Instead, I view the universe as beginning from nothing and evolving through eons of lifeless & mindless stages until living & thinking being emerged, and worked their way to the top of the food chain. — Gnomon

Anthropomorphic where we need to be anthropic. Human intelligence was never the goal. A heat sink that could make sense of a Big Bang negentropic beginning is the mission the Cosmos has in mind.

I'm not interested in "creationist mind fables" or inflationist myths -- such as ballooning of a vast universe from a dimensionless mathematical quantum fluctuation. — Gnomon

So you are neither interested in religion or physics. Just some fable arising from the mathematical fictions of Turing universal computation.

Or maybe 'cueball': 'The cueball on the table is white' is true if and only if the cueball on the table is white. — TonesInDeepFreeze

Hah! Replace the "real object" with the abstract object and thus reveal the semiotic game being played. If you can't see a difference, there never was a difference. The claims about reality were always indirect and mediated. Conditioned on some abstract definition. :up:

The problem is that we don't want it to be the. case that one doesn't know what snow is until one knows it is precipitation in the form of small white ice crystals formed directly from the water vapour of the air at a temperature of less than (0°C). — Banno

But that's not snow on the lawn. It's sleet! Etc, etc. :grin:

But then these numbers - growth constants like e and phi – are ratios and so are dimensionless unit 1 values more than they are some weird real number. — apokrisis

To correct myself, e and phi are different in that e is transcendental and phi is algebraic. That's something I need to dig into further.

My argument is that the whole potential vs actual infinity thing comes from the fact that our ideas about numbers are based on systems of constraints. We want to close some space of values in a way that creates a set of numerical objects with shared properties. And so we end up with a set of "all the integers" that is a class of objects with tightly specified properties. And then relax some of those constraints and we find the integers nested in the larger set that is "all the rationals".

This is a subsumption hierarchy in hierarchy theory. Each successive set becomes larger as you relax the constraints that form its boundary. So from the point of view of the integers, they are potentially infinite when seen from inside their closed world - a closed world that is unbounded in its openness as an integer generator – and then become viewable as actually infinite in being a crisply restricted domain within the larger and more relaxed space that is the set of rationals.

So virtual vs actual infinity is a point of view. Each level of number can contain within it a more constrained notion of number. And also itself be contained within a less constrained one.

Each such set is a machine for cranking out sequences according to some set of rules. It is a symbol generator, and so is open in that it possesses the finite means for spitting out infinite steps. But then from the point of view of some less restricted generating algorithm, the set looks to be closed in terms of all the values that can be produced in that way. There is now some larger set of values that becomes possible by a generator with less constraints producing values with less intrinsic structure.

This nested view is illustrated in diagrams like this...

No.

Hah, no. Not Bergson. The more general structuralist notion of a hierarchy of scales of spatiotemporal integration. So what Stan Salthe would call cogent moments. And physics would call lightcones.

The cosmos is structured in terms of the scales at which interactions have had time to complete whatever change was going to happen. And beyond that event horizon ate all the possibilities yet to be actualised.

So time has a fundamental grain determined by c. A moment or duree is the completion of a change. And the Planck scale is the size of the smallest such moment.

It is indeed measured by a rotation and translation as it is the the time and space large enough to contain the first Planck scale energy fluctuation - a wave with the Planck frequency. So a single beat of a helical spiral. A sine wave. A rotation and translation that begin at the same size. But then a beat later, the space has doubled and so the energy halved. The fluctuation has already been redshifted. The difference between local spin and global translation is already established.

The fact we measure time with clocks is just showing how general the logic is. We have to have something that changes and yet that makes no difference to be able to measures the changes that do make the difference.

But then really accurate clocks wind up actually using atomic vibrations.

You did it again! — TonesInDeepFreeze

:lol:

That being said, the human mind dreams about how the world could be better, even if it contradicts fundamental constraints of reality. — _db

My argument is that this is a historically recent thing. And predicated on the "unlimited" energetic resources unleashed by the Industrial Revolution.

The Enlightenment was the precursor in it got us thinking about how to transcend the old social order to become more rationally organised as a species.

But inadvertently that led to the world of "satanic mills". Dreams of better became dreams of power and consumption.

@schopenhauer1 says this means the whole Enlightenment project is a sham, a ruse, an enslavement. I say it could be merely the right dream derailed. We could fix it.

(Of course that is a little too late now. We don't have the controls even to lay our hands on.)

Metaphors aside, humans want more than reality can provide. We always have and we always will. — _db

Ever had contact with people living simple lives? It isn't that impossible to match your ambition to your possibilities. It is only been a short time – since the industrial revolution – that the dream of being the "limitless" species has become socially institutionalised.

Just do it, as the adverts say. And why would they say that?

I don't know that I am so terribly relatively weak. — TonesInDeepFreeze

That is my hypothesis. The evidence continues to mount.

Forumcombing is itself a distraction that I probably shouldn't allow myself as it eats so terribly into my time needed for my main pursuits. — TonesInDeepFreeze

Of course. We are not worthy of you. That makes your pointless asterisking of "dangerous disinformation" even more pointless.

(By the way, this poster is not as overtly dogmatic as usual cranks. Indeed his skill is to deflect by feigning that he is considering the corrections, which I perceive to be disingenuous.) — TonesInDeepFreeze

So someone is different in lacking a prime characteristic of the true crank. And yet you only hammer harder when that someone finds you being overly hostile and wants to laugh you off?

Your comments in your above post are well taken though. Even if I am in countering mode in this post, probably soon later I'll reflect more and benefit from your point of view. — TonesInDeepFreeze

Great.

Your annoyance with me should not permit you to read into my plain words things that are not in them, not even plausibly, not to willfully misconstrue what I say in the worst way, and not to strawman me over and over as you did yesterday. That is beneath you. — TonesInDeepFreeze

You wildly exaggerate. But it is true I hadn't read any of your posts before this thread.

However, I feel like you're mentioning a lot of physical phenomenon but not explaining clearly how they relate to mathematics. — keystone

One could always be clearer. But then there is also the issue of how much you are equipped to understand. I can't be held responsible for all the work you might need to do.

However I'm not complaining. At least I'm make progress on making my ideas clearer to myself at times. :grin:

I can draw a line with open ends on a piece of paper and label the ends negative and positive infinity. This unbounded object is entirely finite. — keystone

You can draw a sign that you then interpret in a certain habitual fashion. The issue then is how does this sign relate you to the reality beyond. Does is create a secure bridge? Or is it wildly misleading?

It appears that you are looking at the universe from a point-based perspective in that there's a first instant which is followed by the next instant, and so on. — keystone

Nope. I've said I'm starting the world from its Planckscale cut off. To start the world from a point would be to start it from the singularity where all physics has been scrambled to nonsense.

And the logic is the same whether we are talking in terms of fundamental intervals or fundamental durations.

My triadic systems approach says intervals and durations are irreducibly complex entities. They are born not as some monistic given but from an emergent, self-referencing, dichotomy.

And this is Planck scale physics. It is what the maths says.

How do we measure time? In the usual approach we spatialise it. We call upon the fundamental contrast between a rotation and a translation. We imagine a length that is constrained to a self-repeating local cycle – a clock hand that goes round in a local circle. And then we use that locally fixed symmetry as the standard unit to then create some unbounded sequence of length intervals. Every time the big hand completes one sweep, the day adds another hour of temporal distance travelled.

And there is nothing in this mental picture to say why it can't continue forever. Physical change has been anchored at one of its ends by being made to spin forever in the one spot. And that then frees up the possibility of change being turned into an infinity of time steps in its other direction. Globally, time becomes as infinitely large as it likes.

So you can have a proper definition of an instant or an interval only when you have nailed the rather ambiguous or vague notion of "a change" to a dichotomous coordinate system – a symmetry breaking. One end has to be fixed. You do this by creating a cycle that just goes round and round the same 0D point. The other then is allowed to flap completely free. It can follow a straight line forever as a straight line is simply an endless repetition of steps that never repeat rather than the other thing of an endless repetition of steps that only repeat.

A moment in time – a durée - thus is an irreducibly complex object. It combines rotation and translation to create the emergent thing of a "fundamental time step". And length intervals are also the same trick. They just get stripped of the philosophical nod to energy and change (the things time must measure) and become a story of the 0D point and its 1D line.

At least with clocks you can see how repetition and difference are the partners in crime. The idea of the spatial interval becomes shrouded in mathematical mystery.

But if we add back the physics – the irreducible quantum indeterminacy found in nature – then the clock of the length interval becomes visible. Any point must vibrate. It will have a resonant motion ... because QFT says so. And we can see the reciprocal relation between location and momentum as plain as your face in Heisenberg's uncertainty principle.

Nature has a fundamental frequency. Physics says it is so. A systems metaphysics says it is only to be expected.

If maths has been left behind in this grand and still unfolding adventure, tough shit.

But I'm not a philosopher. — TonesInDeepFreeze

Hey. Now you are on a site where you get the chance to learn! Don't waste it.

Your strength is deductive rigour. Pragmatic philosophy stresses that rational thought involves the three steps of abduction, deduction and induction.

A scientific mindset means making the creative leap of forming a hypothesis, properly deducing the general constraints of that hypothesis, then inductively confirming the truth or otherwise of that hypothesis in terms of the observed particulars or practical consequences.

So think of this site as presenting you a true intellectual challenge. There is an arc to thought that transcends all forms of human rationality. If you are strong in one of the three aspects of reasoning, why would you be content with leaving the other two weak?

Can you just make an inspired guess, a creative leap in the dark. Can you follow through a formal model to its practical and measurable consequences?

The deduction of a theory is indeed a formal exercise. But pragmatism explicitly recognises that its inductive confirmation is necessarily informal. And that is OK. Theories make predictions and we find confirmation in the messy real world business of making measurements. We say the facts fit, even if we only have the first two or three significant digits. Three sigma could be good enough if not a lot is at stake.

So when you hammer on posters, some are indeed just fools or cranks. But also, they might at least be discovering something about how to abductively form hypotheses, or inductively confirm their theories.

You clearly are confident in your logical rigour. But Pragmatism tells you that that is only one third of what you need to be a "reasonable person" in this world we share. Time to be properly humble and get involved with PF in ways that challenge your weak spots.

Having no philosophy is not a disqualifier. Posting is not paintball where you can't participate unless you you are on one of the teams. Not having a philosophy doesn't entail that one doesn't have meaningful things to say. And I find it refreshing when a person doesn't have a philosophical ax to grind. — TonesInDeepFreeze

Have you noticed how much you assert the negative so as to avoid having to support the positive?

What is life without some form of ontological commitment?

Oh come on. I didn't "gatecrash" anything. You posted essentially a one-liner on the subject, itself not an argument. That's fine. And it should be allowed that one may reply in kind. And even if a poster replies tersely to a longer argument, that's not "gatecrashing" or necessarily even rude or whatever. — TonesInDeepFreeze

Oh come on. You yourself have said you have no philosophy to defend on this forum, just a self-appointed need to police it for its mathematical thoughtcrimes and disinformation campaigns.

Of course not. It's not even a formal claim. — TonesInDeepFreeze

I was teasing. If you gatecrash a comment, you could at least have the courtesy to set out your reasons for your assertions.

For myself, even though I am not a mathematician, I happily study ZFC without having the platonist commitment that the abstract objects of mathematics exist independent of mind. — TonesInDeepFreeze

So you reveal yourself as a pragmatist. Infinity is a useful idea as far as it goes in the real world of doing things – like deciding whether some circle is in fact a very fine construction of flat lines, or a polygon is in fact a very fine construction of flattish curves.

Truncating pi is practical. One can be a finitist and it looks exactly the same as being an infiinitist. Outside the culture wars of philosophy of maths, who could tell the difference? It becomes a difference that doesn't make a difference.

You might believe it, but can you supply a formal proof of that claim?

As I've pointed out, finitism (or worse, ultrafinitism) leads to some odd results : you have to truncate ππ (which turns circles into polygons), you have to deny irrationals, you destroy the foundations for calculus, lines no longer consist of an uncountably infinite set of points, etc. — Real Gone Cat

That's a list of features, not bugs. It's long past time to drive the Platonists out of maths. Pragmatism makes for a sounder metaphysics when it comes to how one would model reality. :smile:

It seems that mass-energy is convertible to spacetime. Does that argue for monism... — Art48

If there is a conversion, it is to spacetime warp and hence gravitational potential. So the matter - as one kind of structured energy - is being converted to spacetime as another. A gravity field is created that continues to suck in matter as its fuel. It is a kind of reverse star – a dissipative structure – in that sense. :smile:

And the situation can be measured in the higher order currency of information/entropy. The black holes event horizon is where the transaction is taking place. If everything – matter. warpage, and even energy – are subsumed under the more general notion of information, then it can seem physics speaks to metaphysical monism. Thales said the fundamental substance was water. Physics now says it is Shannon's "information entropy" – countable degrees of freedom or fundamental bits of physical uncertainty.

But dig deeper and Aristotle's hylomorphic understanding of substance is a better fit. There, substantial being arises at the intersection of form and matter. Naked potential for action being given a shape and direction.

The monism of "basic stuff" becomes a dialectical relation between a raw material potential and its formal structure. Random action being given coherent direction. And this reappears in modern physics – especially if you are on the ontic structural realism bandwagon.

So the Comos can be understood simply as a spacetime container giving direction to its quantumly impulsive contents. General relativity (GR) is the theory describing the container. Quantum field theory (QFT) accounts for the energetic vacuum which fills it with potential action. A substantial world of enmattered objects arises at the intersection of the two. Particles pop out of the hot soup as Big Bang universe expands and cools. Symmetries are broken and so local structure is imposed. Matter arises to the degree antimatter has been cancelled away, and the Higgs field has enforced the mass couplings that finally split the fundamental particles into a distinctive set of elements.

So what we think of as monistic substance is in fact a hierarchy of development in which increasing structure is being imposed on raw undirected action – the vacuum's sea of virtual quantum fluctuations. You get protons, neutrons and electrons as the complicated crud – particles with mass and some particular combo of force interactions.

In a cold and empty universe, atomic matter can become stable and eternal. Part of the reason for this is that the gravitational side of the equation is a reckoning postponed to the infinite future.

All forms of mass and energy create gravitational warpage. But the Big Bang produced a spacetime so flat that it will take "forever" for all the separated bits of warp associated with every lump of enmattered particle to fall back together.

In a general balancing way, the positive energy represented by the creation of matter is matched by the negative energy of creating this great big gravitational well. A debt is incurred at the start and only comes due at the end.

Black holes can be considered the debt collectors. At least locally, in the interim.

Particles get sucked into a vortex of warpage and give up their structure at the event horizon. At least that is how it looks from the outside. Kinetic energy disappears and gravitational potential appears in its place.

Yet even black holes live in the larger story of an expanding~cooling Cosmos. Eventually they get dissipated too as the temperature of the surrounding vacuum falls so low that the black holes evaporate. They melt away, turning the gravitational warp back into a flood of radiation – but radiation of extreme wavelength and chill. Radiation with the temperature of the cosmic Heat Death.

So there is this general duality where action is being given a direction. Random potential is being formed into persisting structures with varying degrees of complexity and stability. Spacetime is the gravitational field whose curvature tells stuff how to move. Mass and energy are the formed particles, or localised persistent quantum excitations, that tells spacetime how to bend. Substantial being is the intersection of this relation.

Mostly this results just in the vacuum. So as a substance, there is nothing much to see. Just a sea of virtual excitation with some general temperature. A hot and condensed soup that becomes a cold and expanded soup. It does look pretty monistic.

But scattered in the generalised vacuum state are the more interesting forms of structured potential. Black holes and fundamental particles. Local features with some measure of persistence.

We could call both of them energy structures. But even then, they are divided, being made of either the negative potential of spacetime curvature, or the positive potential of quantum fields.

And even a fully unified view of general relativity and quantum field theory – a theory of quantum gravity – is going to be some form of hylomorphic metaphysics. The emergence of actions with directions. A classical Pythagorean unity in being a unity of opposites.

So there is the familiar metaphysical debate. Is reality monistic or what? The alternative to monism is in fact the triadicism of Aristotle's systems metaphysics. You have the three things of the material potential, the formal (indeed Platonic) structure, and the resulting substantial state of being that results when these polar opposites achieve stable unity.

That maps nicely to the expectation that GR + QFT = QG in some neat mathematical operation.

The whole deal is scaled by its trio of Planck constants – c, G and h. Or the speed of light, the strength of gravity, and the grain of quantum indeterminacy.

So GR unites c and G as a maths. QFT unites c and h as a maths. Therefore the task of QG is to unite c, G and h in the one mathematical structure. That is when we can truly convert between G and h as the constants representing direction and action, form and matter, gravity as the spacetime container and quanta as the energetic potential that are its fluctuating contents.

I wish life were an endlessly fascinating riddle to be solved.

Oh wait. It is!

So I am not sure what you are getting at. — schopenhauer1

Do you believe that being an airatarian is conceivable dietary choice?

Foremost Breatharian, Jasmuheen, formerly Ellen Greve, is credited with starting today's Breatharian movement. Her Prana Program advises followers to convert to Breatharianism gradually: Become a vegetarian; become a vegan; move to raw foods, then fruits, then liquids and finally prana. You replace physical food with air and light as well as metaphysical nourishment.

Apokrisis thinks that we should X, so we should X. — schopenhauer1

Why do you persist with this strawman? I simply point out that there are constraints. And so also the resulting freedoms.

You can pick your nose or scratch you bum and it makes no difference to me. You just can't pick my nose or scratch my bum without some very good medical reason and appropriate qualifications. :razz:

Not really what I am getting at. Rather, why we do anything. Our motivation. Our goals. Our decisions. It isn't simply dictated by instinctual drives. It isn't even that we have some learning mechanisms. We have symbolic brains that make meaning of the world by parsing them out into conceptual frameworks, by iterative interactions of individual and the group. — schopenhauer1

So now you are rehashing what I said about semiosis in humans involving a hierarchy of levels.

But @180 Proof said it. The giving of lingusitic reasons for every action we take is (mostly) ex post facto rationalizations. A rational society doesn't require that kind of deliberation beyond the point that it has some collective utility.

We aren't doing things because apokrisis thinks there needs to be balance. — schopenhauer1

Strawman.

It's just apokrisis' ideas on X, nothing more. — schopenhauer1

Again you have utterly failed to reply to my argument, just tried to strawman your way out of it in tedious fashion.

I believe that irrationals are algorithms which describe this mysterious other object - continua. — keystone

I've already raised this point, asking if sqrt(2) is the exception or the rule. Higher dimensional generators could produce generators of some number that looks to be an irrational point of the line. But then these numbers - growth constants like e and phi – are ratios and so are dimensionless unit 1 values more than they are some weird real number.

The status of any regular irrational seems different. They would lack generators apart from decimal expansion. Something else is going on.

I don't believe there is a fundamental length since any length can be divided. — keystone

Can the Planck length be divided? Not without curling up into a black hole.

What you believe and what the Universe would like to tell you seem two different things. Who wins?

I appreciate that you are using a lot of physics analogies here but I feel like you've gone to far. — keystone

Reductionism in either maths or physics is showing its age. I am just exploring the holism that would give the larger view. And in being triadic, that is irreducibly complex. Tough to deal with perhaps. But it is what it is.

I can imagine a mind that lives in a 4D universe that can picture a 4D hypersphere as easily as a sphere. — keystone

Yea, nah. I'm not buying these feats of your imagination.

In this analogy, the interaction is the act of cutting. — keystone

That's taking a point of view. Performing a figure~ground gestalt discrimination. So it would indeed be a good analogy of how an observer reads information into the world. It is how the brain sees reality in terms of collections of bounded objects.

We are getting towards Peirce who completed Kant's project of creating a metaphysics that begins in the world-constructing mind. But we can only go far taking this semiotic path before wondering how to take the step to a pansemiotic view – the one where the world is "thinking itself" into definite being in ontic structural fashion.

If all potential images popped out simultaneously then the whole page would pop out resulting in no image at all. — keystone

Well the trick is that there is enough contour information to allow only the one possible stereoscopic reading once the brain has filtered out all the pixillated noise of the random colours. The hidden rabbit or seagull is merely hidden while the brain finds a way to suppress the shapelessness of the coloured pixels from the intelligibility of a depth perception-based contour.

So as a stimulus it is fixed - designed to play off two different boundary constructing visual subsystems. We are being informed of an incoherent surface by the random field of colour pixels. We have to stop looking at it as a flat incoherent surface to find the quite different depth-based reading.

The page contains the potential of infinite images, — keystone

The problem is that it doesn't. It plays on a dichotomous rivalry of brain subsystems. You have to switch off the one and employ the other. The search is for the single hidden interpretation. Only one of the two points of view can spot it.

Can the image and background be the 'measure of the other' that you're referring to? If so, then that makes sense to me. — keystone

That is the standard logic of Gestalt psychology. Figure and ground arise as a holistic calculation. The whole brain is organised by this contrast-creating logic. Neuroanatomy is a collection of useful dichotomies or symmetry breakings we can impose on the world to make in intelligible.

This is why the brain is not a computer. It works holistically. It imposes contrast so as to separate the world into signal and noise. It doesn't crunch data. It constructs meaning by suppressing randomness. To be attentively focused is to have defocused on everything else.

So some things about your magic eye analogy hold. It certainly explains why reductionism has such a grip on our psychology. The brain is so skilled at ignoring backdrops and seeing only the foreground events that we might indeed believe that suppressing meaningless noise is an effortless and costless mental affair.

But the brain has vastly more inhibitory connections than excitatory ones. It has to work on ignoring as much of the world as it can so as to then see it in an object-oriented fashion.

Putting a finger on an irrational value has this sort of extreme cost. Unless we have some generating algorithm to shortcut the whole decimal expansion, we just have to plough on using infinite resources. Every next digit is just as much a surprise at the last. Even if we might be thinking after even five decimal places, well how many more do I pragmatically need here.

So your general approach – to root the question in actual psychology – is right. And that is Brouwer/Peirce for you. There is a cost to decimal expansion where there is no shortcut algorithm. This is the Kolmogorov complexity approach I mentioned. What could be more pointless(!) than a numerical value without the constraint of a generator?

The Diagonal Paradox can be extended in principle to any curve in 2D. For example, a circle of radius 1 has a circumference of 2pi, but if I apply my system of sine curves to the circumference I find that as they converge uniformly to the existing circumference, their lengths tend to infinity. Hence I am staring at what appears to be the simple circle I began with, but I now have one with infinite circumference, and hence infinite area.

Thus infinity is everywhere in plane geometry where it shouldn't be. — jgill

Hah! In the spirit of the infinite fractal coastline paradox. Nice paper.

I consider the Paradox an aberration that results from collapsing one dimension to a lower dimension in certain circumstances and insignificant although bizarre. But Wolfram claims that this crops up in Feynman diagrams. It goes to the very nature of lines and points. — jgill

No, I think it is significant and general. To relate it to my own interests – the Cosmos – there is this same virtual vs actual wrangle over renormalisation in quantum theory. Either renormalisation is some horrible kluge to be eliminated by better maths ... or in fact finitude and its dichotomous cut-offs have to be brought into the maths of the infinite somehow.

What I would point out again is how complex numbers may have their Penrosian "magic" as they speak simultaneously to the symmetries or conservation principles of rotation and translation. The incommensurability arise at that point – the foundational distinction between spinning at a spot and moving away in a straight line.

A 0D point could be spinning, it could be moving. It has no context, so we can't yet tell. It is technically vague. No symmetries have been broken and so no symmetries have been revealed.

But as soon as we imagine anything happens, the foundational symmetry breaking is the Noether symmetries that close the world for Newtonian mechanics.

Newton starts the world already in motion. The first derivative. The zeroeth doesn't really exist even at a Gallielean level of relativity. And this Newtonian world is defined by its twin inertial freedoms – to rotate and translate. One keeps things anchored at locales. The other sends them moving and so carving out the global largeness of space.

This would be why you find that converging to a limit has this fractal coastline property. Rotation and translation want to be different. They exist by being incommensurate.

It is the old squaring the circle story. Pi is irrational as curves and straight lines are at root incommensurate. They have to be that to co-exist in the same world and so be the symmetry-breaking making that world.

Complex numbers then speak to how the two directions of free action – one closed and cyclic, the other open and expansive – can be united under a unit 1 symmetry description. They explain how the symmetry is selectively broken in a way that is special to a 3D continuum. You get the chirality and commutative order arising as something that materially matters – unique in that it can produce those local knots, or Newtonian particles, that can't unknot, in the style modelled by twistor theory or fibre bundles..

So it is not a mistake resulting from the simple collapse of a higher dimensionality into a lower one. It is about a complex collapse – a reduction of dimensionality to a 3D continuum that then sets you up in a world where the number of spin directions finally match the number of momentum directions.

The collapse produces the internal gauge symmetry where rotation and translation become the new thing – a breaking of the symmetry achieved in 3D. You can get a cosmos founded on Newtonian mechanics with the Noether dichotomy to close it as a world, make it safe for local knots of energy that can't come untied, just endlessly shuffled about like bumps in a rug.

In short, you can collapse dimensionality to SO(3) and discover it then spits out SU(2). The magic happens. Commutative order becomes a thing. Time is born. Space is anchored in a way that can be described symmetrically by spherical or Cartesian coordinates. Etc, etc. :grin:

And what of the cut off issue? I'm thinking this gives an argument in terms of the Planck scale representing a dimensional ratio.

The problem with infinities and infinitesimals is this urge to give them a concrete value. Or if not that, then they are processes without bounds. And neither answer is truly very satisfying in the light of physical reality.

The point about the Universe is that it is a story of fractal dimensionality or scalefree growth. The universe exists as a log/log story of cooling and spreading. This is both open and closed in some sense. And I've explained that in terms of it being an inversion at a deeper level.

It is going from very hot to very cold by going from very small to very large. Something is increasing as something is reducing. And if we look at a light ray, we see it is the same thing from opposite perspectives. Light waves – as your simplest sine wave or helix (the helix making the rotation~translation deal explicit) – are both stretched to their maximum possible extent and also redshifted to their maximum possible extent. They become as big as the cosmic event horizon and as cold as absolute zero.

So while we do like to measure all this using yardsticks like rulers and thermometers, it is essentially a dimensionless ratio. The Planck triad does not stand for some actual independently measurable number. It stands for a Platonic ratio - just like e scales unit 1 growth or pi scales unit 1 curvature. The cut off becomes simply the point where local spin and global translation first measurably come apart. And this is a qualitative distinction, not a quantifiable one.

The same goes for the Heat Death where everything arrives at its other end where the Planck triad are inverted - 1/planck - to give the cut off marking the other end of the effective 3D continuum. (Again, inflation and dark energy are unsolved aspects of this view.)

And this is why I argue for the numberline in these same terms - as the infinitesmal and the infinite as each other's reciprocal measure. A way to have the small and the large being both unboundedly open and yet also finitely closed.

The missing bit is that the numberline is based on naked spatial intuition. Peirce and Brouwer were trying to bring in time and energy (the two being complementary under quantum uncertainty) as the way to achieve the trick of an "open closure". Sure you can count forever. But that then takes time an energy.

You have two actions in opposition. This means that you can only expand until you run out of energy. And you can only contract until you run out of space.

Adding this to the numberline conception builds in the self-limiting finitude that the conventional spatial version lacks.

As I've said, Turing computation has run into a similar story of physical constraint. Infinity only reaches so far in a world where the gravity of being a hunk of circuits curling up into a black hole at a certain critical energy density – a cut off point.

So rather than either/or when it comes to taking sides on virtual infinity vs actual infinity, I've been pushing "both" in the dichotomistic sense for this reason. Openness and closure are what must emerge as themselves something that co-arise from the firstness of Peircean vagueness and become a combined continuity within the thirdness of Peircean generality.

A tricky business.

Okay, I accept that substance (continua) and void (0D points) and are both fundamental! — keystone

I'm thinking of something more irreducibly complex. A dimensionality that is "completely" void can't help but have some residual degree of local fluctuation. And likewise, a dimensionality that is "completely" full, can't help but have some residual degree of fluctuation – but of the opposite kind. Particles can appear in the coldest vacuum state. But holes or local voids can appear in the hottest vacuum states.

So you have here a system – like the Universe – with its reciprocal Planck cut-off conditions. Finitude that seals both its ends. The hot Big Bang is where there is so much of everything that there is no room at all for local somethingness – except as the smallest void-like fluctuations. Some fleeting patch of coolness.

This becomes the eternal spawning multiverse of inflation, for example, where the inflation field rages, but here and there, by a quantum fluctuation, some spot cools just slightly and that results in a phase transition. Another bubble universe – such as our Big Bang – starts to form at that place.

And then that nipped off bud of dimensionality keeps growing, keeps cooling and expanding, until it eventually flips over into its de Sitter state of a vast void – a space as cold and empty as it can quantumly get. And now it is the expression of the opposite thing of a nothingness with its residual minimum entropy particles. The void is now the hole that hosts the faintest possible sizzle of its own blackbody radiation – photons so cold that their wavelength is about 38 billion lightyears.

The point is that mathematics can conjure up all kinds of models based on simple premises. It can just take concrete starting points for granted, and take the resulting paradoxes as something to either ignore or even be a little proud of.

But physics is now pushing maths rather harder. It is time to be a bit more serious about eliminating those confusions. It is time to stop being so content with a reductionist metaphysics and to get serious about the modelling of holistic reality.

Physics and cosmology are highly concerned about how the Universe could exist – how finitude could be extracted from potential infinity.

Space, time and energy all look to have had a definite start at the Planckscale that defines the dimensionality of the Big Bang. The continuum was born of one cut-off that could separate the nothingness that could be found in the everythingness. The fluctuations that were the holes.

And then this dimensionality – by expressing the reciprocal actions of spreading and cooling – is on the long path to the other end of space, time and energy. The story gets inverted. The cosmos has become "all hole" – the largest nothingness – with only the faintest possible remaining sizzle of particle fluctuation.

So maths can have its petty wrangles over how to model infinity. It's inconsequential. But to the degree that the interpretation is holistic, it is going to be on the right side of history. And so the intuitionists and finitists feel more correct for that reason.

However what really matters – if we are interested in models of reality as it actually is – is the fact that finitude can be extracted from pure unboundedness. Closure can be extracted from openness ... if that openness is also being transformed from a vagueness to generality (in Peirce-speak).

The universe can exist as it is making the heat sink that it is falling into.

Although there are still big questionmarks. We still seem to need eternal inflation at the front end as a kind of somethingness to get the Big Bang ball rolling, and dark energy at the back end as also a kind of somethingness to deliver the de Sitter state that ensures an eternalised Heat Death cut-off at the other end.

The metaphysical riddle isn't yet solved. However the physics of the residual "somethings" has become highly constrained. And overall, they point to a holistic or pansemiotic view of existence – the triadic systems story where the container and its contents co-emerge from unbounded potential.

The small grows large. The hot grows cold. Symmetries are broken in ways that are themselves symmetric. By heading to infinity in either of these directions, you encounter the infinitesimal as a consequence.

The universe has an irreducibly complex generator in that it is a triadic and recursively self-referencing knot of relations. And any proper notion of a continuum would have to pull off that trick too.

I know, but as usual you don't see where I'm coming from. — bongo fury

I hope this is a prelude to you making an attempt to explain then. :meh:

...and with those abstract nouns. — bongo fury

So abstractions are banned from a metaphysical discussion. :up:

Do you mean, an indiscriminate application of colour words to the domain of things (or patches)? — bongo fury

Nope. As usual you don't see where I'm coming from.

Do you mean, you are able to apply the words in a manner that begins to distinguish two different though still overlapping colours? — bongo fury

Back to the abstract nouns I guess. Semiotics as a maximally general theory of meaning tells us signs point out the differences that make a difference, not just merely the differences. But then there must be a spectrum of differences of some kind such that there could indeed be the differences that make a difference that are then different from the differences that don't. ie: we want to be able to separate signal from noise in a crisp and dichotomous fashion.

So before acts of signification can be a thing, there must be a spectrum of differences to be thus divided into its opposing classes. And where does this spectrum arise in a fashion that can leave it also the generalised indifference which is merely the noise against which the difference that makes a difference stands out?

Confused yet? :lol:

Primal difference must be resolved back to an indifferent sameness that allows meaningful difference to exist – be actualised – as a second order contrast.

Its thermodynamics. Let loose a bunch of particles in a box. They all have different velocities and directions. In time, they will still all be moving differently, but they will have collectively arrived at some constant macrostate equilibrium. You have a baseline of indifferent difference that can now support a measure of significant difference. A negentropic fluctuation.

Whatever linguistic distinction that Goodman might want to make in terms of how the world is can now be made in a measurable fashion. We can have the particularity of actual events as we have the generalised anonymity of an indifferent ground – a state that is concrete and actual too.

So maybe you don't even realise that to make a mark on reality, you need a stable surface on which such a mark can endure. There are steps to take to reach the place in which you want to set up your metaphysical camp.

Goodman's approach is concrete and clear. Yours is abstract and poetic.

A discrete classification in no way has to imply a continuous one. — bongo fury

Goodman can kiss my arse then.

So not necessarily a matter of degree. Arguably a matter of discrimination. — bongo fury

I am talking about how the spectrum that allows your 50 shades of grey arises. This is confusing for sure. But after the separation of the potential, you get the new thing of the possibility of a mixing.

So we start with a logical vagueness - an everythingness that is a nothingness. We have a “greyness” in that sense. Something that is neither the one nor the other. Not bright, not dark. Not anymore blackish than it is whitish. You define what It “is” by the failure of the PNC to apply. You are in a state of radical uncertainty about what to call it, other than a vague and uncertain potential to be a contextless “anything”. It is not even a mid-tone grey as there are no other greys to allow that discriminating claim.

But then you discover a crack in this symmetry. You notice that maybe it fluctuates in some minimal way. It is at times a little brighter or darker, a little whiter or blacker. Now you can start to separate. You can extrapolate this slight initial difference towards two contrasting extremes. You can drag the two sides apart towards their two limiting poles that would be the purest white - as the least degree of contaminating black - and vice versa.

Once reality is dichotomised in this fashion, then you can go back in an mix. You can create actual shades of grey by Goodman’s approach.

I once had a holiday job mixing industrial paint in monster vats. It was amusing how my recipe for the morning for some company’s shade of white, used to paint their fridges, requires drums and drums of bright white, and then a few teaspoons of black, and indeed a touch of red, to make it “theirs”.

So once you separate, then you can create. With a vat of white and a fat of black, you can mix every shade of grey inbetween. But if you only have a vat of light grey and a vat of dark grey, your range is way more limited. And if you have two middle of the range greys, then it might be hard to know whether the two have already been mixed as your efforts at mixing look to be making no further difference.

This is the ontology. Potential gets divided, the divisions produce the further thing of a space of free possibilities - a spectrum of mixed states.

Everythingness Is turned into a set into of local particulars within some global bounding constraints, At which point, our everyday notions of t reality as a collection of medium sized dry goods takes over. We take the atomic particulars for granted and get on with constructing the mixtures that have become concretely possible. We don’t seem to need a theory of how this generalised somethingness itself came to be.

Your “argument” offers no evidence. Just makes rash and unreasonable claims.

For example, are you as free to be an airatarian as a vegetarian or carnivore? You can have all the “reasons” you like. The question is do you have actual choices?

And then, civilisation as the ultimately rational social structure is meant to maximise your personal choice. You can head to the supermarket gluten-free or Asian aisle.

Life in general is like that. A mix of general constraints and particularised choices. We can turn food into a moral dilemma. But we still must eat food. Go figure. And I didn’t invent this world. I just comment on how it is.