I was admitting that I may have made a mistake in my analysis of what you've been arguing. Perhaps a direct question would help.

Do you hold that universals are independent from language? — creativesoul

I’ve explained. Universals are constraints. Constraints are causal. Causal is real.

And then language is a semiotic constraint on meaning. Language can be generalised pansemiotically to talk about the machinery of constraints in general.

So in a loose sense - one far more general than your locution hopes to imply - all universals depend on language, or rather the semiotic relation by which constraints on being develop.

Most universals of course don’t rely on human language - human socio-cultural constraints. Tables and chairs do. Constructs like masculinity do. But a horse is a horse due to genetic level information, or constraints over bioiogical development. An electron is an electron due to more fundamental symmetry constraints over material development.

So the way you pose your question fails to recognise the greater metaphysical generality of the metaphysical framework I employ. Your question only seemed direct as it depends on a far more limited notion of causality and existence.

MU right, the world wrong. MU accepts unbroken as an antonym of continuous, but not as a synonym of undivided.

You’re in a hole. Quit digging.

And so we wind up in the usual place with you denying the most standard philosophical definitions....

We are all familiar with the idea of continuity. To be continuous[1] is to constitute an unbroken or uninterrupted whole, like the ocean or the sky. A continuous entity—a continuum—has no “gaps”. Opposed to continuity is discreteness: to be discrete[2] is to be separated, like the scattered pebbles on a beach or the leaves on a tree. Continuity connotes unity; discreteness, plurality.

1. The word “continuous” derives from a Latin root meaning “to hang together” or “to cohere”; this same root gives us the nouns “continent”—an expanse of land unbroken by sea—and “continence”—self-restraint in the sense of “holding oneself together”. Synonyms for “continuous” include: connected, entire, unbroken, uninterrupted.

2. The word “discrete” derives from a Latin root meaning “to separate”. This same root yields the verb “discern”—to recognize as distinct or separate—and the cognate “discreet”—to show discernment, hence “well-behaved”. It is a curious fact that, while “continuity” and “discreteness” are antonyms, “continence” and “discreetness” are synonyms. Synonyms for “discrete” include separate, distinct, detached, disjunct.

https://plato.stanford.edu/entries/continuity/

A short quiz.

Q1) When something is undivided, is it:

A) Divided?
B) Continuous?

Q2) When quantifying an amount of water, do we ask:

A) How many water is there?
B) How much water is there?

Q3) When quantifying an amount of apples, do we ask:

A) How many apples are there?
B) How much apples are there?

Q4: When you have fallen into a pit of logical incoherence, do we:

A) Keep digging?
B) Cease to dig?

(Answers on a back of a postcard...)

Thanks.

You make less sense with every post.

Sounds legit. Goodness knows why we always find ourselves talking about them in the same breath.

That a unit is potential divided into other discrete units does not imply any continuity. — Metaphysician Undercover

Sounds legit.

It calls things that are existentially contingent upon language 'independent' of language. — creativesoul

Where exactly?

Ignoring/removing... no difference. Setting them aside either way. — creativesoul

But it is a big difference. It is the difference between atomism and a structural holism.

One view needs to presume fixed parts. The other presumes a fundamental instability that can become suitably regulated.

So they claim opposite things about reality at a fundamental level.

Language is related to the world by virtue of the attribution of meaning — creativesoul

Nope. Meaning arises out of the relating. The meaning of words is stabilised through the functionality of habits of use. Language is shaped by the work it does, the purposes it serves, in our interactions with the world.

My participation in this thread was motivated by my own unconventional use of 'universal' which is more about being a common denominator... being universally extant within all X after removing the individual particulars. — creativesoul

No need to remove them. A constraints-based logic simply ignores them as differences that don't make a difference.

So a compositional approach - one predicated on construction or addition - wants to understand its "other" of universality or generality as that which can survive all particular acts of subtraction. That is how it seeks dichotomously to complete itself. What can you take away and so arrive at "the particular essence".

But this ontology doesn't really work, as we know.

So a constraints-based approach is more like the pragmatism of Wittgenstein's family resemblances, or even ways of life. A state of constraint merely has to tolerate difference. Stability of identity emerges once a system is in some equilibrium balance and further change ceases to create significant change.

So no need to remove individuals. They are only noticed if they matter.

Is a penis definitional of a male? Well biologically, there is a family resemblance to speak of. But maybe it is a stunted micro-penis or maybe this male has two of them.

The identification of this individual as a true male might come into question on biological functional grounds. Is there still some possibility of this individual impregnating a mate with his appendage? At some point, the "penis" will have such a low probability of functioning as intended that it is not fit for purpose.

But the line is somewhat arbitrary precisely because probability is involved. A misfit penis might on occasion still do the trick. The difference might not make a difference as a matter of chance.

So a constraints-based approach is the one that gets the probabilistic nature of reality. It is flexible in its definitions, whereas a compositional approach has this unnatural brittleness when applied to the world.

(Hence Bayesian reasoning!)

Divide the inch into halves, quarters, however you wish, they are still all discrete units. — Metaphysician Undercover

And yet all still capable of further sub-division apparently. And how can there be further division if there is nothing further that counts as the undivided?

Your mathematical logic doesn't really seem all that water-tight, eh?

You have been switching back and forth at will, — Metaphysician Undercover

I was simply trying to keep pace with your flip-flopping. One second, measurement units. The next second, actual things.

I would think that clearly penises are not existentially contingent upon language. Thus, "penis" sets out something that is properly called "independent" of language, for it is not existentially contingent upon our taking account of it via naming it. — creativesoul

Dicks are real and not linguistic inventions. This must be progress!

As mentioned earlier, the difficult part seems to be devising a method by which we can assess something with regard to whether or not it is existentially contingent upon language. — creativesoul

So you won't answer the direct ontic question - are you backing realism or nominalism. Instead your issue is epistemic - how could we determine the matter either way. Where is our "access" to reality.

And yet pragmatism has already been "devised" as a method. :-}

A penis does not a man make. Geckos have those. — creativesoul

What? Even the females?

If being a universal requires existential independence from language, then all universals must consist entirely in/of that which is not existentially contingent upon language. — creativesoul

Are you continuing with this nonsense even after I explained why it is nonsense?

A structuralist approach to language use emphasises its role in the construction of a social reality. A semiotic generalisation of linguistic structuralism shows how reality in general is the product of structuring constraints.

So if we are talking ontology, then human language use really does construct humans - at a social level. But it doesn't construct them at a more basic neurological or biological level. You need the language or neurons or genes to do that.

So when Aristotle started the business of thinking about reality in structuralist terms, he could see that the universal definition of "a man" would have to reflect these levels of organisation. Men were reasoning animals that might even participate in an even more abstracted logical realm of semiotics.

But Aristotle didn't know about genes and neurons. So that is why his approach to substantial being was a little hazy on the details of what might properly constitute the different levels of structuralism going on.

So my complaint - which you have so far failed to answer clearly - is that you are bringing an epistemic quibble to an important ontological debate. You are simply saying all knowledge of reality is linguistic and so every concept a cultural construct.

Well, yes. It is a pragmatic fact that we need a more abstract semiotic machinery - like language - to do the meta-structuring of our biologically and neurologically structured experience of the world. Pigeons can categorise. But speech let's us take it to another level. And formal mathematical language can take us a step even beyond ordinary language. All this is epistemically understood.

But then it is an ontic category error to confuse the linguistic basis of knowledge with the knowledge claims then being made.

So "being a universal known as a man" has to be understood in terms of what constraints really form "a man". And it is an ontic mixture. Social constraints - our shared cultural image of masculinity - clearly play a real part in producing "real men". A man can be measured by the degree to which he does or does not conform to some generic cultural stereotype.

But then there are also the neurological and biological constraints in play. Any reasonable use of language is going to acknowledge this at least implicitly. A man has a dick, two balls, and the usual complement of X-chromosomes, on the whole.

He is generically an animal while also generically a reasoning being. And neither of these generalisations are "social constructions". They are both accounts of the reality. It is just that the cause of this reality is on some levels genetic and neurological, on others social and cultural.

Maybe you get this, maybe you don't. But you seem to be striving to blur the line between social construction as an epistemic issue and social construction as a cause of substantial being.

You keep repeating your magic phrase - "existentially contingent upon language". Well some aspects of "being a man" are clearly existentially contingent on the cultural ideas that only language encodes.

It we were talking about bacteria, or stars, then no, our conceptions of them have very little bearing on their existence. We can exert some constraints on bacteria - like inventing antibiotics and seeing them evolve resistance. But really, we don't construct their existence through just talking about them.

However palaces and fences and iPhones are examples of other kinds of objects - artifacts - that are clearly very dependent on the games of linguistic social construction. Through our conceptions, we are the causes of their existence - the reason why they exist materially.

Perhaps it is unfortunate you picked on such a confusing example of "a man" as your example of a universal. It could be a good example as it illustrates the hierarchical nature of structured being. But only if you are already clear about the pansemiotic underpinnings of structuralist holism.

Snore....

Having done so, I'm waiting for a sensible reply. I realise that will never come.

Of course not, that would be contradictory to say that a continuity has bounded lumps. If it has bounded lumps, it is not a continuity. This is simply a matter of avoiding contradiction. — Metaphysician Undercover

So how do you divide up a foot into inches unless there is some underlying continuity to be divided?

The "unit", being an individual thing cannot be defined by a dichotomy, it can only be described. — Metaphysician Undercover

So now you have switched track from epistemology back to ontology? One second we are talking about units of measurement, the next about actual substantial objects out there in the real world?

Always a pleasure doing business with you, MU. ;)

But sure, a complex substance is going to be predicated of multiple dichotomies or universal contrasts. But surprise. That is why Aristotle defined complex being in terms of hierarchies of constraints.

Your compositionalism vs Aristotle's structuralism.

So you are going to bore me with repetition as usual? I've already told you why I don't agree. Your move.

The candidate is what counts as being "a man". Are you saying that being a man doesn't involve - in large part at least - of being a composition of things that are not existentially contingent upon language? — creativesoul

I'm saying that counting shaping or structuring constraints is different from counting compositional elements.

So you are thinking like a reductionist. Aristotle was thinking like a holist.

Ad homs are a sure sign that one doesn't have an argument. — creativesoul

Hey, you just invented a new category of fallacy!

I said that a continuity is measured by discrete units. — Metaphysician Undercover

So are these discrete units bounded lumps of continuity or not?

What dichotomy properly defines your notion of "unit" here. Clearly you have in mind the idea of a sameness that repeats. We can cut the whole into a set of similar parts. The one can stand for the many.

I see a whole tangle of metaphysical dichotomies in play here. The usual story. As it should be.

First, the concept would need to be one that sets out the elemental constituents of the candidate in question — creativesoul

So I am right that you simply fail to get what a structuralist ontology is about? You are wedded to logical atomism. Aristotle wasn't.

A degree is a discrete unit. By measuring a continuity in degrees, you are applying discrete units to the continuity. — Metaphysician Undercover

So now you are saying that a unit is a continuity chopped into discrete pieces? That is, it places limits on the continuous so that bits of continuity can be treated as the same and thus counted as repetitions. A degree is a difference that isn't a difference fundamentally, just the very same thing happening all over again?

Hmm. Seems familiar.

If a thing is hot, then it is not cold. To say that a thing is hot to the degree that its not cold, is to replace a clear logical principle with an ambiguous one, allowing contradiction that the thing be both hot and cold, qualifying this with the ambiguity of "by degree". — Metaphysician Undercover

So much for Aristotle's distinction between contradiction and contrariety then. What a goof that guy was!

The temperature is meant to be objective and any temperature in itself, is neither hot nor cold. — Metaphysician Undercover

Depending on the application, what is hot by one standard might be cold by another, but the independent standard allows us to avoid the nonsense of "it is hot to the degree that it isn't cold". — Metaphysician Undercover

Do you ever read what you write? Or is making sense utterly irrelevant here.

The difficulty, it seems, is developing a method for taking account of which constructs set out that which is existentially contingent upon language, and which ones set out that which is not. — creativesoul

Pragmatically, where is the difficulty?

You seem to want to turn an ontological question into an epistemic one. Your tactic seems to revolve around emphasising the doubt that we can truly know reality because we only know reality via the structure of words.

But while that is a routine epistemic challenge, it is pretty irrelevant once you accept a pragmatic approach to belief and just get on with ontologising.

Yes, language is a reality-making game. But then was Aristotle using ordinary speech or pioneering a new logical level of semiosis to "talk about" the universalised concept of "a man". Are you actually critiquing Aristotle here if you are only merely carping about ordinary language usage?

His method seems inadequate, or 'hazy' as you say. — creativesoul

What I am emphasising is the structuralism that was implicit in his substance thinking. The holistic causality used to account for the nature of Being.

So your comments seem overly focused on linguistic structure. And even linguistic structuralism - of the familiar Continental/Saussurean type - strives after a more sophisticated triadic or holistic reading.

Proponents of structuralism would argue that a specific domain of culture may be understood by means of a structure—modelled on language—that is distinct both from the organizations of reality and those of ideas or the imagination—the "third order".

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

And then we now know enough about biology and neurology to see how those are also levels of organisation that are the product of semiotic codes. Maths and logic - as languages - are a still higher level of structuration.

So there are men as biological animals, men as socialised humans, and men as rationalising scientists and mathematicians. Three levels of substantial being right there. :)

What counts as being a "man" is what one is taught counts as being a man. That varies tremendously from group to group, or it can at least. — creativesoul

So is a penis a social construct? Is an X chromosome a social construct?

Sure, social construction is a thing. But so is biological construction. And semiosis recognises other kinds of "language use" beyond just words, like the language of the genes.

Aristotle was right about humans as substances as their being is organised by a structure that is more than accidental. Genes and neurons encode a purpose and a design. There is a reason why bodies and behaviour hang together, or endure.

Aristotle was hazy about the detail. Yet he was a structuralist. And a social level of construction - the one that employs actual language - needs to be understood in similar structuralist fashion.

He initially learned what counts as being a man the same way everyone else does. — creativesoul

So you are talking past what counts in terms of biology so as to focus on what counts in terms of culture. And yet both of these are realities of the experienced world, not imaginative fictions.

Definitions of masculinity might change as the needs of particular social systems evolve. But anthropologists can find the structural logic, the evolutionary sense, that explains the prevailing definitions. Or else they can show how some signifier of masculinity - like wearing a tie - is a symbolic "accident".

Social constructionism is properly a theory about social realities. It doesn't mean culture lives in a fictional world. Culture is all about the symbols that are the language which can be used to structure a world of social meaning.

What makes the measurement meaningful is its relationship to something outside the category of the things being measured. — Metaphysician Undercover

So when you measure a degree of continuity, what else do you measure that against except a corresponding degree of absence of discreteness?

A is continuous to the degree it isn’t .....

Go on. Try to fill in the blank with a word that doesn’t mean discrete.

As I said, you have no description of the qualitative difference between what has already been, and what will have being in the future. What you express is the description of an agent at the present, who has constraints relative to the past, and freedoms relative to the future. You have no description of what it means to be constrained or to be free. — Metaphysician Undercover

Agents?

My account was rather more general than that.

Here's an example. Say we have hot and cold, as dichotomous terms which define each other, with degrees of difference assumed to be "between" them. By defining hot with not-cold, and cold with not-hot, and degrees of difference, we have no description of those qualiies, what it means to be hot, or what it means to be cold. So if you proceed in this direction now, to define what it means to be hot, and what it means to be cold, you'll see a fundamental difference between them, such that hot and cold are completely distinct ideals which cannot be related through the degrees of difference. — Metaphysician Undercover

Hot and cold are defined by a temporal asymmetry - a direction in which time or change flows. So cold is more than just not-hot. It is a state of maximum entropy. While heat is then the opposite in being an order or energy - a negentropy - available for dissipation.

We have some exact maths that describes what we now mean by differences in temperature.

Hot and cold are discrete, while the degrees of difference are continuous. — Metaphysician Undercover

This is rubbish.

In all such instances there is an incommensurability between the discrete (hot and cold, constraint and freedom) and the continuous (degrees of difference). Incommensurability is beyond the capacity of mathematics. So we have an incommensurability between the continuous existence of the agent at the present, and the two discrete things, constraints of the past, and freedoms of the future. That incommensurability cannot be grasped with mathematics. — Metaphysician Undercover

Good try. But completely irrelevant argument.

The maths of limits works. My approach explains metaphysically how it could in fact work. It explains in what sense there are limits to approach even if these limits could never be reached.

If one extreme of a dichotomy is defined by its "distance" from the other, then it is both possible always to be measurably moving towards one limit - by measurably moving away from the other limit - while also never arriving at this other limit, as then that would result in the nonsensical claim of having left the other limit "completely behind". The other limit would have to have vanished. And what then could measure a distance from it?

You're missing the point. — Metaphysician Undercover

You're avoiding the point. If we were still sitting around on our chuff, not doing the maths, we'd still be convinced by Aristotelian level physics no doubt.

But there are fundamental differences which cannot be expressed as mathematical relations, such as the dichotomy between future and past, the difference between what has been and what has not yet come to be. — Metaphysician Undercover

Huh? The past is the constraints on future degrees of freedom. The future is the remaining free possibility that the past hasn't managed to constrain. Of course the definition is reciprocal.

The patterns of nature are revealed to us before we apply mathematics to them. — Metaphysician Undercover

Maybe before science got going and the game changed.

Did pre-scientific folk intuitively believe that cannonballs followed a parabola, or that a rolling ball on a frictionless plane would roll forever?

Was that much of nature really revealed by an Aristotelian level of physics?

Three centuries of mathematical empiricism have bent the modern mind to a single interest in the invention of engines for the control of phenomena - a conceptual network, which procures for the mind a certain practical domination over, and a deceptive understanding of, nature, where thought is not resolved in being but in the sensible itself.

Maritain, The Degrees of Knowledge

There's your 'immanent metaphysics' in a nutshell. — Wayfarer

A silly reply if my immanent metaphysics is what I've said it is - a full four causes naturalism.

He was hardly a systematic or monolithic thinker. — Wayfarer

Are you kidding?!? That's like saying Led Zeppelin was hardly a rock band. :-O

The fact that he was an idealist philosophy is something you continually try to deprecate, but it is a fact nonetheless. — Wayfarer

And yet he started from psychology - from a proper kind of cognitive and evolutionary idealism, not a muddled mystical one - and worked his way outwards to recover the material world.

That's only a matter of perspective. The other perspective claims that making categorically distinct things, like the sensible and the intelligible (the particular and the universal, material and immaterial), into two poles of one category, with degrees of separation, is the real mistake. — Metaphysician Undercover

Well if a dichotomy is a mistake, you should be able to expose that fact.

For instance, the material and the immaterial is indeed a weak-arse dichotomy. It is just a simple negation. It is the claim that there is the material .... and the not-material.

Well what can you really make of a vague distinction like that - one without proper self-grounding context?

Matter and mind is also a bad dichotomy - one that doesn't really make intelligible sense as I keep telling you. There is no formal reciprocal relation being described.

A properly formed dichotomy is one that is self-grounding, self-contextualising, in being reciprocal or inverse. A is not B because it A is 1/B. That is, A-ness contains or partakes of the least possible degree of B-ness. And B-ness in return is defined by containing or partaking in A-ness to the least possible degree.

That is why information and entropy make a nice dichotomy. Informational certainty is inverse to entropic disorder. There is a formal connection via the reciprocal relation. Each others its other to become itself. The greater the separation, the more sure the polar distinction.

It's the same with the infinite and the infinitesimal. They are defined as each other's reciprocal. And physics has found the same duality in the Planck scale. And that is what has got physics so excited about holography - the duality of fundamental theory found in the AdS/CFT correspondence.

So there are clear rules for forming proper dichotomies. It's not a matter of "perspective". It is an exact mathematical relation.

Again, that is why I champion semiotics. The possibility of information arises at exactly the point when physics is at its most constrained, or mechanical. One can see the connection by which a fundamental distinction must emerge. If you limit physical dimensionality - degrees of freedom - so that it approach zero, then you get the emergence of the counterfactual possibility of a symbol or informational mark.

Life is chemistry reduced from its 4D chaos down past 2D surfaces and 1D chains all the way to the possibility of zero-D codes. DNA is a strand - a linear sequence. Any codon could be the next in line. That reduction of physical causality - the fact that any codon could be next - then allows DNA to represent pure information. Or at least a variety of amino acids that can be connected in a 1D chain to curl up and act as a 3D shaped message, an effective cause, in a 4D brew of cellular action.

It is this form of idealism, the desire to make all things mathematical, which drives this mistake. So of course the mathematics will support it. — Metaphysician Undercover

Mathematics reveals nature's fundamental patterns. So a lack of mathematical rigour is always going to be the actual mistake.

Writing helps clarify thought. — Mitchell

Exactly. And an unreceptive audience is a help in making the effort as you get old and lazy. :)

It keeps the ideas circulating as well as making some fresh connections. I used to write books. I might well start another next year. The problem is I don't feel any burning need to.

It's only for my own benefit. I don't expect people to read them. ;)

This means that in the case of sense knowledge, the form is still encompassed with the concrete characters which make it particular; and that, in the case of intellectual knowledge, the form is disengaged from all such characters. To understand is to free form completely from matter.

This is an example of the bad thought habit I just highlighted - turning a "soft" contrary into a "hard" contradiction. It is the reductionism you always complain about.

So it is not a problem that knowledge is structured by it having two poles of being - ideas and impressions, concepts and percepts, rationality and empiricism.

Psychologically, we know it is just a fact that our mentality is divided in this fashion. But the big mistake is to turn it into some absolute ontological separation - the duality of a hard contradiction - when really it is only the relative thing of a dichotomous contrariety.

If you turn to a powerful model of a "knowing system" - like Stephen Grossberg's Adaptive Resonance Theory (ART) neural networks - you can see this point made mathematically and explicitly. He models awareness in terms of a "long term memory" layer in interaction with a "short term memory" layer. So the basic potential here is "memory" - a state of encoded representation or response. And then hierarchically, all you need is a contrast of characteristic timescales. Sense data or impressions are the immediate reaction to the events of the moment. Concepts or ideas are the long term memory states that create the more general context that can interpret the particular events forming a perceptual state in the short term memory layer.

It is an important fact that the best mathematical models of psychology support the view that ideas and impressions are not hard contradictions - a dualism - but only a soft or relative state of dichotomisation.

All mindfulness boils down to a "memory response" - some intra-layer neural competition that is an adaptation of internal state to some applied perturbation (a changing environment). And then you get a useful structure, a complexity of response, just by a separation of spatiotemporal scales of adaptation. Ideas vs impressions is a natural divide that "processes" the world in a balance dichotomous fashion.

So you are enthusiastic about philosophical approaches that appear to endorse full-on dualism. Science misses something as it rejects a hard division of reality into the material and the immaterial. Science is wrong in thinking that materiality vs immateriality is only a relative affair so far as its physicalism is concerned. You take it as just an obvious fact that there is an empirical world that is available to the senses, but then an actually separate rational world that is available to ... the nous, the mind, the secret sauce spirit.

Yet natural philosophy rejects actual dualism. And science supports its immanent understanding of nature.

Dichotomies or symmetry-breakings are how nature achieves intelligible structure. So - in its highly developed state - nature will appear to be broken by its dualities. But mystery is avoided by recognising that any such duality can only be soft or relative. A pair of developmental contraries, not a pair of existent contradictions.

But if you want to keep lapsing into a reductionist ontology, and then complaining bitterly that "science" doesn't accept the resulting hard dualism, that must be your private psycho-drama in the end. A properly organic conception of nature doesn't even need to go there. It can show that the dualism is always the product of a semiotic or epistemic "cut". Any division must arise out of a shared commonality.

And resolving that division means dissolving it back into a state of vague potential. It is not logically permitted to collapse all the material aspects of the account to immaterial ones, or vice versa.

If Peirce were an "objective idealist" in the sense that you keep wanting to claim, then he would simply be wrong by his own lights. There would have to be something very queer about his thinking. He would have to be contradicting himself.

But if you read him as talking of structuring contrarieties, then you can see he was emphasising the complementary nature of reality - its hylomorphic organisation where even the Cosmos at its most physically simple can be considered to have mind-like features.

Poetically, matter is effete habit, deadened routine. Substance at its most unlively.

You can read it as an endorsement of transcendent theism if you like. Plenty read it as an endorsement of immanent panpsychism.

But perhaps it actually is just this organic thing, this middle path between hard realism and hard idealism, that one would dub pan-semiosis.

Essential attributes and accidental attibutes are both properties, and properties are universals. — Mitchell

What is more important here is that the accidental and the essential (or the necessary) are a dialectical dichotomy - defined as a mutually exclusive and jointly exhaustive pair of complementary terms. And so through the unity of opposites, we can track their emergence from pure possibility (vagueness) as each other's mirroring generality.

In the view I am taking, all universals are not singular but dual. True generality is defined by matched pairs that speak to opposing extremes of realised being.

So if I say form, you say matter. If I say discrete, you say continuous. If I say chance, you say necessity. If I say flux, you say stasis. And so on through all the fundamental ontologically-basic categories.

Once the duality, or complementary logic, of "metaphysical strength" universals is accepted, then it becomes obvious that the two need the third thing of a ground of common being from which they can arise as the opposed limits of "the possible". They point back to their own grounding in vagueness - pure potentiality - by the very fact that they represent the counterfactual extremes on that possibility.

For the discrete to be distinct from the continuous - for that distinction to be actualised in a general way by a world - then each must successfully exclude all possibility of its "other". Thus also, the possibility of the "other" must exist to actually get excluded in this fashion. The potential is defined (in dichotomous contrast to the actual!) as then the state where nothing is yet excluded. So before the dichotomy can be the case, there must be the third thing of a vagueness that is neither discrete nor continuous in any degree ... a state that is just the potential for such a division to arise.

Of course, not all "universals" are metaphysical strength dichotomies. That is where a lot of confusion starts. Whiteness is a reasonably strong universal, in being the complete opposite of blackness. But a horse is really a fairly particular "universal".

The concept of "a horse" sort of excludes donkeys and mules and zebras. But the boundaries are vague. And more importantly "a horse" does not stand completely opposed to any other generality. A horse is a living organism as opposed to an inanimate object. A horse partakes of more fundamental metaphysical dichotomies. It is a continuous whole in terms of itself, a discrete part in terms of its world. But even here, the boundaries of the concept of "a horse" remains vague. Is the sweat that is about to drop off the horse still part of its structural continuity or now part of what counts towards defining its structural discreteness?

The problem with the conventional take on universals is that people try to reason about them using the logic of particulars - the predicate logic secured by the three laws of thought. Peirce unpicked that logic by showing that generality is rightfully defined by the LEM failing to apply, and vagueness by the PNC failing to apply.

This opens up the system of reasoning so that we can see that what defines the metaphysically fundamental categories is the absolute division they achieve via dialectical opposition. The discrete and the continuous mutually define the extremes of a certain kind of universal possibility. And in defining the extremes, they together point back to the undivided potential that must have been there to birth them.

Aristotle of course tackled this in his Organon in contrasting contradiction and contrariety.

Two statements are contradictory if one affirms or denies universally what the other affirms or denies particularly. But two statements are contrary if one affirms or denies particularly what the other affirms or denies particularly of the same thing.

So a contradiction excludes a middle, but a contrariety admits to a middle. The same substance - your soup - could be hot, or it could be cold, or it could be anywhere in between. If all soup is hot, then it is a contradiction if your soup is cold. But if my soup is hot, then it is only a contrary fact that yours is cold.

The trick then is to see that when we speak of universals as the product of dichotomies or dialectical opposition, we are now contrasting two particulars. They are only contrarieties (as if they were contradictions, then one couldn't even be considered a possibility, and if one wasn't possible, then its "other" can't even be crisply defined).

If the poles of a dichotomy are only contraries, then only the vague, or pure potentiality, counts as some actual monistic universal - but now an apophatic one, defined by its actual non-existence.

What actually exists is not the "oneness" of this potential but the "many-ness" of the divisions that proved to be possible. So universality unfolds hierarchically in the manner first articulated by Anaximander (well, metaphorically by the Hesiod also). That is, metaphysics seeks to identify the most general dichotomies (or symmetry breakings) that then led to the increasingly more specific ones.

Anaximander actually managed a strikingly thermodynamic view. The Apeiron first separates into the hot and the cold, then follows the division into the dry and the wet. Earlier I highlighted the fundamental division that modern physics appears to have arrived at - the two basic "directions of action" of a (gravitational) integration and a (quantum) differentiation.

But whatever the story, the logic is the same. A first most general symmetry breaking paves the way for a casade of further symmetry breakings. Universality has hierarchical organisation - an unfolding direction in time. The most general change sets the scene for more particular change. And every metaphysically significant change takes the logical form of a dichotomisation.

Hence why hylomorphic substance was taken by Aristotle to be the foundational state of being. The combo of en-mattered form and in-formed matter. Everything definitely begins only when material cause and formal cause are brought together in an actualised state of contrariety - when they are realised with the middle ground that connects them as the matched extremes of a state of possibility.

But then when did these two "actions in directions" first arise? The talk of prime matter and prime mover tries to bypass this question by just claiming their actuality, their divided particularity, as something static or eternal. So again, to get beyond the usual impasse, we have to have a triadic metaphysics where the grounding potential is defined apophatically in terms of what we consider to be the most fundamental pair of universals. If this is form and matter, then that is what a vague beginning swallows up.

Substance can't be the substrate of substance. But a potential could be divided in any fashion by a dichotomisation. And logically - reversing the hierarchical story to be seen in metaphysical development - the first dichotomy is then going to be whatever is the most general possible one. If generality has to set the scene for specificity, then that is why Anaximander (or the Hesiod) intuitively sought the most general possible dichotomy as the first act of world-creating symmetry breaking. And - back to modern physics - why a theory of quantum gravity seems fundamental to explaining the "how" of a Big Bang creation event.