I will add that the expression that mathematics is 'in the world' is meaningless, just as it would be to say that a carton of eggs contains the number 12. Mathematics gives us a common symbolic means to describe, quantify and understand the world in a way that is not just based on individual perception but is grounded in a shared understanding and inherited knowledge. — Wayfarer

That summation should put an end to this thread. But of course, we can argue about the pertinent meaning of each word in the last sentence. The short answer is "Yes". But what do you mean by "in", or "embedded", or "grounded"? :wink:

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This summary of Tegmark's mathematical universe is interesting — Lionino

The universe isn’t math unless the ‘same thing different time’ applies to natural phenomena rather than our pretending to hold it still so as to calculate it.

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The universe is not math unless the regularity of the laws of physics is true? I have not read "Our Mathematical Universe" but I am convinced Tegmark addresses that — Lionino

The truth of the regularity of the laws of physics is not relevant to the question I raised. Truth as correctness comes from comparing a model of the phenomenon to the phenomenon. If they correspond then the model is ‘true’ to the observed phenomenon. What is at issue in my question is whether an abstraction may be involved in treating the model and the phenomenon as self-identical during the comparing process. There is no question we have produced a large collection of true mathematical statements in physics, and that these true statements of mathematical physics make many technologies possible. The question is whether we can come to a more fundamental understanding of modeler and phenomenon, subject and object than that which begins from the assumption that both hold still during the comparing process. Such an understanding does not invalidate mathematical truths , it shows them to be derivative and opens up new possibilities for understanding the world and ourselves

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the mathematics of the phenomenon is pretty much the phenomenon itself lato sensu — when a neutron decays into a proton and an electron, the only things happening are numbers changing — Lionino

Think about what is happening when a number changes. In the first place, what must be assumed about a phenomenon such that a number can be assigned to it? The phenomenon must be assumed to have a qualitative core that remains the same while we count increments of change within it. We usually think of numeric change in terms of the model of motion. When we measure the movement of a ball we count changes in degree of spatial displacement of something that is assumed to remain continually self-identical as the qualitative meaning ‘this ball’ throughout the countable changes in its location. But what if the quality we label as ‘this ball’ never persisted from one moment to the next as the same qualitative thing?

There would be nothing self-identical about which to count increments of change. Put differently, numeric quantification depends on our ability separate difference in degree from differences in kind, qualitative change from quantitative change. This is what ‘same thing, different time’ means. What poststructuralist authors argue is that it is only by abstracting away, that is, by not noticing, the continual qualitative changes in the substrates of our counting that we end up with a universe of objects which appear to behave mathematically. They argue that in fact every change in degree is simultaneously a difference in kind. And this applies not only to objects in the world, but our cognitive schemes. It is not simply that there are no perfect shapes in nature, but that even in our own imagination there are no perfect shapes.

As Heidegger writes:

“The most insidious manner of forgetting is the progressive "repetition" of the same. One says the same with a constantly new indifference; the mode of saying and interpreting changes.”

It is only as a result of our own conjuring trick that we produce a world that is remarkably amenable to numeration.

This does not at all mean that our physics is incorrect, that we have to go back and change all our calculations. It just means that there is a more intricate kind of behavior taking place in what the physicists observe and model , a behavior the requires a non-numeric language in order to understand it. The need for this language, and its advantages over mathematical forms of description become more clear in the social sciences than in the natural sciences. This is not because we understand these phenomena less well than we do the physical realm. On the contrary, newer approaches within psychology reveal an understanding, still lacking among most physicists, of the qualitatively shifting dynamics underlying mathematical objectification.

You likely will not agree with any of this, but at least it may give you a better sense of why postmodernists have a bug up their ass about the mathematical grounding of science, truth as correctness and propositional logic.

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Numbers are not assigned to things, but they are all that things are, and our scientific theories seem to support this to a certain extent. Fundamental particles are in fact a collection of numbers, among which mass, electric charge, isospin, weak hypercharge, spin, lepton number. You may say these are the qualitative core(s), but that is a simple rebuttal that suffers from the same gaps as just stopping at the fact that they are quantitative. — Lionino

Numbers wouldn’t be assigned to things, but since number implies a process of identical repetition, it would commit things to a certain structure, that a thing repeat some attribute or property identically. Why does quality suffer the same gap as stopping at the fact of quantity?Doesnt quantity require quality but not the reverse? Can there be a quantity without a quality, category, whole, entity, species to be counted? Put differently, when Tegmark says mass, electric charge, isospin, weak hypercharge, spin, lepton are numbers, don’t we have to ask what it is that continues to be the same again and again ( number) in these entities, qualities , categories, properties?

Ball would be a human label (baggage) emerging from a collection of things (atoms and such). It is always changing as everytime it bounces it loses atoms off its surface, but then we end up not in metaphysics but in a discussion of semantics — Lionino

This isn’t just semantics but the fundamental basis of number as the repetition of ‘same thing, different time’. As soon as we say something ‘is’ a number, we have committed ourselves to a certain way of defining that something, as persisting self-identity. If Ball is a human label, what is a collection of things in themselves? The ball may change every time it bounces, but, what do we say about the atoms it loses off its surface? Are these not treated like the ball , as self-identical objects in motion? Or as fields of forces with assigned properties which are enumerated as identical repetitions of the same entity?

a lot of philosophy relies on the validity of the idea of repetition and of identity. We can throw those out at a very fundamental level, but at some point we will have to grant them if we want to progress.
There is no such thing as tissues, just a collection of cells that are made of molecules. Yes, but we can't derive biological laws from chemical laws due to the sheer complexity and also to possible emergent features. We must grant that there is such a thing as tissues if we want to come up with medicine. — Lionino

you could say sociology comes from psychology, which comes from neurology, which... from physics. But you can't say the converse, that physics comes from biology or that chemistry from neurology. The more derivative a field is, the more baggage it has, specifically because it goes away from the foundations of the universe. Another issue is that sociology and psychology are very unreliable (papers have very low reproducibility) while physics is almost always reliable — Lionino

A main reason why we cannot reduce the higher order sciences to the lower ones is that typically, the lower ones , such as physics, use a more traditional scheme of understanding than the higher ones. Physics today for the most part stays within a model of realist causation , although there are strands of newer thinking within the field, such as Karen Barad, which are allowing physics to catch up with the thinking that has been available within philosophy and psychology for a while now. For a long time, physicists, including Hawking, denied the relevance of time for the understanding of physical phenomena. But Lee Smolen and others, thanks to their embrace of ideas from biology and philosophy, are showing the absolutely central importance of time for understanding physics. So while it should in theory be the case that we can reduce philosophy to cognitive psychology , cogsci to neuroscience , neuroscience to biology, biological to chemistry and chemistry to physics , it turn out to be a circle , where the most complex human sciences come up with new ways of thinking that eventually make their way down to the natural sciences, which are reliable precisely because they are so abstractive. But the broad, simplifiying abstractions of physics have their downside, such as pushing into the convenient category of randomness whatever their simplifications cannot model.

We can progress in different ways. One form of progress relies on repetition of identity. Another form of progress relies on showing how the repetition of identity is derivative from differences upon differences. The first form of progress leads to normative ethics based on an empirical realism that assumes we are all living in the same natural world, thanks to the grounding of empirical certainty in the identical repetition of properties within natural objects. Since it assumes a verifiably same world for everyone, there are correct and incorrect, true and false understandings of this same world for all. As a consequence, political polarization, holocaust, atrocity and other forms of social violence must often be explained on the basis of wayward intentions and motivations of individuals and groups ( greed, dishonesty, evil, immorality, hunger for power, sadism) or ignorance (‘drinking the Koolaid’), rather than the result of an ethically legitimate worldview askance from one’s own.

The poststructuralist can claim all he wants ("every change in degree is simultaneously a difference in kind"), but until he proves Π, I can just ignore him on this topic because it has explanatory power for me to do so. Mathematical universe is a theory about the universe, it takes our perceptions as they are, without doubting our modes of cognition as they appear, without taking phenomenology into account. — Lionino

Again, I’m not denying that physics has explanatory power. Accepting poststructural thinking doesn’t take away any of that power. It leaves it completely intact, but enriches it. My mode of perception makes things appear for me exactly as I described it to you. Since we are accustomed to seeing our world in terms of self-identical objects , it take a bit of practice to make ourselves explicitly aware of what is already implicit within that perception. Husserl’s method of phenomenological reduction through bracketing our naive naturalistic attitude ( which physics remains stuck within) is one way of gaining entry into this implicit intricacy hidden within the abstraction of self-identical persistence that we place over what presents itself to us as a continually qualitatively changing flow of sense.

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Very importantly, as a matter of empirical fact, we have not found anything in the universe yet that cannot be reduced to numbers. — Lionino

Think of 3 dogs, 3 apples, and 3 cups. They are all 3s, but denoting the different objects.

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How do we know whether quality or quantity is fundamental? Or rather two sides of the same coin? Does a quality, to exist, need not to show quantity too, being either one or many, zero being not existing?

The idea of the mathematical universe is not that quantity or quality are fundamental, but that all the properties that there are are mathematical. There are no non-mathematical properties, science seems to support this — Lionino

There are, of course, widely varying ways of understanding the relation between quality and quantity. For instance, one could follow Henri Bergson, who distinguishes between non-numeric qualitative duration and the empirical multiplicity of magnitude.

“Bergson presents duration as a type of multiplicity opposed to metric multiplicity or the multiplicity of magnitude. Duration is in no way indivisible, but is that which cannot be divided without changing in nature at each division.'On the other hand, in a multiplicity such as homogeneous extension, the division can be carried as far as one likes without changing anything in the constant object; or the magnitudes can vary with no other result than an increase or a decrease in the amount of space they striate. Bergson thus brought to light "two very different kinds of multiplicity," one qualitative and fusional, continuous, the other numerical and homogeneous, discrete. It will be noted that matter goes back and forth between the two; sometimes it is already enveloped in qualitative multiplicity, sometimes already developed in a metric "schema" that draws it outside of itself.

I think Tegmark’s idea of a mathematical universe is tied not just to the simple idea that we can locate cardinal and ordinal numbers in everything in the universe, which I think Bergson would agree with. Rather , he is wedded to a specific theory concerning how number applies to things in terms of mathematical concepts. Tegmark’s theory cannot allow Bergson’s idea that matter goes back and forth between qualitative and quantitative multiplicity. Instead, he wants to enclose qualitative differences within the platonism of fixed mathematical structures and schemas. For Tegmark, platonic schema has the last word, where for Bergson qualitative change in nature does.

The mathematical universe does not address matters such as solipsism, différance, phenomenology or idealism. It takes our perception of things as they are and goes from there, just like science does. Just like the correspondence theory of truth assumes there exists an outside world to which beliefs would correspond to — Lionino

Husserl’s position on the relation between qualitative and quantitative change is more radical than Bergson’s. His phenomenological project aims at taking our perception of things as they are after we have bracketed our presuppositions. For instance ,Husserl would ask you, when you look at a table in front of you, what do you actually see, a three dimensional object or one perspectival view of that object which hides the back of the table from you? Do you see an unmoving thing or one whose appearance changes as you move your head and eyes, or walk around to the back of it? How do we come to think of this thing we only ever see in perspectively changing dimensions in terms of a fixed set of properties Tegmark would say that , yes, we construct these objective properties , but that doesn’t mean that what we construct doesn’t correspond to the real mathematical nature of physical matter. Husserl depicts Tegmark’s realist view in the following way:

“Each individual object (each unity, whether immanent or transcendent, constituted in the stream) endures, and necessarily endures -that is, it continuously exists in time and is something identical in this continuous existence, which at the same time can be regarded as a process. Conversely: what exists in time continuously exists in time and is the unity belonging to the process that carries with it inseparably the unity of what endures in the process as it unfolds. The unity of the tone that endures throughout the process lies in the tonal process; and conversely, the unity of the tone is unity in the filled duration, that is, in the process. Therefore, if anything at all is defined as existing in a time-point, it is conceivable only as the phase of a process, a phase in which the duration of an individual being also has its point. Individual or concrete being is necessarily changing or unchanging; the process is a process of change or of rest, the enduring object itself a changing object or one at rest. Moreover, every change has its rate or acceleration of change (to use an image) with respect to the same duration. As a matter of principle, any phase of a change can be expanded into a rest, and any phase of a rest can be carried over into change.”

But Husserl argues that the above description does not take our perception of things as they are for us in the most primordial sense. Once we have bracketed all of the presuppositions we draw from memory to fill in for what we don’t actually experience in front of us, what we actually experience is devoid of the quantitatively measurable constancies that Tegmark’s mathematical universe depends on.

“Now if we consider the constituting phenomena in comparison with the phenomena just discussed, we find a flow, and each phase of this flow is a continuity of adumbrations. But as a matter of principle, no phase of this flow can be expanded into a continuous succession, and therefore the flow cannot be conceived as so transformed that this phase would be extended in identity with itself. Quite to the contrary, we necessarily find a flow of continuous "change", and this change has the absurd character that it flows precisely as it flows and can flow neither "faster" nor "slower." If that is the case, then any object that changes is missing here; and since "something" runs its course in every process, no process is in question. There is nothing here that changes, and for that reason it also makes no sense to speak of something that endures. It is nonsensical to want to find something here that remains unchanged for even an instant during the course of its duration.

“Can one speak in the strict sense of change in a situation in which, after all, constancy, duration filled out without change, is inconceivable? No possible constancy can be attributed to the continuous flow of appearance-phases. There is no duration in the original flow. For duration is the form of something enduring, of an enduring being, of something identical in the temporal sequence that functions as its duration…Objective time is a form of "persisting" objects, of their changes and of other processes involved in them. "Process" is therefore a concept presupposing persistence. But persistence is unity that becomes constituted in the flow, and it pertains to the essence of the flow that no persistence can exist in it. Phases of experience and continuous series of phases exist in the flow. But such a phase is nothing that persists, any more than a continuous series of such phases is.

We could have come up with a whole different numbering system than the one we have now. — L'éléphant

I agree. I noted in a You Tube "documentary" recently that there is a tribe in the Amazon that counts by 2s. Was that embedded? I think math, like Language, and everything else accessible to human mind/experience is a posteriori constructed by Mind and accepted if functional, rejected if not.

I noted in a You Tube "documentary" recently that there is a tribe in the Amazon that counts by 2s. Was that embedded? I think math, like Language, and everything else accessible to human mind/experience is a posteriori constructed by Mind and accepted if functional, rejected if not. — ENOAH

Sure thing.

For example, every number is predefined, so when we build an equation or a formula, each one of the terms have already been defined -- and no wonder the equation works! :scream:

One of the things that we like to use as math object is the circle or a sphere because of the circumference, diameter, and arc angles. So, from this, we claim that math is out there waiting to be discovered and the proof of this is that circle and sphere exist in nature. We are obsessed -- no we lose our mind to it. In our mind the circle signifies antiquity and wisdom. It signifies disciplined and scholarly thoughts. Hey, the solar system is full of round things!

Agreed. I like your example regarding circle.
I wish I was proficient enough in math to dig deeper for artifacts of math's artifice. But I chuckle at where it may have taken off: this idea that Math pre-exists our constructions.
When Plato has the slave draw the triangle proving forever the pre-existence of that Form. As if the slave didn't figured it out because he was born into a culture that had triangle constructed as a useful signifier.

The original question seems sort of trivial on second thought. Math exists in thought. Thought is part of the universe. Ergo math is in the universe. For if we are "embedded" in the universe, surely math must be.

But more questions follow: "is math only in us? If so, where does it come from? What causes it?"

I guess this would probably depend on your views on perception. If we see apples because apples exist, then it doesn't seem to be much of a stretch to say we see numbers because numbers exist. But if we construct our apples out of an inaccessible noumena, then perhaps there are no apples or numbers — or other people to discuss the existence of numbers with for that matter.

I think math, like Language, and everything else accessible to human mind/experience is a posteriori constructed by Mind and accepted if functional, rejected if not.

Constructed out of what? Or is it creation ex nihilo?

Constructed out of what? Or is it creation ex nihilo? — Count Timothy von Icarus

Short reply: Constructed (like everything else displacing Nature with Consciousness) out of images stored in memories, developing over maybe hundreds of millennia by the same or a similar Darwinian process familiar enough that it requires no describing. What is functional is adopted and input then revised by future generations , so far, reaching the extremely functional stage it has today.

No, not ex nihilo, yet, ultimately empty and nothing. A useful Fiction, like the rest of Mind and its constructions.

Why not that?

I guess I'm not understanding, "out of images stored in memories." Is Mind ultimately empty because everything in comes out of images and memory and these aren't part of Nature?

Normally Darwinian processes are described as occuring in and through nature to natural things. There is actually a somewhat pathological insistence that "Mind" not he allowed to enter the picture, so I don't know if I am familiar with how you mean it.

How does conciousness "displace" nature? Could we also say it emerges from or is embedded in nature? Or is it something wholly different?

Short reply:

Unless I misunderstand, (in which case, sorry) a pathological insistence that Darwin cannot be applied to Mind is only evidence of folly, or at best dogma, not evidence that it cannot be.

And, yes, Mind is ultimately empty. It is not Natural, but being empty, it ultimately is not Real, either. It's a Fiction made of fleeting images, applied as Signifiers to code the Body to feel (not as in emotions, as in those organic process which we organically sense) and act. Not dualism or physicality, but a qualified physicalism: Body/Nature real, Mind exists as a separate "entity" but is Ultimately empty and fleeting.

And as for how does it displace Nature? That's exactly what it does. There was a now mythical, time when a human might have looked at an apple and seen what a (mythical) equally intelligent animal sees. But you and I cannot see apple without it being structured by the chains of Signifiers, images in your memory, structuring that experience for you as seeing an apple. In Nature I.e. in Reality, you or that mythical animal wouldn't see apple; as a Real Being, you would just be be-ing; not seeing apple, just see-ing, an incessant present, not chopped up by the structures of Mind into successive objects and moments of time.

In fairness to this post, our experiences, all of them including MATH, as amazing as they are, are Fictional constructions which, in effect, displace Reality. There's no essence, Spirit or being behind Mind, nor its constructions. You already are that Being, as a living body. We just want it to be the Fiction that's real. We want it to be Mind. Hence everything from Plato to Hegel.

A quick addendum, and I'll leave it.

One of the ways we arrive at truths, as you know, is by convention. This is a powerful structure for triggering the settlement commonly called belief.

I don't know about you, but when it comes to math beyond a Senior highschool level, I cannot test my beliefs, and must rely on convention.

If you were in the same boat, (l accept likely not,) and you and I agreed, Math has some essence of The Truth of The Universe to it, what the hell would we even be talking about?

And, my point is not what you think. It's not to say we should stay out of things we cannot be certain about. My point is tgat is what we all do, necessarily, all the time.
We construct Fiction, and settle upon the functional places, whether because of convention, reason, or fantasy; all of them also Fictions.

But more questions follow: "is math only in us? If so, where does it come from? What causes it?"

I guess this would probably depend on your views on perception. — Count Timothy von Icarus

Hmm, I find the issue more intimately entwined with whether or not quantity in fact occurs within the cosmos. I find the stipulation that it does not hard to even fathom, much less entertain. But if quantity does occur within the cosmos, then the means of addressing this quantity in the cosmos is, and can only be, what we term maths. Maths is a language with quantity as its referent. No quantity, no maths.

It is only when we humans get into axiomatized maths that maths can be deemed to become fully relative to the axioms we humans concoct.

No lesser animal has a clue about axiomatized maths, but some lesser animals can and do engage in rudimentary maths just fine; again, with quantity as their referent.

Hence, to my mind, the only way of appraising all maths as strictly within us and thus as having nothing to do with the quote unquote "real world" is by appraising the "real world" to be fully devoid of quantity.

Hence, to my mind, the only way of appraising all maths as strictly within us and thus as having nothing to do with the quote unquote "real world" is by appraising the "real world" to be fully devoid of quantity. — javra

If you replaced the word math, with symbols, or representations, would the above also hold true for you?

If you replaced the word math, with symbols, or representations, would the above also hold true for you? — ENOAH

As I tried to explain, to my thinking quantity can only be represented via math - such that at the very least rudimentary math is a representation of quantity (I should add, and its relations). Because of this, my answer will be "yes".

Bear with me then, I might need to think it through. But it seems, that while I recognize the contradiction of submitting Mind cannot know Reality, but only construct a (Fictional) reality, still I'll state a hypothesis about Reality, at least as I understand that fiction.

Is the so called real world, Reality, and not the world I am submitting we construct in Mind? And if so is Reality devoid of representation, as you are suggesting?

Isn't it devoid of representation by so called definition? Isn't Reality present, by "definition" (the past has vanished, the furure has not happened). Reality is necessarily that which is, and not that which is re-presented? The instance of re-presentation is the irretrievable loss of presence, and Reality.

And you might say, I meant that within Reality, representations exist, the lion's roar, etc. But the simplest way to adress that is we run from a lion's roar, its a drive, a bird is attracted to another's "dance," it's a drive. The representation status is a construction of mind. While the so thought of, "real world" of Mind may have math and representations, and we are inescapably attuned to that, Reality does not anywhere have representations and math hiding in it somewhere, waiting, like everyone from Plato to Heidegger have said, to be gleaned out by us through some real process of becoming. We are not a special species with a God given spirit (who else then, but God?) called consciousness. Consciousness is a structure of Fiction, in perpetual construction of Fiction with effects on Nature through the human body and human culture.

We're that super weird conceited ape who somehow evolved its internal sense of imaging and memory, into an autonomous System which has taken over our organic aware-ing. So much are we attuned with that system that we invent theology, create civilizations, and math too, and insist that they are real, that uniquely we discovered them in Nature, instead of proudly admitting we made them all with our brains.

Quantity only exists in Nature because we displace Nature with quantity, etc. Think of quantity without reference to any form of representation, but on its own, in its allegedly pure and essential form as it supposedly inhabits Reality. You can't, that's absurd, right? The very thinking utilizes representations. Then why do we shy away from acknowledging that our uniquely human Conscious experiences are structured by representations and as such, they are not ultimately Real?

Quantity only exists in Nature because we displace Nature with quantity, etc. Think of quantity without reference to any form of representation, but on its own, in its allegedly pure and essential form as it supposedly inhabits Reality. You can't, that's absurd, right? The very thinking utilizes representations. Then why do we shy away from acknowledging that our uniquely human Conscious experiences are structured by representations and as such, they are not ultimately Real? — ENOAH

I should start with the observation that we don't share the same ontological models of reality. That mentioned, I think of it this way when I put my ontological/metaphysical cap on:

If there happens to be two or more coexistent psyches, then quantity necessarily is existentially in the cosmos in an objective manner: for here there factually co-occur a plurality of psyches (if absolutely nothing else). If, on the other hand, there is no quantity in reality, then this will entail the fact that there is no plurality of coexistent psyches: with this directly resulting in solipsism - wherein the one solipsist by unexplained means "fictionalizes" everything, quantity very much included. I in no way uphold the possibility of solipsism - though I'm not here to argue this out. Because I don't, I then conclude that it is logically impossible for quantity to be illusory, or fictional - again, this because at the bare minimum a plurality of psyches co-occur.

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I'll also add that, as I so far interpret them at least, representations are such precisely because they re-present that which is present. Without that which is present, no representations could obtain.

Getting back to the thread's topic, our representations of present quantities might well be deemed mental constructs, but the quantities themselves (which our representations re-present) are not (unless one starts entertaining notions such as that of objective idealism wherein everything is mind stuff, but even here quantity would yet be a staple aspect of the universal effete mind ... which is not the fully localized and active minds that you and I are, individual active minds which represent portions of this same universal effete mind which all coexistent active minds share).

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If, on the other hand, there is no quantity in reality, then this will entail the fact that there is no plurality of coexistent psyches: with this directly resulting in solipsism - wherein the one solipsist by unexplained means "fictionalizes" everything, quantity very much included. — javra

Solipsism--only one psyche exists (in Reality)

What about the position that psyche--including its constructions--doesn't exist at all in Reality? Nihilism? No. Nature exists in/is Reality. Mind is a system "reflected" in the organic body, which functions as it does because it evolved, inter alia, a logic that it must be real. But it is not. So no one mind only; but rather, no mind. Just the be-ing body.

And we intuitively "know" this. If we didn't, there wouldn't be these challenges in philosophy, particularly epistemology and metaphysics including ontology.

I guess I'm just not understanding why you say Nature exists at all. If all we ever have access to is Mind, and this is empty fiction, wouldn't Nature just be another of our fictions? Can we know anything of Nature? If not, why suppose the body and nature? Is it an article of faith?

Shankara similarly has it that all is illusion, Maya, part of the infinite creativity of Brahaman. But in Advaita Vedanta, being is one, a unity, and we are not cut off from the recognition of Brahman and recognition of our true nature. I'm not sure if this works in a case where there isn't knowledge of the Absolute, since we end up with no grounds for the fiction/reality distinction.

Hmm, I find the issue more intimately entwined with whether or not quantity in fact occurs within the cosmos.

Well, in an important way, it doesn't seem to. Everything bleeds into everything else, there are no truly discrete physical systems. We have a "bloboverse." There is one universal process, and this would seem to preclude quantity.

Indeed, it's unclear what it would mean to have multiple things "be" without them interacting (and thus forming a unity). In what sense totally discrete things all "be" and be part of the same singular category of "being?"

But processes necessarily change. A toy universe needs at least some variance to have content. A world that consists of just a single undifferentiated point is essentially the same thing as nothing. It's like how a signal of just 1s or just 0s cannot transmit any information. Floridi has a good proof of this in his "The Philosophy of Information," and Spencer Brown's Laws of Form and Hegel's Logic get into similar territory.

For something to be, there has to be some variance, as sheer indeterminate being reveals itself to be contentless. And in variation, you get the seeds of quantity.

For what would it mean for something to have unity if plurality is not a possibility? From the one comes the many.