Could it be that maths, like space and time are part of our human cognitive apparatus in some way? — Tom Storm

Einstein took Kant’s essentially unmanageable space and time verities of cognition and said, in effect, “No.” Spacetime works its ass off in the everyday world of narrative continuity, making over our lives into personal histories as malleable spacetime wraps history around the curvature of gravitational fields. So, nowadays, someone can perhaps show us how waveform physics such as energy might be related to super-position, say, as its substrate? If it sustains the super-position of highly excited elementary particles, then energy as the motion of super-position stands as a platform within Magical Physicalism. In my usage here, magical doesn’t mean contrary to logic and reason; instead, it means subtle and sometimes absential materialism. Prime example:

$e = mc^2$ turns energy-substrated super-position (macro scale) into massive, material objects in motion all around us. Under this scheme, Einstein is a magical physicalist who took unworkable metaphysical principles like Kant’s space and time and proved them physical.

MHO, cosmology (physics) concerns only modelling the development of what we call "the observable universe" and not "beginnings" or "origins" or "essences" of all things (metaphysics). — 180 Proof

Your definition, being correct, improves my post. For clarity, let me ask about a particular detail. If one models the universe as beginning-less, and thus origin-less, does cosmology then cover the totality of existence? Perhaps a categorical essence is out of domain, but essential things aren’t.

This raises the question whether metaphysics has any place within a physicalist universe. You clearly credit metaphysics with real status. How do you reconcile this with your physicalist identity? Is it the case you think metaphysics not a categorical separation from physics but instead a higher-order physics?

With ucarr's indulgence and as a retired teacher of Computing Science, I would assume that ucarr is referring to quantum computings use of the very real physical phenomena of superposition. — universeness

In quantum computing a qbit can have more states than the two of the traditional binary bit.

"Just like classical bits, a quantum bit must have two distinct states: one representing “0” and one representing “1”. Unlike a classical bit, a quantum bit can also exist in superposition states, be subjected to incompatible measurements, and even be entangled with other quantum bits."

These states are quite 'real.' For me, its a bit like fully accepting the three physical states of solid, liquid and gas, and then being a little disturbed when you find out about 'plasma.' — universeness

Is this what you were referring to ucarr? with:
Quantum computing has something contrary to say about the last part of your claim.
— ucarr — universeness

Hear ye, hear, ye! All y’all students come to order! Professor universeness is in the house! So listen up. Some foundations ‘bout to get laid.

Or maybe there are two and 57 at the same time, objectively. There can also be 4 and 57 at the same time. Are there also two pairs? where is the rule for counting? Surely it is not in the thing itself! Isn't it the case that when I said "two" I have given something that wasn't there… — JuanZu

If none of these numbers are there, then how do you assign the number-signs to what you see? If you’re a brain in a vat, how do you find meaning in articulating sounds as signs for number signs?

a difference, a partition, a slice, a rule, a number simply different from 57 regardless of whether they are melons, apples or anything else? — JuanZu

Here we have a chance to see how things differentiable can still be linked and thus are not different.

So number is different from numbered things. — JuanZu

Here, again, we have a chance to nuance our understanding of the relationship between material objects, the substrates to which number-signs attach themselves, and abstracted number signs, manipulable per math grammar in absentia with respect to their referents. The in-absentia status of pure numbers gives the impression of their categorical independence, but no, numbers never completely exit the natural world.

If you feel that crude metaphor conveys anything about the point at issue, perhaps it is because you don't understand it — Wayfarer

I beg your pardon for my digression into crude raillery.

Practicing mathematicians pay virtually no attention to this philosophical discussion.
— jgill

And thus you are a dearly valuable exception to the rank and file establishment.
— ucarr

What does this mean, exactly? That paying no attention to a philosophical discussion is a virtue? And 'the rank and file' of what organisation, exactly? — Wayfarer

I’m crediting jgill with being an exception to the practice of mathematicians giving the blind eye to jabbering conversationalists. I’m also giving him his props as a legit arbiter of math truth. Blowhards like me, being a repellent to legit folks, survive by being especially grateful to such as jgill for hanging tough and dialoguing. And let me also note your scholarship, which I witnessed through your linked article.

Well, if he doesn't know how to count he probably doesn't know that there are two things. He knows that there is a difference and that they are separated in space, that one thing is not the other, that they are similar, etc — JuanZu

If we can agree that the toddler sees a difference between one lollipop and two lollipops, then we know this person understands magnitude as something that varies; this is what math signifies. We therefore see also that a toddler can see numbers in the world without knowing the math signs for what is seen.

I wouldn't say it "responds", it's not a mechanism. It's intentional content… — Hallucinogen

The exercise of reason is sometimes a transitive verb, meaning it has intentions about acting upon and affecting some object of its attention. If that object is not the world it seeks to manipulate, then it’s seeking to act upon information about the world. Either way, it’s a response to the world, whether directly or indirectly.

If numbers are physically_materially real, then how long and heavy are they? What shape and colour are numbers? — Corvus

Name a material object with any of the following: length, weight, form or color that you can’t count. If you find all such material objects are countable, you have your answer.

https://thephilosophyforum.com/discussion/14901/numbers-a-physical-handshake-with-design/p1

What do you mean by differentiable here? — Lionino

Can the starting point be localized to, say, the post-Big Bang? Right now pre-Big Bang is, for me, unmanageable.

If our universe has no beginning, then we know that the limit of science is general existence. Like Philosophim says in his thread: Things exist axiomatically. There can be no explanation of cosmology because a beginning-less universe, with respect to its existence, is pre-analytical. Likewise, a beginning-less universe is pre-epistemological and pre-ontological with respect to its existence. The limit of science is the analysis of sequentiality.

You failed to show how that follows but since it is too early into the argument to be making contentions, I will just grant you. — Lionino

My premise to be proven by my arguments is that material object and physical number are biconditionally linked as equivalent.

Everything from "There’s no reductio ad absurdum re:" to "Since any and all material objects, individually, present as a countable one, oneness, a countable number, acts as an essential attribute of each and every material object." sounds like Christopher Langan, meaning complete gibberish. — Lionino

If a starting point and a number are separate, then it’s a contradiction to claim a starting point is an origin since it implies another, separate and co-eternal thing. Curiously, the contradiction contradicts itself if you figure starting point implies number and vice-versa. If the two are really one thing, then that’s a strong argument that number as a priori abstraction only is wrong. It is my argument.

…lots of mathematics deals with infinities. The natural numbers are an infinite set, and the set of real numbers are infinitely bigger than the set of natural numbers, and it gets worse as you go into the complex field. Calculus relies on the concept of infinity. You can have an infinite amount of infinities in mathematics that just keep growing. This does not seem to relate to the physical world. There is something about mathematics that is not about just the physical world. — Lionino

I suspect the reason why infinite sequences are not other-worldly is tied to the math solution to Zeno’s Paradox. If it’s true we move through the world without getting entangled in the asymptosis of the infinitely divisible number line, then it’s also true that infinite series are real but ontically undecidable.

I should maybe be excluded from this discussion..
I don't believe in pure mental concepts at all, not the way you guys are talking about it
— mentos987 — mentos987

You’re welcome to continue weighing into this conversation on the physicalist side, if that position isn’t also averse to your inclinations. Hoping you’ll give us more goodies like the tree-bridge.

With this I seek to claim that our concept of math did not build the bridge. It was a fallen tree over a creek a long time ago that did — mentos987

Excellent example of the natural world practicing physical number for counting! What person in the village thinks two trees or four trees have fallen over the creek?

No. A natural number one let’s everyone pass over the risen creek without getting wet. Real number in the real world built number sign within the head. What are number signs in the head without real number in the real world? They’re Kant’s empty concept without percept.

To you it seems that apples and oranges are numbers, to me their numeration may simply be external properties that are only acquired in relationship. — JuanZu

Ever seen a toddler who, knowing next to nothing about numbers in their head, fails to distinguish one offered lollipop from two offered lollipops?

"How can mental “objects” have causal effects upon the physics of the natural world? The answer is numbers." -- To me it seems incorrect, since our numbers are just us mimicking what is already there. — mentos987

Your premise presupposes what it seeks to contradict. Don’t take my word for; take your own words for it. Re-examine your closing sentence.

All of it? A priori reasoning doesn't come from sensory stimuli, by definition. — Hallucinogen

What does it come from? If you say reasoning about reasoning about the world, that lands it in higher-order reasoning about the world. Now, I challenge you to name what a priori reasoning responds to in total separation from the world.

Practicing mathematicians pay virtually no attention to this philosophical discussion. — jgill

And thus you are a dearly valuable exception to the rank and file establishment.

Tosh. Kant detested materialism, as do I. — Wayfarer

So, you detest materialism? Post herein a picture of your right index finger after you’ve chopped it off.

Pure math has connection to the natural world only as indecipherable signification representing thermodynamic equilibrium.

Since mathematicians only use pure math for investigation of the ground rules concerning applied math, pure math is merely higher-order applied math.
— ucarr

Mysteries never cease :roll: — jgill

Thank-you for your time, attention and commentary. Its not easy to get them from authentic experts. I like having the attention of important people. What you say in your below quote is what I attempted to say in my above quote. One salient difference is the absence of arrogance and pretension, hallmarks of my statement. I was trying to characterize pure math in total isolation, whereas you nuanced the separation of pure and applied math with anecdotes from your professional experience. Your nuanced separation speaks to my theme: math applies well to the natural world because it’s of the natural world. It’s of the mind a well; It’s not simply of just one or the other. However, in my opinion, it is more at discovery than at invention.

The distinction between pure and applied math is somewhat vague, one reason being that pure math may become applied math at times. A researcher in applied math could be working on a math scheme to solve a particular problem, like calculating the stresses on a modern fighter plane during sharp turns. Or, he could be pursuing a topic purely for its own sake, curious about what comes next - and then finds someone has used his results in an applied manner.

This happened to me. My interests are always in "pure" math (complex analysis) and I published a paper in 1991, I think, with no thoughts of it ever being "useful", only to find my principle result was employed in a multiple author sociology paper about decision making in a group. Of course, the author who cited and used my result paid no attention to the details. — jgill

Not uncoupled from the material world' does not mean 'material in nature' — Wayfarer

Percept + concept = complex materialism. As with complex numbers, there is a real part and another type of part. In the case of materialism, the other type of part is non-local materialism: collection across time-interval-positive of a set of conditionally connected members reified into a gestalt, with gestalt in this context being a synonym for concept.

A particle moves through space; some formulae do a good job of describing that movement and even predicting how it might go. But the particle and its movement are clearly prior. Mathematics, then, would seem to be derive from the world, the world in every sense prior. — tim wood

:up:

Speak! Without antecedent, existential fact, science and math can’t even get started.

In what sense is pure maths concerned with physical objects?
28 minutes ago — Wayfarer

Since mathematicians only use pure math for investigation of the ground rules concerning applied math, pure math is merely higher-order applied math and thus it is not uncoupled from the natural world. — ucarr

It has to be, since mathematical concepts are more general than physical entities, which only exist at a given coordinate in space. Mathematical truths whoever enjoy far greater comprehensivity. — Hallucinogen

Quantum computing has something contrary to say about the last part of your claim.

I don't presuppose the existence of "physical minds" — Hallucinogen

If mind emerges from brain, then no brain, no mind. Yes, mind is independent of brain as mind, but the absential materialism of mind is its constraints upon dynamical, material processes. Again, no dynamical, material processes, no mind. Functional mind that has impact upon existentiality, meaning and usefulness is never uncoupled from the physicality of the natural world.

What a priori axioms does physics possess? — Hallucinogen

What a priori reason is practiced by brain in a vat never in contact with the world?

Any that math possesses supports my position. — Hallucinogen

Math, like brain in a vat without the worldly mediation of conscious human, can only instantiate the circularity of thing-in-itself, and that without cognition. Pure math has connection to the natural world only as indecipherable signification representing thermodynamic equilibrium.

Since mathematicians only use pure math for investigation of the ground rules concerning applied math, pure math is merely higher-order applied math and thus it is not uncoupled from the natural world.

Suppose the Riemann hypothesis finds its solution in pure math. So, pure math establishes that all primes calculable by the zeta function locate themselves on the critical line of the complex number plane.

Now let’s blink out the natural world of physics, thus leaving us with pure math with no physical referents, no matter how far down the line you evaluate. What are we left with? A system of interrelated signs with meaning and use resting upon nothing but the conventions implied by the system of signs itself, as established by the precedent, again, of the system itself.

What do we have? An endless loop of circular reasoning with no other meaning than its circularity. That’s why I say math is a physical property of the natural world. Only there does number possess existentiality, meaning and usefulness.

don't follow your line of questioning, ucarr. What's your point? — 180 Proof

Suppose the Riemann hypothesis finds its solution in pure math. There it’s established all primes calculable by the zeta function locate themselves on the critical line of the complex number plane.

Now let’s blink out the natural world of physics. Pure math has no physical referents, no matter how far down the line you evaluate. What do we have? We have a system of signs denoting numerical relationships resting upon only the conventions of the signs themselves. The precedent for these conventions is, again, the signs themselves. This is a closed loop of circular reasoning grounded in nothing but its own circularity. This is why I say number is a physically real property of the natural world. Only there does math possess existentiality, meaning and usefulness.
————————————————————————————————————————-
As I read your lineout, I feel need to defend starting point of analysis as arbitrary because axioms, the necessary starting point of the scientific method, are pre-analytic, and thus arbitrary. Your no-beginning postulate necessitates arbitrary points of departure within its domain.

You seem to be backing up your line out with the claim maps, unlike their referents, have logical antecedents that constrain the methodology of their construction and thus the scope of their content. This ranges out ultimately to your separation of signs from their referents. I’m opposing this because my physicalist argument thoroughly entangles sign with referent so that maps do forever approach their referent terrain. There is no merger however.

The physicality of words and numbers makes them approach being bi-conditional with their physical referents.

All of this is to say, within a realm unbounded, finite and without beginning, everything is a map to another thing.

Your bifurcation of sign/referent is harder than mine.

We do not know. — JuanZu

If I have 5 oranges in one basket and I have 5 apples in another basket… — JuanZu

If this is something you cannot know, then your argument above has no grounding in fact and therefore no logically attainable truth content, only blind guesswork. On that basis, why should I accept it?

My 'anti-platonist pragmatics' (finitism?) comes to this: pure mathematics is mostly invented (re: pattern-making) and applied mathematics is mostly discovered (re: pattern-matching) — 180 Proof

Pattern-making in total abstraction from physical reference, beyond convention established by precedent, tells you what?

…every physical fact depends on facts about this mathematical structure, but not vice versa. — Hallucinogen

So, pure math includes relationships without reference to physical things inhabiting the natural world. This is an intriguing argument for idealism. What do math theoreticians say about the physical mind’s ability to cognize these supposed ideals-in-themselves?

Do you believe math is metaphysically prior to physics? If so, what say you about the fact that math, like physics, possesses pre-analytical axioms? (They’re solely existential.). Also, what say you about math axioms being incomplete? (If they’re incomplete, they’re not ideals.)

If apples and oranges have intrinsic physical properties then the number (if it is different from numbered things to avoid breaking with the principle of identity) does not participate in those physical intrisic properties either. Therefore, the number is not something physical and is extrinsic to intrinsic physical things which are numbered — JuanZu

Assuming you possess proper vision, have you ever been unable to distinguish five oranges from two oranges?

It is also necessary to define what you mean by a physical thing. — JuanZu

Physical: anything subject to the spacetime warpage of gravitational fields.

f I have 5 oranges in one basket and I have 5 apples in another basket, the 5 does not seem to participate in Appleness nor the orangeness. So the number is not the same as numbered things. — JuanZu

You say number stands apart from apples and oranges . When we look at number five apart from them, we know nothing about their number. How do you know both have number five?

If it were the same (or if the number is an intrinsic property of numbered things), we would have to say that 5 apples are 5 oranges and vice-versa (or that 5 apples have the property of been 5 oranges and vice-versa) breaking the identity principle. — “JuanZu

Since number five, in abstraction, tells us nothing about apples, oranges or any other physically real thing, that tells us pure math, in order to be physically real and thus inhere within particular, physical things, and thus be existentially significant, meaningful and useful, must evaluate down to physical particulars. Universals are emergent from particulars, but they are not existentially meaningful in abstraction.

…requires an arbitrary starting point re: sequential processes. It can be considered a “working” starting point, but there’s no logical — 180 Proof

Why do you line out “an arbitrary starting point for a sequential process”?

A starting point not logically necessary = a starting point arbitrary. Agree or disagree?

Logic is rooted in sequentiality, thus arbitrary starting points, such as the axioms of the scientific method, being pre-sequential, are also pre-logical. Agree or disagree?

Axioms have no logical support. Agree or disagree?

Referents without beginnings have models without beginnings. This is a simplification of saying: Referents without beginnings have models no less arbitrary than themselves. Agree or disagree?

…we ought not mistake the maps we make for the territory itself? — 180 Proof

You’re citing the sign/referent relationship?

"Must be"? Why must there be? If you look closely enough, you will find the imperative securely rooted in your need for one, in the (your, and mine too) logic of the thing. But logic is descriptive and only seems to be prescriptive. That, or show, extra-logic, how and why it must be. — tim wood

The idea here is that with any and all experiences of sentient existence, the sentient being must make a start, i.e., embark upon their personal history. Making a start and making a starting count are one and the same. This isn’t the logic of the starting; there can be no logic of the starting as there is, as yet, no logic. Starting is pre-analytic, thus pre-logical. Starting with an arbitrary start_starting count is an existential necessity that has no logical support. This is evidenced by the scientific method: science starts with an arbitrary starting point, the axiom.

This is a continuation of the first part of my OP.

Conclusion: number-as-property, being essential and physically real, and being tied inextricably to material objects, is discovered. They are not purely conceptual objects, accessible to the mind only.

Numbers are discovered, not invented. Numerical properties and numerical relationships likewise are discovered, not invented.

The number zero shows how emptiness is permeated by these same numerical relationships, so existence presupposes number-as-property.

If number-as-property is physical and essential, then there is an answer to an important question: How can mental “objects” have causal effects upon the physics of the natural world? The answer is numbers.

This is the necessary conclusion of both the number-idealist and the number-realist.

Example: Civil engineering demonstrates idealist control of the physical if you’re a number idealist: The building of a suspension bridge across a body of water as, say, San Francisco’s Golden State Bridge, demonstrates numbers manipulated to specifications required for a stable road across a bay. How ideal number shakes hand with real object remains to be explained.

If, on the other hand, you’re a number-realist, then you understand there’s no unexplainable interface of ideal and real in the design and build of a suspension bridge. Numbers, like the bridge itself, are physically_materially real. The two are integrated and holistically consistent.

Is this a correct paraphrase of your response to Philosophim’s thesis: spacetime, an unbounded, finite, beginning-less phenomenon, requires an arbitrary starting point re: sequential processes. It can be considered a “working” starting point, but there’s no logical necessity guiding the choice of a particular starting point.

Why include me in your reply to Gnomon? — 180 Proof

In my post to Gnomon, I'm continuing our debate about his interpretation of $e=mc^2$and, additionally, his application of his interpretation to his arguments supporting his EnFormAction proposition. I think it's fundamentally wrong because he has m = matter instead of m = mass, the correct equivalence.

I was interested in your post because it lays down some foundational definitions of physicalism as you see it. (In another minute, I'm going to ask you some questions in reaction to your postulations. This is for clarification of my understanding.)

I'm thinking what you have to say is germane to our debate. He has EnFormAction covering a wide terrain including: material, spiritual and undefined. Much of what he's claiming as metaphysical_spiritual I'm claiming as physical.

Also, I've been criticizing him from the standpoint of execution of his argumentation. I've characterized it as being slapdash and error-laden. Your execution of argumentation, meticulous, precise and funded by in-depth research, stands at the opposite end of the spectrum from his and, for that matter, from mine as well until very recently.

----------------------------------------------------------------------------------------------------------------------

...the abstraction, or concept, of "consciousness" ...a self-reflexive activity — 180 Proof

If firstly we picture Einstein sitting at his desk writing out the equations for special relativity, and then secondly we read his paper published in 1905, can we next conjoin these two events via memory to the effect that we can claim them public and therefore physical?

...because by definition consciousness is excluded from this paradigm. — Unknown

This is a claim made by Wayfarer?

Physicalism only excludes non-physical concepts from modeling (i.e. explaining) how observable states-of-affairs transform into one another. In this way "the paradigm" is epistemologically modest, or deflationary, limiting its inquiries to only that which can be publicly observed – accounted for – in order to minimize as much as possible the distorting biases (e.g. wishful / magical thinking, superstitions, prejudices, authority, etc) of folk psychology/semantics. — 180 Proof

You're saying physicalism is rooted in the scientific method's demand that scientifically measurable things be public?

We physicalists do not "exclude consciousness" (i.e. first-person experience) but rather conceive of it as a metacognitive function – e.g. phenomenal self-modeling – of organisms continuously interacting with and adapting to each other and their common environment. — 180 Proof

Is metacognitive, within your context, higher-order cognition, i.e., cognition of cognition?

Might selfhood entail a three-tiered hierarchy of cognition: empirical cognition (seeing the world directly); analytical cognition (elaborating the grammar and syntax of the seen world); hyper-cognition (seeing your seeing of your seeing of the world).

Actually, I didn't comment on the visibility of Mass & C. But, for the record, all of the equation's elements are imaginary & invisible abstractions. And none of them is tangible Matter, although Mass is a numerical measurement (mentalization) of Matter, a concept, not an object. So, I don't know how you decided that the invisibility of of numerical concepts contradicts my description of Einstein's equation, in which I referred to Matter, not Mass, as "tangible". Does any of that "matter" to you? :joke: — Gnomon

I call EnFormAction a "shapeshifter", because like physical energy, it can transform into a variety of manifestations. The most famous example is Einstein's E=MC^2 equation of invisible Energy and tangible Matter and a non-dimensional number. They are different expressions of the same essential substance. — Gnomon

Here's why I read your examination of Einstein's equation as commentary on the invisibility of m and $c^2$:

Einstein's E=MC^2 equation of invisible Energy; this is your description of the left side of the equal sign: (one term) E = energy (characterized by you as invisible).

and tangible Matter and a non-dimensional number.; this is your description of the right side of the equal sign: ( two terms) M = mass (characterized by you as tangible matter) and $c^2$ = the velocity-of-light$^2$ (characterized by you as a non-dimensional number).

Tangible = perceptible by touch, so tangible matter is stuff that can be picked up and handled. Your mistake: M = matter; no, M = mass.

You say:

Mass is a numerical measurement (mentalization) of Matter, a concept, not an object. — Gnomon

The signs denoting measurements of mass are abstractions, and the meaning of these measurements are concepts, but the referent for this signification and conceptualization of its meaning is physical reality. The material reality of mass is experienced whenever a weightlifter attempts to lift a three-hundred pound barbell. The barbell's disinclination to move is not visible.

Regarding C = velocity-of-light$^2$, light, being a physical phenomenon, has a constant velocity, another physical phenomenon. C = velocity-of-light$^2$, being a sign, arguably has no expanded spatial dimensions. However, the subject of importance here is the referent of the sign, the velocity of light squared. Being physical, it is spatially three-dimensional, not non-dimensional.

You talk about the abstractions that populate $e=mc^2$. Yes, they're abstractions not simply tangible, but questions about the ontic status of signs and their relationship to their physcial_phenomenal antecedents lies within the domain of linguistics. The framing context for your description of $e=mc^2$ is Enformaction, a proposition within your theoretical philosophy as based upon physics. Herein you're talking physics, not linguistics. Argumentation about the immateriality of signs is irrelevant within your context.

I call EnFormAction a "shapeshifter", because like physical energy, it can transform into a variety of manifestations...They are different expressions of the same essential substance. — Gnomon

This is where you're heading with your examination of $e=mc^2$. You seem to be claiming Enformaction is a substance that is the material platform for energy, mass and the velocity of light.

You bite off a big challenge. The ontic status of energy not being well understood, its conceptualization remains largely undefined.

...I'm always looking up words, the definitions of which often lead me to other words I have to look up, — Patterner

...we might say, snowflakes, in general, have a design, and each one has its own unique design. — Patterner

...is that the kind of thing you’re talking about? — Patterner

A pattern, when it's catchy, presents itself a thing worth keeping. I delight in sweet melodies arising from ingenious tunes. Might your experience of music resemble this?

A world without patterns is not something I wish to experience, too much like trudging Dresden after the Allied bombing.

I suppose we can say ideas are a type of pattern; they're the type favored by the mind.

I'm guessing now and then you marvel at the creativity of a clever idea. A familiar example is a good joke. When a good joke is current and passing word-of-mouth like wildfire, we catch glimpse of many minds joining together like kindling.

How about a choice piece of hot 'n juicy gossip? That brings us together like a gaggle of squawking busybodies, right?

Yes. We're all immersed in a world of patterns.

We grew within the universe, which has consistent principles, and are made of the universe's materials, which are subject to those principles. Is there a reason to think an intelligence that developed in such a way would not be able to recognize these principles? — Patterner

I agree with your first sentence and I believe it to be a sufficient explanation of our recognition of order within the matter_energy realm.

What is the relationship between numbers and order? To what degree can you have one without three other? To what degree are they not the same thing? — Patterner

I believe the number line is sine qua non to both math and order. The positions along the number line and their relationships are why math is the language of the ordering of spacetime phenomena. A number is a number line. A position along the number line is just an idealization about the ultimate compactness of a dimensionless point.

Is a random number sequence an instance of numbers separated from order? Even in this instance, the numbers still map to the number line. Furthermore, this question dovetails into the difficult question whether we can rationalize outside of order. A requisite for postulating about numbers, a rational entity, depends on numbers being coupled with order. Rationalizing outside of order also raises a difficult question about whether intelligibility can exist separate from order. You explanation for how humans internalized the consistent principles of the universe places heavy reliance upon intelligibility. How could humans recognize scientific truths without being engulfed within an environment essentially ordered?

I want you to give more thought to your decision to sign off from all discussions of design. Principles, being organizing, foundational truths, have an intimate relationship with design. If I'm not mistaken, you embrace them as essential components of metaphysics. How could organizing principles, acting in the role of designers, not be involved in the high ordering of atoms? As you say, the universe's materials are subject to the universal principles.

No. I did not, and do not, declare the order is designed. — Patterner

Again, I did not, and do not, acknowledge design. — Patterner

No, I did not, and do not, describe cosmic mind. — Patterner

Yes. The order pre-existed the life that arose within it. — Patterner

What I mean is, will thinking that objects 'possess an inherent attribute that can be labeled "number"' lead to a dead end? Will thinking it is not an attribute of objects, but of the universe's order, that we are recognizing lead to a dead end? After all, we might approach things differently, depending on which we take as our starting point. — Patterner

You have raised the central question: Where is the starting point of order? If we can accept, within the confines of our discussion here, that number is the peerless marker of position and therefore of order, then we can acknowledge that there's presently toleration of the notion number and order are discovered not invented.

A second, central question: How did number and order pre-dating humans get internalized within the human understanding? This form of the question evaluates down to: Where is the starting point for order and design for humans? Is it the human hand suggesting to the inquisitive mind of its possessor that two fingers not looking like five fingers is both meaningful and useful? Is it, instead, the abstract mind of humans navigating the environment via notions of number relations abstracted from counting fingers? Is number an attribute of material objects, or is it an incorporeal abstraction confined to the realm of cognition?

A third, central question: does the biconditional operator in logic link number with order? If N = number and O = order finds true expression as n ⟺ o, then finding the start of one entails finding the start of the other.

I’ve already given my answer: both claims about number are true. Counting fingers is no less essentially mathematical than perceiving the obscurities of pure math. This is so because the foundation of math cognition is its necessary antecedent: counting fingers. As justification, I cite Aristotle’s Agent Intellect (human) meets intelligibility (material object first, then both material and cognitive objects).

Patterner, by implication, agrees with the equivalence of the two modes of discovery with his response to my question:

Do you believe a brain confined to a vat will eventually start counting? — ucarr

Certainly not. I don't believe a human could come to any intelligence or consciousness under those circumstances. I believe sensory input is essential. — Patterner

Now we come to the hotly controversial topic of design and its location within the cosmic history.
If it’s possible to pinpoint the advent of design within the phenomenal universe, where in the timeline of events does it lie?

Firstly, let’s consider a fourth central question: If O = order and D = design finds true expression as o ⟺ d, then finding one entails finding the other.

If there’s a hierarchy, it might be number, order, design.

Most importantly, if the two biconditionals are true, then we have a triad.

Can we make a theoretical placement of the triad of number_order_design within the infinitesimal interval of time following the Big Bang?

If we answer is “yes,” all we’re doing is tracking the start of the triad as natural phenomena.

If super-hot plasma is the first form of the material universe during inflation post-Big Bang, then we can infer its ontic status as pre-cursor to the formation of elemental atoms. With atoms clearly, we have number and order, whether as independent, unobserved entities, or as entities contingent upon observation. You ask what agent could act as observer in the micro-seconds following inflation? The question must be raised during the early expansion of the universe because the reflexivity of end-oriented consciousness, per our discovery-rather-than-invention thesis, requires a pre-cursor no less than does the triad. Remember, when I claim the early universe knew itself, even if only pre-cursively, I’m claiming nothing in scope beyond the phenomenal universe.

To summarize, we have a defensible argument to the effect that the triad of number_order_design was extant from the start of the universe because the highly ordered status of the atom and its sub-atomics must be assumed as prior to all assemblages thereof.

The universe is consistent. Laws of physics, mathematics, and whatever else, are the same everywhere...If they were not, we would have chaos, and I doubt life would have arisen at all. — Patterner

You argue that our phenomenal universe of forces and material objects has an innate order founded upon principles likewise innate. You go on to declare that life wouldn't be possible without the designed and pervasive order of the universe as its ground. You present a picture of naturally ordered life arising from pre-existing order.

We evolved, and exist, in this universe, with its consistent principles. Meaning they are within us. I think counting is our recognition of these attributes, these consistent principles, of the universe. It makes sense that we recognize the principles of our own existence when we see them outside of ourselves. — Patterner

You acknowledge designed order is imbibed into human genome from the forces and materials from which it has arisen. This is your description of cosmic mind meeting human mind. The human mind, once attaining to the requisite cognitive prowess, recognizes essential attributes of order of the surrounding creation. So, order, and number, the peerless marker of position and therefore of order, are discovered within the natural world. You don't believe numbers are a human invention:

Do you believe a brain confined to a vat will eventually start counting? — ucarr

Certainly not. I don't believe a human could come to any intelligence or consciousness under those circumstances. I believe sensory input is essential. — Patterner

You make it clear human mind and the innate order of the natural world are an interface, a complex surface interwoven from the coming-together of the two conversationalists. You answer the question: Why do two fingers look different from five fingers? It is because Aristotle was right and Descartes was wrong: human learns from natural world as part of an Aristotelian Duet wherein Agent Intellect meets intelligibility.

Do you believe a brain confined to a vat will eventually start counting?