My original question was, if number is material and physical (as claimed by the OP), then what measurements in size and weights does it have? And what shape and colour does number have for its physical and material existence? — Corvus

Your best friend sings tenor in the church choir. His buddies call him “Golden Pipes.” The women call him “Boy Wonder.” He serenades the sighing of lungs on starry nights.

What size and weight, what shape and color, his tenor voice? The width of his nostrils, the length of his lungs, the breath of his chords, is it? These numbers are sizes of music and song, but one man is he. Oh, glee of sweet nighters.

Number one, our silent partner, never leaves us from cradle to grave.

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.
— ucarr

:lol: Not sure if I've just been complimented or insulted. I kinda like it that way. — universeness

I got a little carried away with my vernacular. With the above salutation I’m praising what you posted.

So at the most fundamental level, surely its the ability to differentiate between different objects, attributes, properties, patterns that is the essential ability for a sentient to be able to experience the universe. The quantity of a particular object within a particular volume in spacetime, seems to me secondary to the more fundamental need to be able to differentiate. — universeness

Your supposition about differentiation points our attention to something essential: we gain knowledge of the world through our differentiations separating our experiences of things into their distinctions and, might it be, as I’m thinking right now, that number is a general distinction amongst a welter of more local and specific distinctions, and thus the essential importance of math. I think we can claim generally that all humans of sound mind use math every day as an essential part of their navigation of the world. Distinctions of the senses: color, sound, taste, smell and touch have in common the theme of number running through all of them: how many colors, sounds, tastes, smells and touches is absolutely essential to everyone’s personal history, albeit not necessarily fully cognitively.

Without the contrast of changing stimuli, humans, no matter how rested, fall asleep. Number is essential to those contrast-producing changes.

I’m not ready to claim number is the minimum distinction required for the intelligibility of sensible experience, but you’ve done much to help me advance in that direction.

Perhaps a categorical essence is out of domain, but essential things aren’t.
In this statement, for clarity's sake, I prefer fundamental to your term "essential". — 180 Proof

How are “essential” and “fundamental” distinct? Webster’s Thesaurus lists each word in the other’s list of synonyms.

This raises the question whether metaphysics has any place within a physicalist universe. — ucarr

The doesn't make sense to me because I think of "physicalist universe" itself as a metaphysical construct, that is, merely a speculative supposition – way of observing and describing nature. — 180 Proof

I wonder if you, when talking of metaphysics in the context of this post, refer to the metaphysics of a particular field, physicalism, whereas I, when talking of metaphysics in general, refer to the metaphysics of all fields.

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

In the context of my general usage of metaphysics beyond the metaphysics of a particular field (the latter being the grammar local to that specific field), “beginnings,” “origins,” and “essences” cannot be excluded. When you say:

…I think of "physicalist universe" itself as a metaphysical… way of observing and describing nature. — 180 Proof

You seem to be referencing the particular metaphysics of “physicalism,” not the general metaphysics of ontology.

There is nothing in nature (or in mind) that i refers to, we call it irrational for a reason, and yet, i is the basis of lots of our mathematics. From that it should follow that mathematics is not just about physical things, and thence that either numbers are not real objects or that numbers are real but not physical. — Lionino

Your post is interesting. Let me clarify: that math covers more than the simple physical I don’t deny. Math, like other abstractions represented by signs, has significant, extensive, even complex distinction from the natural world.

As I learn about emergence and emergent properties, I become more inclined to think math is an emergent property, with material objectivity in the role of its substrate. By this claim I mean to say that math as an emergent property, though like a world unto itself with immersive complexity and broadly inclusive parameters radically different from those of the material world, nevertheless falls short of categorical independence from its substrate, the material world.

Abstraction in general I think a phenomenon that can aptly be labeled: complex materialism. Complex materialism involves 3D compositing of serial empirical experiences linked by similarity and theme. The mind takes these strings of remembered experiences and composites them into an abstraction that thematically generalizes their similarities into an abstraction represented by signifiers. This process, if a reality, makes its clear that abstractions have emergence from the material world, but not independence from same.

Note: regarding complex numbers, which have an imaginary part, they, like the ratio of the diameter of a circle to its circumference, express themselves through an unbounded, asymptotic progression. What’s important to note is that no human has directly perceived infinite magnitude. Complex numbers, like irrational numbers, are neither real nor unreal, but rather ontically undecidable. Thus the infinite sets and the imaginary sets don’t work as evidence of math’s categorical independence from the material world.

Thanks for weighing in. I hope you’ll keep doing so.

:up:

I consider methodological physicalism only a paradigm for making/evaluating 'physical models' and interpreting their results, or problematics. — 180 Proof

Methodological, the adjective that attaches to physicalism, tells us your brand of physicalism gets practiced via model making, model evaluating and data crunching? Moreover, it is itself a model for model making?

How do you find countable objects from the object you can't count? — Corvus

Since your question asks about the “object” you can’t count, a word single in number, haven’t you already counted it?

Isomorphism. — JuanZu

It just preserves from one pair to another pair what the eyes perceive. Number signs, in order to be assigned meaning, must first be referenced to something tangible and countable. Counting by number signs arbitrarily assigned to tangible counting sets of things examples tangible things acting as substrates for a math language that only has meaning with reference to tangible things within the natural world. I infer this is what you’re thinking of when you talk of numbered things. The tangible things numbered substantiate in meaning what the signs represent. You can imagine yourself inventing a language that has no tangible referents, but only as an abstraction from your knowledge of numbered things exampling number signs arbitrarily attached to tangible things.

Well, given what I've said independence is real. Otherwise we fall into contradiction and the complete uselessness of mathematics. — JuanZu

I can give you an example of math attached to tangible things and thereby being meaningful and useful: civil engineering.

Give me an example of math independent of tangible things that is meaningful and useful. Pure math investigating foundational math grammar won’t work because that’s higher-order applied math examining math grammar which, in turn, is grounded in tangible things countable.

If the number were not different from the numbered things, it would not be possible to give us two apples after giving us two oranges. Since if the number is not a third with respect to apples and oranges, this number falls into the essence of some of the objects, which would lead to saying that two oranges ARE two apples. Violating identity. — JuanZu

You have a three-year-old. You ask him to go to the big fruit bowl on the table across the room and get you two apples and two oranges. You don’t ask him with words because he’s not good with number signs. Instead, you hold up two fingers and say, “apples.” Next, you hold up two other fingers and say, “oranges.” You don’t think your three-year-old can complete the task without knowing number signs?

If a child cannot distinguish and understand two apples and two oranges without knowing counting numbers, then neither child nor adult could ever see two of each. This is not a description of our daily experience.

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.