• Material Numbers
    The fact that God hasn't showed himself only means he hasn't showed himself yet...EugeneW

    Before the 20th century, ocean floors were public, repeatable, measurable i.e., subject to scientific examination & description.

    From antiquity until now, God, by definition, transcends the material.

    Since science has entered into the 4D realms of spacetime & QM, further expansion in 4D might lead to an upward dimensionality of materialism that includes a 4D empirical God consciousness (which is not God) that might well serve organized religion.

    In light of the above statement, the premise God consciousness has no 4D empirical existence is, in my opinion, not a well-supported conclusion.
  • Material Numbers
    Not subjective materialism, but philosophical dualism. The rational intelligence, nous, recognises numbers and forms, among other attributes, which are among the qualities which make material things intelligible.

    “EVERYTHING in the cosmic universe is composed of matter and form. Everything is concrete and individual. Hence the forms of cosmic entities must also be concrete and individual. Now, the process of knowledge is immediately concerned with the separation of form from matter, since a thing is known precisely because its form is received in the knower. But, whatever is received is in the recipient according to the mode of being that the recipient possesses. If, then, the senses are material powers, they receive the forms of objects in a material manner; and if the intellect is an immaterial power, it receives the forms of objects in an immaterial manner. This means that in the case of sense knowledge, the form is still encompassed with the concrete characters which make it particular; and that, in the case of intellectual knowledge, the form is disengaged from all such characters. To understand is to free form completely from matter.
    — Brennan, Thomistic Psychology
    Wayfarer

    Breaking this down,

    EVERYTHING in the cosmic universe is composed of matter and form. Everything is concrete and individual. Hence the forms of cosmic entities must also be concrete and individual.

    Is Brennan herein referring to the (individual) gods? Are you polytheist? Do you hold with the premise monotheism is false?

    the process of knowledge is immediately concerned with the separation of form from matter

    Do you hold that such separation is empirically literal, or do you have an understanding such a separation is a benign procedural fiction of the reasoning mind? I ask this because form and matter in separation (to me) seem to be unintelligible. This bifurcation gives the reasoning mind a stronger handle on what it's trying to understand, however, we don't see such separation in our everyday world, do we?

    whatever is received is in the recipient according to the mode of being that the recipient possesses.

    So, humans are a mixture of the material & the immaterial i.e., a mixture of form & content? If so, this tells us humans encompass a brain/mind bifurcation. This leads us to a crucial question for the immaterialist: How do the material & the immaterial {connect, interface, bridge} to form a common ground and what does such common ground look like?

    Might it be the case QM has some answers to this question?

    To understand is to free form completely from matter.

    Do you experience purely abstract thought without material imagery acting as a supporting substrate making it intelligible?

    I'm inclined to think the easy, discrete separation of matter & form is a useful fiction, but a fiction nonetheless.
  • Material Numbers
    Being countable is part of the makeup, part of the being of material things.
    — ucarr

    Could that something that makes them countable be their presence?
    Sir2u

    Here's where things get interesting because what you have written above is a full, unconditional affirmation of what I've been claiming from the start.

    Yes! The physical presence of material things is what makes them countable, and the language of math does the counting; it does not create or ascribe to material things their countability. The countability of material things, as you say above, is their physical presence.

    In a world without material things, I suppose pure math could busy itself with the counting of abstract numbers. Of what use would that be? Might it serve as a Buddhist chant that aids in calming the mind for the sake of meditation? I say this because the counting of abstract numbers without referents is a vacuous circularity.

    Mankind will have to find another way to describe the universe and they will chuck applied math out of the window as obsolete.Sir2u

    Why should applied math, that works in the real world, be chucked out the window? While it's true that Einstein physics has superseded Newton physics to some extent, the world still uses Newton physics everyday to great advantage.
  • Objective evidence for a non - material element to human consciousness?


    When I see your raise & raise that , I'll süss the pot with gold coins featuring the faces of Einstein, Bohr & Planck.
  • Material Numbers
    Your central point is that numbers do not exist in the material world, apart from human mind inventing them, then using mind to count material things, right?

    Recently, you've said material things are countable. So, if numbers are not a physical attribute of a material thing, and yet numbers, which are of the mind only, can count material things, then the counting of material things by mental numbers is mixing a mental thing with a physical thing, subjective materialism (Berkley).

    Bear in mind, numbers as symbols must have a material thing as their referent, if they are to keep separate from material identity, otherwise, you're mixing the two.

    Do you think that math cannot be applied to non material objects.Sir2u

    Following from your claim numbers are purely mental, non-material things are the only things they can count without becoming entangled with the material world.

    Are you okay with science reverted back to the period before the scientific method?
    — ucarr
    Apart from the fact that it is a bloody stupid question, how do you think my answer would help you to prove that the universe is mathematical?
    Sir2u

    It's not a stupid question because the lynchpin of modern science is the belief that the physical attributes of material objects persist in the absence of sentience naming them. The three pillars of the scientific method, as you know, are public, repeatable, measurable. If the state of material things were dependent upon sentience naming them, as you claim with numbers, material things would forever be shape-shifting like mad in accordance with the many points of view of various individuals. Material things are measureable to a standard because their attributes don't change under the influence of sentience, which means said attributes are independent of sentience.
  • Material Numbers
    A cognitive-leap whopper is a conclusion that might be correct, but is based upon on a small volume of evidence and needs much more evidence to start becoming probitive.

    If universe is non- mathematical, how does this impact status of applied math? Huge question that needs answering by your claim.

    There's something external to the Big Bang singularity?
  • Material Numbers
    ...because quarks can never be asymptotically free...EugeneW

    Asymptotic freedom ≈ forever approachable but never arrived at? Quarks are really solitary?

    Since I'm curious, I'll spout off with a shot in the dark. Is there at least a faintly tangential connection between elementary particle perturbation & the introduction of asymmetry, with rapid inflation of the pre-Big Bang universe?

    If there's a scintilla of truth in this speculation, doesn't that tell us the pre-Big Bang universe was unstable?
  • Atheism & Solipsism
    ↪ucarr Pro tip: "ontological status" =/= pragmatics (or cognition) aka "the behavior that supports it ..." :roll:180 Proof

    You're implying ontological status of a thing is metaphysical?
  • Material Numbers
    Regarding,

    QFT in curved spacetime was used by Hawking in his description of the eponymous radiation. But the calculation is approximate. It's rather well understood, but there is no connection involved between the information inside and the radiation.EugeneW

    You say,

    So the math never describes exactly and at most approximations can be made. Which simply means no exact structures exist. Which means they don't exist at all.EugeneW

    I think your above quote is the gist of your premise our universe in not mathematical. With these three sentences, I think you're conflating the signifier with the signified.

    If we look retrospectively at Newtonian physics through the lens of Relativity, we can assert that, beyond a certain region of velocity, Newton's Laws are (now) unacceptable approximations. To go on from there to say,
    Which simply means no exact structures (for near-light velocities) exist. Which means they don't exist at all.EugeneW

    Entails making a cognitive leap that is a real whopper.

    I say you make the same cognitive-leap whopper when you claim the present day limitations of the Hawking Radiation measurements amount to probitive evidence the universe in non-mathematical.
  • Material Numbers
    Math, by definition, does make material things countable.Real Gone Cat

    Numbers do not represent objects they specify the quantity of objects, the length of object, the weight of objects. But not the objects themselves.Sir2u

    Do you know you're entangling mental objects with physical objects? I suspect your premise here is rooted in subjective materialism.

    Subjective Materialism -- The only knowable reality is the represented image of an external object. Matter as a cause of that image, is unthinkable and therefore nothing to us. An external world as absolute matter unrelated to an observer does not exist as far as we are concerned.The only knowable reality is the represented image of an external object. Matter as a cause of that image, is unthinkable and therefore nothing to us. An external world as absolute matter unrelated to an observer does not exist as far as we are concerned.

    An external world as absolute matter unrelated to an observer...

    I think this is the lynchpin of the scientific method. Are you okay with science reverted back to the period before the scientific method?
  • Objective evidence for a non - material element to human consciousness?
    Okay. Very clear. Can I think of Kuhn as one who examines the (scientific) zeitgeist?
  • Material Numbers
    Since you've made this statement, do you acknowledge that material things are countable?
    — ucarr

    Of course they are, did I not make it clear enough that was the reason for inventing numbers.
    Sir2u

    I think your affirmation here forms the heart of our discussion.

    We both know that material things are countable. This means material things can be counted.

    Something about material things makes them countable.

    Mind you, the language that does the counting, math, does not make material things countable.

    Being countable is part of the makeup, part of the being of material things.

    Math, the language of counting, only entails the means of counting; it doesn't create the possibility of something being countable; it merely provides a means for doing the counting of countable things.

    We know this because, as you've been saying, human mathematicians are still struggling to count certain things for which the mathematical expression is not yet resolved.

    We suspect that these as yet uncountable things will eventually become countable, when their mathematical expression gets resolved, but the fact of their being countable prior to math being able to actually do the counting makes it logically clear that math does not impart countability to these material things, otherwise we would not struggle to count them. Instead, all we would have to do is create some math that imparts countability to these things and then they would be countable.

    We both know that's not how the world works.
  • Material Numbers
    f a thing has many uses within the real world, is that proof of its reality?
    — ucarr
    I suppose you're indirectly asking if Reality is necessarily Material or Physical.
    Gnomon

    I don't take it that far. With the above I'm implying that establishing the physicality of a thing is a good means of establishing the reality of a thing.

    I haven't jumped to the conclusion physical reality precludes non-physical reality.
  • Material Numbers
    ...most of the universe has no mathematical structure. Already three bodies interacting gravitationally do not move on mathematically well-defined ways, unless specific boundary conditions are fulfilled. So a mathematical universe is a fiction, a myth.EugeneW

    I say "not mathematically well-defined" and "non-mathematical" are two different things. Moreover, "not mathematically well-defined" does not do away with the abundance of mathematically well-defined physics. (Is not the warpage of spacetime by celestial bodies well-defined?)

    This tells me your conclusions that, "most of the universe has no mathematical structure" and "the mathematical universe is a fiction," in light of the evidence provided, are cognitive leaps. Can you support them with evidence more decisive?

    P.S. You can throw open the shutters onto a new vista for me by detailing a non-mathematical physics.
  • Material Numbers
    Wittgenstein has elaborated an argument against numbers being metaphysical.

    My questions originate from the opposite end of the continuum.
    ucarr

    I take this to mean you think numbers are metaphysicalMark Nyquist

    Your inference about my intentions makes perfect sense, however, my language is faulty, and thus your conclusion is opposite of what I tried & failed to communicate.

    In the above statement, I was trying to say that while Wittgenstein was promoting the physicality of numbers by attacking their metaphysicality, I am promoting the physicality of numbers by establishing their objective materiality.

    What you inferred is much closer to what I wrote but didn't intend, hence you correctly misinterpreted what I incorrectly expressed. (How's that for labrynthine mishegoss?)

    All of the above is to inform you that, given my physicalist intentions re: numbers, your position & mine are not on opposite sides of the aisle.

    I'm not perfectly clear on whether or not you allow that number is a physical attribute present in material objects. Since the brain is a material object, and you believe information is answered by brain state and brain state only, this would seem to indicate you do make such allowance.

    But then you conclude by saying,

    If your brain projects some meaning to the external environment that would be a false perception and it is still only a physical brain state holding a concept of numbers.Mark Nyquist

    Since you put stock in the physicality of numbers via neural networks, how do you reconcile this with saying the ascription of numericality to the external environment is a false perception?
  • Objective evidence for a non - material element to human consciousness?
    They are modular , but in a different sense than relative space-time location. The latter is a relativity defined as objective relations structured mathematically. Kuhn’s paradigmatic relativity isnt based on objective structures but subjective values systems.Joshs

    I'm thinking subjective values systems, almost by definition, are rooted in relativity, as subjectivity is always local to the individual. Paradigmatic subjectivity therefore implies zeitgeist, ethos. How does Kuhn separate his ideas from such?
  • Objective evidence for a non - material element to human consciousness?


    So, our sense of good & evil, no less than our sense of true & false, gets instantiated by neural processing?

    Does the literature of neural concept processing say anything about neural networks doing something akin to statistical analysis of individual instances of "right" and "wrong," leading to a model?
  • Material Numbers
    ...numbers were invented for counting...Sir2u

    Since you've made this statement, do you acknowledge that material things are countable?

    Could something be described mathematically if math has not been invented?Sir2u

    Could something be described fluxmatically if math has not been invented? Could something be described noxmixically if math has not been invented? Could something be described (fill in the blank with your own word) if math has not been invented? Could something be described...

    Colors have always existed, drab brown being one of the worst ever imagined. But until someone invented a method of naming them. Now it has the illustrious name of Pantone 448 C. Could it be possible that the same has happened to numbers?Sir2u

    Since I can write a sentence in parallel to your sentence, do you acknowledge that if your sentence is valid, then my sentence is valid? See my parallel sentence below.

    Numbers have always existed, 3.1415929... being one of the worst ever imagined. Then [but until] someone invented a method of naming them. Now it has the illustrious name of Pi. Could it be possible that the same has happened to colors?

    We now use math to describe the universe...Sir2u

    Since you have made the above statement, do you think if follows that the universe, which pre-dates human math, has always been describable via the language of math?

    we had to invent the math(numbers and equations) to explain it, to make the calculations fit reality. And a lot of explanations turn out to be wrong.Sir2u

    Do you agree that when you say, "humans had to invent the math to explain the universe," you are saying, again, that math was invented to explain the innately mathematical nature of the universe?

    Do you agree that from this it follows that math expresses its form and content in connection with the form and content of the universe?

    Do you agree that when you talk of math striving to fit reality, and sometimes failing, you imply that math fails in its core mission when it doesn't fit reality?

    I have asked you if you would give 2-stone and 3-stone the same number. Are you unwilling to answer this question?
  • Material Numbers
    Since I acknowledge that humans spoke of the numbers of things (perhaps without using the word "number") thousands of years before they developed the writing of numbers, you, therefore, per your stipulation, acknowledge that humans put numbers onto material objects to describe what was already there before they developed the writing of numbers?
  • Objective evidence for a non - material element to human consciousness?


    Does the Kuhn content you've quoted contain a component of relativity?

    Is Kuhn's statement implying that just as the rate at which time elapses is specific to a local inertial frame of reference, so is an artistic or scientific paradigm (frame of reference) comprised of local beliefs and local evidence that warrant consideration on ther own terms, thus crediting such paradigms as being modular?
  • Objective evidence for a non - material element to human consciousness?


    You say,

    Modern neuroscience puts the idea that they cannot be accounted for to sleep, definitively.Garrett Travers

    I infer that they has moral values for its antecedent.

    and then you provide us with,

    By leveraging well developed computational models to interrogate neural mechanisms and representations, this work has significantly advanced our understanding of concept learning by characterizing the nature of the component mechanisms and their underlying neural machinery. The result is a converging neurocomputational account of concept learning that integrates brain systems involved in attention, memory, reasoning, cognitive control, and reward processing.Garrett Travers

    Is the above quote the section of your evidence that specifically accounts for moral values (through the lens of materialism-physicalism) neuroscientifically?

    Is the upshot that moral values are one example of concept learning that is processed by the neural machinery of the brain?

    Are the component mechanisms of concept learning physical or conceptual? I ask this question because "component mechanisms and their underlying neural machinery" suggests a bifurcation, with "component mechanisms" being conceptual and "underlying neural machinery" being physical.
  • Material Numbers
    ↪Sir2u Sorry for butting in, but the universe was behaving in a mathematical way (physics + chemistry) long before humans (biology) even entered the fray so to speak. I dunno, just saying.Agent Smith

    :grin: :up:
  • Material Numbers
    Nothing has numbers as part of their make up, numbers were invented...Sir2u

    Seeing pile-of-2-stones and pile-of-3-stones, would you give each pile the same number?ucarr

    If it were discovered that Germany has already established Fluxmax-stones = 3-stones, would the equation 2-stones = Fluxmax-stones have to be changed to 2-stones ≠ Fluxmax-stones?ucarr

    That is sort of like asking if the cowshit you found was discovered to come from a bull would we have to call it NOT COWSHIT.
    No, we would just call it bullshit.
    Sir2u

    Do you agree that COWSHIT ≠ bullshit?

    When you look at 2 material objects, say, 2 stones, do you see 2 stones, or do you see the number 2 as it is written on paper?

    Since writing first appeared thousands of years after human first started walking the earth, do you accept that 2 stones first appeared long before the first appearance of number 2 as it is written on paper?

    And of course we see numbers everywhere, we put them there.Sir2u

    Do you acknowledge that the numbers we put onto material objects describe what was already there before human started writing numbers?
  • Material Numbers
    we do see number everywhere in the everywhere,Janus



    :up:
  • Material Numbers
    Giving them a label is the key there, if the number label where part of the stone no one will need to "give" them anythingSir2u

    Pile of 2-stones sits on a red square. Close by, pile of 3-stones sits on a green square.

    Seeing pile-of-2-stones and pile-of-3-stones, would you give each pile the same label?

    Do you think 2-stones can be replaced with Fluxmax-stones and would make no difference?
    — ucarr

    Of course it could be replaced with anything, as long as it is universally accepted. Fluxmax-stones could quite easily be 2-stones in some sort of technical language.
    Sir2u

    If it were discovered that Germany has already established Fluxmax-stones = 3-stones, would the equation 2-stones = Fluxmax-stones have to be changed to 2-stones ≠ Fluxmax-stones?
  • Material Numbers
    We were discussing the materialistic qualities of numbers, which is no existent.Sir2u

    What about the materialistic qualities of number?



    There's a stone sitting on a red square. Close by, there's a stone sitting on a green square. A person sees them and gives them a label. Label = 2-stones.

    Do you think 2-stones describes something that's there in the stones?

    Do you think 2-stones completely different from stone on red square and stone on green square?

    Do you think 2-stones is a label randomly given to stone on red square and stone on green square?

    Do you think 2-stones can be replaced with Fluxmax-stones and would make no difference?

    If you think the replacement makes no difference, what can be done to let people know
    2-stones = Fluxmax-stones?
  • Material Numbers


    Ever read a biology book?

    You've been debating me about pure math & how it's uncoupled from the material world & I've been arguing that applied math is about the material world & that pure math, being about how math logic works, is also, ultimately, about the material world because logic has no meaning outside of the continuity of interrelated material things.
  • Material Numbers


    Can you elaborate a bit more? I've been thinking that with more loops per fixed interval of time,
    A. I. will become self aware.

    If so, this leads me to thinking the self (maybe the soul) lives in the interstices of the loops, and is immaterial, epiphenomenally speaking.

    The self is an associate of the material world, but is not local to it.
  • Material Numbers
    Indeed. An imagination is a simulation that is seen. With the minds eye?EugeneW

    Now you're talking about feedback looping with vertical stacking.
  • Material Numbers
    I would think that it would be impossible to have a man made physical object without there being a concept on which to base it.

    But it would be impossible to form a concept of something natural without having at least some of the characteristics being known.
    Sir2u

    Let's reverse the order.

    But it would be impossible to form a concept of something natural without having at least some of the characteristics being known.

    I would think that it would be impossible to have a man made physical object without there being a concept on which to base it.

    Human concepts are based on observations of surrounding natural forms. Proceeding from there, humans make alterations to their naturalistic concepts. These alterations are derivatives of the naturalistic concepts that preceded them. They are still natural forms because human nature, as the name indicates, stands as another form of nature, so the products of human nature, whether naturalistic or altered, also stand as other forms of nature.
  • Objective evidence for a non - material element to human consciousness?
    The priest just wants to be remembered for his good deed. As he should. By doing so he shows that there exists something non-material, something non-explainable by material processes. Something contained in the matter. Call it love, hate, divine, good, or bad.EugeneW

    :up:
  • Objective evidence for a non - material element to human consciousness?
    The theory involves the idea of ancient pedigree that, concomitant with the material brain, there exists also a distinct and irreducable non-material mind, this being proposed as the fundamental agent of our moral awareness capable of enabling a type of insight not explicable in terms of the neural processes...Robert Lockhart

    How is that different from what dualists have been saying for thousands of years? From your original post I had assumed that we are talking about physical evidence.T Clark

    In context, the claim seems to be about a certain type of human behavior i.e., moral behavior. Proceeding from there, the claim is that moral behavior is not traceable to cognitive operations rooted in neural networks.

    So, the objective (physical) evidence of non-material cognitive operations is moral behavior.

    As I see it, the argument now focuses upon whether or not moral behavior is traceable to cognitive operations of neural networks.

    Suppose moral behavior is merely an effect of the logical operations of neural networks.

    One counter-narrative to this supposition relates the example of self-sacrifice motivated by agape love, as in the case of the Catholic priest who took the place of a prisoner sentenced to death within a Nazi concentration camp. There's nothing blatantly self-serving or logical about such behavior.
  • Material Numbers
    An imagination is a simulation but a simulation doesn't need to be an imagination. They are both simulations. An imagination is an imagined simulation. A simulation is just a simulation.EugeneW

    I think EugeneW is saying there is, in the case of human, a SELF which has intentions, whereas, in the case of computer, there is NO self, and thus there are no intentions, just a programmed, logical continuity of coded commands.

    A simulation "borrows" the selfhood & the intentions of the computer programmer, a human.

    A computer simulation program is like an appendage of human, an extension, like an arm, under the control of human.
  • Material Numbers
    Each day recently arXiv.org has received about 200 research papers in math. Many of these are "uncoupled from empirical experience", yet thousands of math people find them intelligible.jgill

    As you may have seen in my statement to Sir2u above, pure math is concerned with the innate workings of the language of math itself. Any brief survey of the sciences with show you just how worldly is math in application to many, many real world events. An examination of how this language works by its own lights is thus an examination of our real world, although not directly.
  • Material Numbers
    But they both are only physical representations of concepts.Sir2u

    The connection you name above goes in both directions.

    Concept - Philosophy - an idea or mental picture of a group or class of objects formed by combining all their aspects. -- The Apple Dictionary

    Consider a) Mental representations of material objects; b) material representations of concepts

    Which comes first?

    Even when we form concepts of mental things i.e., concepts of concepts, the line of reality traces back to material objects within our empirical world.

    Pure math is a language about how the language of math works logically.

    What is logic? It is an examination of the continuity that connects events of our lives into an intelligible narrative. A narrative is intelligible when a group of people all recognize noteworthy actions & reactions of humans bound together within cause-and-effect relationships.

    Apart from our conscious experiences within our daily world, logic has no intelligible meaning or value.

    Since math & logic are interwoven into our daily experiences, a study of how math works logically, pure math, likewise is intimately interwoven into our daily experiences.

    You should ask a pure mathematician whether their mind enters an immaterial realm while they're working.
  • Material Numbers
    These are very rigid statements that are beliefs, not facts. You should indicate as such. Should a philosopher state their beliefs as facts?jgill

    The key word in my statement is signification. I'm tempted to argue that my claims are true by definition, since a sign without a referent is like a material object without elements or compounds. I sense, however, that is a weak argument.

    As for my etiquette as a person making claims (you compliment me with the title of philosopher), your response exemplifies what it denounces.

    Saying,

    These are very rigid statements that are beliefs, not facts.jgill

    Is like saying,

    This statement is false.

    What fun is philosophy without bold claims subject to refutation?

    By the way, what is your refutation of my bold claims?
  • Material Numbers
    The positional grid is not a material thing, it is an abstract.Sir2u

    If I remember Battleship correctly, there is a plastic platform full of holes, the grid where a player's battleship moves to various positions.

    Writing words and numbers down does not make them physical objects, it just makes it easier to transmit ideas.Sir2u

    No argument with you here. Yes, number symbols & words are signs that refer to material things.

    I'm saying that number symbols refer to & derive meaning from material things whose set of attributes includes one particular attribute I call number. All of this verbiage is an attempt to say material objects are numericalizable because they have a built-in property of being movable, which is to say, positionable.
  • Material Numbers
    So physical systems, given satisfying conditions, can instantiate mathematical structures just as ideas in our heads can.Kuro

    Abundant thanks with much gratitude to you, Kuro. Your input here is tremendously substantial and, I presently like to think, more encouraging than otherwise. There's much in your input I must study further. If warranted, I hope additional input from you is forthcoming.
  • Material Numbers
    Will you go to my world devoid of spacetime and think about the role of numbers there?
    — ucarr

    There's not a lot to go on based on what you've said, but if by that you mean: are numbers real in the absence of reference to space-time?, my response would be again: 'well what about pure mathematics'?
    Wayfarer


    Pure mathematics is the study of mathematical concepts independently of any application outside mathematics.

    ...the appeal is attributed to the intellectual challenge and aesthetic beauty of working out the logical consequences of basic principles.

    ...presently, the distinction between pure and applied mathematics is more a philosophical point of view or a mathematician's preference than a rigid subdivision of mathematics.
    -- The Apple Dictionary

    It seems to me -- especially in light of paragraph 3 above -- that pure math, in order to be intelligible beyond the circular reasoning of logical truth by definition, must trace back to material objects interrelated.

    ...almost all mathematical theories remained motivated by problems coming from the real world or from less abstract mathematical theories. Also, many mathematical theories, which had seemed to be totally pure mathematics, were eventually used in applied areas, mainly physics and computer science. -- The Apple Dictionary

    ...intellectual challenge and aesthetic beauty of working out the logical consequences of basic principles

    Logic is continuity, which is to say, interrelationship, rooted in inference. Would anyone have any notion of continuity & interrelationship between material things without firsthand experience of a spacially-extended, material world that affords empirical experience?

    Pure math, and all other forms of signification, once uncoupled from empirical experience, become unintelligible.

    Numbers, uncoupled from interrelated material objects, become random, unable to signify anything intelligible.

    Abstract thought is non-specific WRT our material world; it is not uncoupled from our material world.
  • Material Numbers


    I didn't say an abstract conception of a number is a material thing. I implied it is a sign that has a material referent.

    I'll go to your references. Will you go to my world devoid of spacetime and think about the role of numbers there?