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. — ucarr

Music to my ears. My standpoint is this: Humans are not capable of truly original thought. What we call original thinking is just small pieces of prior experience (originating from the physical worldfrom the physical world) that we recombine in a new pattern.

The reason why I think this is because we know that the wavelengths of light goes far beyond the spectra that we call visible light, so if our eyes where constructed differently we would be able to see new colors. And yet, when you are asked to imagine a new color, you find that it is utterly impossible. We are not even capable of doing any truly original imagination.

Maybe I haven’t tried enough different drugs, I hear good things..

Music to my ears. My standpoint is this: Humans are not capable of truly original thought. What we call original thinking is just small pieces of prior experience (originating from the physical worldfrom the physical world) that we recombine in a new pattern. — mentos987

That agrees with Kant even, that all knowledge starts from experience. However, not all knowledge is derived from experience (even if it can be in some traced to it). The concept or image of a golden mountain does not come from experience but from the our ability to synthetise the gold and the mountain.

Likewise, continuing from my original post, even if many things such as vector spaces and analytic geometry ultimately derive from Peano arithmetic (I am not sure if it does, I would have to check on the axioms but I don't have time), they extend from the arithmetic, as the complex field extend from the naturals. 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.

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.

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.

The concept or image of a golden mountain does not come from experience — Lionino

original thinking is just small pieces of prior experience that we recombine in a new pattern — mentos987

Yes, the golden mountain is a combination of Gold + Mountain. I agree that it is original but the elements of it originate from nature. A randomizer of all existing physical combinations could achieve the same.

There is nothing in nature (or in mind) that i refers to — Lionino

"i" was crafted to fill up a gap in mathematics, it was not directly inspired from nature, true. But, we have found out that it does correspond to real natural behavior in electricity. I still believe that math is fully derived from physical reality, even if we have taken "leaps" of logic to reach where we are.

derive from Peano arithmetic (I am not sure if it does — Lionino

I am not sure either, but I remember that “deriving from simpler math” was a constant exercise in all of my higher math courses. So I assume that you can derive it all the way back to + - / * .

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.

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.

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.

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.

IMHO, 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).

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.

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?

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.

I still believe that math is fully derived from physical reality — mentos987

It depends on what you mean by that. All knowledge starts from experience, we open our eyes as a baby before we are even able to reason and thus form knowledge.
Math, however, does not seem to fully derive/be apprehended from physical reality, because otherwise all mathematics would be applicable to physics, and that is clearly not the case — yet at least.

Math, however, does not seem to fully derive/be apprehended from physical reality, because otherwise all mathematics would be applicable to physics, and that is clearly not the case — Lionino

Maybe, I am unsure. It all comes back to not being able to imagine a new color as I stated here

The reason why I think this is — mentos987

From this exercise, I deduce that it is more likely that all the constituents of our most advanced math are still basic physical elements that we have prior experience of.

"would be applicable to physics" We can make plenty of new combinations of elements and most of them have no place in reality.

A toddler can see the difference but does not see it as a numerical difference. He can see the difference between an isolated object, and see objects of the same type, or similar, together and separated in space. But there is no number there that he sees. If we tell the toddler to repeat what he has found (difference, spatiality, similarity, etc.) as an order (like in a market) he will not be able to. He needs the objectification that a symbol gives him, for example, in such a way that this symbol can enter into a relationship with other symbols. If we ask what a '9' is, we cannot answer with difference, nor with spatiality, nor with similarity. We respond in relation to other numbers with which this 9 is contextualized, as an addition, of unity, for example, among many others.

The case is that "the number" always appears as another of the things we count. Someone who has already learned elementary mathematics (such as simple numbering) can ask them to give you two oranges or two apples. 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. That is why we must differentiate between the number and the numbered, and in fact in practice we always do.

With respect to the topic in question we cannot say that the number (in this case the number "1") is an essential (or internal) property of the thing. It is an external property of the thing.

If none of these numbers are there, then how do you assign the number-signs to what you see? — ucarr

Isomorphism.

The in-absentia status of pure numbers gives the impression of their categorical independence, but no, numbers never completely exit the natural world. — ucarr

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

If one models the universe as beginning-less, and thus origin-less, does cosmology then cover the totality of existence? — ucarr

We don't know – possibly not. The observable universe is the only "existence", however, that matters significantly to us (i.e. terrestrial life).

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".

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

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.

You clearly credit metaphysics with real status. How do you reconcile this with your physicalist identity?

These terms don't make sense to me. I am not a (logical) positivist or (Humean) empiricist. My methodological physicalism is a function, or corollary, of my philosophical naturalism which is a metaphysics (or speculative supposition).

Is it the case you think metaphysics not a categorical separation from physics but instead a higher-order physics?

No. I think metaphysics concerns 'a priori speculative suppositions about nature (i.e. humanly knowable aspects of existence)' and physics concerns 'explaining transformations in nature by making testable, hypothetical-deductive models'. I consider methodological physicalism only a paradigm for making/evaluating 'physical models' (sans non-physical ideas or entities) and interpreting their results, or problematics.

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. — ucarr

Could you provide some examples of such material objects? How do you find countable objects from the object you can't count?

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.

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.

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?

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

This makes sense to me. Space is extension and extension implies measurability, quantity. Something similar may be said of time. Space and time are also dependent on differentiation, and differentiation entails individuation. Where there is difference and similarity there is also number and category. I think it arguably all comes down to real configurations and patterns that are reflected in our cogntions and recognitions.

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?

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.” — ucarr

In that case "two fingers" is the third one I am referring to. "Two fingers" is the sign here. To the "two fingers" you have to ADD "oranges" or "apples". Why do you have to add them? Because with the number the numbered thing is not given. The child already understands this autonomy of "2" (for example with the other fingers of the hands) and is able to apply it to different things. He has evidently learned it as something third that is not between apples and oranges. Well, let's remember, if the number were intrinsic to things there would never be two pairs of fruits, the "2" would not be a third; the "2" would belong to one thing and not another (so as not to violate identity).

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 — ucarr

No. Relating them (reference) to something "tangible" does not imply their identification. The relationship in this case presupposes two terms, the number and the numbered as something different. The effective relationship implies only that we can do it and that there is a passage from the number to the thing numbered. How is it possible that we can manipulate things by counting them and not fail at every attempt to manipulate them? It is not because there is something numerical in the thing, but because the thing allows itself to be chiseled, so to speak (that is why in general geometric figures do not exactly adjust to the tangible things to which we apply, the same thing happens with numbers, there are always a rest).

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

Chiselling. You have to adapt the raw materials for their numerical application. Only then can you successfully manipulate them (numerically, in a exact way) and build bridges, pyramids, etc.

Paradigm =/= model.

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

My original question was about number, not object. But your reply was about object, and I was asking about them too. Why do you want to count object which you can't count? And " a word single in number,"??? - what does it mean?

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?

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.

I like this thread, as I think it pushes folks to dig deep, to try to explain some of their 'fundamentals,' when it comes to how they personally perceive the universe and their personal existence in it. it's interesting and useful to try to analyse the level of 'rationality' and 'logical rigour,' expressed whilst at the same time, attempting to self-examine your own rationale and logical rigour against others.

Imagine we were as sentient as we are now, but had no ability whatsoever to memorialise any data at all, outside of our physical beings but we did have a 100% eidetic memory ability and a memory capacity that means each of us can recall everything we have ever observed/encountered etc.

We could identify an apple and express the idea of a unitary value, by some kind of language mechanism. We can't use any kind of 'glyph' but we could say agree on an emitted sound, that represented a unitary amount, like one apple. Making the sound twice would mean two apples.
Over time, we could employ different sounds to mean different quantities and develop base number sets such as base 10 etc. But this is what we do now, yes, 'ten' and 'twenty' are just different sounds.
We don't have to 'glyph' them and write them for such to exist. 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. What would you say is the absolute minimum required to be able to differentiate one 'thing' or 'existent' from another? What minimum process is required? Would it be something like awareness of unitary durations? as a minimum fundamental. Time units must pass and something must be aware of that?

Number is an essential, material property. — ucarr

Hylomorphism? :chin:

IIRC paraphrasing Peirce / Wittgenstein, arithmetic (e.g. counting) is a practice, therefore material in effect; numbers, however, signify patterns (i.e. ideas) abstracted from the arithmetic practice and so themselves are not material. In other words, we assign "properties" to objects (à la Kant) rather than "discover" that objects "have" them. Or as Meinong might say: 'arithmetic exists' whereas 'number subsists'.

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.

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.