Numbers: A Physical Handshake with Design
This OP keys off Philosophims conversation: A first cause is logically necessary.
There must be a starting-point physical entity, whether differentiable, or not. So, there too must be a starting-point counting number.
Theres no reductio ad absurdum re: two simultaneous starting-point things because these two starting point things are bi-conditionally connected. They are one-and-the same in the sense that they are essential attributes of each other. Where there is thing there is number, and vice versa.
These paired starting-points, operating in spacetime beginning-less, unbounded, finite and relativistic, exemplify the necessary arbitrariness of pre-analytic beginnings.
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.
When we postulate any object, we necessarily, bi-conditionally postulate a number one. Material object and number cannot be divorced.
Number is an essential, material property.
Moreover, given the multiplicity of solo ones, we must conclude all material objects are countable, both individually and collectively.
Therefore , material objects can always be gathered together into collections, that is sets.
Solo ones and sets entail physically real numbers as one of their essential, physical attributes. That we never fail to differentiate differently numbered sets, neither perceptually nor conceptually, evidences the essential status of number, the physical property.
Herein, there is no conflation of sign with referent because of the number zero. It is an absentially real number whose presence changes other numbers in its field of influence. As the mind, another, absentially real, presence, in parallel physically changes material objects within its field of influence.
There must be a starting-point physical entity, whether differentiable, or not. So, there too must be a starting-point counting number.
Theres no reductio ad absurdum re: two simultaneous starting-point things because these two starting point things are bi-conditionally connected. They are one-and-the same in the sense that they are essential attributes of each other. Where there is thing there is number, and vice versa.
These paired starting-points, operating in spacetime beginning-less, unbounded, finite and relativistic, exemplify the necessary arbitrariness of pre-analytic beginnings.
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.
When we postulate any object, we necessarily, bi-conditionally postulate a number one. Material object and number cannot be divorced.
Number is an essential, material property.
Moreover, given the multiplicity of solo ones, we must conclude all material objects are countable, both individually and collectively.
Therefore , material objects can always be gathered together into collections, that is sets.
Solo ones and sets entail physically real numbers as one of their essential, physical attributes. That we never fail to differentiate differently numbered sets, neither perceptually nor conceptually, evidences the essential status of number, the physical property.
Herein, there is no conflation of sign with referent because of the number zero. It is an absentially real number whose presence changes other numbers in its field of influence. As the mind, another, absentially real, presence, in parallel physically changes material objects within its field of influence.
Comments (142)
Conclusion: number-as-property, being essential and physically real, and being tied inextricably to material objects, is discovered. They are not purely conceptual objects, accessible to the mind only.
Numbers are discovered, not invented. Numerical properties and numerical relationships likewise are discovered, not invented.
The number zero shows how emptiness is permeated by these same numerical relationships, so existence presupposes number-as-property.
If number-as-property is physical and essential, then there is an answer to an important question: How can mental objects have causal effects upon the physics of the natural world? The answer is numbers.
This is the necessary conclusion of both the number-idealist and the number-realist.
Example: Civil engineering demonstrates idealist control of the physical if youre a number idealist: The building of a suspension bridge across a body of water as, say, San Franciscos Golden State Bridge, demonstrates numbers manipulated to specifications required for a stable road across a bay. How ideal number shakes hand with real object remains to be explained.
If, on the other hand, youre a number-realist, then you understand theres no unexplainable interface of ideal and real in the design and build of a suspension bridge. Numbers, like the bridge itself, are physically_materially real. The two are integrated and holistically consistent.
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 isnt 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.
If 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. "5" is not oranges, nor apples, it only applies extrinsically. Therefore is wrong to say that "5" is physical "because apples and oranges are physical". You must say that numbers are physical things by itself to the extent of numbered things (apples and oranges).
Then it is necessary to define what you mean by a physical thing.
Counting numbers originate from the fact that the identity self-distributes its own Boolean algebra. The set in its entirety (unity) corresponds to "1" and the empty set to "0". Subsetting allows the construction of von Neumann ordinals - sets that correspond to counting numbers.
Because physics consists of a set of points with trajectories in a mathematical space, this structure is everywhere-distributed in physics. That explains the connection between your "starting-point physical entity" and your "starting-point counting number". They do not "begin" simultaneously though - every physical fact depends on facts about this mathematical structure, but not vice versa.
Quoting 180 Proof
Like the rules and strategies of (e.g.) chess, respectively (i.e. grammars and narratives).
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?
[quote=JuanZu;868783]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.[/quote]
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.
Assuming you possess proper vision, have you ever been unable to distinguish five oranges from two oranges?
Quoting JuanZu
Physical: anything subject to the spacetime warpage of gravitational fields.
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 minds 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? (Theyre solely existential.). Also, what say you about math axioms being incomplete? (If theyre incomplete, theyre not ideals.)
Pattern-making in total abstraction from physical reference, beyond convention established by precedent, tells you what?
We do not know. "Have" refers to property. I prefer to say apples and oranges can be counted as something potential. We learn to count. But first things appear differentiated. The number is also differentiated, and in that case we would speak of isomorphism.
Quoting ucarr
Well, they always tell us something significant and meaningful about themselves. Whether they are useful or not would be something extrinsic.
Quoting ucarr
How is number 5 deformed by gravitational fields
Quoting JuanZu
Quoting 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?
I have said "I have" as I can say "I have counted." 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. The latter is true and the former is false (due to impossibility to identify the number and the numbered).
Quoting ucarr
Because I have also indicated something that I do know: That the apples and oranges have been counted and have been subjected to number. And because they are differentiated (they are in a different place, for example, or do not share the same space) they can be counted.
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.
Quoting ucarr
I don't presuppose the existence of "physical minds".
Quoting ucarr
What a priori axioms does physics possess? Any that math possesses supports my position.
Quoting ucarr
They are more general than physical rules but less general than logic and also less general than the global identity.
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 lets 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. Thats why I say math is a physical property of the natural world. Only there does number possess existentiality, meaning and usefulness.
Why 'material'? In what sense? In what sense is pure maths concerned with physical objects?
Quoting ucarr
Rather an odd expression, but surely one of the confounding things about mathematics, is its applicability to physics. That is the basis of Eugene Wigner's celebrated essay, The Unreasonable Effectiveness of Mathematics in the Natural Sciences. I will not propose to explain this 'unreasonable effectiveness', as Wigner himself could not, and he a Nobel-prize winning mathematical physicist. But I would defend the modest claim that one of the grounds for the great successes of modern mathematical physics, was the discovery of the means by which to express the measurable attributes of physical bodies using mathematical logic. This enabled for great predictive success, whereby predictions are made that appear to 'fall out of the equations', but which lead to real-world discoveries such as Dirac's discovery of anti-matter. (And think about the etymology of the word 'discovery', for that matter.)
You would think that if mathematics were purely conventional, it would lack this ability to make genuine, unexpected discoveries about nature. The surprising effectiveness of mathematics in making accurate, sometimes unexpected predictions about the natural world suggests a deeper connection between mathematical structures and physical reality. This view opposes the idea that mathematics is just a tool invented for practical purposes, instead hinting at some intrinsic relationship between mathematical concepts and the fabric of the universe.
But in all this, I fail to see why we should accept that numbers are material properties. They may be applied to the measurable attributes of material bodies, but that is completely different to saying that they are material entities.
Could it be that maths, like space and time are part of our human cognitive apparatus in some way?
Quoting Hallucinogen
Quantum computing has something contrary to say about the last part of your claim.
Quoting 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.
Quoting Hallucinogen
What a priori reason is practiced by brain in a vat never in contact with the world?
Quoting 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.
Quoting ucarr
Speak! Without antecedent, existential fact, science and math cant even get started.
Something very like Kant's 'concepts without percepts are empty'. 'Not uncoupled from the material world' does not mean 'material in nature'. Humans are metaphysical beings - we can peer into the intelligible domain and return with things like computers and airplanes.
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.
There are so many kinds of mathematicians and so many kinds of mathematics it's foolish to try to generalize. I'm guessing about 1200 PhDs are granted each year in the USA, with about half being American citizens. Probably a large majority never publish more than, say, two papers in their careers - for various reasons. But there are those, like myself, that find the exploration of new ideas fascinating.
That's how I see myself and many others: Explorers. It's no wonder you find mathematicians among rock climbers and mountaineers.
Quoting ucarr
Mysteries never cease :roll:
Could be. :up:
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.
Tosh. Kant detested materialism, as do I.
Another mathematician, but one who ventured into philosophy and cognitive science, was Charles S. Pinter (whom I discussed briefly with jgill in the past (although I learn Pinter has since died, but then, he was 96 at time of death)). Anyway, his maths books are here, about which I know nothing, but his final work was the very interesting Mind and the Cosmic Order, published in Feb 2021, a
detailed abstract of which can be found here, and to which I would look for a possible answer to this question:
Quoting Tom Storm
Creativity can enter when one speculates on new topics and definitions. If a flight of imagination leads to a new concept (if, in fact, there are any), then what flows from a logical analysis of this concept can be considered discovery. In other words, once the initiating concept is delineated, all that follows is in a sense immediately established - to be discovered. But the process of math research is almost always a sometimes convoluted combination.
Practicing mathematicians pay virtually no attention to this philosophical discussion.
Everything that quantum computing allegedly does is mathematical. If by physical you mean something more generic than existing at a point, then you'd have to mention what it is.
Quoting ucarr
I don't think it does.
Quoting ucarr
An abstract mind could have an impact on the natural world without being identifiable in it, if abstracta are more generic than concreta.
Quoting ucarr
All of it? A priori reasoning doesn't come from sensory stimuli, by definition.
The issue I see is that math is like physical law. We have a mental concept for it yes, but that concept was brought about from observing the physical world, which already operates on math. Any action we take, based on our concept of math or physical law, will still have its origin in physical reality. We observe -> we form concepts -> we let the concepts affect our physical actions.
"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 math is just us mimicking what is already there.
Quoting 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 its of the natural world. Its of the mind a well; Its not simply of just one or the other. However, in my opinion, it is more at discovery than at invention.
Quoting jgill
So, you detest materialism? Post herein a picture of your right index finger after youve chopped it off.
What do you mean by differentiable here?
Quoting ucarr
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.
Everything from "Theres 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.
The text after is confusing as well, though not undeciphrable.
Quoting ucarr
Now I understand what you are saying. It seems that, for you, numbers are something found physically in every object. That 2+2=4 is the law manifested when you push a pile of 2 objects onto another a pile of 2 and you end up with a pile of 4 objects every time. The problem with that 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.
Quoting mentos987
I can't see how things such as calculus, vector spaces, and higher dimension geometry are somehow derived from our physical world.
Quoting ucarr
If numbers are physically_materially real, then how long and heavy are they? What shape and colour are numbers?
All complicated math is derived from simpler math. The basics of math are taken straight from reality. More complicated math is simply us running away with the tools we have formed.
And thus you are a dearly valuable exception to the rank and file establishment.
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.
Your premise presupposes what it seeks to contradict. Dont take my word for; take your own words for it. Re-examine your closing sentence.
Quoting mentos987
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. The mental concept of math is an intermediary.
Quoting ucarr
I claim here that our concept is mimicking a more complete set of math that is governing the universe.
Take all this with a bucket of salt, I am on loose footing here and I know it ^^
Edit: Thinking about it some more... I don't believe in pure mental concepts at all, not the way you guys are talking about it, so I don't know what I am arguing. I don't think that a human mind can conceive of anything that is completely outside our prior experience, and I think our experience is locked to physical reality.
I wouldn't say it "responds", it's not a mechanism. It's intentional content and it's abstract and propositional. You have a mind, so you have it.
Ever seen a toddler who, knowing next to nothing about numbers in their head, fails to distinguish one offered lollipop from two offered lollipops?
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 lets 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? Theyre Kants empty concept without percept.
Well, I mention this because you used bridge building as an example of mental concepts taking physical form. I am trying to add to that that the mental concept in turn came from an original physical form.
Quoting ucarr
I am unsure what we are talking about. I do not claim that math isn't real, just that it isn't man made. The symbol "3" may be manmade, but the symbol isn't building any bridges, it is just part of the shared concept. We have constructed ourselves a concept that we implement in engineering sure, but I think that all inspiration for it comes from physical reality.
I should maybe be excluded from this discussion..
Quoting mentos987
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. Then perhaps a proto-two will appear in his mind that will then finally be objectified and solidified as knowledge thanks to teaching and learning. But obviously "the two" will not have arisen from the thing itself, rather it is something that happens to the thing when it enters into a relationship with someone who defines the measure and sees the difference between the two, and the Lollipops.
Greed. Even a toddler have enough inbuilt math to enable them to be greedy and want what they think is "more".
I wouldn't say "in-built math". Toddler can differentiate and identify. The quantity appear in another level perception. After all, when we think in numbers we don't think at the same time all the things we have counted.
If you feel that crude metaphor conveys anything about the point at issue, perhaps it is because you don't understand it.
Quoting 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?
Quoting JuanZu
Ye "in-built" may not be true. I do think toddlers do a calculation to determine what is more and what is less. It is a form of math.
But! The imaginary worker-philosopher might have told me "there are not two, there are 57." I wonder, is number two in number 57? But objectively there are not 2 melons, there are 57. 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, a difference, a partition, a slice, a rule, a number simply different from 57 regardless of whether they are melons, apples or anything else? So number is different from numbered things.
Oh my, you are on a roll. :gasp: First you suggest machine gunning people crossing the Rio Grande, and now you suggest the obvious. Sad days, indeed. :cool:
Perhaps this is the Tarantino inspired version of Johnson's, "I refute it thus!"
(although, not being one to point the finger.... :lol: )
I love that statement, it's so ........ exciting, when thoughts of "well what can I do with my life, what 'meaning' or 'significance,' can I nurture and what legacy can I produce?", dominate a persons rationale.
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.
Giant Molecules Exist in Two Places at Once in Unprecedented Quantum Experiment
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.'
Is this what you were referring to @ucarr? with:
Quoting ucarr
Youre welcome to continue weighing into this conversation on the physicalist side, if that position isnt also averse to your inclinations. Hoping youll give us more goodies like the tree-bridge.
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 havent tried enough different drugs, I hear good things..
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.
Quoting 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.
Quoting Lionino
My premise to be proven by my arguments is that material object and physical number are biconditionally linked as equivalent.
Quoting Lionino
If a starting point and a number are separate, then its 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 thats a strong argument that number as a priori abstraction only is wrong. It is my argument.
Quoting Lionino
I suspect the reason why infinite sequences are not other-worldly is tied to the math solution to Zenos Paradox. If its true we move through the world without getting entangled in the asymptosis of the infinitely divisible number line, then its also true that infinite series are real but ontically undecidable.
Name a material object with any of the following: length, weight, form or color that you cant count. If you find all such material objects are countable, you have your answer.
Quoting 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.
Quoting 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.
Quoting 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 + - / * .
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 its seeking to act upon information about the world. Either way, its a response to the world, whether directly or indirectly.
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.
Quoting Wayfarer
I beg your pardon for my digression into crude raillery.
Quoting Wayfarer
Im crediting jgill with being an exception to the practice of mathematicians giving the blind eye to jabbering conversationalists. Im 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.
If none of these numbers are there, then how do you assign the number-signs to what you see? If youre a brain in a vat, how do you find meaning in articulating sounds as signs for number signs?
Quoting JuanZu
Here we have a chance to see how things differentiable can still be linked and thus are not different.
Quoting 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.
Quoting universeness
Quoting universeness
Quoting universeness
Hear ye, hear, ye! All yall students come to order! Professor universeness is in the house! So listen up. Some foundations bout to get laid.
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 arent.
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?
Quoting Tom Storm
Einstein took Kants 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 doesnt mean contrary to logic and reason; instead, it means subtle and sometimes absential materialism. Prime example:
[math] e = mc^2[/math] 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 Kants space and time and proved them physical.
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.
Maybe, I am unsure. It all comes back to not being able to imagine a new color as I stated here
Quoting 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.
Quoting ucarr
Isomorphism.
Quoting ucarr
Well, given what I've said independence is real. Otherwise we fall into contradiction and the complete uselessness of mathematics.
We don't know possibly not. The observable universe is the only "existence", however, that matters significantly to us (i.e. terrestrial life).
In this statement, for clarity's sake, I prefer fundamental to your term "essential".
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.
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).
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.
Could you provide some examples of such material objects? How do you find countable objects from the object you can't count?
Quoting 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 dont ask him with words because hes 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 dont 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.
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 youre 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.
Quoting 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 wont work because thats higher-order applied math examining math grammar which, in turn, is grounded in tangible things countable.
Since your question asks about the object you cant count, a word single in number, havent you already counted it?
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.
Quoting 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?
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).
Quoting 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).
Quoting 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.
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?
: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?
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'.
Quoting Lionino
Your post is interesting. Let me clarify: that math covers more than the simple physical I dont 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. Whats 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 dont work as evidence of maths categorical independence from the material world.
Quoting 180 Proof
How are essential and fundamental distinct? Websters Thesaurus lists each word in the others list of synonyms.
Quoting ucarr
Quoting 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.
Quoting 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:
Quoting 180 Proof
You seem to be referencing the particular metaphysics of physicalism, not the general metaphysics of ontology.
Maybe you should consult a 'dictionary of philosophical terms'. :roll:
Quoting universeness
I got a little carried away with my vernacular. With the above salutation Im praising what you posted.
Quoting 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 Im 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 everyones 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.
Im not ready to claim number is the minimum distinction required for the intelligibility of sensible experience, but youve done much to help me advance in that direction.
No problem and thank you.
Quoting ucarr
I would like to pursue this a little more and press you on your thoughts on trying to take human thought down to some notion of a very 'fundamental' or 'essential' minimum. We don't even have to be restricted by the notion of human thought. Let's consider what we think would be required for any existent in the universe to be aware of, or be able to distinguish any other existent. Must all such exercises always land at the problem of hard solipsism? I have always considered solipsism to be nonsense but I still can't prove hard solipsism is incorrect, no-one currently can.
What is needed for such a notion as a quantum fluctuation or a singularity or a god origin? are the two fundamentals required, simply duration and space? and then something must be aware that such has happened so that the notion 'event' can become the next most essential happening.
Quoting 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.
As I typed to @ucarr, I like this thread as it obtains deeper clarification from folks, as to their position on the notion of fundamentals. My question here will not assist the OP discussion but it will help me understand your position a little better. It's based on a recent episode of Matt Dillahunty on the call-in YouTube show, 'The Line.' A theist called in to talk to Matt about his materialist/naturalist stance. Matt interrupted him to say that he was not a philosophical materialist/naturalist (he considered the two terms synonymous) but he was a methodological materialist/naturalist. He then went on to clearly explain the difference. So, are you declaring the same as him, in the quote above? You are a methodological naturalist and not a philosophical one as you refuse the burden of proof that is assigned if you state that there IS no existent outside of the natural universe.
Isn't the measurement of his body just a form of data? Data is not material or physical. Is it?
Quoting ucarr
Do music and song have size? Is it a metaphor or what?
Quoting Corvus
Your questions are good. They point to my main point in all of my jabbering: number-signs (which are not number, the physical property) attach themselves to physical things. Together, number-signs and their substrates, physical things and physical properties, form something that can be called complex materialism. It has two parts: physical things and number-signs. The latter denote their material substrates in the language games humans must play.
You ask about the singers body in my little story. The measurement of his body is data, but that data has no meaning without his body to which it refers.
You ask about the measurement of music. The measurement of music in signs, whether math or verbal, takes its meaning by its attachment to the existential reality of its substrate, the singing man.
Whats the meaning, which is to ask, Whats the reality, of musical notation on paper if it doesnt refer to the singing man, or even to the leaves rustling in the breeze?
Abstractions of the human mind are emergent from the physics of the natural world, but not wholly independent from same.
But isn't the measurement data of the body, the property of the body, or a part of description of the body, rather than the body itself? For example, a person has a certain data associated with him such as DOB, name, sex, place of birth, height, weight etc etc. DOB is just one of the properties of the person, but it is not the person. There will be millions of other people with the same DOB, so DOB itself doesn't say anything about a person until it had been attached to a person.
It is not meaningful itself until it is attached to a person, but that is what the relation is about. You have measured and attached the measurement, hence related the numbers to the body and gave meaning to the numbers as the measurement of the body. Hence numbers are concepts, not physical or material?
Quoting ucarr
Again the musical notation on the paper has no meaning until it had been performed by the singer. The notation itself is not the music, but an instruction how the singer must perform the music? Therefore, should we not class it as a concept too? Once the singer masters how to sing the song according to the instruction, the singer no longer needs the instruction. He throws it away in the bin, and just sings away as he pleases and wants on his own style and moods. He would still follow the instruction for the singing, from his memory, not from the notation on the paper.
Quoting Corvus
Apparently without intending to, you state my premise exactly.
Quoting Corvus
Here you are expressing my premise again with a more complex model. Music, a complex interweave of numerical values of vibrating strings, exemplifies, more nobly, the physicality of number. The signs on the scoring sheet have physical, vibrating strings as their substrate, giving them meaning and usefulness as data.
Your height, weight, age etc. are not abstractions; theyre represented by abstract signifiers, but the number of your height, for example, remains consistent throughout your adult life. Your and everyone elses senses will register this consistency, regardless of what the signifiers say on paper. Probably youre thinking this is an argument for your premise that numbers are a separate reality from the physics of the natural world. If someone changes your height measurement significantly on paper, everyones senses will continue to see your same, established height. This is because the ontic meaningfulness of the height measurement signifier is tied directly to the physical number of your height as registered by the senses. Signifiers divorced from their referents are just line drawings on paper faithful to established patterns without meaning or usefulness. When you say data is separate from the physical body, being able to call the patterned line drawings data contradicts your claim the patterned line drawings are a separate reality without physicality. Without their direct connection to physical reality by reference, as mediated by the brains memory, the line drawings are NOT data, but rather just patterned line drawings. This difference between meaningless line drawings and data is crucial. The latter cant exist as we understand and use it without being referenced to the physics of the natural world. Clearly, this means number, as represented by number signs, really is out there. Number, as distinguished from number-sign, is complex (meaning two-part) materialism: pattern recognition of similar things into sets composited into abstract signs as mediated via the memory.
Your points were that numbers are material and physical. My point is that numbers are mental and conceptual.
Quoting ucarr
Again as above, your points were that numbers are physical. My point is that numbers and data are conceptual. Until you link the numbers to the physical objects, they have no meanings. But once you have attached the numbers to the objects, they have meanings. Still my point is that numbers are concepts even after they are linked to the objects.
Quoting universeness
Terrence W. Deacon, in his book Incomplete Nature: How Mind Emerged from Matter, does important work towards a physicalist explanation of the mind as emergent property of matter. From the small, limited understanding of his book Ive been able to glean, the core of his thesis puts the burden of the emergence of physicalism-based consciousness onto a multi-tiered paradigm of dynamical processes, with thermodynamics as the base. From the start, then, Deacon highlights the seminal (pun intended) importance of thermodynamics WRT life. The three-part paradigm links thermodynamic processes to morphodynamic processes and, in turn, these two are linked to teleodynamic processes. This paradigm has for its theme: the appearance of the ententional within nature. The ententional domain includes dynamical processes that are, ultimately, end-directed processes rooted in strategic absences, thus Incomplete Nature. These critical absences are effected by constraints as imposed by each level of dynamical processing. I think, if Im not mistaken, and I might be, that the critical absences due to critical constraints are part of an encompassing phenomenon Deacon implies with his frequent references to far-from-equilibrium states. The far-from-equilibrium state of being might well be labeled one of the fundamentals of living organisms. One can say maintaining this state of being is what is commonly know as the struggle to survive.
The peculiar feature of mind is its particular method of striving toward the goal of maintaining the contra-grade processes of the major organ systems of living organisms. The end-directedness of mind is rooted in what is not yet but, by design, eventually will be. It is chiefly this feature of mind, I think, that gives the impression mind is not physical. My adjustment, accordingly, features now the notion of complex materialism, an absential phenomenon rooted in the critical constraints of the three-tiered process towards sentience and cognition.
Quoting universeness
Fanfare from the band as complex materialism comes onstage and, in doing so, kicks hard solipsism up into the rafters. Mind is not divorced from the physics of the natural world.
Quoting universeness
Youre in the hunt for naturally occurring abiogenesis. Might the biggest question in science be: by what means the quantum leap from non-life into life?
My point is that number-signs, fundamentally distinct from physical number, are concepts only after theyre been cognitively_mnemonically linked to the physics of number. I think youre fundamentally wrong in your thinking number-signs hold the status of data before such linkage.
Without the necessary cognitve_mnemonic linkage to the physics of number, a natural occurrence, there are, in effect, no such things as meaningful number-signs (what your refer to as numbers), only patterned line drawings, which you can label numbers, or whatever you wish to call them.
No. I never said that. You are either misquoting me, or not reading my posts properly.
Before the linkage numbers are concepts. After the linkage, they become data.
Quoting ucarr
What is the physics of number? I am trying to clarify the concepts, so that we can understand the points of the agenda better.
Quoting Corvus
Concept - an abstract or generic idea generalized from particular instances.
With our definition of concept (Websters), we have the same relationship as the one obtaining between number-signs and the physical property of number: the physical thing, in this case particular instances, is the substrate conferring meaning onto concepts. Example: you have a concept of muscle cars as a potent instrument of seduction by men trying to make time with women. Herein concept like number, takes its meaning from observation of physically real muscle cars seen over the years. Neither concepts nor data, divorced from physical reality, have any meaning or use.
Given this similarity of concepts and data, (one is general is focus while the other is more specific in focus) arguing numbers are concepts before their linkage to physical things and data afterwards is both wrong and irrelevant to the crux of my argument: the linkage of physical substrate and numbers (which are concepts) is necessary for the latter to have meaning and use. You argue for the separate reality of numbers. Point to line drawings labeled number-signs to make that claim if you wish; its a claim for a reality without meaning or use.
Quoting ucarr
Quoting Corvus
In my statement you dont see any quotation marks, so thats evidence Im not quoting you.
Suppose I change my statement: Quoting ucarr
If my argument for the similarity of the terms is correct, I dont need to make any further changes to my above claim.
Quoting Corvus
Concepts and data can exist without the physical objects purely in the minds. Do you need the physical reality and objects when you imagine, remember or think about something?
Quoting ucarr
In that case, you have been reading my posts not properly. :D
Quoting ucarr
The description of "number" in the OP sounded muddled, and seemed to be vague and incorrect, hence I was trying to clarify the concept with you.
Yes, they can, and they do. However, they do not exist there purely. It is the interweave of world and perceiving mind that fuels experience-based memory, thoughts, understanding, imaginings and ideas.
Quoting Corvus
Memory and imagination, via the interweave of world and mind, play a game of give-and-take with environment. Ask any courtroom lawyer, or prosecutor, and he/she will tell you about the unrealiability of memory on the part of witnesses. Ask any senior citizen whos just visited their childhood home after decades absent from it and theyll tell you about seeing a world smaller than the one they remember.
Not even the young, of sound mind and fit body, are wholly exempt from forgetfulness.
The discipline of psychology can go on and on about the vagaries of human memory under various circumstances.
Mind has a partial, complicated independence vis-a-vis the experiential environment, the bank that funds the cognitive capital that is our consciousness.
Why do I think mind is never wholly independent from our physical world?
Have I ever been counted as zero, or as two? No. Ive only been counted as one. I am a one, an individual. My holistic oneness is my state of being. I, along with 7 billion others, am a human one. I count myself, and I am counted by others, as one.
I fight to be counted as one. Thats why, periodically, I go into the ballot box and make my marks on paper in order to be counted as one.
I have a physical life thats always been counted as one; physical number, counting my wholeness as one, has always been with me.
At the time of my birth, I stretched my lungs and vibrated my chords and cried out as a new one, just ejected into the spectacle of life. A stillborn has no life, and has no number, not even zero.
If we are not born with number, we are not whole and, probably have no life. I say probably because some human individuals are born and do live without essential parts of themselves. However, even the most bereft of the permanently disabled count as a one. There are no partial humans. All humans are whole and complete in their oneness.
You can check the summary from Cerulean-Lawrence below my inital post, its spot on.
To quickly note the relevance here, I basically determine that the core foundation of knowledge is our ability to 'discretely experience'. Discrete is to take many and make it one. I believe it is the origin of math. Of course, though we can create a discrete identity, it must be applied to reality for confirmation. Thus while we can construct discrete abstracts or 'ones' in our head, to test the accuracy of this measure it must be applied outside of ourselves.
:up:
Thanks for the link. Ill read them and then respond.
Yes, there's a difference ... (Btw, I adopt both positions as the latter, I think, is a function of, or entailed by, the former.)
[quote=universeness]You are a methodological naturalist and not a philosophical one as you refuse the burden of proof that is assigned if you state that there IS no existent outside of the natural universe.[/quote]
As a philosophical naturalist, I speculate that
Whatever is "outside of the natural universe" supernaturalia I further surmise natural beings like us are naturally incapable of both perceiving and cognizing (i.e. more than merely fantasizing about) and that, therefore, does not contribute anything explicable to our understanding of either nature itself or the flourishing of natural beings.
This is only a 'metaphysical supposition' not an axiom, theorem or statement of fact so no "burden of proof" required. :smirk:
Furthermore, consistent with this supposition, I'm also a methodological naturalist, by which I mean that
Does that clarify my position?
Saying memory can be unreliable therefore numbers are physical is a poor logic. Memory is an ability of the brain which is a biological organ. Of course its capacity can degrade with ageing, and other factors. It is like saying your eyesight got bad, and cannot see the road, therefore the road doesn't exist.
Imagine the ancient primeval times when the folks had lived in the caves, and hunting for survival. They had no numbers or languages, but they must have been fine with the living just going out roaming the forest looking for the food source. I am sure they had lived like that with no major problems for thousands of years. Numbers were discovered much later in human history, and it is just a mental concept.
It is strange why on earth you keep claiming that numbers are material and physical in the OP, and I was just trying to figure out your logic for the claim.
Numbers are concept and purely mental in its nature, and that is why they are universal. If you read Kant, you might have noticed that is what A priori concepts are about. Number works with material and physical objects, but it is not the same existence in nature.
If numbers were material and physical, then your numbers and mine would be different and contingent, which would make the universally necessary concepts and knowledge (Mathematics, Geometry etc) impossible.
I understand logic as an exacting type of continuity; it is continuity that adheres to strict rules of inference as they pertain to conjunction; disjunction; implication, mutual implication and the negation of these logical operations.
Quoting Corvus
Memory, by definition, is referential to antecedent, empirical experience internalized cognitively. Therefore, the relationship between experience of the environment and its subsequent, memory, directly entails the five logical operations listed above. Degrading memory exemplifies a breakdown in the conjunctive logical operation connecting experience of the environment to mind. This relationship lies at the center of my claim abstract math calculations of the mind are tied to experience of the environment. Were they not, the fitness of memory would not affect abstract thought. This applies no less to higher orders of abstract thought because all its levels, ultimately, reduce to experience of the environment. Mind is emergent from environment, but the two remain coupled.
Quoting Corvus
Youre uncoupling seeing the road from the roads existence as a thing-in-itself. Your implicit assumption in lobbing this uncoupling action as a missile attacking my position is that memory of seeing the road internalized is NOT sufficient to establish the REALITY of the road as a thing-in-itself. Believing this, you attack the uncoupling of mental impression from thing-in-itself, with the former being insufficient evidence of the true state of the road as thing-in-itself. Your attack assumes as true what it tries to deny: mental impressions are not categorically separate from their antecedent material objects making up the environment of the natural world. That mental impressions of number as cognitive math in abstraction are not categorically separate from their antecedent material objects making up the environment of the natural world is specifically what I mean when I say number is physical.
Numbers are universal? Theres a reason why teaching math to elementary students usually involves the use of material things that can be counted like, for example, wooden blocks. Without use of countable things named in the counting process, many elementary students, when shown equations on a blackboard, would see nothing but meaningless chalk scribbles.
Quoting Corvus
You imply there are no logical relations between material things. The sum of my car parked on the street next to yours is no less calculable than one equation solved in our heads, respectively.
Now, to this you will say, but counting the cars is a mental operation that is separate from the cars themselves. To this I will say, see my above argument about material-things-in-themselves being sufficient to establish the reality of relationships whereas mental impressions alone are not. The upshot of this has me saying, again, mental activity is emergent from but not ultimately uncoupled from its physical substrate, material things.
Quoting Philosophim
Yes. I agree with the points you make here.
After reading your Knowledge and induction within your self-context and some of your interactions with Bob Ross, Im willing to venture a tentative overview of a key part of your thesis. Your hierarchy of induction, which has four levels: probability, possibility, plausibility, and irrational induction, serves as a guide for passage from Distinctive Knowledge to Applicable Knowledge. Let me begin by saying these four levels, that progressively move further away from knowledge, respectively, are a quartet of inductions already known to the general public superficially. Therefore, your work details these four general precepts with a schematic overview and a collection of algorithms for rigorous calculations. Through use of your guide, members of the public can do more precise assessments of truth content at each level.
On a speculative basis, Im wondering if your scheme can be used with logical truth tables towards rigorous assessments at each of the four levels.
Note - This note is, admittedly, a somewhat fanciful suggestion: in order to keep your quartet alliterative, consider replacing your last level, irrational induction, with pretension.
It makes me incredibly happy to hear you understood the paper and what the goal was.
Quoting ucarr
Possibly. If there is a need for it, I will.
Quoting ucarr
Honestly I've never been satisfied with the last phrase. Originally I was going to call it faith, but I thought that word had too much baggage attached to it. I love the alliterative suggestion, but pretention has a lot of negative connotation to it. I'll think about it. :)
What branch of Logic is this?
Quoting ucarr
What do you mean by this? Could you please rephrase it?
Quoting ucarr
How do you uncouple seeing the road from the road's existence as a thing-in-itself? Does the road have a thing-in-itself? Or the thing-in-itself has the road? How were they coupled in what way?
Is using the countable things only way teaching and learning the elementary maths?
Quoting ucarr
This was not about material things. It just meant to say that you can perform math calculations and geometrical proof works without having to perceive the actual objects in front of you, which proves that numbers and geometrical axioms are A priori concepts, which are universally necessary truths.
They are universal in the way that if you calculate 5+7=12, and whoever in the world sees it will accept as a truth. You didn't need any objects to calculate the math with the numbers.
For example, if you had 5 cars parked in the front yard, and 7 cars at the back yard, then you don't need to personally visit the yard to count the cars whenever you want to know how many cars in total you own. You can do 5+7=12 in your head without seeing the cars or counting them, you get the answer. The reason you can do this is that because numbers are A priori concepts. Numbers are not material or physical.
But if something is physical, what properties does it have?
Quoting Corvus
If you dont know the five logical operators, then you need to open a book of logic for beginners. Thats the book Im studying.
Quoting ucarr
Quoting Corvus
At the bank, when the teller pays out thirty dollars cash to you from your account, you get pieces of paper with numbers on them. The pieces of paper, by themselves, have no value. In the bank at Fort Knox, the U.S. gold reserve holds thirty dollars that back the value of your paper money in the form of pieces of gold, which, by definition, hold monetary value intrinsically. This is a conjunctive relationship between paper money and gold with respect to monetary value.
In a parallel relationship, when your math teacher solves an equation on the blackboard, s/hes paying out math information to you just as the bank teller pays out paper money to you. Just as the gold in Fort Knox, by conjunction with the paper money, gives it value, the natural world of material things, by conjunction with the number signs on the blackboard, gives them value. The mind perceives countable material things in the natural world and, through the process of abstraction, a process that composites multiple experiences linked by a theme into one representative abstraction, links number signs with the property of being countable, an intrinsic property of material things.
Break this connection and number signs, like paper monies, lose their value. Just as gold funds the value of paper money, material things fund the value of number signs. For this reason, I claim number is a physical property of the natural world. Numbers, then, are, ultimately, physical.
I didn't ask about the five operators. There are around 50 - 60 different type of Logic schools all dealing with different type of events and contents with different forms. I asked which school of Logic was it? Anyhow, I thought it was quite odd for you to have written the operators in words rather than the symbols.
Quoting ucarr
Money can lose its value from many different factors. It has nothing to do with breaking the connection between the paper money and numbers. Your arguments seem to have deep flaws and don't add up at all.
Numbers are concepts which describe the objects and the world with the values. They are not the objects themselves, and they are definitely not physical in nature.
Quoting Corvus
You dont. This has been my point all along.
Quoting Corvus
You say above its poor logic to claim My eyesight is bad and I cannot see the road; therefore, the road doesnt exist. I agree this is bad logic because of the objectivist assumption the road is there whether one sees it or not.* A central implication of this assumption is that the truth content of eyesight depends upon what is really there that it sees. This, in turn, implies eyesight, which is perception of the mind, depends on the physical things populating the natural world. Now we arrive at my premise that the mind is an emergent, cognitive operator ultimately rooted in the physical. This means, specifically, that numbers, which are of the mind, likewise are, ultimately, part of a complex of physical world_brain_emergent mind.
*An unseen road might be quantum mechanically uncertain, but that uncertainty is collapsible.
I didn't quite understand what you meant by "uncouple seeing the road from the road's existence as a thing-in-itself." in your replies, hence asked to clarify what you mean by that.
Quoting ucarr
Yes, I was trying to say to you that numbers exist as concepts, whether one remembers them or not. The road exists in front of you, whether you see it, or not (because you had a bad eyesight.)
If numbers were physical, as you have claimed all along, then they might not exist, or stop existing due to some external reasons or ageing, deaths or destruction = Do numbers get old or die? What a baloney even to suggest that !
People get old. But numbers don't get old, because they are concepts. Numbers are not physical, and you cannot break them or throw out in the bin. You cannot uncouple numbers from anything. Numbers are concepts.
Quoting Corvus
Dont confuse number-signs with physical number as countable-things-in-the-world. Ive never denied what you claim here about number-signs. But even with number-signs, the issue of ontic status is debatable.
If you think numbers existed as concepts before the Big Bang, then youre attaching yourself to Cartesian Dualism. This attachment parallels claiming God existed before the Big Bang.
Youre positing two worlds, one physical, one non-physical. If non-physical numbers have a relationship to the physical things they describe, but are not themselves physical, then you, like Descartes, have to explain how non-physical numbers have any practical relationship to the physical world.
How do non-physical numbers attach themselves to the physical brain in your head? You will say you have a mind thats not physical. I then ask you how your non-physical mind attaches itself to your brain. This conversation has always been about how concepts, supposedly non-physical, connect with the physical humans who create and propagate them.
Quoting ucarr
Ive already presented this explanation in our dialog more than two times.
It is good to see you are now accepting that numbers are concepts. It is a progress. But you still seem to insist that there are numbers which are physical. So now we notice that you have changed your claim, and brought in the Cartesian dualism into the argument.
Please bear in mind, the Cartesian dualism is not about numbers as concept and physical existence at the same time. To start, that is a contraction for something being both physical and mental at the same time.
Cartesian dualism is about mind and body as separate two distinct substances. It is not what you are trying to claim.
Descartes was a rationalist, and dualist. He would be the last one who would have said numbers are material or physical. No, he would never have said that. I have not read Descartes, but that is my gut feeling. Please correct me if I am wrong on Descartes on this point.
I tried to understand cases where numbers are physical entities, but I must admit that I couldn't possibly think of any case number that can be regarded as a physical object. You need to come back with a more convincing argument for your claim.
:up:
Quoting Corvus
You say this is bad logic because the road is there whether the eyes see it or not.
One day at the dinner table a husband tells his wife that afternoon he saw a statue of George Washington. Your wife tells him hes wrong. The statue you saw at the location you gave is a statue of Thomas Jefferson, she says. Next day he returns to the location and, going much closer to it than on the previous day, he sees that, indeed, its a statue of Thomas Jefferson.
Do you acknowledge that in order to check the truth content of the husbands first mental impression of the statue, he had to return to the site and try to verify or revise that first impression?
You know that even if your eyesight is bad, and cannot see the road, the road exists.
You know when your memory and eyesights are both bad, so you can't tell what the statue was, and you must go back to it to check it out, but you know that the statue exists.
Therefore even if your memories can be unreliable, numbers do exist in your mind. To say that numbers are material and physical, is a bad logic.
Quoting ucarr
Of course, you need to go back and see the statue to confirm what it is. Therefore it proves, even of your memory is unreliable, things exist as they are, be it physical or mental. Just because your memory is unreliable doesn't mean that mental objects become physical. Even if you memory becomes bad, numbers are concepts in the mind.
Quoting ucarr
Quoting Corvus
During the week following the husbands discovery about the statue, he goes out walking and steps onto a patch of ice hidden under snow. He takes a hard fall and hits his head on the pavement. That night in his hospital room, his wife, visiting him, cheers him up with stories. At one point, she asks him if he remembers telling her about the statue of George Washington in the town square. She uses a mocking tone while speaking the name of George Washington and laughs, expecting hubby to laugh along with her little joke about his mistake. The husband, instead of laughing, doubles down on his claim that, indeed, the statue in the square depicts George Washington. At this point, the wifes smile is overtaken by a sad expression as she realizes the head injury mustve destroyed his correct impression of the statue. All that remains now is his earlier, incorrect impression.
The correct impression in husbands head is either damaged or destroyed. Does this correct version of his impression, that was previously operational within his head, but now is not, still exist somewhere outside of his head?
Well, whatever happened to the man's head, the statue exists. Someone's head going off, doesn't affect the physical or mental existence which has been exiting before.
If the statue was there before, it would still be there existing as it was unless someone moved it away. If it didn't exist before, then it doesn't exist now unless someone placed one at the location.
Numbers will always be existing in the minds of humans. Because someone died, or someone's head gone off doesn't mean numbers turn to physical or disappear into non-existence.
Quoting Corvus
Quoting ucarr
Quoting Corvus
We have different mental impressions in our heads. This variety includes: grocery list items, images of statues observed, numbers learned in grammar school now being used to count grocery list items.
Quoting ucarr
Quoting Corvus
Weve been talking about mental objects. This category includes numbers as well as other mental objects as, for example, the memory of the statue.
Quoting Corvus
Quoting ucarr
Is it the Humean impression are you talking about?
Quoting ucarr
You are using the concept impression wrong, if it is the Humean. It would make more sense if you used ideas instead of impressions. Numbers are mental concepts, and they would have no matching impressions according to Hume. Humean impressions are not associated with knowledge, judgement or concepts. They are passions, emotions and feelings viz. sensations in nature.
Well, the idea of the statue is from the external object, and the idea of number is from the mental concept, so you are talking about totally different ideas in nature. You cannot have an idea of the statue without seeing the statue, and having the impression of it. But you can have an idea of a number without having to see any external objects or impressions of the object.
Quoting ucarr
Quoting Corvus
Quoting Merriam-Websters Dictionary
Regarding the statue as impression from the external object and number as impression from a concept, are they both non-physical contents of the mind?
Quoting Corvus
Have you directly observed passions, emotions, feelings, and sensations? Mind you, this question is very specific. Im not asking if youve directly observed humans (or other animals) experiencing passions, emotions, feelings, and sensations. Im asking if youve directly observed passions, emotions, feelings and sensations divorced from humans (or other animals) experiencing them?
Quoting Corvus
Youre claiming numbers and their relations are understandable a priori, regardless of age, situation, and personal experience?
Do you, or anyone you know of, have knowledge of a human society that does no counting of material things whatsoever?
Do you, or anyone you know of, have knowledge of a human society with children who cant see the difference between one lollipop and two lollipops?
Quoting IP060903.
In your opinion, do these two attributes of number bind abstract numbers to physical things and physical things to abstract numbers?
You still seem to be misunderstanding the difference between the act of counting physical objects, and the ontology of numbers. The two are not the same thing. I have given you enough explanations for the reasons that they are not the same.
If you are talking using a religious language, then yes you can say even rocks have minds, because they are created by God, and even say the recent frequent volcanic eruptions around the world were the acts of God showing his frustration for the Global warming trend. However we want to reject that type of metaphors, when we are debating the point in philosophical analytic perspectives.
Quoting ucarr
Quoting ucarr
[quote= https://en.m.wikipedia.org wiki";871859"] Hume followed John Locke in rejecting the existence of innate ideas, concluding that all human knowledge derives solely from experience.[/quote]
I was just wondering if your use of the word "impression" was Humean, or from the ordinary language. But even for Hume, numbers are concepts which is part of the rationality or reason. I don't believe that any philosopher in history has said that numbers are physical.
Debaters, using words instead of fists, throw punches by asking questions. When the battle is engaged, the questions start flying.
If, on the other hand, only one of the fighters enters into the middle of the ring and just stands there awaiting engagement with the other boxer until, finally, its clear the other boxer will not leave his corner, its universally understood that that fighter has conceded the fight.
Ive answered your questions over and over. As a recent example, Ive responded to your citation of Hume with a quote from him that supports my position. As another recent example, when you attempted to distance concept from impression, I cited a dictionary definition that establishes their similarity along the axis of non-physicality, a central element within our battle.
You, however, have lately been refusing to answer my questions. Youre like a boxer who refuses to leave his corner to engage with the other boxer.
Your avoidance began with this question:
Quoting ucarr
Youve avoided it three times. Youre still talking, still asking questions, but youre doing this over in your own corner, where the fight cannot continue.