Material Numbers
02-25-22
Material Numbers
If a thing has many uses within the real world, is that proof of its reality?
If a thing has intimate association with material objects, does that suggest its objective materiality?
Let’s examine numbers in the context of these questions.
Number – a unique marker of position.
Number as unique marker of position allows human to conceptualize, manipulate & measure material objects arrayed in interrelationship.
Motion – the changing values of the x,y,z and t of an object. As an inertial frame of reference x,y,z and t changes its values, the shape of its array changes.
Observation of these changing values allows human to use notation to track the motion of an object.
The Physicalization of Numbers – Can we conceptualize numbers as physical objects?
Material Numbers – because a material object can hold a position, perhaps we can understand that any material object has a built-in property of number. The number property of a material object is its ability to afford a slot wherein a set of possible numbers gives value to its position within an array of other material objects in interrelationship.
This property of number of a material object, like its mass, is therefore understood to be one of its physical attributes.
The number of a material object is then a kind of measure of the built-in positionality of a material object.
Proceeding from here, perhaps we can characterize math as a property of material objects inhabiting the neighborhood of epiphenomenon.
The number line is then a continuum of signs with the positionality of material objects as their referents.
Does measuring a material object for appraisal of its physical dimensions entail measuring its positionality?
Wittgenstein has elaborated an argument against numbers being metaphysical.
My questions originate from the opposite end of the continuum.
Material Numbers
If a thing has many uses within the real world, is that proof of its reality?
If a thing has intimate association with material objects, does that suggest its objective materiality?
Let’s examine numbers in the context of these questions.
Number – a unique marker of position.
Number as unique marker of position allows human to conceptualize, manipulate & measure material objects arrayed in interrelationship.
Motion – the changing values of the x,y,z and t of an object. As an inertial frame of reference x,y,z and t changes its values, the shape of its array changes.
Observation of these changing values allows human to use notation to track the motion of an object.
The Physicalization of Numbers – Can we conceptualize numbers as physical objects?
Material Numbers – because a material object can hold a position, perhaps we can understand that any material object has a built-in property of number. The number property of a material object is its ability to afford a slot wherein a set of possible numbers gives value to its position within an array of other material objects in interrelationship.
This property of number of a material object, like its mass, is therefore understood to be one of its physical attributes.
The number of a material object is then a kind of measure of the built-in positionality of a material object.
Proceeding from here, perhaps we can characterize math as a property of material objects inhabiting the neighborhood of epiphenomenon.
The number line is then a continuum of signs with the positionality of material objects as their referents.
Does measuring a material object for appraisal of its physical dimensions entail measuring its positionality?
Wittgenstein has elaborated an argument against numbers being metaphysical.
My questions originate from the opposite end of the continuum.
Comments (136)
No. They're only graspable by an intelligence capable of counting. They're intelligible objects.
Did you ever play battleship? The numbers are part of the positional grid, not properties of the object.
I think the OP is referring to an argument where numbers are represented by a physical/material concept, not a metaphysical one. At least, he said Wittgenstein had some arguments in this points
Quoting Hello Human
You pick up a rock & it weighs 1 pound.
You pick up another rock & it weighs 4 ounces.
The second rock weighs only 25% of what the first rock weighs. Holding each rock feels different because of their different weights.
Rock 1 pulls down on your left arm harder than Rock 2 pulls down on your right arm.
Weight, as you know, is a physical property of each rock. The weight of each rock gives you an impression of the identity of each rock.
I'm saying that another way to get an impression of the identity of the two rocks is by putting them into a line with other rocks & then counting up the total number of rocks.
Instead of the weight of the two rocks being experienced by you by holding them & feeling how hard they pull down on your arm, the number of the two rocks is being experienced by you by putting them into a line of other rocks & experiencing how the counting of the line of rocks changes after adding the two rocks.
With this idea, I'm just repeating to you things you already know.
What is slightly different here is how I'm asking you to look at what you already know.
Instead of looking at a number as a thing way over there, while a rock as another thing way over here, I'm asking you to look at a rock as being a physical number made of material we call granite or agate or diamond or (you fill the blank).
Are you saying the positional grid, a material thing, possesses the property of number?
What does an intelligence grasp when it counts?
I say an intelligence grasps a material thing, as when it counts a line of stones, en route to understanding numbers & counting.
Even a written number symbol, let's say, ink on paper, exists as a physical thing as, in our example, ink on paper.
The stones are material - well, according to materialism - but the count, the quantity, is not. What the intelligence grasps is number. Ink on paper is physical, but what it signifies may not be. And the fact that the same information can be represented by different symbolic forms demonstrates that the meaning and physical representation are separate. And what about pure math? Nothing physical is involved at all in that.
You're barking up the wrong tree, wanting to justify the reality of number by saying it's material. I'm very interested in mathematical Platonism, and my view is in line with traditional platonism, i.e. numbers are real but not material. They can only be grasped by an intelligence capable of counting, but they are the same for all who count.
See the discussion in What is Math?
Note referece to 'the fear' - this fear is real and profound. If number is real but not material, then materialism is false, and as mainstream culture assumes that it's true - well, that's a big problem for it.
An alternative to the Platonist view is Aristotle's 'moderate realism'. It holds that numbers (etc) are real, but only encountered in relation to material particulars (although again this has a problem accounting for pure math in my view.) See Aristotle was Right about Mathematics After All.
See also The Indispensability Argument in the Philosophy of Mathematics.
Also Sir Roger Penrose, Is Mathematics Discovered or Invented?
In my fruit bowl I see three oranges. What do they have in common with the lamps? Taken all together there are three lamps just as there are three oranges. We see number everywhere in the environment. We don't see numbers, we don't see abstract ones or twos anywhere. We have developed a system of symbolic numerals to represent numbers; our recognition of those symbols and their relation to the number that is everywhere in the environment is the closest we can get to seeing an abstract number.
What is a number without a material referent?
It's just another material thing, but unlocateable.
Number = position. Only material things can have position.
What is counting without a world of material referents?
It's just a series of neural networks oscillating.
In a world without spacetime, do numbers have any meaning?
It's not a material thing. It's an idea. You know what a number is, because you're h. sapiens. But your dog, if you have one, does not.
You should read some of those refs I gave, or come with some other argument, because this one's a dud.
Looks like you see numbers as I do.
I didn't say an abstract conception of a number is a material thing. I implied it is a sign that has a material referent.
I'll go to your references. Will you go to my world devoid of spacetime and think about the role of numbers there?
There's not a lot to go on based on what you've said, but if by that you mean: are numbers real in the absence of reference to space-time?, my response would be again: 'well what about pure mathematics'?
(I hasten to add, I'm appallingly bad at mathematics, unlike several accomplished contributors here, but I don't think the point I'm trying to make necessarily depends on that.)
I recall an anecdote I read decades ago about Arabs who used to play chess whilst riding camels across the desert - without a board. That level of mental acuity and recollection also far exceeds anything I'm capable of, but I remember thinking at the time that it was a sterling example of the power of abstract thought.
One, Descartes believes quantity is proper of physical multiplicities in the sense of extension:
Quoting Descartes
From the second part of Principles of Philosophy.
And in fact Avicenna had a similarly veined argument, a sort of identity between quantity and ostensibly the extension it "models," to forward against the atomists (not the same as the Greek tradition, rather, atomists only in the mereological sense) of his era. That is, because, Aristotle's critiques, which more primarily concern the broader metaphysical doctrine rather than the specific atomistic thesis, Epicurus had developed atomism a tad bit more and the Arabic Kalam tradition had numerous proponents of atomism (who were only considered with the thesis of a discrete space rather the Greek doctrine in full). Since they'd take the notion of discreteness to be a literal representation of space, Avicenna argued that the functionality of the Pythagorean Theorem in physical space, and its utter incompatibility with discreteness even at a level of approximation, disproved atomism.
Finally, in more recent literature, material numbers have been a charge utilized to dispense away various logicist accounts of the philosophy of mathematics. This is known as the "Julius Caesar problem," namely that in accounts where numbers are objects, the principles to which we designate numbers can't tell us when exactly something is or isn't a number. What I mean is, take something like Hume's Principle, we wouldn't know when to identify an arbitrary object, i.e. Julius Caesar, with a number.
However, this bit of your post, I don't understand. Perhaps instead of the very extension of the object itself, you're referring to spatial or temporal location, if I understand you correctly. If so, this is an example of an extrinsic, relational predicate (or an impure property). There is debate about whether these are truly proper to the objects they designate or not, but here, the quantity would moreso be a reference of things like physical distance (presumably "material"). The way this would be treated would depend on if the underlying metaphysics for space & time is absolute or a container, i.e. Platonic or Newtonian, versus if they're reductionist, like Leibniz, Hume, or Einstein (how they are treated right now in modern physics!) So there's that.
While I can tell you that it's unlikely you'll be able to account for all of mathematics this way, I shall inform you as to a view known as structuralism in the philosophy of mathematics, where mathematical ideas are really just structures that are instantiated by various things. So physical systems, given satisfying conditions, can instantiate mathematical structures just as ideas in our heads can. However, there are various forms of structuralism with various committal status, and I'm not sure how you would tame those with a materialist doctrine (not saying they're incompatible at all, rather just making a comment WRT my knowledge on the subject).
The positional grid is not a material thing, it is an abstract. And numbers are also abstract ideas that have physical representations or icons so that dumb people like most of us can use the concepts.
Just like an word does, they represent ideas. Writing words and numbers down does not make them physical objects, it just makes it easier to transmit ideas.
Try playing telegraph with a few friends using a complicated idea, see if the idea can be passed on accurately.
Quoting Wayfarer
[i]Pure mathematics is the study of mathematical concepts independently of any application outside mathematics.
...the appeal is attributed to the intellectual challenge and aesthetic beauty of working out the logical consequences of basic principles.
...presently, the distinction between pure and applied mathematics is more a philosophical point of view or a mathematician's preference than a rigid subdivision of mathematics.[/i] -- The Apple Dictionary
It seems to me -- especially in light of paragraph 3 above -- that pure math, in order to be intelligible beyond the circular reasoning of logical truth by definition, must trace back to material objects interrelated.
...almost all mathematical theories remained motivated by problems coming from the real world or from less abstract mathematical theories. Also, many mathematical theories, which had seemed to be totally pure mathematics, were eventually used in applied areas, mainly physics and computer science. -- The Apple Dictionary
...intellectual challenge and aesthetic beauty of working out the logical consequences of basic principles
Logic is continuity, which is to say, interrelationship, rooted in inference. Would anyone have any notion of continuity & interrelationship between material things without firsthand experience of a spacially-extended, material world that affords empirical experience?
Pure math, and all other forms of signification, once uncoupled from empirical experience, become unintelligible.
Numbers, uncoupled from interrelated material objects, become random, unable to signify anything intelligible.
Abstract thought is non-specific WRT our material world; it is not uncoupled from our material world.
Abundant thanks with much gratitude to you, Kuro. Your input here is tremendously substantial and, I presently like to think, more encouraging than otherwise. There's much in your input I must study further. If warranted, I hope additional input from you is forthcoming.
If I remember Battleship correctly, there is a plastic platform full of holes, the grid where a player's battleship moves to various positions.
Quoting Sir2u
No argument with you here. Yes, number symbols & words are signs that refer to material things.
I'm saying that number symbols refer to & derive meaning from material things whose set of attributes includes one particular attribute I call number. All of this verbiage is an attempt to say material objects are numericalizable because they have a built-in property of being movable, which is to say, positionable.
These are very rigid statements that are beliefs, not facts. You should indicate as such. Should a philosopher state their beliefs as facts?
The key word in my statement is signification. I'm tempted to argue that my claims are true by definition, since a sign without a referent is like a material object without elements or compounds. I sense, however, that is a weak argument.
As for my etiquette as a person making claims (you compliment me with the title of philosopher), your response exemplifies what it denounces.
Saying,
Quoting jgill
Is like saying,
This statement is false.
What fun is philosophy without bold claims subject to refutation?
By the way, what is your refutation of my bold claims?
Before that was invented we used to play on 2 pieces of paper. Draw lines with a pencil to form a grid, letters on the top numbers down the side. But they decided to make easier and dumb down the people. But they both are only physical representations of concepts. The location C12 is not a physical thing, ask any kid that learns about map coordinates or Excel in school.
Quoting ucarr
Could you then please indicate to me where I can appreciate a nice looking number 69. I doubt that you can.
This is the image of a Greek road sign. Is it a physical number? No, it is only the paint on a piece of metal that has been manipulated so at to form what is commonly accepted as the visual representations of the numbers 6 and 9. The paint is physical, the metal is physical but the idea is still an abstract.
Numbers do not refer to physical things either, they refer to the quantity(another abstract) of physical objects.
645,798,845,635,345,665,332,313,464,655,876,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.
If numbers derive meaning from material things, then the number above either has no meaning or a meaning that is unknown. Which do you think it is.
Numbers do not represent objects they specify the quantity of objects, the length of object, the weight of objects. But not the objects themselves.
I'm reading this book on Mathematics, The Art of More it's called, by a Michael Brooks. It gives an account of how expert abacists can work sums with imagined/simulated abacuses. I find that quite fascinating, don't you? Do you think I can simulate a fully operational computer in my brain; you know, turn the idea of computer simulation on its head by reversing the roles - instead of a computer simulating a mind, why not let the mind simulate a computer for a change. Do you see any relevance/importance of this in the philosophy of mind?
Each day recently arXiv.org has received about 200 research papers in math. Many of these are "uncoupled from empirical experience", yet thousands of math people find them intelligible. However, the general public will not.
Quoting ucarr
A good calculus student might disagree.
The connection you name above goes in both directions.
Concept - Philosophy - an idea or mental picture of a group or class of objects formed by combining all their aspects. -- The Apple Dictionary
Consider a) Mental representations of material objects; b) material representations of concepts
Which comes first?
Even when we form concepts of mental things i.e., concepts of concepts, the line of reality traces back to material objects within our empirical world.
Pure math is a language about how the language of math works logically.
What is logic? It is an examination of the continuity that connects events of our lives into an intelligible narrative. A narrative is intelligible when a group of people all recognize noteworthy actions & reactions of humans bound together within cause-and-effect relationships.
Apart from our conscious experiences within our daily world, logic has no intelligible meaning or value.
Since math & logic are interwoven into our daily experiences, a study of how math works logically, pure math, likewise is intimately interwoven into our daily experiences.
You should ask a pure mathematician whether their mind enters an immaterial realm while they're working.
As you may have seen in my statement to Sir2u above, pure math is concerned with the innate workings of the language of math itself. Any brief survey of the sciences with show you just how worldly is math in application to many, many real world events. An examination of how this language works by its own lights is thus an examination of our real world, although not directly.
Good to know. Simulation, aka...acting: Data (Star Trek), Robocop, Terminator, etc. humans acting like computers (AI).
Humans can act like computers but can computers act like humans?
The first part of the statement is what's interesting. Just like there are computer games in which a vehicle's engine is simulated, why not let a human brain do the same simulation? Isn't our imagination a simulation software?
No. But I can imagine simulation software.
Yes, and...
So my imagination isn't simulation software. Simulation software contains no imagination. But the imagination can contain simulation software. Simulation software is a part of the imagination but the imagination is not a part of the simulation software. So computers can't act like humans.
Simulation: unreal/testing a scenario
Imagination: unreal/(also) testing a scenario
Notice how simulated worlds are fantasy worlds.
The computer isn't aware of the simulation. It's programmed. We are aware of a simulation in our brain. It's not programmed. The computer or robot has no dreams. Nature isn't programmed.
An imagination is a simulation but a simulation doesn't need to be an imagination. They are both simulations. An imagination is an imagined simulation. A simulation is just a simulation.
I think EugeneW is saying there is, in the case of human, a SELF which has intentions, whereas, in the case of computer, there is NO self, and thus there are no intentions, just a programmed, logical continuity of coded commands.
A simulation "borrows" the selfhood & the intentions of the computer programmer, a human.
A computer simulation program is like an appendage of human, an extension, like an arm, under the control of human.
But it is not always necessary to have physical representations.
Quoting ucarr
I would think that it would be impossible to have a man made physical object without there being a concept on which to base it.
But it would be impossible to form a concept of something natural without having at least some of the characteristics being known.
Let's reverse the order.
But it would be impossible to form a concept of something natural without having at least some of the characteristics being known.
I would think that it would be impossible to have a man made physical object without there being a concept on which to base it.
Human concepts are based on observations of surrounding natural forms. Proceeding from there, humans make alterations to their naturalistic concepts. These alterations are derivatives of the naturalistic concepts that preceded them. They are still natural forms because human nature, as the name indicates, stands as another form of nature, so the products of human nature, whether naturalistic or altered, also stand as other forms of nature.
[1] Yes
[2] Yes
[3] :chin:
Indeed. An imagination is a simulation that is seen. With the minds eye?
Indeed!
Now you're talking about feedback looping with vertical stacking.
Well, almost. More like nested loops. I'm the outside loop watching and influencing the inside loops that affect me as a loop.
Can you elaborate a bit more? I've been thinking that with more loops per fixed interval of time,
A. I. will become self aware.
If so, this leads me to thinking the self (maybe the soul) lives in the interstices of the loops, and is immaterial, epiphenomenally speaking.
The self is an associate of the material world, but is not local to it.
Which natural forms are the base for books? On which natural form is animal training based?
And how does this all intertwine with the OP?
Ever read a biology book?
You've been debating me about pure math & how it's uncoupled from the material world & I've been arguing that applied math is about the material world & that pure math, being about how math logic works, is also, ultimately, about the material world because logic has no meaning outside of the continuity of interrelated material things.
Yes.
Quoting ucarr
No, I cannot remember even mentioning it. We were discussing the materialistic qualities of numbers, which is no existent.
What about the materialistic qualities of number?
There's a stone sitting on a red square. Close by, there's a stone sitting on a green square. A person sees them and gives them a label. Label = 2-stones.
Do you think 2-stones describes something that's there in the stones?
Do you think 2-stones completely different from stone on red square and stone on green square?
Do you think 2-stones is a label randomly given to stone on red square and stone on green square?
Do you think 2-stones can be replaced with Fluxmax-stones and would make no difference?
If you think the replacement makes no difference, what can be done to let people know
2-stones = Fluxmax-stones?
Giving them a label is the key there, if the number label where part of the stone no one will need to "give" them anything
Quoting ucarr
Of course it could be replaced with anything, as long as it is universally accepted. Fluxmax-stones could quite easily be 2-stones in some sort of technical language.
Whatever they are called is because of human constructed language, not because of stones having built in numbers.
Pile of 2-stones sits on a red square. Close by, pile of 3-stones sits on a green square.
Seeing pile-of-2-stones and pile-of-3-stones, would you give each pile the same label?
Quoting Sir2u
If it were discovered that Germany has already established Fluxmax-stones = 3-stones, would the equation 2-stones = Fluxmax-stones have to be changed to 2-stones ? Fluxmax-stones?
:up:
I doubt that many would call two or three stones a pile, but who knows. The same applies here as I said above, if the piles of stones already had a label there would be no need to give them one. Nothing has numbers as part of their make up, numbers were invented by man so that he could work out how the universe works.
Quoting ucarr
That is sort of like asking if the cowshit you found was discovered to come from a bull would we have to call it NOT COWSHIT.
No, we would just call it bullshit.
And of course we see numbers everywhere, we put them there.
I love these Einsteinian thought experiments ! :nerd:
Quoting ucarr
Quoting ucarr
Quoting Sir2u
Do you agree that COWSHIT ? bullshit?
When you look at 2 material objects, say, 2 stones, do you see 2 stones, or do you see the number 2 as it is written on paper?
Since writing first appeared thousands of years after human first started walking the earth, do you accept that 2 stones first appeared long before the first appearance of number 2 as it is written on paper?
Quoting Sir2u
Do you acknowledge that the numbers we put onto material objects describe what was already there before human started writing numbers?
:rofl:
You have a point, monsieur/mademoiselle!
:grin: :up:
If you acknowledge that humans spoke the numbers for thousands of years before they wrote then yes, I can do that.
But that just means that numbers were invented for counting before writing was invented for accounting. It in no way shows that numbers are part of the articles they describe.
Quoting Agent Smith
Actually, you are right and wrong. Could something be described mathematically if math has not been invented?
Colors have always existed, drab brown being one of the worst ever imagined. But until someone invented a method of naming them. Now it has the illustrious name of Pantone 448 C. Could it be possible that the same has happened to numbers?
We now use math to describe the universe, but we had to invent the math(numbers and equations) to explain it, to make the calculations fit reality. And a lot of explanations turn out to be wrong.
I see. I'm right and wrong. Right in that the mathematical laws of nature preexisted humans, but then, this is where I err, humans had to invent the math necessary to describe these laws.
Since you've made this statement, do you acknowledge that material things are countable?
Quoting Sir2u
Could something be described fluxmatically if math has not been invented? Could something be described noxmixically if math has not been invented? Could something be described (fill in the blank with your own word) if math has not been invented? Could something be described...
Quoting Sir2u
Since I can write a sentence in parallel to your sentence, do you acknowledge that if your sentence is valid, then my sentence is valid? See my parallel sentence below.
Numbers have always existed, 3.1415929... being one of the worst ever imagined. Then [but until] someone invented a method of naming them. Now it has the illustrious name of Pi. Could it be possible that the same has happened to colors?
Quoting Sir2u
Since you have made the above statement, do you think if follows that the universe, which pre-dates human math, has always been describable via the language of math?
Quoting Sir2u
Do you agree that when you say, "humans had to invent the math to explain the universe," you are saying, again, that math was invented to explain the innately mathematical nature of the universe?
Do you agree that from this it follows that math expresses its form and content in connection with the form and content of the universe?
Do you agree that when you talk of math striving to fit reality, and sometimes failing, you imply that math fails in its core mission when it doesn't fit reality?
I have asked you if you would give 2-stone and 3-stone the same number. Are you unwilling to answer this question?
How could they exist if math had not been invented. The universe exist before humans did, and humans wanted to describe it. So they invented the names of colors, shapes, sizes and many other characteristics that objects have. Mathematical laws are made by mankind to do that job, describe. They are nothing more than a specialized language.
Math is the human's way of describing the universe's characteristics as well but they had to do a lot of trying to get the formulas to fit the reality. And they have still a very long way to go and a lot of methods to invent to get to the end.
We humans believe that it must be a universal way of describing things, even going to the extent of send mathematical messages into space in the hope that beings from other worlds will understand the concepts. Maybe they will but there is always the possibility that they have other methods of doing it.
Yes, just as they put colors, shapes and lots of other stuff.
Quoting ucarr
Of course they are, did I not make it clear enough that was the reason for inventing numbers.
Quoting ucarr
Oh dear, you do go on a bit don't you. And you are good at invent gobbledygook. Humans need to describe things, they will always find a way to do so. A river gets deeper one day and some measures it at 5 meters, the next day someone else measures it a 17 feet. Did the level rise or lower? Metric and standard are two methods of measuring, but both describe the depth of the river. There are many examples of measuring systems for anything that can be measured. And they have all been invent by humans.
Quoting ucarr
Would we even know about Pi if someone had not invented a method to work it out and describe it? The same goes for black holes, they say that they have always been there, but until recently they have invent the mathematical equations to more or less prove their existence.
Quoting ucarr
I suppose it has, and I know that is the only method of doing so that humans have discovered. But I cannot be sure whether other methods exist or not, and neither can you. All we know is what the science department has told us.
Quoting ucarr
That is what humans made it for, it would not exist still if it did not work to some extent.
Quoting ucarr
If math was perfect why did it take so long and have so many theories thrown out or overturned by new theories? If the math had been there all along why does it need to change. The simple reason is that while the universe is describable mathematically humans have still not figured out all of the math necessary to do the job and are still working on invent new ideas and methods to do so.
Quoting ucarr
I honestly thought you were joking when you asked such a ridiculous question. But I think that you yourself answered it when you called both of them piles of stones. Same name would even fit 20-stone.
The reason is more likely that most of the universe has no mathematical structure. Already three bodies interacting gravitationally do not move on mathematically well-defined ways, unless specific boundary conditions are fulfilled. So a mathematical universe is a fiction, a myth.
I suppose you're indirectly asking if Reality is necessarily Material or Physical. The Non-Physical Reality thread is seeking a similar clarification of Realness. :nerd:
https://thephilosophyforum.com/discussion/12585/non-physical-reality
I take this to mean you think numbers are metaphysical, however everything you listed as properties of numbers originated from your personal brain state which in a neurological sense is entirely physical and doesn't need a metaphysical explanation.
Likewise, the use of numbers by others is always inseparable from brain state. Can you show any way numbers exist in the absence of a biological brain state?
For me, the question of 'what is information?' is answered by brain state and brain state only. The question of 'what are numbers?' is a sub category of information and answered as brain state and brain state only. If your brain projects some meaning to the external environment that would be a false perception and it is still only a physical brain state holding a concept of numbers.
Quoting Mark Nyquist
Your inference about my intentions makes perfect sense, however, my language is faulty, and thus your conclusion is opposite of what I tried & failed to communicate.
In the above statement, I was trying to say that while Wittgenstein was promoting the physicality of numbers by attacking their metaphysicality, I am promoting the physicality of numbers by establishing their objective materiality.
What you inferred is much closer to what I wrote but didn't intend, hence you correctly misinterpreted what I incorrectly expressed. (How's that for labrynthine mishegoss?)
All of the above is to inform you that, given my physicalist intentions re: numbers, your position & mine are not on opposite sides of the aisle.
I'm not perfectly clear on whether or not you allow that number is a physical attribute present in material objects. Since the brain is a material object, and you believe information is answered by brain state and brain state only, this would seem to indicate you do make such allowance.
But then you conclude by saying,
Quoting Mark Nyquist
Since you put stock in the physicality of numbers via neural networks, how do you reconcile this with saying the ascription of numericality to the external environment is a false perception?
I say "not mathematically well-defined" and "non-mathematical" are two different things. Moreover, "not mathematically well-defined" does not do away with the abundance of mathematically well-defined physics. (Is not the warpage of spacetime by celestial bodies well-defined?)
This tells me your conclusions that, "most of the universe has no mathematical structure" and "the mathematical universe is a fiction," in light of the evidence provided, are cognitive leaps. Can you support them with evidence more decisive?
P.S. You can throw open the shutters onto a new vista for me by detailing a non-mathematical physics.
I don't take it that far. With the above I'm implying that establishing the physicality of a thing is a good means of establishing the reality of a thing.
I haven't jumped to the conclusion physical reality precludes non-physical reality.
Well, yes, I see it as my brain holding or containing the physical or numerical attributes of an external material object. That's my view and thanks for clarifying your original post. I'll try to read some more here.
I went round and round last summer on the 'What is information?' question and there never was much consensus so you might find the same pattern for a 'What are numbers?' question.
I think your affirmation here forms the heart of our discussion.
We both know that material things are countable. This means material things can be counted.
Something about material things makes them countable.
Mind you, the language that does the counting, math, does not make material things countable.
Being countable is part of the makeup, part of the being of material things.
Math, the language of counting, only entails the means of counting; it doesn't create the possibility of something being countable; it merely provides a means for doing the counting of countable things.
We know this because, as you've been saying, human mathematicians are still struggling to count certain things for which the mathematical expression is not yet resolved.
We suspect that these as yet uncountable things will eventually become countable, when their mathematical expression gets resolved, but the fact of their being countable prior to math being able to actually do the counting makes it logically clear that math does not impart countability to these material things, otherwise we would not struggle to count them. Instead, all we would have to do is create some math that imparts countability to these things and then they would be countable.
We both know that's not how the world works.
Being countable means being able to be placed in a one-to-one relationship with the integers (or counting numbers). The integers are a human invention. Being placed in a one-to-one relationship is a human activity. Being countable is not a property of material things sans humans. Or minds, at least (corvids, monkeys, etc. may be able to count).
Math, by definition, does make material things countable.
Well, what about cosmology - the Big Bang Theory for example? Scientists project backwards from the knowns of the present - speed of expansion of the universe (accelerating), estimates of mass of the universe, etc. - and they find that the universe must've begun 13.8 billion years ago. Then they searched for corroborative evidence and found it as cosmic microwave background radiation (CMBR). All these projections into the past are mathematical in nature. In other words, given humans are only a 300k year old species, it follows that the universe was mathematical way before humans came into existence.
Thank you. At least someone else understands that math is just another language used to describe the universe. :100: :party:
Something to test any model of material numbers is to understand that material numbers can only exist in the physical present. Any numbers that references the past or future cannot physically exist in a past or future location but must exist in a present physical form (brain state only). This should point out the necessity of numbers physically existing as brain state only. So references to past numbers can only exist in the physical present and the most obvious form is physical brain state...dynamic neural networks that physically exist in the physical present only.
When we think about material numbers it may be in a framework of a time continuum but the material state can only be in the physical present and located in a physical brain.
Let me open the shutter and give you a bright shining vista. A belvedere. Spacetime is curved, and curvature can be quantified, by tensors. Ricci tensors, Einstein tensors, metric tensors, Riemann tensors, mass-energy tensors, or whatever tensors. The are collections, tuples of tuples, of number concerning positions and lengths, time and durations, a lot of (partial, directional, single or multiple) derivatives thereof, and a dual flat, Minkowskian, (co)tangent space is introduced locally, to facilitate calculations.
Then on this space particles fields couple with an eternal and all-pervading field of virtual particles by means of which they reach out to other particles (Haag's theorem says virtual particles are math constructs, but a similar argument can be constructed for real particles). If they get no interaction, they will get lost in space hopelessly.
These particles and their couplings to the virtual field (by charges, which are considered the generators of the force mediating fields, giving the misleading image of force being the result of particle exchange, which doesn't happen), these particles and their couplings to the to the virtual fields between them (the intermediary fields, like the field of intermediary vector bosons in the weak interaction, or the photons between charged particles), are described by quantum fields, as you certainly know.
The coupling to the virtual fields, and the couplings of these fields to other virtual fields, is represented by Feynman diagrams. There are an infinity of them, corresponding to increasing numbers of interactions with and of the virtual "glue". The charge of particles determines the glue strength, i.e. the coupling strength. If this coupling is strong, like is the case for the color force in the strong nuclear force holding quarks together, the
Feynman diagrams contribute more and more instead of less and less, as is the case in the electrons interacting. And because quarks can never be asymptotically free, the perturbation approach can't be used to describe quark interacting with other quarks, as the perturbation approach assumes the particles to be free before and after the interaction. If the quarks are close to each other, the effective coupling is small, letting them run fairly free while forming a proton, neutron, pion, or more generally, hadrons and mesons.
To describe the motion of these quarks the approach with Feynman diagrams (the perturbative approach) won't work. There are other non-perturbative approaches like those lattice calculations assuming a discrete structure of spacetime. Supercomputers are used to do calculations in this color charged realm.
So perturbative QFT is applicable in a very limited domain, and extending it to curved spacetime complicates the the app. QFT in curved spacetime was used by Hawking in his description of the eponymous radiation. But the calculation is approximate. It's rather well understood, but there is no connection involved between the information inside and the radiation. This connection has been established recently (by entanglement), but there is no consensus.
So the math never describes exactly and at most approximations can be made. Which simply means no exact structures exist. Which means they don't exist at all.
Indeed. And anyone claiming it to be a universal language is unconsciously adoring an absolute god. Which is present for everyone. The universal god.
Could that something that makes them countable be their presence? Based on the idea that you cannot count things that are not there to be counted, maybe this is so.
I can count my ideas about how to solve a problem, I can count sheep on the field or in my mind, I can even count how many times you have failed to provide any detailed proof to back up your way of thinking. But I find it incredibly hard to count nothing. You try it, how many diphthongs are in the following paragraph?
How many did you find? None I guess.
You did not find any because there were none to find, If I had written any there they would have been easy to find.
The logical conclusion is that what makes objects countable is simple their presence.
Quoting ucarr
I don't know who we are but maybe you are right, or not. Who knows, mankind might be extinct before the can invent languages complicated enough to describe the rest of the universe.
Yes they do just that. They have invented a language that describes the universe in its current state and they use that to. Then they use the same language to look for evidence of it being true. From that it follows that it has only been possible for humans to describe it for a few years.
You can do the same with a couple of photos of someone that were taken a few years apart, you can guess what they looked like in the past and what they will look like in the future. Then go and look for pictures of them in the past to see if you were right or hang around for a few years to see if they change the way you predicate.
I'm beginning to have doubts about this though - the reverse extrapolation into the past leads us to the big bang singularity (the mathematical models we have seem to, as physicists like to say, break down). Does this mean the universe wasn't mathematical? What if retracing a series of logical syllogisms finally led back to a contradiction or meaningless statement? What then?
Fact is that most of the universe can't be mathematically described and a lot of math can't be found in the universe. Because it's non-mathematical.
Quoting Sir2u
Do you know you're entangling mental objects with physical objects? I suspect your premise here is rooted in subjective materialism.
Subjective Materialism -- The only knowable reality is the represented image of an external object. Matter as a cause of that image, is unthinkable and therefore nothing to us. An external world as absolute matter unrelated to an observer does not exist as far as we are concerned.The only knowable reality is the represented image of an external object. Matter as a cause of that image, is unthinkable and therefore nothing to us. An external world as absolute matter unrelated to an observer does not exist as far as we are concerned.
[b]An external world as absolute matter unrelated to an observer...
I think this is the lynchpin of the scientific method. Are you okay with science reverted back to the period before the scientific method?
Quoting EugeneW
You say,
Quoting EugeneW
I think your above quote is the gist of your premise our universe in not mathematical. With these three sentences, I think you're conflating the signifier with the signified.
If we look retrospectively at Newtonian physics through the lens of Relativity, we can assert that, beyond a certain region of velocity, Newton's Laws are (now) unacceptable approximations. To go on from there to say, Quoting EugeneW
Entails making a cognitive leap that is a real whopper.
I say you make the same cognitive-leap whopper when you claim the present day limitations of the Hawking Radiation measurements amount to probitive evidence the universe in non-mathematical.
Asymptotic freedom ? forever approachable but never arrived at? Quarks are really solitary?
Since I'm curious, I'll spout off with a shot in the dark. Is there at least a faintly tangential connection between elementary particle perturbation & the introduction of asymmetry, with rapid inflation of the pre-Big Bang universe?
If there's a scintilla of truth in this speculation, doesn't that tell us the pre-Big Bang universe was unstable?
I think the pre inflation era was an era of a kind of time that is characteristic for virtual particles. They don't move forward nor backwards in time but oscillate. That state, present on a 3D Planckian volume residing on a 4D bulk space (which with it can gravitationally interact, somewhat like the Randall-Sundrum model, explaining the weakness of gravity), is set in motion not by an internal breaking of symmetry (symmetry breaking has no place in this model) but by an external condition that exceeds a critical value: the negative curvature of the bulk space on which two 3D branes (universe and its mirror version) can
inflate into real existence.
Quarks can't be asymptotically free. Only when together they can move freely.
What's a cognitive leap whopper?
If universe is non- mathematical, how does this impact status of applied math? Huge question that needs answering by your claim.
There's something external to the Big Bang singularity?
No, it was only describable. Then math was invented to help describe it.
Do you think that math cannot be applied to non material objects. I had two dreams last night and three the day before.
Holy shit!!! Non material things are mathematical as well. OR NOT.
I suspect you have no idea how to continue proving your point so you are trying to confuse the topic.
Quoting ucarr
Apart from the fact that it is a bloody stupid question, how do you think my answer would help you to prove that the universe is mathematical?
You are the one that has stated that mathematics was clearly a part of the universe before humans existed, therefore the universe is mathematical. Exactly what proof have you offered?
Mankind will have to find another way to describe the universe and they will chuck applied math out of the window as obsolete.
Recently, you've said material things are countable. So, if numbers are not a physical attribute of a material thing, and yet numbers, which are of the mind only, can count material things, then the counting of material things by mental numbers is mixing a mental thing with a physical thing, subjective materialism (Berkley).
Bear in mind, numbers as symbols must have a material thing as their referent, if they are to keep separate from material identity, otherwise, you're mixing the two.
Quoting Sir2u
Following from your claim numbers are purely mental, non-material things are the only things they can count without becoming entangled with the material world.
Quoting Sir2u
It's not a stupid question because the lynchpin of modern science is the belief that the physical attributes of material objects persist in the absence of sentience naming them. The three pillars of the scientific method, as you know, are public, repeatable, measurable. If the state of material things were dependent upon sentience naming them, as you claim with numbers, material things would forever be shape-shifting like mad in accordance with the many points of view of various individuals. Material things are measureable to a standard because their attributes don't change under the influence of sentience, which means said attributes are independent of sentience.
You mean to say the universe wasn't mathematical before humans got here? The earth was not revolving around the sun in an elliptical orbit determined by the mathematical laws of gravity before humans came into existence!? :chin:
I'm sorry, I don't follow.
Quoting EugeneW
:up:
Quoting EugeneW
Okay ...
O ... kay :chin:
I can't follow this leap. Explain how you get to "no exact structures exist" and from there to "they don't exist at all".
Here's where things get interesting because what you have written above is a full, unconditional affirmation of what I've been claiming from the start.
Yes! The physical presence of material things is what makes them countable, and the language of math does the counting; it does not create or ascribe to material things their countability. The countability of material things, as you say above, is their physical presence.
In a world without material things, I suppose pure math could busy itself with the counting of abstract numbers. Of what use would that be? Might it serve as a Buddhist chant that aids in calming the mind for the sake of meditation? I say this because the counting of abstract numbers without referents is a vacuous circularity.
Quoting Sir2u
Why should applied math, that works in the real world, be chucked out the window? While it's true that Einstein physics has superseded Newton physics to some extent, the world still uses Newton physics everyday to great advantage.
Not subjective materialism, but philosophical dualism. The rational intelligence, nous, recognises numbers and forms, among other attributes, which are among the qualities which make material things intelligible.
[quote=Brennan, Thomistic Psychology]“EVERYTHING in the cosmic universe is composed of matter and form. Everything is concrete and individual. Hence the forms of cosmic entities must also be concrete and individual. Now, the process of knowledge is immediately concerned with the separation of form from matter, since a thing is known precisely because its form is received in the knower. But, whatever is received is in the recipient according to the mode of being that the recipient possesses. If, then, the senses are material powers, they receive the forms of objects in a material manner; and if the intellect is an immaterial power, it receives the forms of objects in an immaterial manner. This means that in the case of sense knowledge, the form is still encompassed with the concrete characters which make it particular; and that, in the case of intellectual knowledge, the form is disengaged from all such characters. To understand is to free form completely from matter.[/quote]
This is the closest you've come to saying something philosophically interesting in this thread.
If an exact structure can't be described exactly, it doesn't exist. Otherwise you could describe it exactly.
The fact that it can't be described exactly just means there isn't an exact structure. If the exact structure is the approximation then what is the exact structures? And what it approximates? There are many possible approximations.
No. "The fact that it can't be described" only implies that it hasn't been described yet (either by you or maybe anyone). For instance, the ocean floors of Earth could not be mapped until the 20th c, yet the ocean floors have existed for billions of years before they were mapped.
The fact that God hasn't showed himself only means he hasn't showed himself yet...
Breaking this down,
Is Brennan herein referring to the (individual) gods? Are you polytheist? Do you hold with the premise monotheism is false?
Do you hold that such separation is empirically literal, or do you have an understanding such a separation is a benign procedural fiction of the reasoning mind? I ask this because form and matter in separation (to me) seem to be unintelligible. This bifurcation gives the reasoning mind a stronger handle on what it's trying to understand, however, we don't see such separation in our everyday world, do we?
So, humans are a mixture of the material & the immaterial i.e., a mixture of form & content? If so, this tells us humans encompass a brain/mind bifurcation. This leads us to a crucial question for the immaterialist: How do the material & the immaterial {connect, interface, bridge} to form a common ground and what does such common ground look like?
Might it be the case QM has some answers to this question?
Do you experience purely abstract thought without material imagery acting as a supporting substrate making it intelligible?
I'm inclined to think the easy, discrete separation of matter & form is a useful fiction, but a fiction nonetheless.
Before the 20th century, ocean floors were public, repeatable, measurable i.e., subject to scientific examination & description.
From antiquity until now, God, by definition, transcends the material.
Since science has entered into the 4D realms of spacetime & QM, further expansion in 4D might lead to an upward dimensionality of materialism that includes a 4D empirical God consciousness (which is not God) that might well serve organized religion.
In light of the above statement, the premise God consciousness has no 4D empirical existence is, in my opinion, not a well-supported conclusion.
Is someone rushing to judgment about boundary ontology?
Where's the argument, supported by evidence (Hadron Super-Collider), that the boundary ontology of, say, elementary particles, must be exact & discreet in order to be extant?
Action-at-a-distance of elementary particles raises questions about existing boundary ontology being simple, exact & discreet.
Likewise the event horizon of black holes>likewise the holographic theory of the universe.
Likewise dark matter.
Likewise the 2nd law of thermodynamics being preserved within black holes.
What judgement is there to be made?
Quoting ucarr
What's the boundary ontology of elementary particles? They are only supposed to be asymptotically free.
Quoting ucarr
Which questions?
Quoting ucarr
Likewise in being simple, exact, and discrete?
Consider, an approximation is such in relation to another thing it resembles, as a kind of isotope, or variant. As a thing in itself, it's just another thing, no less extant than the other thing it resembles.
Should we reverse engineer our thinking about the applied math models that seem to fit real things, like bridges? Is engineering a fiction that, by luck, happens to work, through no rational intent of engineering science?
Is acceleration due to gravity a fiction?
What's the pivotal evidence that all of the universe is non-mathematical, not just some of it?
Yes. My examples are supposed to show non-discrete, real boundaries, or unknown boundaries, yet to be mapped mathematically.
I think the evidence is that we don't see perfect mathematical structures. Plato delegated them to a mathematical extramundane world, from where they are projected as shadows, I think we project math from the mind to the physical world and in some situations, when asked in mathematical language, the physical world answer in a back mathematically, but in most cases she doesn't have an answer.
Not 'gods' - individual particular things. Whatever you see, any object or being, is a combination of matter and form.
Quoting ucarr
I think we do - because that is how the mind recognises and classifies things. Whenever you see an object, there's an immediate chain reaction of apperception, assimilation, and recognition - this is going on all of the time. If you loose that functionality you literally couldn't make sense of experience - like that Oliver Sachs book The Man who Mistook his Wife for a Hat. (I think the technical term is 'agnosia'.)
This type of 'matter-form' dualism goes back to Aristotle and ultimately to Plato. It is derived from the understanding of the platonic Ideas or Forms. The very rough drift is that individual particulars are always a composite of form and matter - but the Aristotelian notion of 'matter' is different to the modern. It is more like 'unformed chaos', which is brought into being by bring 'impressed with form' (as a seal is impressed on wax).
Of course it's true that a great deal of Aristotelian philosophy was abandoned in the transition to modernity, chiefly due to the very great deficiencies of Aristotelian physics, which was demolished by Galileo. But some elements of Aristotle's metaphysics, such as 'hylo-morphism' (matter-formism) have made a comeback.
The basic idea behind that Brennan quote is that the senses 'receive' the sensory data from a particular, but the mind (nous) recognises the form or idea or principle of the particular, and that rational knowing is always a combination of these two elements, the sensory with the intellectual.
It goes some way to addressing your concern with whether numbers must always have material representation, I think. That's because the operation of the intellect is purely rational, it is concerned only with ideas, which are immaterial in essence. But where Aristotle departed from Plato, is that Plato held that the ideas have real existence in their own right, whereas Aristotle said they were real only when they were instantiated in material form. (That is called 'moderate realism'. There's an Aeon article about Aristotelian realism here and another article which discusses Platonic realism in relation to maths here.)
Look at your favorite coffee mug, now describe it. You use words to describe right? Did it have the properties you used before you described it or did they come into being when you did it? Now imagine try to describe something without the words to do it. Impossible right?
That is what math does. Describes the properties of things using numbers instead of words.
Could you just go back to the OP and point out exactly where you stated that. No, don't bother.
You are repeating yourself using different words but saying the same thing. I doubt that anyone has any possibility of change your way of thinking and you have no way of changing anyone else's. The argument has been running for years with advancing at all.
One last question. You don't have to answer.
If mankind had never invented and renovated and updated mathematics to fit into the little bit of the universe that it actually manages to describe reasonably well, would we be stuck with describing it as a very big colorful place with lots of stuff floating around?
My answer would be yes, because math has nothing to do with the universe. It is just the method of describing the properties. We would still be able to describe a lot of the properties because ordinary langue suffices for that.
Indeed, description is only possible once we develop the language to do it with and math is a language, but more too.
When and if I invent a language, the words, their definitions, can't be arbitrary i.e. if I coin a word and define it as I please, the properties listed in my definition will not/should not magically appear in the world. Will it/should it? The words "leprechaun", "elf", "fairy" are such kinds of words - their extension is empty. If math were invented, many of the concepts in it would be similarly affected - they would not apply to the real world.
If, as you say, "math has nothing to do with the universe," and, as you say, "It is just the method of describing the properties." then, by your own words, the properties described by math must belong to the material things and not to math. As you've said earlier, these material properties include length, width, height, weight, etc. So, math describes these physical properties of material things that are external to math.
Let's look at the two statements below.
First, I make a claim about material things,
then you elaborate what I assert with an additional detail.
Quoting Sir2u
Now, let's look again at what you said just before> math describes the properties of material things i.e., length, width, height, weight, etc. Let's remember you also said "math has nothing to do with the universe," and thus we conclude these properties are external to math.
Let us now assemble the physical properties of material things external to math. When we assemble length, width, height, weight, etc., what do we get?
We get PRESENCE. You know as well as I do that a material thing that possesses the properties just described has presence within the real world of material things.
Now, let's look again at your most important statement in this discussion,
Quoting Sir2u
I know you don't think math bestows upon material things the physical properties listed above because you've just said, "math has nothing to do with the universe. It is just the method of describing the properties."
So, if math doesn't bestow physical properties upon material things, and these physical properties add up to presence then, the presence of material things is likewise independent of math.
Therefore, given that presence is independent of math, and presence, by your own words, is that something that makes material things countable, then, by the transitive property, the countability of material things is also independent of math.
The logic here is airtight, is it not?
Ask almost anyone to describe a leprechaun or an elf, maybe even an angel. I bet they can do it.
These are words that are used to describe things, whether concrete or abstract. Math is used to describe the properties of the universe and uses words such as inches, meters, degrees, numbers. None of which appear magically in the world but all are just as "real" as a faerie.
PSsssssssssssssss. :smirk:
I'm not sure. Are we talking past each other?
An invention, in my view, is essentially imagination based. Ergo, what's invented needn't correspond to reality (unicorns, leprechauns, fairies don't exist). If math were also an invention, the same would be true - nothing mathematical would have any physical correlate so to speak.
This, however, isn't the case. Mathematical objects do correspond to things in the real world (mathematical theories in physics). This has to mean something; it can't be ignored, oui?
Quoting ucarr
In the second line, without realizing it, you affirm the claim I make in the first line.
Quoting Sir2u
In the third line, I make the observation that your statement is an affirmation of my claim.
Quoting ucarr
In the fourth line below, you accuse me of moving the goal posts.
Quoting Sir2u
In lines 5, 6, 7 I quote myself from the OP. Any reader can clearly see that my later statement, Being countable is part of the makeup, part of the being of material things. was made earlier, with slightly different wording, in the OP. To elaborate a bit further, when, in the OP, I talk about a material object's ability to hold a position as being essential to its physical attribute called number, I'm using different words to talk about the very thing, PRESENCE, which you affirm as the thing that makes material things countable.
Quoting ucarr
Quoting ucarr
Quoting ucarr
There's no wiggle room here.
In my previous post, wherein I show, through your own statements, your belief in my central claim, the logic is sound.
In this post, I show, through my own statements, the fact I've never deviated from my OP.
The evidence supporting these two claims is here before the reader in black & white. Any reasonable person can evaluate the carefully worded statements and make their decision where the truth lies.
Together they form an infinite continuum to move in. Space is the only real infinity.
Most, if not all languages spoken on earth were invented or came from someone's imagination. So you think that languages need not correspond to reality then? That they would not correlate to anything physical?
This has to mean something; it can't be ignored, oui?
Only your word for that, and I am a non believer. The key to your concept is the "built in" bit. But nothing can be proven to contain any mathematical information. If you can show any definitive proof of this claim, please do so. But stating that it is true does not make it so.
If a stone contains that information about itself, which of the stones in a quarry contains the data about the pile? None of them.
As I said already, you are repeating yourself. Please stop.
Languages are used to describe something i.e. they aren't invented in a vacuum. There are two aspects of this whole description process:
1. Things/objects: In this we're at full liberty, naming can be done in whichever way we fancy e.g. water could've been assigned to the word "dex" or ",loi" etc. Naming needn't possess a rationale.
2. Patterns: We have no choice in this regard. If what goes up must come down or if rolling stones gather no moss, then that's how we have to say it is (assuming we're concerned about truth). These patterns are not invented by us, they're out there, independent of us. The universe exhibits mathematical patterns and these weren't imposed on the universe by us with the aid of language.
As you wish. I will stop. Excelsior.
:up:
The counting process is a brain process. And not just an abstract process. To count to ten takes me five seconds and counting to 100 would take 50 seconds and 1000 would take 500 seconds. Since all this counting is taking place in a brain, why not identify the brain as the source of Material Numbers?
So it seems the choice is do material numbers reside in matter or in brains? If a brain was absent then counting wouldn't even be possible.
I remember the first time I saw a number raised to a negative power. "How does that work?" I wondered. "Take the square root of a negative number? But you said..." Who thought up imaginary numbers? "Say, they look like real numbers."
Right, gravity exists without human intervention. Even without humans coming up with the idea of describe it by using numbers it would still hold us on the ground, but there would be no description of it. Math is in the human mind.
Quoting Agent Smith
As I have said, everything has properties.
OK, so Banno's red cup actually has red as part of it's being. Or does it just have a property we call red?
Does 'reality' have an exact, context-independent meaning? Is such a situation even possible? (And what exactly do I mean by 'possible'?)
I proceed with the assumption you read the premise of my quoted line as being,
Reality has an exact, context-independent meaning.
Isn't the premise you ascribe to me a pretty good definition of Platonic Idealism?
Anyone who uses possible assumes an existence-accommodating context of some sort.
As for the degree of generality of an existence-accommodating context, I'm presently of the opinion that metaphysicians want to push that degree of generality towards infinity. So, yes. The metaphysician believes reality has an exact, context-independent meaning.
Doesn't the utilitarianism (and thus locality) folded into my quote protect it against Platonic Idealism?
Possibly. (I see what you are getting at, but I've learned (with difficulty) to be wary of dragging in foggy grammatical habit as ethereally hyper-logical necessity.)
Quoting ucarr
You seem to have one foot on the station and the other on the train. If 'reality' has only the foggiest referent (or more plausibly a dizzying infinity of unique context-dependent referents), the game loses its charm. 'No matter, never mind.'
[quote="ucarr;664270"]
I think the bolded statement is correct and important.
The first statement might admit some exceptions, but one must allow for the ineluctable ambiguity of the smoke signals we are trading here. (You mentioned 'Wet-gloom-shine' in the OP. I think he generalized his discovery about math to 'lung wrench' in general. But 'every talk has its stay.')
Statement one above is my general statement creating context for the following three statements.
Statements two & three are a response to a debater's extreme position that numbers exist only within the human mind, without material presence within our material world.
Statement four is my acknowledgment of the connection between the abstract thought of the human mind & our material world.
Abstract thought is non-specific WRT our material world; it is not uncoupled from our material world.
— ucarr
I think the bolded statement is correct and important.
The above commentary upon the "abstract thought" statement is attributed to me, but I don't recognize the words as being mine. III, are they your words?
Also,
Quoting ucarr
The above commentary re: 'Wet-gloom-shine' etc is not mine & does not appear in my OP.
:lol: :rofl: