The necessary truth of mathematics (?)

[Write4U]

Not even after failing to even attempt an answer to a basic question that was put to you no less than seven times? A question, I note, that goes to the central core of the claims you make repeatedly.

If you have no answer, then your entire thesis falls in a heap.

The question of the meaning of the term "value" that does not represent a quantity but a "quality"? That question?

 

[Write4U]

Not even after failing to even attempt an answer to a basic question that was put to you no less than seven times? A question, I note, that goes to the central core of the claims you make repeatedly.

If you have no answer, then your entire thesis falls in a heap.

The question of the meaning of the term "value" that does not necessarily represent a quantity but can also represent a "quality"? That question?

I am still researching for examples of intrinsic (non-numerical) values, but let me try this as a starter.

Intrinsic vs. Extrinsic Value​

Abstract​

If we presume mathematics is universal while morality is cultural, these practices demand distinct pedagogies: Mathematics becomes a uniform requirement while ethics becomes a variable elective. However, the idea that mathematics is an essential part of the core curriculum is relatively new. Why must everyone be taught mathematics given that mathematicians are so rare?

Studying mathematics and ethics expands the scope and unity of our world through abstract and analogical reasoning. From an evolutionary perspective, these disciplines are co-adaptations, mutually sustaining cognitive capacities with shared origins in our distant past.

Concepts such as equality and fairness depend upon mathematics for their meaning, if not their merit. No formal instruction is ever value-free and the most efficacious teachers can answer the perennial question, “what is this course good for?” Humans vary with respect to abstract reasoning skills and a variety of mathematical languages are spoken around the world.

Even so, we should promote mathematical literacy by cultivating those cognitive capacities that make mathematical reasoning and moral deliberation possible. Integrated approaches to mathematical and moral instruction may be more efficacious than teaching each in isolation. We need to value math education if we want to make moral progress just as we need to value human intellectual variation if we want to make mathematical progress.

https://plato.stanford.edu/entries/value-intrinsic-extrinsic/#

 

[James R]

The question of the meaning of the term "value" that does not represent a quantity but a "quality"? That question?

I already asked you seven times.

Go back and find one of those times. Read what I actually asked you, carefully. Try to find an answer that addresses what I asked you, rather than posting your usual irrelevancies.

 

[exchemist]

Not even after failing to even attempt an answer to a basic question that was put to you no less than seven times? A question, I note, that goes to the central core of the claims you make repeatedly.

If you have no answer, then your entire thesis falls in a heap.

He seems to conflate “description” with “cause”. Mathematics describes various physical entities and processes. But obviously, being abstract, it cannot cause anything in the physical world.

This appears to be the error at the root of everything he says on this subject.

 

[Write4U]

He seems to conflate “description” with “cause”. Mathematics describes various physical entities and processes. But obviously, being abstract, it cannot cause anything in the physical world.

This appears to be the error at the root of everything he says on this subject.

My position is that human mathematics describe observed Universal physical functions and therefore can be used to argue that Universal functions are mathematical in essence.

Generic Universal maths do not cause universal physical functions, they logically regulate physical functions. (The Black Box works mathematically)

Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity).

The concept of a function was formalized at the end of the 19th century in terms of set theory, and this greatly enlarged the domains of application of the concept. Functions are widely used in science, and in most fields of mathematics. It has been said that functions are “the central objects of investigation” in most fields of mathematics.[5]

Function (mathematics) - Wikipedia

en.wikipedia.org

If humans can use mathematics to copy or imitate natural physical functions to a high degree of accuracy, what precisely is the objection to the concept that Universal functions are in fact based on what humans have named "mathematical in essence"?

If human symbolic mathematics are used to prove Universal functions, is it not logical to deduce that Universal functions have mathematical underpinnings?

What you are saying in essence is that when it looks like a duck, walks like a duck, quacks like duck, it isn't a duck!?

Forget human symbolics They are just human codified tools to describe the mathematical nature of spacetime itself.
No one argues with that analogy.

But if mathematics are a human tool and humans are part of this Universe, then it logically follows that the Universe has mathematical properties.
Humans are not creator gods, our brains are products of Universal evolved physics. No mysteries, just plain logic.

 

[exchemist]

My position is that human mathematics describe observed Universal physical functions and therefore can be used to argue that Universal functions are mathematical in essence.

Generic Universal maths do not cause universal physical functions, they logically regulate physical functions. (The Black Box works mathematically)

Function (mathematics) - Wikipedia

en.wikipedia.org

If humans can use mathematics to copy or imitate natural physical functions to a high degree of accuracy, what precisely is the objection to the concept that Universal functions are in fact based on what humans have named "mathematical in essence"?

If human symbolic mathematics are used to prove Universal functions, is it not logical to deduce that Universal functions have mathematical underpinnings?

What you are saying in essence is that when it looks like a duck, walks like a duck, quacks like duck, it isn't a duck!?

Forget human symbolics They are just human codified tools to describe the mathematical nature of spacetime itself.
No one argues with that analogy.

But if mathematics are a human tool and humans are part of this Universe, then it logically follows that the Universe has mathematical properties.
Humans are not creator gods, our brains are products of Universal evolved physics. No mysteries, just plain logic.

You can describe the physical processes of the universe in French. That does not make caused by something French.

 

[Write4U]

You can describe the physical processes of the universe in French. That does not make caused by something French.

Correct me if I'm wrong, but I see that as a false equivalence.

Using the example of the duck, a canard in France is still a duck. Or more popularly, "a rose is a rose by any other name".

The Fibonacci Sequence in daisies is the same all over the world, regardless of the symbolic language used to "describe" it.

IMO, in nature, "evolution via natural selection" is a mathematical, albeit probabilistic process.

Price equation​

The Price equation is a mathematical relationship between various statistical descriptors of population dynamics, rather than a physical or biological law, and as such is not subject to experimental verification. In simple terms, it is a mathematical statement of the expression "survival of the fittest". https://en.wikipedia.org/wiki/Price_equation#

IMO, it is very much subject to experimental verification.

Does this look like a mathematical process?
Figure 1: A selective sweep
Under natural selection, a new beneficial mutation will rise in frequency (prevalence) in a population. A schematic shows polymorphisms along a chromosome, including the selected allele, before and after selection. Ancestral alleles are shown in grey and derived (non-ancestral) alleles are shown in blue. As a new positively-selected allele (red) rises to high frequency, nearby linked alleles on the chromosome ‘hitchhike’ along with it to high frequency, creating a ‘selective sweep.’

Evolutionary Adaptation and Positive Selection in Humans

What Is Selective Breeding And How Does It Work?​

Selective breeding, also known as artificial selection, allows for the passing on of traits deemed desirable by breeders to subsequent generations. Without human interference, populations of plants, animals, and other living organisms reproduce under natural selection where the environment determines which traits are passed down. https://www.newrootsinstitute.org/a...ing-the-methods-motivations-and-implications#

 

[DaveC426913]

Correct me if I'm wrong, but I see that as a false equivalence.

Using the example of the duck, a canard in France is still a duck.

You're wrong.
You made exactly the point Exchemist was making. Describing a duck as a canard doesn't make a duck French.
Just like describing the universe with math equations doesn't make the universe math equations.
As always, you mistake the map for the territory.



:braces for the inevitable onslaught of equivocations and irrelevant links and quotations:

 

[James R]

Write4U:

Try to focus.

I asked you not to post irrelevant links and extracts from irrelevant articles, but you went ahead and did that anyway. (Can't you help it? Is this a kind of involuntary spasm?)

Here's the task I set you AGAIN:

----> What you need to do is to explain to me how mathematics could possibly cause anything in the physical world.

I have now asked you to try to justify your claims no fewer than NINE times in this thread. Each time, you duck and weave and avoid the question.

Tenth time lucky, maybe?

If you won't even try to answer the question honestly, then I think we're done.

 

[James R]

Addressing the latest distracting blather...

My position is that human mathematics describe observed Universal physical functions and therefore can be used to argue that Universal functions are mathematical in essence.

Nobody observes "Universal physical functions". They probably don't exist. (Assuming the use of the word "function" here implies the mathematical meaning of that word rather than actual physical processes.)

Generic Universal maths do not cause universal physical functions, they logically regulate physical functions. (The Black Box works mathematically)

Regulation of a physical process requires something to cause that regulation.

----> What you need to do is to explain to me how mathematics could possibly cause anything in the physical world.

You're claiming there is something called "Generic Universal maths" that can somehow affect physical things and "logically regulate" them.

Explain to me how "Generic Universal maths" can affect physical things. What is "Generic Universal maths", anyway? Is it a physical thing, or is it conceptual, like all the other maths we know of?

If humans can use mathematics to copy or imitate natural physical functions to a high degree of accuracy, what precisely is the objection to the concept that Universal functions are in fact based on what humans have named "mathematical in essence"?

Humans use mathematics to describe and theoretically model physical processes.

Mathematics cannot "copy" a physical thing, because mathematics can't bring physical things into existence (unless you can show how it can do that).

If human symbolic mathematics are used to prove Universal functions, is it not logical to deduce that Universal functions have mathematical underpinnings?

What's a "Universal function"? Give me an example or two, please. And how does "human symbolic mathematics" prove anything about those? Give an example or two.

What you are saying in essence is that when it looks like a duck, walks like a duck, quacks like duck, it isn't a duck!?

A concept does not look or act very much like a physical object or process. There's a fundamental distinction between map and territory. You have had that distinction explained to you many times before. Don't you understand it, yet?

Forget human symbolics They are just human codified tools to describe the mathematical nature of spacetime itself.
No one argues with that analogy.

Just a sentence or two earlier, you were saying that "human symbolics" are "used to prove Universal functions", and can therefore - for unexplained reasons - be used to "deduce that Universal functions have mathematical underpinnings".

Now you want to throw all of that away? Just two or three sentences further. Okay, then. But you're not making any kind of coherent argument, you realise. You flip flop from one thing to another, almost as if you forgot what you wrote two sentences earlier. Are you okay?

But if mathematics are a human tool and humans are part of this Universe, then it logically follows that the Universe has mathematical properties.

By proxy, you mean? The universe has mathematical properties because mathematical properties are made up by humans in their descriptions of the universe?

That's not particularly controversial, but it is very different to your core claim and to the claims of people like Tegmark.

Humans are not creator gods, our brains are products of Universal evolved physics. No mysteries, just plain logic.

What's "Universal evolved physics"?

Where's the logic?

The Fibonacci Sequence in daisies is the same all over the world, regardless of the symbolic language used to "describe" it.

The Fibonacci sequence is not "in" daisies. A physical daisy does not contain a mathematical concept.

IMO, in nature, "evolution via natural selection" is a mathematical, albeit probabilistic process.

Nobody cares about your opinion on such things, until you can show that a mathematical concept can cause a physical change.

So far, you haven't even come up with an in-principle argument for how it could conceivably do anything like that.

 

[Write4U]

Regulation of a physical process requires something to cause that regulation.

Yes, a dynamic environment is causal to the interaction of its constituent parts. How they deterministically interact is a mathematical function.

The Universe describes itself via expressed mathematical functions, regardless of the existence of humans. Regular durable patterns have been forming since the Beginning.
Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals and self-organization.[3]
https://en.wikipedia.org/wiki/Chaos_theory

James R:
Humans use mathematics to describe and theoretically model physical processes.

Self-organization into regular patterns is a mathematical function, regardless of any descriptive symbolic representation. A rose is a rose...
Is this description true or not? If not, what is it?

I believe that scientific "observations" are cognitive of naturally occurring regularities and the one thing about mathematics is its regularity.
And therefore, in essence, regular pattern forming is a mathematical process.
If it is true, what is it that guides the self-organization of these recurring "underlying patterns"? There is only one known candidate, and that is an abstract guiding principle of what we have discovered, symbolized, and codified as "mathematical functions"

https://www.sciencefocus.com/science/was-maths-invented-or-discovered

The term "physics" does not describe anything other than the science, nor does the term "mechanics" unless these processes are explained via mathematical symbolization.

A nuclear power plant is regulated by mathematical controls of the environment. If something goes wrong the physics becomes uncontrolled and that little patch of land becomes uninhabitable for many years.

James R:
Mathematics cannot "copy" a physical thing, because mathematics can't bring physical things into existence (unless you can show how it can do that).

Higgs did the very thing you asked. Program a collider with the proper dynamics based on the right mathematical formula and presto a boson materialized where none existed before and promptly decayed because bosons cannot exist independently.
The dynamics within the collider were causal. The mathematical control of the dynamics produced the desired result.

The Higgs boson can't be “discovered” by finding it somewhere but has to be created in a particle collision. Once created, it transforms – or “decays” – into other particles that can be detected in particle detectors. Physicists look for traces of these particles in data collected by the detectors. https://home.cern/science/physics/higgs-boson#

In nature all possible forms of dynamics are present and where the dynamics and constituent parts are similar, similar results may be predicted to emerge with mathematical regularity.

----> What you need to do is to explain to me how mathematics could possibly cause anything in the physical world.

No, I don't need to do that. That is not my claim which you persist I am advancing. Universal maths does not cause, they guide the orderly and predictable interactive functions as we can observe and initiate down to very small scales.

Mathematics is not causal to physical interactions, they are the Universal abstract rules that "determine" predictable results of physical interactions.
Input --> mathematical function --> Output

But rather than grilling me about a descriptive language that works "reasonably well", is it not time that you explain this mainstream description of natural interactive functions that are not based on the physical interactive properties of the constituent parts that are so accurate that they can be applied for practical human applications, by copying natural physical processes!

 

[exchemist]

You're wrong.
You made exactly the point Exchemist was making. Describing a duck as a canard doesn't make a duck French.
Just like describing the universe with math equations doesn't make the universe math equations.
As always, you mistake the map for the territory.



:braces for the inevitable onslaught of equivocations and irrelevant links and quotations:

Exactly.

And, as I have pointed out more than once previously, one can only describe aspects of the physical world in mathematics if one has already defined the mathematical quantities whose relationships are being described, in words. F=ma remains a purely abstract piece of algebra until you have defined what F, m and a mean, as physical quantities - something you have to do in words. Those definitions are what connect the abstraction of mathematics to the physical world.

So mathematics cannot even claim to be a free-standing description of the physical world. It relies on physical terms and concepts first defined in words.

 

[James R]

---> What you need to do is to explain to me how mathematics could possibly cause anything in the physical world.

No, I don't need to do that. That is not my claim which you persist I am advancing. Universal maths does not cause, they guide the orderly and predictable interactive functions as we can observe and initiate down to very small scales

You can't weasel out of the problem you've created for yourself that way, Write4U.

"Guiding" something so that outcome A happens rather than outcomes B, C or D is equivalent to causing A to happen.

Suppose you assert that a mathematical equation of some kind is the thing that causes balls placed on slopes to roll down towards the bottom. That would be saying that a conceptual thing (the equation) somehow produces a physical effect (rolling down the slope) on a real-world object (the ball).

"Guiding" doesn't get you out of jail. If you assert that a mathematical equation is what "guides" the ball on the slope to roll down the slope rather than up it or across it, then you're still asserting that a conceptual thing (the equation) somehow determines the behaviour of a physical system made up of real-world objects.

You have now failed TEN times to justify your assertion that concepts can have physical effects on things.

Don't you think it's time to quit while you're behind?

 

[Write4U]

You're wrong.
You made exactly the point Exchemist was making. Describing a duck as a canard doesn't make a duck French

No, that is the wrong analogy. Describing a duck in any language does not change the duck!

So mathematics cannot even claim to be a free-standing description of the physical world. It relies on physical terms and concepts first defined in words.

I agree. It relies on cognition of physical properties and interactive concepts first defined by words and later more accurately defined by the language of mathematics which are universal. Even as we have developed a codified symbolic language to describe maths, the maths remains intrinsically the same regardless of the language.

What else is the regulating principle that produced regular and durable patterns from chaos? I did not invent Chaos Theory.

I have yet to see a theoretical replacement that even approximates the power of mathematics.

 

[James R]

Regular durable patterns have been forming since the Beginning.

It is people who recognise "patterns". Pattern is a regularity that we notice. The universe doesn't recognise patterns.

Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals and self-organization.[3]
https://en.wikipedia.org/wiki/Chaos_theory

Chaos theory is a theory - a conceptual description of various physical systems.

Self-organization into regular patterns is a mathematical function, regardless of any descriptive symbolic representation.

Patterns do not "self-organise". Patterns are regularities that human beings observe. We "organise" them.

There is no pattern that has no "descriptive symbolic representation", because patterns are descriptive representations.

I believe that scientific "observations" are cognitive of naturally occurring regularities and the one thing about mathematics is its regularity.

Observations don't involve thinking. They involve looking. Ideas like "regularities" are just that - concepts that we have in our heads. They refer to observations - sometimes.

And therefore, in essence, regular pattern forming is a mathematical process.

You're not keeping track of whether you're talking about physical things or ideas, now. In fact, that's the fundamental problem we have here: you apparently have trouble telling the difference.

A nuclear power plant is regulated by mathematical controls of the environment.

No. A nuclear power plant is regulated by physical things: control rods, pumps, coolant, human beings at the controls, etc. etc.

Literally none of that is "mathematical".

Mathematics has no "controls". It doesn't - CAN'T - control physical things. How could it? (That's ELEVEN times now, notice.)

If something goes wrong the physics becomes uncontrolled and that little patch of land becomes uninhabitable for many years.

Ah! The physics.

The physics is not the same as the mathematics, though. Is it?

Higgs did the very thing you asked. Program a collider with the proper dynamics based on the right mathematical formula and presto a boson materialized where none existed before and promptly decayed because bosons cannot exist independently.

The Higgs boson was formed in that collider because two physical things (protons) that were going very fast in opposite directions collided head-on with one another. Mathematics didn't cause the Higgs boson to pop into existence. How could it? (TWELVE.)

The dynamics within the collider were causal.

The dynamics, eh? Would that be the physics, again?

See the root of that word? Physic- . Same root as in the word "physical".

The mathematical control of the dynamics produced the desired result.

Mathematics wasn't at the controls. People were.

In nature all possible forms of dynamics are present and where the dynamics and constituent parts are similar, similar results may be predicted to emerge with mathematical regularity.

Word salad. Now you're back to just wasting time blathering about nothing again.

But rather than grilling me about a descriptive language that works "reasonably well", is it not time that you explain this mainstream description of natural interactive functions that are not based on the physical interactive properties of the constituent parts that are so accurate that they can be applied for practical human applications, by copying natural physical processes!

I can't even tell what you're trying to ask me. Maybe try using smaller words.

 

[Write4U]

You have now failed TEN times to justify your assertion that concepts can have physical effects on things.

Ten times , you have failed to give me the courtesy of considering the concept of mathematically regular Universal functions emerging from a naturally ordered and ordering spacetime geometry.

 

[James R]

Ten times , you have failed to give me the courtesy of considering the concept of mathematically regular Universal functions emerging from a naturally ordered and ordering spacetime geometry.

Word salad excuses.

You can't explain how a concept can affect a physical object, can you?

Why not be honest about that?

 

[Write4U]

Is is people that recognise "patterns". Pattern is a regularity that we notice. The universe doesn't recognise patterns.

It doesn't need to. It produces them!

I am not talking about motive or intent. Mathematics are a necessary property of spacetime.

What is Mathematics?​

Mathematics is the science and study of quality, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.

There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions". Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."

But Einstein was talking about the human symbolization of generic natural mathematics. And he was right. But that does not negate the concept of naturally occurring maths.

 

[James R]

While we're at it...T

Ten times , you have failed to give me the courtesy of considering the concept of mathematically regular Universal functions emerging from a naturally ordered and ordering spacetime geometry.

I have done the exact opposite of "failing to give you the courtesy" of considering your silly claims and your invented, ill-defined concepts.

I have engaged with your nonsense more than anybody else on this forum.

How dare you accuse me of failing to give your writings fair consideration.

 

[exchemist]

Ten times , you have failed to give me the courtesy of considering the concept of mathematically regular Universal functions emerging from a naturally ordered and ordering spacetime geometry.

Meaningless verbiage does not give its author the right to demand courtesy. Even if one were to extend you that courtesy, how can one "consider" something that seems just a random jumble of sciency terms?