Applicability of Maths to the Universe

[Peebothuhlu]

At work.

Wait! Go back a step or two!

I really want to see some one counting in 'Cat'!

[GrandizerII]

Example, if there's symmetry involved in the real world, then the maths that makes use of symmetry will naturally be applicable to the real world.

I don't think anyone doubts that math has applicability to the material world. We could barely get through a day without it.

I know. I'm trying to point out that it shouldn't be a surprise at all in this scenario.

The controversy starts up when people say that math is always and only a description of the material. The metaphor that math is only a language to talk about the material appears to break down at some point.

How though? Would be good to have some specific examples. I forgot which clip it was (whether it was this one or another I watched), but Penrose mentions something about precision, but to me that doesn't really do much to support his POV. Because the other position explains this rather adequately.

And it's not only Platonists who say that numbers have a kind of independent existence, in a non-language kind of way. The number 2 exists in a way that the word "cat" doesn't, for example. That's what Popper, Penrose, and many others say is the case.

I might be inclined to agree. But again, unless there's something specific to go by here, I cannot say for sure.

In the end it's a metaphysical question, not a scientific one. People who are fully committed to a material-only kind of metaphysics will deny that there is anything else. Since I don't know the answer, and I take Popper and Penrose et.al. seriously, I have to keep an open mind on this.

At some point some specific examples are going to be required to challenge what may be referred to as the materialist perspective when it comes to mathematics. I'm keeping an open mind as well, but that doesn't mean I can't provisionally go with what is more reasonable to me. What is the problem with the materialist perspective when it comes to this topic? I'm not considering here consciousness or the mental world by the way. That may perhaps be a mystery (I can certainly understand how some people see it as such), but I don't see what is the mystery exactly regarding the applicability of mathematics to the physical/real world.

[Jehanne]

I don't think anyone doubts that math has applicability to the material world. We could barely get through a day without it.

The controversy starts up when people say that math is always and only a description of the material. The metaphor that math is only a language to talk about the material appears to break down at some point. 

And it's not only Platonists who say that numbers have a kind of independent existence, in a non-language kind of way. The number 2 exists in a way that the word "cat" doesn't, for example. That's what Popper, Penrose, and many others say is the case. 

In the end it's a metaphysical question, not a scientific one. People who are fully committed to a material-only kind of metaphysics will deny that there is anything else. Since I don't know the answer, and I take Popper and Penrose et.al. seriously, I have to keep an open mind on this.

Yes, there is an aspect of math that cuts across cultures. But this is also true of other basic linguistic concepts. So, cat, chat, gato, mao, etc as opposed to two, deux, dos, er.

One difference is that math  is a *formal* language: it has internal rules that are not present in most natural languages. And, for mathematicians, playing with and exploiting those formal rules are the essence of the game.

And, yes, mathematics really is like a very complex game for those doing mathematics. It has rules about what 'plays' are legal, it has goals (theorems), etc. It can even be helpful to *think* of the mathematical concepts visually and in other ways.

In exactly what sense do numbers have an 'independent existence'? From what I can see, the 'number 2' is a shorthand for all the cases where counting two objects is a useful thing to do. And the mathematical object 2 allows for such modeling.

WLC does not accept ZFC, and in particular, the Axiom of Infinity.  He is an ultra finitist, except, of course, when it comes to his God's attributes.  Dr. James Lindsay's book Dot, Dot, Dot: Infinity Plus God Equals Folly has a in-depth look at this.

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Craig has abandoned that so-called line of "reasoning":

RationalWiki -- William Lane Craig

Even though WLC is not the main point, the debate I was referring to happened like very recently and he was using this line of reasoning. Do you mean he abandoned it very recently?

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WLC does not appear to be very active any more.  His Reasonable Faith calendar is mostly empty.

[polymath257]

Yes, there is an aspect of math that cuts across cultures. But this is also true of other basic linguistic concepts. So, cat, chat, gato, mao, etc as opposed to two, deux, dos, er.

One difference is that math  is a *formal* language: it has internal rules that are not present in most natural languages. And, for mathematicians, playing with and exploiting those formal rules are the essence of the game.

And, yes, mathematics really is like a very complex game for those doing mathematics. It has rules about what 'plays' are legal, it has goals (theorems), etc. It can even be helpful to *think* of the mathematical concepts visually and in other ways.

In exactly what sense do numbers have an 'independent existence'? From what I can see, the 'number 2' is a shorthand for all the cases where counting two objects is a useful thing to do. And the mathematical object 2 allows for such modeling.

WLC does not accept ZFC, and in particular, the Axiom of Infinity.  He is an ultra finitist, except, of course, when it comes to his God's attributes.  Dr. James Lindsay's book Dot, Dot, Dot: Infinity Plus God Equals Folly has a in-depth look at this.

I didn't realize he had actually weighed in on that issue.  I know he doesn't like an actual infinite past, but I wasn't aware he disliked either the axiom of infinity or, more broadly, ZFC.

On the other hand, there is a type of consistency there. It is pretty likely that Plato would be considered a finitist by today's standards. On the other hand, it is difficult to do an honest job of even Euclidean geometry without actual infinities.

[GrandizerII]

Yes, there is an aspect of math that cuts across cultures. But this is also true of other basic linguistic concepts. So, cat, chat, gato, mao, etc as opposed to two, deux, dos, er.

One difference is that math  is a *formal* language: it has internal rules that are not present in most natural languages. And, for mathematicians, playing with and exploiting those formal rules are the essence of the game.

And, yes, mathematics really is like a very complex game for those doing mathematics. It has rules about what 'plays' are legal, it has goals (theorems), etc. It can even be helpful to *think* of the mathematical concepts visually and in other ways.

In exactly what sense do numbers have an 'independent existence'? From what I can see, the 'number 2' is a shorthand for all the cases where counting two objects is a useful thing to do. And the mathematical object 2 allows for such modeling.

WLC does not accept ZFC, and in particular, the Axiom of Infinity.  He is an ultra finitist, except, of course, when it comes to his God's attributes.  Dr. James Lindsay's book Dot, Dot, Dot: Infinity Plus God Equals Folly has a in-depth look at this.

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Even though WLC is not the main point, the debate I was referring to happened like very recently and he was using this line of reasoning. Do you mean he abandoned it very recently?

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WLC does not appear to be very active any more.  His Reasonable Faith calendar is mostly empty.

Ah go on YouTube. Search Graham Oppy and WLC

[Belacqua]

Yes, there is an aspect of math that cuts across cultures. But this is also true of other basic linguistic concepts. So, cat, chat, gato, mao, etc as opposed to two, deux, dos, er. 

The word "cat" and its cognates refers to material objects of a certain type. The question we're working on now is: what does "two" refer to?

One difference is that math  is a *formal* language: it has internal rules that are not present in most natural languages. And, for mathematicians, playing with and exploiting those formal rules are the essence of the game.

And, yes, mathematics really is like a very complex game for those doing mathematics. It has rules about what 'plays' are legal, it has goals (theorems), etc. It can even be helpful to *think* of the mathematical concepts visually and in other ways.

You use words that sound unserious when you talk about pure mathematics -- "playing with," "game," "plays," etc. 

Would you say that math is only serious when it is used to describe the material world? That any other time it's just a game? 

I think that many mathematicians would disagree with you. I'm also concerned that if we define seriousness as utility, we're repeating a common anti-intellectual assumption.

In exactly what sense do numbers have an 'independent existence'? 

Since you've already ruled out all of Plato (without bothering to explain why), we can talk about numbers having independent existence in exactly the way that Popper describes. I suppose I could type that all out in my own words, but the original paper is not long. And if you're going to go around declaring that Popper is wrong it might make sense for you to read what he says. 

https://tannerlectures.utah.edu/_documen...pper80.pdf

From what I can see, the 'number 2' is a shorthand for all the cases where counting two objects is a useful thing to do. And the mathematical object 2 allows for such modeling.

So a number is the memo we use after looking at two objects and counting them? If that's all numbers are, then you're begging the question and assuming that they only exist when used in reference to physical objects. 

But then, you use the term "mathematical object 2." Is this the same as the number 2? Do people doing pure mathematics use "mathematical objects" but not numbers?

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I really want to see some one counting in 'Cat'!

  

No one counts in "cat." 

The question is: does a word like "two" refer to an object in the same way that a word like "cat" does.

[Jehanne]

Ah go on YouTube. Search Graham Oppy and WLC

Okay, it's a recent radio debate; perhaps that is what Craig is doing these days, as opposed to his regular "stand ups".

I'll listen to it, eventually; but, Craig's arguments are absolutely lame.  Here's the Nobel physicist J. J. Thomson's "plum pudding" model of the atom that you can find in a stared, optional section of Modern Physics, 3rd Edition by Professor Kenneth S. Krane, a modern-day physicist:

"

As you can see, Professor Thomson's model is completely coherent from a mathematical point of view, but, it's not the way Nature (at least in our Universe) works.  And, so, Dr. Craig's claim that the Universe is mathematical is true, but only in a weak sense.

[Belacqua]

What is the problem with the materialist perspective when it comes to this topic? I'm not considering here consciousness or the mental world by the way. That may perhaps be a mystery (I can certainly understand how some people see it as such), but I don't see what is the mystery exactly regarding the applicability of mathematics to the physical/real world.

If by "mental world" you are referring to an individual's mental activity and memory, then I agree that's not relevant to the issue. That's phenomenology -- what Popper calls "World Two." It depends on, but is different from, the purely material. We don't have to solve the mystery of exactly how the mental world of personal ideas arises from the physical world of brain tissue. 

Nor is there any problem with the applicability of math to the physical world. 

However, if you take "physical world" and "real world" to be synonyms, then you're begging the question. Because for Popper and others, the material world (World One) is real, but so is World Three, which is the non-physical world of numbers, symphonies, fictional characters, etc. etc.

[Jehanne]

Nor is there any problem with the applicability of math to the physical world. 

The anthropic principle explains it.  WLC is recasting the antiquated fine-tuning argument.

[GrandizerII]

What is the problem with the materialist perspective when it comes to this topic? I'm not considering here consciousness or the mental world by the way. That may perhaps be a mystery (I can certainly understand how some people see it as such), but I don't see what is the mystery exactly regarding the applicability of mathematics to the physical/real world.

If by "mental world" you are referring to an individual's mental activity and memory, then I agree that's not relevant to the issue. That's phenomenology -- what Popper calls "World Two." It depends on, but is different from, the purely material. We don't have to solve the mystery of exactly how the mental world of personal ideas arises from the physical world of brain tissue. 

Nor is there any problem with the applicability of math to the physical world. 

However, if you take "physical world" and "real world" to be synonyms, then you're begging the question. Because for Popper and others, the material world (World One) is real, but so is World Three, which is the non-physical world of numbers, symphonies, fictional characters, etc. etc.

You're right. Should avoid equating physical world with real.

That said, let me share with you how I intuit numbers like 2. Based on how I currently see things, there is no number 2 floating out there in the Platonic sense and serving as some form of cause for the concept of 2 in our minds. For me, number 2 strictly exists in our minds, as a way to "visualize" a certain quantity of identical things. The quantity is out there in a "vague" sense, but it is not decipherable as "2" without a mind to see separateness and "identicalness" of the objects of interest. What would be the biggest challenge to this view?