Applicability of Maths to the Universe

[Belacqua]

[polymath257]

[Belacqua]

Plato liked to use math as a key point in his argument that there are 'eternal forms', but I think the revelations of modern math have made that a rather untenable position.

The fact that there are different maths that derive from different sets of axioms doesn't affect Plato's thought at all.

math is a sport for mathematicians

You make it sound unserious.

Burtt's book is limited by it focus (necessary at the time of publication) to Newtonian physics. But the metaphysical problems that arose from relativity and quantum mechanics go far beyond those presented by Newtonian physics. That this book was written in 1932, just after the formulation of Schrodinger's equation, is quite enough to question its applicability to modern science.

The book is an accurate history of the changes in scientific epistemology that happened because of Newton. Much of what he says remains the same despite the switch from classical to quantum physics. The fact that science agrees NOT to explain many things, instead accepting them as brute facts ("it happens that way because it just happens that way") and considers them explained when they have been given a math formula remains the same.

Most importantly, the book is important for people who say that science and only science gives us truth. We can see that science is a contingent system -- it could be different -- with a genealogy. The kind of answers it looks for determines what it will and won't find. That means that it leaves huge aspects of the world unexplained and, in the current paradigm, unexplainable.

[Jehanne]

[Cepheus Ace]

listen here my young apprentice, what WLC is doing is pushing for platonic realism and substance dualism in order to sneak in the idea that his god exists without evidence

This is why it's far better to ignore WLC and read the good people who raise the same issue.

WLC also argues against platonic realism in his writings but he shamelessly uses it when it comes the kalam cosmological argument.

christian apologists are shameless frauds at best

[GrandizerII]

[UtilitarianDeist]

I'm terrible at math but that must mean that God doesn't want me to be good at math so I'm fine with that. God obviously wants plenty of other people to be a good at it.

[Belacqua]

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.

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.

[The Grand Nudger]

Penrose and Popper, both, were committed and vocal materialists. You're reading what you believe into the things they wrote.

Three worlds is not a dualist conjecture. It's the observation that these three categories - the world as it is, how we experience the world, and what we know about the world, are not equivalent. It's a useful conjecture in that world three, of which science is a representative subject, is not necessarily equivalent to world one, the world as it is. The aim was to improve world three, so that it might be closer to world one.

In that context, it works. However, in the context of mind, it doesn't. Our brains are a representative of world one, our experience is a product of that brain, and what we know (or think we know) is a consequence of that experience. Penrose's contention is not that mind is immaterial in any way shape or form. It's that classical physics and computation might not be able to explain how our brains work, that we need a better understanding of the quantum world for that.

If you insist on making these constant appeals to authority, then it might help to pick an authority that actually does express the argument that you're trying to make.

[polymath257]

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.

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.