Math's existence

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I know this is a large, large question.

Where do people like Hawking and Dawkins think the math that we see in nature originated?

THANKS!
 
According to them, if you’re serious, where did nature get it?

THANKS!!!
 
Jim_Baur said:
According to them, if you’re serious, where did nature get it?

THANKS!!!
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Well, are Hawking and Dawkins self-proclaimed atheists? I don’t know the answer to that.

However, not all scientists are atheists.

I think your real question should be “where do atheists think math came from?”. Just because science doesn’t mention God, doesn’t mean that all scientists are atheists. Remember there are many Priests who are scientists.

So for non-atheist scientists, God plays the major, underlining role.

God Bless.
 
I can’t speak for Hawking or Dawkins, but it seems to me that mathematical properties are necessary in a materialist existence. I can’t imagine matter, energy, space and time without mathematics as at least a by-product.

It seems to me that a non-materialist existence would be sufficient for mathematics too, though.
 
How could math or science be described in terms of God? Just because there appears to be this concrete order does not mean that they are the work of God. Perhaps humans’ have attributed their own axioms to build an order for them. Or perhaps mathematics are just inventions of the human mind in its attempt to explain the natural world. Or perhaps there is no order at all and the order we perceive is just based on these constructed axioms and further investigation might show that these axioms or theorems are inadequate forms of explanation.
 
andyklein said:
How could math or science be described in terms of God? Just because there appears to be this concrete order does not mean that they are the work of God. Perhaps humans’ have attributed their own axioms to build an order for them. Or perhaps mathematics are just inventions of the human mind in its attempt to explain the natural world. Or perhaps there is no order at all and the order we perceive is just based on these constructed axioms and further investigation might show that these axioms or theorems are inadequate forms of explanation.
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This. Both andyklein and tonyrey hit it on the head in saying that they wouldn’t assume that nature has to “get” mathematics from somewhere. I’m assuming that, if we’re trying to get inside the mind of a Hawking or Dawkins, we would need to posit a form of ontological naturalism, meaning that there really is not anything that is not reducible to natural/material causes. That being the case, it would seem that we can either (1) attribute mathematics to some sort of structure or system which we have discovered in nature, or (2) we can posit that mathematics is not truly existent outside of our minds, but rather is a paradigm by which we interpret the data we are given which seems to produce consistent and reliable results, as andy pointed out. The former seems much less dangerous for the objective quality of the results of mathematics, to me at least, if I were to adopt such a position.
 
phil19034 said:
However, not all scientists are atheists.

I think your real question should be “where do atheists think math came from?”. Just because science doesn’t mention God, doesn’t mean that all scientists are atheists. Remember there are many Priests who are scientists.
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I don’t know if these guys were atheist or not (their work isn’t contingent on anything I can identify as either a religious or anti religious proposition) but here is a work that aims to answer the question.

amazon.com/gp/aw/d/0465037712/ref=mp_s_a_1_1?qid=1388705833&sr=8-1
 
This answer is coming from an atheist and a math major. In math we speak of idealized objects that behave according to certain rules. We deliberately contrive the objects and the rules so that the objects will behave much like the “real” objects we see in nature. This is why most mathematics appears to be useful–it is usually invented for the sake of modeling a real-world phenomenon.

Indeed, it’s quite possible to describe types of math which are not very useful at all yet are still perfectly valid. You could easily propose mundane axioms for arithmetic that wouldn’t be useful for calculating “real-world” quantities. Again, we simply contrive the math to be useful from the outset.
 
William Lane Craig and John Lennox have recently been defending the following argument:
  1. If God does not exist, the applicability of mathematics would be a happy coincidence. (Premise)
  2. It is not a happy coincidence. (Premise)
  3. Therefore, God exists. (From 1 and 2)
Consider the three major views of abstract objects, of which mathematics is a category: nominalism, Platonism, and conceptualism. If Platonism is true, then mathematics exist in a distinct realm from the natural world, which would make its applicability nothing more than a happy coincidence. Yet, if nominalism is true and mathematics is just a useful fiction, then how is nature written in the language of mathematics? Without God, the applicability of mathematics to the natural world is merely coincidental, regardless of one’s view of abstract objects. On the other hand, on theism, God created the universe with the mathematical structure he had in mind.

Anyway, I find the argument to be an interesting one. It has some promise at the very least.
 
punkforchrist said:
William Lane Craig and John Lennox have recently been defending the following argument:
  1. If God does not exist, the applicability of mathematics would be a happy coincidence. (Premise)
  2. It is not a happy coincidence. (Premise)
  3. Therefore, God exists. (From 1 and 2)
Consider the three major views of abstract objects, of which mathematics is a category: nominalism, Platonism, and conceptualism. If Platonism is true, then mathematics exist in a distinct realm from the natural world, which would make its applicability nothing more than a happy coincidence. Yet, if nominalism is true and mathematics is just a useful fiction, then how is nature written in the language of mathematics? Without God, the applicability of mathematics to the natural world is merely coincidental, regardless of one’s view of abstract objects. On the other hand, on theism, God created the universe with the mathematical structure he had in mind.

Anyway, I find the argument to be an interesting one. It has some promise at the very least.
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Could God have created a universe with another mathematical structure in mind?
 
belorg said:
Could God have created a universe with another mathematical structure in mind?
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Why not? There is no obvious reason why this should be the only universe. There may be others which are utterly different.
 
tonyrey said:
Why not? There is no obvious reason why this should be the only universe. There may be others which are utterly different.
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I would think that if there are several possible mathematical structures and there are several universes each with thier own maths, the “coincidence” is not so surprising
 
phil19034 said:
Well, are Hawking and Dawkins self-proclaimed atheists? I don’t know the answer to that.
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Hawking believes that the laws of physics by themselves will generate the Universe.

Since laws of physics are mathematical in nature (and it’s even more true in case of string theory) then we can say that it’s mathematics which generates the universe.

Of course this leads one to ask where did the laws/maths come from.

Hawking will say that the laws JUST EXIST.

A theist will say that the laws were made by God which JUST EXISTS.

A Gnostic will say that the laws were made by Demiurgos, which was made by God, which JUST EXISTS.

A proponent of multiverse will say that we have the laws we do, because we just happen to be in this particular part of the multiverse. The multiverse is simply a space of all possible universes, each with its own laws. And the multiverse JUST EXISTS.

A proponent of the “baby universe” theory will say that each time a black hole is created, a new universe is created inside it, with its laws of physics slightly modified compared to the parent universe. Of course if you try to go back, then it means that there must be a top-level universe, which, well, JUST EXISTS.
 
A popular misconception is that there is only one type of mathematics. There are in fact infinitely many varieties. To reiterate what I said earlier, we intentionally chose to use some of the types that are most applicable to nature. Math generally is not applicable to nature, however.

I’ll give an example. The field we are most accustomed to is the field of real numbers that we all learned a little about in high school. But it’s possible to define different and simpler fields. Assume the existence of two numbers, 0 and 1, and two operations, addition and multiplication, defined such that 0+0=1+1=0, 0+1=1+0=1, 01=10=00=0, 11=1. These numbers and operations satisfy the requirements for a field, but good luck finding a non-trivial use for this field in nature.
 
weller2 said:
Hawking believes that the laws of physics by themselves will generate the Universe.

Since laws of physics are mathematical in nature (and it’s even more true in case of string theory) then we can say that it’s mathematics which generates the universe.

Of course this leads one to ask where did the laws/maths come from.

Hawking will say that the laws JUST EXIST.

A theist will say that the laws were made by God which JUST EXISTS.

A Gnostic will say that the laws were made by Demiurgos, which was made by God, which JUST EXISTS.

A proponent of multiverse will say that we have the laws we do, because we just happen to be in this particular part of the multiverse. The multiverse is simply a space of all possible universes, each with its own laws. And the multiverse JUST EXISTS.

A proponent of the “baby universe” theory will say that each time a black hole is created, a new universe is created inside it, with its laws of physics slightly modified compared to the parent universe. Of course if you try to go back, then it means that there must be a top-level universe, which, well, JUST EXISTS.
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And then we look at which explanation is the most parsimoniuous. And the winner is…?
 
Oreoracle said:
A popular misconception is that there is only one type of mathematics. There are in fact infinitely many varieties. To reiterate what I said earlier, we intentionally chose to use some of the types that are most applicable to nature. Math generally is not applicable to nature, however.

I’ll give an example. The field we are most accustomed to is the field of real numbers that we all learned a little about in high school. But it’s possible to define different and simpler fields. Assume the existence of two numbers, 0 and 1, and two operations, addition and multiplication, defined such that 0+0=1+1=0, 0+1=1+0=1, 01=10=00=0, 11=1. These numbers and operations satisfy the requirements for a field, but good luck finding a non-trivial use for this field in nature.
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Yep, it is called computer science 😉
 
belorg said:
Could God have created a universe with another mathematical structure in mind?
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I think God could have created the universe with either a Euclidean or non-Euclidean geometry, for example. I don’t think he could have made 2+2=5, since that would be a logical contradiction.
 
Ion said:
Yep, it is called computer science 😉
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Ssshhhhhhhh. 😉 I could have given a more ironclad example, but I figured I was coming across as pedantic enough already.

But if you insist, non-computable functions/numbers are useless for practical purposes. “Non-computable” meaning that not only can we not express the numbers in decimal form, we cannot even reliably approximate the numbers because we cannot determine upper bounds for the error involved in the approximations.
 
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