Mathematical Platonism

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Mathematical Platonism
OP - February 04, 2011, 12:21 PM

Platonism, while being a very rare allegiance for many philosophers, still is the worldview of choice for many mathematicians.
Why is it that mathematicians feel that the principles of maths are real universals? Why do they insist upon calling mathematical acheivements "discoveries" and not "creations"?
Do you think the principles of mathematics, as pythagoras believed almost 3000 years ago, "rule the universe"?

At evening, casual flocks of pigeons make
Ambiguous undulations as they sink,
Downward to darkness, on extended wings. - Stevens
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Re: Mathematical Platonism
Reply #1 - February 04, 2011, 12:24 PM

Mathematics just seems to describe the universe very well, I don't think it is anything more than that. The universe seems to work in quantities, it is really no surprise.

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Re: Mathematical Platonism
Reply #2 - February 04, 2011, 02:45 PM

Maths is a language. It evolved rather than was created. It's only a creation as far as meaningful communication is a creation. Or any meaningful description of the universe. The universe is consistant with itself whether we understand it or not. When it makes sense to us, we can start describing it. The values can be arbritrary, but whether you use imperial, metric, or the medium of dance, the constants still need describing in a way others can understand and apply, a way that is consistant with the universe as it is presented to them.

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Re: Mathematical Platonism
Reply #3 - February 04, 2011, 03:12 PM

@ z10

I was always taught to think of Math as a *natural* science. This is the first time I see this notion questioned/challenged.

Even in my field (signal processing), where we're basically concerned with processing numbers that reflect underlying physical processes, we still think within the boundaries of *nature*. Even numbers are, in a way, instances of nature.

A googolplex is *precisely* as far from infinity as is the number 1.--Carl Sagan
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Re: Mathematical Platonism
Reply #4 - February 04, 2011, 09:03 PM

Yes, I agree with all of you that numbers do describe our universe very well.
However, it's difficult to see exactly what is so "natural" about them. In most discussions on the philosophy of maths, we can oppose platonism to nominalism - which is the theory that all that exists are causal relationships within time/space and are part of the energy/mass nexus. Where do numbers fit in here? Clearly, they are a mental event that is used by us to describe the universe but where do they exist? Just in our mind or do they have an absolute objective existence outside of us that we can discover? If it is the latter then we open the door to something that is beyond the natural world - the world of objective numbers and mathematical principles.
Many famous contemporary mathematicians were platonists, like Godel and Penrose, believing their maths formulations were discoveries and not subjective creations - and thus, holding that there is exists apart from the natural world, an intelligible world of pure reason.

At evening, casual flocks of pigeons make
Ambiguous undulations as they sink,
Downward to darkness, on extended wings. - Stevens
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