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I would be much obliged if you could take a look at the video provided below:

http://www.closertotruth.com/video-profile/Is-Mathematics-Invented-or-Discovered-Stephen-Wolfram-/1384 [Broken]

I certainly wouldn't mind a more general discussion on the Platonic/Invented nature of Mathematics. However, I think that the PF Staff & Moderators would probably prefer, justifiably, if we kept that discussion to a minimum, because it is debated so often and far better elsewhere. Instead, shall we try to keep the discussion centered on the implications for Mathematics of Wolfram's views specifically.

In the way he delivers his answer, he seems to be suggesting that this more general view of mathematics does away with Platonism. Is this true? Surely it just passes the buck one step on. This wider sphere of formal systems could equally be Platonic too.

He states that many (perhaps all) of these formal systems are internally self-consistent. How can this be the case if the method he is using is simply the re-organization of mathematical symbols?

If its possible to produce new, entirely self-consistent axiomatic systems in this way, is there actually any limit to the number of said systems that can exist? Or are they innumerable?

Thanks for your input,

Kherubin

http://www.closertotruth.com/video-profile/Is-Mathematics-Invented-or-Discovered-Stephen-Wolfram-/1384 [Broken]

Stephen Wolfram said:On a couple of pages you can give all the axioms commonly in use in Mathematics. They are quite simple, but they are what you grow Mathematics from. The question is then, are those the only possible axioms?

I certainly wouldn't mind a more general discussion on the Platonic/Invented nature of Mathematics. However, I think that the PF Staff & Moderators would probably prefer, justifiably, if we kept that discussion to a minimum, because it is debated so often and far better elsewhere. Instead, shall we try to keep the discussion centered on the implications for Mathematics of Wolfram's views specifically.

In the way he delivers his answer, he seems to be suggesting that this more general view of mathematics does away with Platonism. Is this true? Surely it just passes the buck one step on. This wider sphere of formal systems could equally be Platonic too.

He states that many (perhaps all) of these formal systems are internally self-consistent. How can this be the case if the method he is using is simply the re-organization of mathematical symbols?

If its possible to produce new, entirely self-consistent axiomatic systems in this way, is there actually any limit to the number of said systems that can exist? Or are they innumerable?

Thanks for your input,

Kherubin

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