Hi,
What do you mean by Platonia?
The kind of Platonia in Tegmark or in Peter's (1Z) post does not make
sense for mathematicians. Even if you are using a theory like Quine's
NF, which allows mathematical universes, you still have no
mathematical description of the whole mathematical reality. Tegmark is
naïve about this.
*Arithmetical* platonia can be said to exist, at least in the sense
that you can prove it to exist in models of acceptable set theories,
like ZF. It is just the structure (N, +, x). It is used in all papers
in physics, math and logic, including Pratt ...
Now, with computationalism, we don't even need such a mathematical
arithmetical Platonia. We need only the idea that arithmetical truth
(even a tiny effective part of it) is independent of you and me. Like
in Plotinus, the ultimate being (arithmetical platonia) is not a being
itself (nor is matter!).
So neither Platonia, nor even arithmetical Platonia needs to exist.
Numbers needs to exist in some sense, and do exist in theories like RA
or PA, in the sense that such theories formally proves that Ex(x =
sssssss0) for example.
Just to be a bit precise.
Bruno
On 18 Feb 2011, at 02:49, Stephen Paul King wrote:
Hi All,
Question: Why must Platonia exist?
Onward!
Stephen
“It is amazing what can be accomplished when nobody cares about who
gets the credit.”
Robert Yates
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