On Feb 18, 9:48 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
> 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 ...
Used as a formalism. It is not the case that everyone
who uses arithmetic is a Platonist
> 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.
> 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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