On Feb 19, 12:34 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 18 Feb 2011, at 17:13, benjayk wrote:
> > Bruno Marchal wrote:
> >> 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.
> > Do you have to have a description of the whole mathematical reality to
> > assert it exists?
> You need it to make sense of it. Mathematical attempts lead to either  
> inconsistent theories, or to a definition of a putative mathematician  
> (like with the theory of topos), which is very interesting but not  
> quite "platonic".

So you can't have mathematics without  a mathematician?

> As a figure of speech Platonia can make sense, but it is doubtful in a  
> theoretical context, like when we search for a TOE.
> > Isn't it enough to say everything that we *could* describe
> > in mathematics exists "in platonia"?
> The problem is that we can describe much more things than the one we  
> are able to show consistent, so if you allow what we could describe  
> you take too much. If you define Platonia by all consistent things,  
> you get something inconsistent due to paradox similar to Russell  
> paradox or St-Thomas paradox with omniscience and omnipotence.

Then let Platonia be all consistent and non paradoxical things

> And then when you try to convey something which is counter-intuitive  
> and against the current main paradigm, like your poor servitor, you  
> have to base things on what the most agree (but this is not an  
> argument, just a methodological remark).

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