On Feb 18, 9:48 am, Bruno Marchal <marc...@ulb.ac.be> 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. 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.
>
> 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
>
> > --
> > You received this message because you are subscribed to the Google  
> > Groups "Everything List" group.
> > To post to this group, send email to everything-list@googlegroups.com.
> > To unsubscribe from this group, send email to 
> > everything-list+unsubscr...@googlegroups.com
> > .
> > For more options, visit this group 
> > athttp://groups.google.com/group/everything-list?hl=en
> > .
>
> http://iridia.ulb.ac.be/~marchal/

-- 
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to 
everything-list+unsubscr...@googlegroups.com.
For more options, visit this group at 
http://groups.google.com/group/everything-list?hl=en.

Reply via email to