On Feb 18, 9:48 am, Bruno Marchal <[email protected]> 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 [email protected]. > > To unsubscribe from this group, send email to > > [email protected] > > . > > 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 [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
