On Feb 19, 12:34 am, Bruno Marchal <[email protected]> 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). > -- 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.
