[EMAIL PROTECTED] wrote: > >But why can't it be reduced to classes of specific physical things? How > >can you show that it is necessary for anything corresponding to this > >description to 'exist' apart from its instantiations as documented > >procedures and actual occurrences of their application? > >David > > I did point out in my last post that there appears to be no simple way > to make such reductions (between math concepts and classes of specific > things). For instance no one has yet succeeded in showing how math > concepts such as infinite sets and transfinite sets (which are precise > math concepts) could be converted into physical notions. A also > pointed to David Deutsch's excellent 'Criteria For Reality':
That doesn't mean math concepts refer to non-physical things. They might not refer at all. Indispensability arguments are dispensable: http://plato.stanford.edu/entries/mathphil-indis/ > Math concepts are super-classes or abstract classes being used to > classify *other* astract classes. I pointed out three different > ontological catgories: > > (1) Abstract entities of universal applicability (like math concepts) > (2) Abstract entities of limited applicability (human constructs like > alphabets or a chair concept) > (3) Concrete instances (like a particular example of a chair) > > I'd say you can make a good case that the entities in (1) are the only > real objective reality. It's (2) and (3) that are actually 'in our > heads'! I don't have a chair in my head. --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
