> >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:


> 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.

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