Re: Mathematical Logic, Podnieks'page ...

From: Kory Heath <kory.heath.domain.name.hidden>
Date: Thu, 01 Jul 2004 03:21:38 -0400

At 03:25 PM 6/30/2004, CMR wrote (quoting www.fact-index.com):
>"Mathematical realism holds that mathematical entities exist independently
>of the human mind. Thus humans do not invent mathematics, but rather
>discover it, and any other intelligent beings in the universe would
>presumably do the same. The term Platonism is used because such a view is
>seen to parallel Plato's belief in a "heaven of ideas", an unchanging
>ultimate reality that the everday world can only imperfectly approximate.

This is a perfect example of what I'm complaining about. The quote implies
that the term "Platonism" can be used as just another term for
"mathematical realism", but then it immediately provides a definition that
goes beyond simple mathematical realism. The belief that mathematical
entities exist independently of the human mind - that humans discover
mathematics rather than invent it - does not automatically entail the
belief that there's a "heaven of ideas" containing (say) the Essence of
Horseness which everyday horses only imperfectly approximate. These two
ideas are logically distinct, and it seems sensible to call them by two
different names. I prefer "mathematical realism" and "essentialism", or
maybe "Platonic essentialism". I'd prefer not to use the term "Platonism"
all by itself, but if I had to use it, I'd use it to refer to "Platonic
essentialism", not "mathematical realism".

-- Kory
Received on Thu Jul 01 2004 - 03:24:54 PDT