Re: Platonism
Victor Yodaiken (yodaiken@sphinx.nmt.edu)
Wed, 9 Nov 1994 12:18:36 -0700
On Nov 9, 11:00am, Randall Holmes wrote:
Subject: Platonism
Quoting DB:
> A-platonism is the idea that when we are talking mathematical
>language, we talk ABOUT something. That "something" is called real
>by A-platonists, imaginary by others. With metalanguage this is
>different, since metalanguage talks about the texts in the
>language, and those texts can have an actual existence in a
>physical sense. They can be recorded in the physical world (like on
>a magnetic disk); retreiving them we get them back in the original
>form. So when we talk about the mathematical texts instead of about
>the mathematical objects, it seems quite reasonable to be
>platonistic. This is so trivial that it is hardly worth while
>mentioning.
>
>Holmes: I don't think this is trivial at all. Reasoning in
>metalanguage can involve "texts" which cannot be produced physically
>at all; certainly there are no restrictions on reasoning in
I don't understand your claim here. Any mechanical system that
"does mathematics" on "texts" will operate on finite objects that
exist in the physical world. Those finite objects may be
representations of infinite objects that may or may not exist
in this or any other world.
>metalanguage which respect physical feasibility of production of texts
>(in most work in this field, at any rate). I maintain that for
>metalinguistic reasoning of a classical type we need at least the
>degree of Platonism which regards the natural numbers as real, and
Why? The computer does not believe or disbelieve, it simply
rewrites bit patterns. If these bit patterns are representations
of "real" numbers or of transfinite sets, it matters not.