FW: FOM: defining "mathematics"

Matt Insall montez at rollanet.org
Thu Dec 30 21:44:01 EST 1999

-----Original Message-----
From: Matt Insall [mailto:montez at rollanet.org]
Sent: Thursday, December 30, 1999 9:59 AM
To: Vladimir Sazonov
Subject: RE: FOM: defining "mathematics"

-----Original Message-----
From: owner-fom at math.psu.edu [mailto:owner-fom at math.psu.edu]On Behalf Of
Vladimir Sazonov
Sent: Thursday, December 23, 1999 12:34 PM
To: fom at math.psu.edu
Subject: Re: FOM: defining "mathematics"

Sam Buss wrote:

> "Mathematics is the study of objects and constructions, or of aspects of
> objects and constructions, which are capable of being fully and completely
> defined.  A defining characteristic of mathematics is that once
> objects are sufficiently well-specified then mathematical reasoning can be
> carried out with a robust and objective standard of rigor."

I am afraid that these "fully and completely defined objects" would lead
us imperceptible again and again back to Platonism. Also what does it
mean "capable of being fully and completely defined"? I think that this
or other way it is inevitable to explain all of these in terms of
formal systems.
I'm not sure, professor Sazonov, why you should be ``afraid'' of being lead
back to Platonism.  Are you convinced that our mathematics has no reality
beyond the marks on the page, as I understand the pure formalist position to
be?  If this is the case, I presume you would agree that your comments above
have no reality beyond the symbols at which I am looking at this moment.
Thus if I do not print out your response to professor Buss, will your
response then never have existed?  This seems tenuous at best.  Anyway, why
must we quibble about these metaphysical issues?  The question was ``What is
mathematics?'', not ``What is your philosophical belief about what parts of
mathematics possess some metaphysical property such as `existence beyond
marks on the page'.''


Matt Insall
montez at rollanet.org

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