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*To*: <fom@math.psu.edu>*Subject*: FW: FOM: defining "mathematics"*From*: "Matt Insall" <montez@rollanet.org>*Date*: Thu, 30 Dec 1999 18:44:01 -0800*Importance*: Normal*Sender*: owner-fom@math.psu.edu

-----Original Message----- From: Matt Insall [mailto:montez@rollanet.org] Sent: Thursday, December 30, 1999 9:59 AM To: Vladimir Sazonov Subject: RE: FOM: defining "mathematics" -----Original Message----- From: owner-fom@math.psu.edu [mailto:owner-fom@math.psu.edu]On Behalf Of Vladimir Sazonov Sent: Thursday, December 23, 1999 12:34 PM To: fom@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 mathematical > 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 appropriate 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 http://www.rollanet.org/~montez montez@rollanet.org

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