[FOM] General Purpose/Special Purpose
MartDowd at aol.com
MartDowd at aol.com
Wed Feb 26 13:35:58 EST 2014
What is the point of this, though? Historically, rigor in topology and
analysis went hand in hand with the development of set theory. In addition
to providing a completely rigorous foundation for all of mathematics, set
theory provided new tools, which resulted for example in descriptive set
theory and concrete results about the real numbers which were previously
unknown. Special purpose methods are just that, and if they can't be formulated
in terns of the "standard foundations" most mathematicians would reject
them.
In a message dated 2/25/2014 12:57:17 P.M. Pacific Standard Time,
hmflogic at gmail.com writes:
As a very crude example that any mathematician or math student can
understand, if you are doing topology, one can envision a foundation where
"continuous function on a space" is taken as primitive, although a lot of issues
have to be resolved if one wishes to avoid bringing set theory into the
picture in a general form.
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