[FOM] General Purpose/Special Purpose

[MartDowd at aol.com]

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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