[FOM] General Foundations Discussion

[Michael Thayer]

The following comment by Harvey Friedman brings up a question I have been wondering about for some time.  In an interesting paper, whose exact title I do not recall, Neil Tennant discussed the difference in viewpoint between what he call "monomathematicians" - people who work with unique objects (like the standard real numbers) and those who deal with structures which come in many flavours (most algebraists, and topologists and some geometers).  Does Harvey's comment below suggest that these latter are farther removed from foundational issues?


>>The apparent lack of THE nonstandard real numbers is a DECISIVE drawback
>>against the use of nonstandard analysis in its most obvious foundational
>>role (although there may be other roles). 
>>
>>Mathematicians wish to concentrate their attention on mathematical
>>structures that are not only explicitly defined, but also are canoncial in
>>various hard nosed senses.
>>