FOM: sharp boundaries/tameness

[Harvey Friedman]

Reply to Insall 6:35PM 2/13/02:

>Dear Professor Friedman,
>     You wrote:  ``Infinitesmals fail on this account because of
>such challenges as "give me an example of an infinitesmal and establish some
>significant facts about it".''
>
>I think I can give you an example of a nilsquare infinitesimal.  I can
>establish some facts about it.  I can not prove that the facts I can
>establish are significant, just as I cannot prove that my facts are
>beautiful.  I can ask you if these facts are either significant or
>beautiful, and if you say no, I must accept your answer.

I was referring only to the "concept" of infinitesmal real number.