FOM: Question: why is category theory viewed as relativism?
wtait at ix.netcom.com
Wed Mar 11 12:26:54 EST 1998
Michael Thayer (mthayer at ix.netcom.com) wrote (3/11)
>does this differ from the discredited view that set theory does not offer a
>foundation for analysis, because there is no distinguished notion of natural
>number. (The tired old "is e a member of pi" objection). I understand why
>relativist foundations is an oxymoron, and I don't wish to defend
>post-modernism or whatever on this list. Just an answer to a simple
I would need first an answer to another simple question: What do you mean
by saying that there is no distinguished notion of natural number? I know
of lots of bad philosophy that seems to imply this, including the one you
suggest (though 0 and 1 make better candidates for natural numbers than e
and pi); but am astounded to find it accepted as a matter of course.
Dedkind long ago answered the `tired old objection' in the case of the
real numbers when Weber asked him why he did not simply identify the real
numbers with the cuts of rationals. His answer, in essence, is that it is
ungrammatical to do so---to ask, e.g. of two numbers whether one is a
subset of the other or not.
The `tired old objection' assumes that if the natural numbers are some
one thing, then they must be sets or something else other than just the
numbers; and then continues by pointing out that there is no
distinguished such thing that they can be. Dedekind's answer is that they
are simply the numbers. The proper answer to *what* they are is
answered---as he answered it---by exhibiting the structure of the system
This seems like a very good answer, and I suggest that the tired old
objection be put to rest.
More information about the FOM