[FOM] predicative foundations

Nik Weaver nweaver at math.wustl.edu
Thu Feb 16 03:37:31 EST 2006

Kenny Easwaran wrote:

> ... it seems that Weaver has a further burden to bear here,
> namely of showing why the arguments in favor of his position are
> substantially better than the arguments in favor of each other
> position ... Until then, it seems that there is no need for a
> third party (like myself, and possibly Friedman) to focus on any
> one stopping point rather than any other.

First of all, I begin to get a bit frustrated at the number of times
I have to deny that I am prescribing a "stopping point".  What I am
saying is that there is a clear philosophical basis for predicative
mathematics and there is not a clear philosophical basis for
impredicative mathematics.  This doesn't mean you have to stop there.
The term "stopping point" was introduced into this discussion by

The idea that I have a burden not only to establish my own view, but
also to separately debunk every possible alternative, and that until
I do this I can be ignored, seems slightly unreasonable.  In any case,
as a matter of fact I have already written fairly extensively along
these lines.  You might start by looking at the messages

However, I rather get the impression that you're simply looking for
an excuse to dismiss me.  Your willingness to accept Friedman at
his word that there are equally compelling justifications for all
sorts of other foundational stances --- he has yet to actually
describe any of these justifications --- and your idea that I
must refute all of these unspecified arguments before discussion
can begin, does suggest this.


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