We are not quite talking at cross purposes.
Part of the historical record is that Aristotle says, over & over again,
that, for the Pythagoreans, arithmos is at the heart of everything,
doesn't he?
Let's drop, for the moment, the ambiguous word *crisis*.
Since the diagonal and square have no common measure [in Euclidean
geometry], then there is no arithmos that can measure both the side and
diagonal. Not everything has arithmos at the heart of it, for the side
and diagonal don't.
Doesn't this deal a death blow to whichever Pythagoreans hold the notion
that Aristotle insists they hold?
Best wishes for a fine '99.
Sam Kutler