I am very glad for Reuben Hersh's clarifications. But I still
think that by not attending to what is as it were phenomenologically
distinctive about the verificational structure of mathematics he gives
aan oveerly fast and loose characterization of mathematics,--
Reuben Hersh wrote:
Its subject matter, mathematical concepts and objects, are
like novels, symphonies, Constitutions, and ideologies--human
creations, part of human culture. But they are different from
the other humanities in being science-like. Science is said to be
distinguished from non-science by possessing reproducible results,
which means high degree
of consensus. Mathematics, even more than any other science,
possesses reproducible results, so in this repect it is the most
science-like of sciences. We prove the Pythagorean theorem,
no only by rereading it in Euclid, but remarkably by finding other,
independent,
unrelated proofs. And of course mathematical calculations
get the same result by means of independdent calculations. When,
rarely a discrepancy appears, it is always straightened out
quickly.
end of quote from Hersh.
All I can say is: Is that fast or loose, or what? He is
using as it were secondary traits of mathematical thought to
represent its first order traits (putting reproducibility and
consensus in place of a careful characterization of the
character of informal, intuitive proof. . .and its apodicity
(not to be mistaken for infallibility).
I find it odd that Hersh did not comment on my references
Rota's charaterization of mathematical Evidenz. I think that
Hersh is so deeply committed to the fallibility,
the post-Lapsarian flawedness,
(= human all too human character) of mathematics, that he
simply cannot get in focus the distinctively apodictic flavor
of mathemamtical Evidenz.