FOM: twin primes again
Peter Schuster
pschust at rz.mathematik.uni-muenchen.de
Wed Jun 21 10:56:21 EDT 2000
Reply to
Joe Shipman shipman at savera.com Mon Jun 19 17:12 MET 2000
I understand from your contributions that the
twin prime conjecture is something different from
Goldbach's conjecture or Fermat's last theorem.
Do I correctly understand that, according to your opinion,
no position is possible which simultaneously
(a) does not assume that the truth-value of such
"highly infinitary" statements as the twin prime
conjecture is determinated from the outset;
(b) does not deny the whole set of integers as
a "completed whole", as something "to quantify over";
(c) does not distinguish between statements like
"for each integer ..." and the corresponding "universally
quantified" formula?
Note that
(a) is a crucial point for every constructive philosophy, if
not for any pragmatic view of mathematics in general;
(b) is just what I tend to assign to (Bishop's) constructive
mathematics, although Bishop possibly would not agree;
(c) seems to be part and parcel of any mathematical practice.
Best regards
Peter Schuster.
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