FOM: twin primes again

Peter Schuster pschust at
Wed Jun 21 10:56:21 EDT 2000

Reply to 

Joe Shipman shipman at 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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