FOM: Reply to Pratt

[JSHIPMAN@bloomberg.net]

Church's thesis says that any sequence of bits we can
effectively generate is recursive.  An experimental prediction
in a physical theory might involve a real number whose bit
sequence was mathematically definable but not recursive.  In
this case it is not necessary to access an infinite amount of
information; ZFC or your favorite axiom system can only
establish the value of a nonrecursive sequence to finite
precision.  If Chaitin's r.e.-complete number omega were
experimentally available (e.g. as a probability) it would
thus provide a source of new theorems.  The "new axiom" would be
that the physical theory involved was correct. -- Joe Shipman