FOM: On "grasping" Con(ZFC)
Robert Tragesser
RTragesser at compuserve.com
Sat Aug 29 12:17:29 EDT 1998
In order to appreciate the difficulty, think in terms of proving
that CON(ZFC) and by limited means. There is an important sense of
"understand" where it makes much good sense to say that we haven't
understood a (mathematical) proposition until we have proved or disproved
it (or have shown that it is absolutely "undecidable"). And even when we
have a proof, there will likely be the possibility of another proof that
enables us to understand it better.(For a clear and direct explication of
this consideration, see G-C Rota, INDISCRETE THOUGHTS, Birkhauser 1997).
There is also the problem of choosing the formula for Con(...),
one that is intensionally correct and not merely numerically correct. (For
example, the Bew of Go"del's proof of his first incompleteness theorem is
intensionally and numerically correct, while the Bew of the corresponding
Rosser version is numerically correct but it is NOT intensionally correct.)
rbrt tragesser
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