I realized in 1957 that I could not subscribe to Platonism, as a Foundation for Mathematics. But I did not then, nor do I now totaly reject some of its tenets. And I appreciate and credit its motation to good mathematics.Elsewhere, I have said of myself, "I'm not a WIMP, I'm a WAMP -- that is, a W(ary) A(ss) M(edial) P(ositioner)." I was driven to this by the fulmations of "both extremes" on so many issues. Contrary to the propaganda, it is not WIMPISH to take a CENTRIST POSITION, since YOU GET BANGED ON BY BOTH SIDES!
Goldlocks was a WAMP in the Cottage of the Three Bears. Aristotle's "Golden Mean" provides tradition for WAMPISM.
And on the issue of MATHEMATICAL PROOFS, I'm a WAMP.
I accept NONCONSTRUCTIVE PROOFS as MATHEMATICS -- not wimpishly, but for good reason. Over and over, I've seen how A NONCONSTRUCTIVE PROOF EVENTUALLY MOTIVATES A CONSTRUCTIVE PROOF.
But I do not accept NONCONSTRUCTIVE MATHEMATICS as FIRST CLASS MATHEMATICS -- not from obstinacy, but again for good reason. There's plenty of EVIDENCE out there that A CONSTRUCTIVE PROOF TELLS US MORE (SOMETIMES MUCH MORE) THAN A NONCONSTRUCTIVE PROOF, HENCE, BEST FURTHERS MATHEMATICAL DEVEOPMENT, IN GENERAL. So, I only value CONSTRUCTIVE MATHEMATICS as FIRST CLASS MATHEMATICS.
And this is got me BANGED ON BY BOTH SIDES. And recipient of scurrilous letters. So be it.
DIG or REDIG.