FOM: Further remarks on models, consistency, and physics
JSHIPMAN@bloomberg.net
JSHIPMAN at bloomberg.net
Tue Nov 4 09:37:54 EST 1997
The impact of Lobachevsky's work was that the parallel
postulate COULD BE false -- his non-Euclidean geometry was so
evidently consistent that everyone stopped trying to "prove" PP
(it doesn't matter if a formal proof of the consistency of his
geometry arrived a bit later). My point was that if Lobachevsky
and Bolyai hadn't existed considerations from physics might
eventually have forced mathematicians to rework the foundations
of geometry in the same way. Today, it is also conceivable
that discoveries in physics could affect FOM. E.g., if Church's
thesis is false we could get new math axioms from experiments.
(And CH or a large cardinal might greatly simplify the physics.)
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