FOM: Reply to Machover JSHIPMAN at
Tue Nov 4 08:43:50 EST 1997

I did not confuse two senses of "necessary".  Prior to Godel's
completeness theorem, the notions of consistency and existence
of a model were distinct. "Necessary" was properly understood as
"true in all models".  Philosophers had tried to PROVE that the
parallel postulate was "necessary"--if they had succeeded it
would have been by a confusing trick of language "unnecessary"
i.e. superfluous relative to Euclid's other postulates.  They
could not prove this but still thought "PP necessary" was true
until Lobachevsky and Bolyai showed models of ~PP.  Before
Riemann, Gauss knew the physical universe might violate PP and
if so a correct physical theory would provide a model of ~PP.-JS

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