FOM: Second-order validities
shipman at savera.com
Wed Mar 17 14:42:51 EST 1999
OK, maybe when you write down axioms and rules of inference for
second-order logic you are really indulging in a species of first-order
logic. But at least it's a logically motivated species of first-order
logic that may be more powerful than the ordinary first-order predicate
calculus. To recast an earlier query, do *logically motivated* axioms
and rules of inference for second-order logic allow one to prove all the
second-order validities that ZF does? If yes, this is a very strong
argument for logicism; if not, let's have an example!
To repeat my other query from March 15th: what are the best known lower
and upper bounds on the Lowenheim number for second-order logic?
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