FOM: second order logic is a myth

Stephen G Simpson simpson at
Thu Feb 25 15:11:45 EST 1999

Harvey, thanks for your concise put-down of second-order logic in 24
Feb 1999 20:08:49.  This is a much better formulation of some of the
points that I have been trying to make.

By the way Harvey, what's your opinion of the views of your Ohio State
University colleague, Stewart Shapiro, as expressed in his book
`Foundations Without Foundationalism: A Case for Second-order Logic'?

You said:

 > idiotic position I once heard a rabidly anti-logic mathematician
 > put forward:
 > "There is no significance to the independence of the continuum
 > hypothesis from the axioms of ZFC. For after all, we know that the
 > continuum hypothesis is decidable in second order logic."

Ye Gods, who is this guy?  No matter how ignorant he is about
technical work in f.o.m., isn't he aware that Cohen won a Fields
Medal?  This illustrates the kind of ignorance/arrogance/hostility
that we f.o.m. professionals have to deal with.  It's a miracle that
f.o.m. still exists as a subject.

-- Steve

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