FOM: Book recommendation
Stephen G Simpson
simpson at math.psu.edu
Mon Aug 21 14:02:05 EDT 2000
Roger Bishop Jones (FOM, 21 Aug 2000) writes:
> The purpose of my posting was to resist the suggestion that any
> possible reduction would settle the case against "alternative
> logics", which I am comfortable doing without having seen
> Manzano's.
Manzano does not present any "case against alternative logics". She
presents reductions of certain alternative logics to first-order
logic, but that does not invalidate the alternative logics, or deny
their interest. In particular, some of the alternative logics surely
have some proof-theoretic properties which the reductions do not
reflect.
> I do not need to consult Manzano's book to know that if he offers a
> reduction from standard second order logic to first order logic
> then that reduction cannot preserve truth, let alone meaning.
Of course it is true that the interest of Manzano's reductions depends
on what properties are preserved. But actually, her reduction of
second-order logic to first-order logic is truth-preserving and
meaning-preserving, in an appropriate sense of these terms. Since you
have not seen Manzano's book, why do you assume otherwise?
-- Steve
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