FOM: second-order logic is a myth
Schalekamp, Hendrik J.
carnun at maths.uct.ac.za
Tue Mar 2 15:34:13 EST 1999
> From: Stephen G Simpson <simpson at math.psu.edu>
> Subject: FOM: second-order logic is a myth
> Boiled down to essentials, Shapiro's case for second-order logic seems
> to be as follows:
>
> 1. There is no sharp boundary between mathematics and logic.
>
> Against 1, the correct view of the matter (going back to Aristotle) is
> that logic is a method or common background shared by all scientific
> subjects, not only mathematics. This key scientific/philosophical
> distinction is reflected in the usual predicate calculus distinction
> between logical and `non-logical' axioms. The logical axioms are
> common to all subjects (i.e. theories), while the `non-logical' ones
> are subject-matter specific.
There seems to be a problem with the understanding of a sharp
boundary. What Stephen has just said seems to support 1, in the sense
that logic clearly has a broader application than mathematics,
especially since one of its applications is to mathematics. This
to me seems to be a sharp distinction (or boundary) as required. Maybe it
would serve to clarify by what statement 1 is supposed to mean and/or what
Shapiro realy meant (sorry but our lib. is limited so I don't have
access to the book).
Regards
Hendrik Schalekamp
Carnun, Son of Danu
===================
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