FOM: second-order logic is a myth

[Schalekamp, Hendrik J.]

> 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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