[FOM] Weak system for SO logic
praatika at mappi.helsinki.fi
Tue Apr 7 07:43:59 EDT 2009
Quoting rgheck <rgheck at brown.edu>:
> we add second-order quantifiers to the language, and take as
> rules the obvious analogues of the first-order rules ...
> This is what makes the system weaker than with predicative
> comprehension. You won't be able to derive something like:
> (EH)(x)(Hx <--> Fx & Gx)
Thanks, Richard, that's what I (vaguely) thought.
Now the question arises, is there any really good reason to take the
more usual rules (which entail even impredicative comprehension) as
more *natural* logical introduction and elimination rules for SO
quantifiers than the above neutral ones?
Ph.D., Academy Research Fellow,
Docent in Theoretical Philosophy
Department of Philosophy
University of Helsinki
E-mail: panu.raatikainen at helsinki.fi
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