[FOM] Weak system for SO logic

praatika@mappi.helsinki.fi 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?

Best, Panu

Panu Raatikainen

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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