[FOM] Weak system for SO logic
praatika at mappi.helsinki.fi
Fri Apr 17 09:46:01 EDT 2009
Richard Heck wrote:
> I think nowadays "the more usual rules" aren't really very usual.
I based calling them "more usual" simply to my quick check in few
books and papers I was more familiar with: e.g. van Dalen, Logic and
Structure; Troelstra & Schwichtenberg, Basic Proof Theory; Prawitz,
"Ideas and results in proof theory"; and Leivant, "Higher order logic"
- all (if I read them correctly) present the rules amounting to the
full impredicative comprehension, and only them.
In addition to Takeuti, at least Manzano, in Extensions of First-Order
Logic, mentions other options. She refers back to the classic (Henkin
But it seems to me that at least in the sources with deal with natural
deduction, these really are the "more usual" ones. However, I would be
very interested in learning about contrary evidence...
> That is how Frege formulates the rules in _Begriffsschrift_, but
> even in _Grundgesetze_ he shows some awareness that there are really two
> things going on. It's worth disentangling these, which of course is what
> happens when we formulate the rules as simply as possible and add
> comprehension axioms.
I whole-heartedly agree!
All the Best, Panu
Panu Raatikainen, Ph.D.
Academy Research Fellow, the Academy of Finland
Docent in theoretical philosophy, University of Helsinki
Department of Philosophy
P.O. Box 9
FIN-00014 University of Helsinki
e-mail: panu.raatikainen at helsinki.fi
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