[FOM] 481:Complementation and Incompleteness
Panu Raatikainen
panu.raatikainen at helsinki.fi
Mon Feb 20 05:11:21 EST 2012
"Michael Lee Finney" <michael.finney at metachaos.net>:
> For the insufficiency of classical logic, there are the books "The
> Principles of Mathematics Revisited" by Jaakko HIntikka and
> "Dependence Logic" by Jouko Vaananen. There are quite a few papers,
> but the basic idea is that first order logic is insufficient to
> characterize common mathematical structures (such as a finite set).
Well, many of us think, in contrast, that the task of logic is, first
and foremost, to provide a theory of valid inferences, and not to
characterize structures. And for this purpose, first-order logic is
the best one can have...
BTW, Hintikka's standard IF logic has the compactness property;
therefore, it cannot characterize many common mathematical structure
either.
And I don't think Väänänen can be used to support such a view; see:
http://www.math.helsinki.fi/logic/people/jouko.vaananen/VaaSec.pdf
http://www.jstor.org/pss/2687796
Best
Panu
--
Panu Raatikainen
Ph.D., University Lecturer
Docent in Theoretical Philosophy
Theoretical Philosophy
Department of Philosophy, History, Culture and Art Studies
P.O. Box 24 (Unioninkatu 38 A)
FIN-00014 University of Helsinki
Finland
E-mail: panu.raatikainen at helsinki.fi
http://www.mv.helsinki.fi/home/praatika/
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