[FOM] 481:Complementation and Incompleteness

[Panu Raatikainen]

"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
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