[FOM] Second-order logic and neo-logicism

[Panu Raatikainen]

The following new paper might interest some here:

Panu Raatikainen: "Neo-logicism and its logic", History and Philosophy  
of Logic (forthcoming)

http://philpapers.org/rec/RAANAI


It has greatly benefited from certain old discussions here in FOM on  
the second-order logic; special thanks to Martin Davis!


All the Best

Panu



Abstract:
The rather unrestrained use of second-order logic in the neo-logicist  
program is critically examined. It is argued in some detail that it  
brings with it genuine set-theoretical existence assumptions, and that  
the mathematical power that Hume’s Principle seems to provide, in the  
derivation of Frege’s Theorem, comes largely from the “logic” assumed  
rather than from Hume’s principle. It is shown that Hume’s principle  
is in reality not stronger than the very weak Robinson Arithmetic Q.  
Consequently, only few rudimentary facts of arithmetic are logically  
derivable from Hume’s principle. And that hardly counts as a  
vindication of logicism.
-- 
Panu Raatikainen

Ph.D., Adjunct Professor 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/