[FOM] computable numbers, independent freindly logic
praatika@mappi.helsinki.fi
praatika at mappi.helsinki.fi
Sun Dec 28 07:08:47 EST 2003
George Kapoulas <gkapou at yahoo.gr> wrote:
> 2) There is an approach for logic
> called independent friendly logic.
> Does anyone know if there is
> proof that the approach used by
> this logic cannot be expressed
> in 1st order logic,
> and references for this?
This logic, isolated by Hintikka and Sandu, essentially
uses "partially ordered" or "branching" quantifiers
(also known as "Henkin quantifiers"). It has been known
for some time that the resulting logic is equivalent to
Sigma-1-1 fragment of second order logic (Enderton 1970;
Walkoe 1970). Hence it is much stronger than the standard
first order logic, and also essentially incomplete.
Hintikka and Sandu have also included partially ordered
connectives to their IF logic, but this does not make it
really stronger.
References:
Enderton, H.B. (1970) 'Finite partially ordered quantifiers',
Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik 16,
393-397.
Walkoe, W. (1970) 'Finite partially ordered quantification'. JSL 35,
535-555.
Best
Panu
Panu Raatikainen
Ph.D., Docent in Theoretical Philosophy
Fellow, Helsinki Collegium for Advanced Studies
P.O. Box 4
FIN-00014 University of Helsinki
Finland
E-mail: panu.raatikainen at helsinki.fi
http://www.helsinki.fi/collegium/eng/Raatikainen/raatikainen.htm
More information about the FOM
mailing list