[FOM] Choice of new axioms 1

tulenhei@mappi.helsinki.fi tulenhei at mappi.helsinki.fi
Tue Feb 14 16:54:17 EST 2006

Quoting Panu Raatikainen <praatika at mappi.helsinki.fi>

who was

> Quoting Andrej Bauer <Andrej.Bauer at andrej.com>:
> > As an innocent onlooker to the current discussion about 
> > "choice of new axioms", I have been wondering all along 
> > why there needs to be one set of standard axioms that 
> > "normal" mathematicians use? 
> Because otherwise one can derive e.g. both MC and not-MC, and 
> consequently, everything. (MC = there exists a measurable cardinal)

I guess this is too simplistic an answer: Derivations are relative to the 
proof system (axioms + inference rules) used. If MC is derivable in one 
proof system and not-MC in another, so what? 

Not everything is thereby derivable, simpliciter. 

Tero Tulenheimo
Ph.D., Post-Doctoral Research Fellow
Academy of Finland, 
Department of Philosophy
P.O. Box 9
FIN-00014 University of Helsinki

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