[FOM] Fwd: invitation to comment

Panu Raatikainen panu.raatikainen at helsinki.fi
Fri May 20 01:59:46 EDT 2011

Lainaus Andre.Rodin at ens.fr:

> I think the message is this. While for the in-consistency of PA and  
> ZFC we may possibly have a sound *mathematical* argument (evidence)  
> any attempted proof of the consistency of these systems will be not  
> a mathematical proof proper but involve some further  
> non-mathematical assumptions. So a mathematical proof of  
> in-consistency of PA and/or ZFC will boost further mathematical  
> research while the lack of such proof leaves us with this  
> controversial mixture of mathematical reasoning and philosophical  
> speculation that we call foundations.

But the consistency of PA, at least, is on an equal footing with many  
theorems of ordinary mathematics, such as Goodstein’s theorem, or  
Kruskal’s Theorem. The former can be derived from the later. I don't  
think it would be proper to say that they depend on non-mathematical  
assumptions or on philosophical speculation.

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

E-mail: panu.raatikainen at helsinki.fi


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