[FOM] infinite logical derivations

praatika@mappi.helsinki.fi praatika at mappi.helsinki.fi
Mon Aug 20 12:02:23 EDT 2007

I was a bit imprecise in my previous posting. 

Infinitary proofs such as those using the omega-rule and discussed e.g. in 
the entry by Hazen I mentioned, are not, literally, infinitely long.  
Rather, they allow steps with infinitely many premises, but a "proof" is 
still finitely long in the sense that it has only finitely many steps. 

I am not sure how much sense the idea of a genuinely infinitely long proof 
makes... What would count as the conclusion (the theorem) of such a proof, 
given it would never terminate ?

(In tableaux systems, an infinite tree represents a failure to find a 
proof rather than a proof.)

Best, Panu

Panu Raatikainen

Ph.D., Academy Research Fellow,
Docent in Theoretical Philosophy

Department of Philosophy
University of Helsinki

E-mail: panu.raatikainen at helsinki.fi


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