[FOM] infinite logical derivations
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.)
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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