FOM: Induction illogical?(corrected version)

Robert Black Robert.Black at
Fri Feb 26 05:27:06 EST 1999

>NOTE: We are talking about lengths of proofs with cuts allowed. I recall
>that Boolos had some interesting lower bounds, but maybe only for cut free
>proofs?? Does anybody recall where Boolos' stuff appeared?

I think you may be referring to 'A Curious Inference', _Journal of
Philosophical Logic_ 16 (1987), 1-12, reprinted as chap. 25 of Boolos's
_Logic, Logic and Logic_.  (Boolos doesn't give the details there, but he
does discuss both cut-free and non-cut-free proofs.  He uses his example
both to argue that no first-order logical system is an adequate
idealization of how we actually recognize first-order validity, and as a
vehicle to distinguish between intuitionistic and finitist acceptability of

Robert Black
Dept of Philosophy
University of Nottingham
Nottingham NG7 2RD

tel. 0115-951 5845

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