[FOM] Ultrafinitism

Alex Blum blumal at mail.biu.ac.il
Wed Feb 11 13:55:46 EST 2009

Walter Read and Dennis Hamilton seem to suggest that Paul Van Bendegem’s
purported counterexample to a generalization of mathematical induction,
“(a) I can write down the numeral 0 (or 1, does not matter),
(b) for all n, if I can write down n, I can write down n+1 (or the
successor of n),
hence, by mathematical induction,
(c) I can write down all numerals."

can be avoided by replacing ‘all numerals’ in (c) by ‘each numeral’. But
by taking ‘each mumeral’ as opposed to taking any one numeral is to take
all numerals,one at a time. The purported counterexample would thus stay 
Alex Blum

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