[FOM] 23 syllables
henri.galinon at libertysurf.fr
Fri Dec 8 03:30:13 EST 2006
"The least number not specifiable-0 in less than nineteen syllables
is indeed specifiable-1 in 18 syllables, but it is not specifiable-0
in less than 19 syllables ; for all I know it is not specifiable-0
in less than 23."
I have submitted my problem to Denis Bonnay who found the trick, so I
give it here. Consider the least number not specifiable-0 in less
than 19 syllables. By assumption, its predecessor is specifiable-0 in
less than 19 syllables (18 or less). Call m one of its
specification-0 of less than 19 syllables, and consider the
specification obtained by writing "the successor of" immediately
followed by the specification-0 m (by concatenation). The result is a
specification-0 having less than 23 syllables ( 5 plus (18 or less)
is 23 or less), and it is one of the least number not specifiable-0
in less than 19 syllables.
I have had a skeptical moment in light of my exegetic aim, for I
thought that such a method would have lead Quine to give an upper
bound, not a lower bound on the possible length of the specification.
That is, Quine should have written : " it is certainly specifiable-0
in less than 23 syllables".
My last doubts vanished when Denis suggested that we could interpret
Quine's phrase "for all I know it is not specifiable-0 in less than
23" as meaning:
a) I know that it is specifiable in 23
b) I do not whether it is specifiable in less than 23.
All is in order then, and well in Quine's spirit.
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