[FOM] 23 syllables

[henri galinon]

"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.

H.G.