[FOM] 23 syllables
henri galinon
henri.galinon at libertysurf.fr
Wed Dec 6 16:43:08 EST 2006
Dear FOMers,
in his essay "The ways of paradox", Quine has a passage on Berry's
paradox. At the very end of the passage (last remark of the following
quote), he offers the reader a little amusing game (implicitly at
least) by hinting at a solution. My question is : what is Quine's
"solution" ?
I quote the entire relevant passage :
" Ten has a one-syllable name. Seventy-seven has a five-syllable
name. The seventh power of seven hundred seventy-seven has a name
that, if we were to work it out, might run to 100 syllables or so;
but this number can also be specified more briefly in other terms. I
have just specified it in 15 syllables. We can be sure, however, that
there are no end of numbers that resist all specification, by name or
description, under 19 syllables. There is only a finite stock of
syllables all together, and hence only a finite number of names or
phrases of less than 19 syllables, whereas there are an infinite
number of positive integers. Very well, then ; of those numbers not
specifiable in less than 19 syllables, there must be a least. And
here is our antinomy : the least number not specifiable in less than
nineteen syllables is specifiable in 18 syllables. I have just so
specified it.
The antinomy belongs to the same family as the antinomies that have
gone before. For the key word of this antinomy, "specifiable", is
interdefinable with "true of". It is one more of the truth locutions
that would take on subscripts under the Russell-Tarski plan. 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."
Best,
H.G.
PhD student
Paris, France
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