[FOM] 23 syllables
henri.galinon at libertysurf.fr
Fri Dec 8 17:49:36 EST 2006
> Richard Heck wrote:
> I'm not sure what the "amusing game" is supposed to be here.
The game I alluded to is in the very last 12 words of the quote
(below). The rest of the quote is fairly clear and standard, as you
emphazise , and not really an "amusing game" . So the point was that
Quine offers a diagnosis that Berry's number is specifiable-0 (in
natural language, even English, I suppose ) in 23 syllables. It is
this I found intriguing: 23. How did Quine get his result ? Was it
the result of a tedious lexical and mathematical research on all ways
of specifying numbers in english (while avoiding to ascend the
semantic hierarchy of course)? Not very "quinean", is it ?
As I've been convinced since, his way was different (see the other
post on the topic).
By the way, I've just read somewhere that Russell thought Berry's
number to be 111,777 ...
>> " 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."
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