[FOM] 23 syllables
henri galinon
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 ...
Best,
Henri
>>
>> " 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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