Re: The modern mathematical concept of infinity is ...

Gus Gassmann wrote:
On Feb 23, 3:17 am, Brian Chandler <imaginator...@xxxxxxxxxxxxx>
wrote:

Japanese, like Finnish, has a plug-n-play system of verb suffixes,
including a causative one we'll call 'sase'. Thus:

taberu : means 'eat'
tabe-sase-ru : means 'cause to eat', as in "feed the children"
tabe-sase-sase-ru : means 'cause to cause to eat', as in "get the maid
to feed the children"
... ["and so on", or not!]

It is normally possible to persuade a native speaker to agree that
tabesasesaseru "is Japanese". But the putative argument is whether
tabe-sase^n-ru "is Japanese" for any natural n. The formal model you
get by writing the obvious grammar in Prolog obviously allows any n,
because (a) it's much easier to do and (b) any limit would be quite
arbitrary. But clearly once the value of n reaches double figures, the
result is something with no relation to the actual Japanese language
as spoken. In this case, to claim that tabe-sase^i-ru (where i is
"Isles's number") is not a Japanese word seems pretty reasonable.

You could do the same thing in English if you want. I recently learned
about the "buffalo" game (http://en.wikipedia.org/wiki/
Buffalo_buffalo_Buffalo_buffalo_buffalo_buffalo_Buffalo_buffalo)

This isn't quite the point -- the "Buffalo" sentence is a curious joke
involving a (very definitely finite!) repetition of the same word
managing to have the same form as verb and noun, in such as way as to
agree. Usually this isn't quite possible because the endings (null and
-s) of singular and plural (3rd person) verb and noun forms are just
the reverse of each other.

To answer Jesse's question: not just Japanese -- they claim that in
English there is a sentence

I live in the house (next to the house)* next to the station.

where ()* means repeat the contents of ( ) um infinitely. (Whatever
that means, exactly)

I suppose they claim that there is also a sentence that looks like:

The digits of pi in sequence are 3, 1, 4, 1, 5, 9, ... [with the rule
about putting 'and' before the last one somehow satisfied]

Well, who knows?

Brian Chandler
.

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