Message-Id: <m0sQglS-0000YjC@xiron.pc.helsinki.fi>
Date:         Tue, 27 Jun 1995 10:42:01 -0700
Reply-To:     Gerald Koenig <jlk@NETCOM.COM>
Sender:       Lojban list <LOJBAN@CUVMB.BITNET>
From:         Gerald Koenig <jlk@NETCOM.COM>
Subject:      Re: ci gerku nicte
To:           Veijo Vilva <veion@XIRON.PC.HELSINKI.FI>
Content-Length: 1462
Lines: 42

xorxes sends  me the feedback I need to work more on this problem:

my sentence:

>> ci remna ku so gerku zo'u ra pencu ri

xorxes translation:

>For each of exactly three humans, there are nine dogs that the human
>touches. (Not necessarily the same ones for each human.)
>
>Jorge

OK, from this I conclude that there can be more than 9 dogs, since on
your interpretation human-1 can touch dog-1 to dog-9, and human-2 can
touch others, "not necessarily the same ones for each human".

Numbers are expressed in predicate calculus by long combinations of
quantifiers and variables. Numbers are exact numerical claims, i.e. "3"
means no more than three and no less than three. It means there are
only 3 things in our universe of discourse. The shorthand way to
express these is this notation: E!=1, E^!2=2, E^!3=3, etc. E^!9(y)
gerku(y) asserts that there are exactly 9 objects satisfying gerku(y).
I am translating the sentence as:

E^!3(x)(remna(x)  E^!9(y)(gerku(y) & pencu(x,y)))

The scope of the quantifier on y is to the end of the sentence.  It
includes the y in pencu(x,y).  We have asserted for the entire length
of the sentence that there are exactly 9 dogs.

Where do the extra dogs come from?


I just don't think that the lojban covers the situation where at O hours
gmt I touch 9 dogs in LA, you touch 9 dogs in Pittsburgh, and pc touches
9 dogs in Washington(?), for a total of 27 dogs. There are only 9 dogs
in this universe of discourse.


djer