Message-Id: <m0sQiaX-0000YjC@xiron.pc.helsinki.fi>
Date:         Tue, 27 Jun 1995 17:54:13 EDT
Reply-To:     jorge@PHYAST.PITT.EDU
Sender:       Lojban list <LOJBAN@CUVMB.BITNET>
From:         jorge@PHYAST.PITT.EDU
Subject:      Re: ci gerku nicte
To:           Veijo Vilva <veion@XIRON.PC.HELSINKI.FI>
Content-Length: 2771
Lines: 65

la djer cusku di'e
> 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.)
>
> 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".

Right. For each human, there are exactly nine dogs that the human
touches, but in the whole universe, there are many more than three
humans or nine dogs.

> 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)))

That is not a good translation, because the Lojban sentence does not
claim that only three objects satisfy remna(x). All the sentence says
is that exactly three objects, out of all of those that satisfy remna(x),
do something. And the same for the dogs. There is no claim that only
nine objects are dogs. The only claim is that for each of three
humans, there are nine objects out of all that satisfy gerku(y),
such that the human touches them.

> The scope of the quantifier on y is to the end of the sentence.  It
> includes the y in pencu(x,y).

The question is whether for each different x, the quantifier on y
selects nine dogs again, or whether they are selected once and for
all for all the x's. The consensus we seem to be reaching is that
they are selected separately for each x. The other option is also
logical, all we have to do is choose one of the interpretations.

> We have asserted for the entire length
> of the sentence that there are exactly 9 dogs.

No, that is not asserted in any of the two interpretations. The sentence
only limits the number of dogs that are touched, not the number of
dogs that there are in all.

> Where do the extra dogs come from?

They were there all the time.

> 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.

{so gerku} means {so lo ro gerku}, "nine of all the dogs of the universe
of discourse". There is no limitation in that sentence as to the number
of dogs in the universe of discourse.

Jorge