From jjllambias@xxxxxxx.xxxx Tue Nov 2 06:49:48 1999
X-Digest-Num: 274
Message-ID: <44114.274.1533.959273825@eGroups.com>
Date: Tue, 02 Nov 1999 06:49:48 PST
From: "Jorge Llambias" <jjllambias@xxxxxxx.xxxx
Subject: Re: 3 dogs, 2 men, many arguments

la xod cusku di'e

>How about "the 3 fastest cars running today"?

If you mean that there were exactly 3 cars equally fast,
and they were all faster than all others, then the 3 is
incidental information. This corresponds to Lojban´s
so called "inner quantifiers": {le ci sutrai karce}.
The number doesn't define the set, it only tells you
how many members the set has.

If you mean the fastest, second fastest and third fastest,
then it is not the case that each car is a fastest car,
so the definition in Lojban will not follow the English
idiom.

Of course you can use numbers as part of a definition
of a set. All I'm saying is that the numbers used as quantifiers
in Lojban are not being used to define a set in the way
you propose. {ci gerku} or {ci da poi gerku} by itself does
not define a set, it only selects three members of the set
of all dogs. The part that defines the set is what comes
after {poi}, not the quantifier.

>What do you mean when you say "Everybody loves somebody"? >Do you mean 
>that each person in "everybody" loves their own "somebody", which may or 
>may not
>be the same person as is loved by another person in "everybody"?

Yes, you know that's what I mean. That is the meaning that
would be hard to say with your scheme.

>pc says we have the whole of Set Theory at our disposal in Lojban. I wonder
>what he meant by that. If that's the case, perhaps what I suggest is
>trivial.

I don't know. Set Theory is available in any language, including
Lojban of course. Perhaps an actual example written in Lojban
might be helpful.

>I haven't yet worked out all the implications of what I am suggesting. Is a
>cross product mapping currently possible?

Do you mean for example:

le ci gerku cu batci le re nanmu
Each of the three dogs bites each of the two men.

>Or a 1:1?

This one is harder. We can say:

le ci gerku cu batci le ri ponse
Each of the three dogs bites its owner.

but there is nothing there to stop some or all of the dogs
from having the same owner.

>So currently I see that
>there are no or very limited ways to describe mappings within the prenex,
>and that the default mapping is sufficiently nontrivial as to break SE 
>symmetry.

I don't know what to say. The scope of quantifiers is an
important issue. You haven't shown how you would handle
it if it's not to be by their order of appearance.

co'o mi'e xorxes