Re: [lojban] More about quantifiers

[pycyn@aol.com]

In a message dated 3/12/2002 5:09:45 PM Central Standard Time, jjllambias@hotmail.com writes:

"Not some" should work just as well for "no", and yet it gets
its own word in English (as well as in Lojban, coincidentally).

True, but the concept behind "no" gets used a lot more -- and "All... no..." is ambiguous in English's loose syntax.

<. It's not so
hard to see that "someone loves someone" means the same as
"not everyone loves no one", or that "everyone loves everyone"
means the same as "no one loves less than everyone". >
As a logic teacher, I can assure that it is hard and, for some people, impossible without a paper and a pencil and ten minutes to work the transformations.

<Not with the quantifiers, only with their import, which
is most often irrelevant anyway.

Here's the rule: if there's an odd number of negatives in front
(that's explicit naku's plus the implicit ones inside of {no}
and {me'iro}) then the import is reversed.>

Sure, but as the depth increases the problems multipy.  And, of course, as the import changes so does the actual quantification, that's what negation does, change all dimensions.

<>Why does Aristotle's system not have {no broda naku} = {ro broda}?

Don't ask me! He has {ro broda} with import and {no broda} with
no import, according to what you reported. Wasn't his system
(A+,E-,I+,O-)?>

Communication failure, perhaps as usual. I read your {ro broda} and {no broda} as mine, in which {no broda} does = {ro broda..naku...},,as indeed it does in your system, too.  I gather that you want to have all the basics of a system be in the {Q broda} format, so that A's system {ro broda no broda suo broda  mei'ro broda}.  In that case, A's system would not have, as you say, {no broda} = (ro broda ... naku ...}; the second implies the first but is not implied by it.  So far as I can find in a quick glance at the central stuff, Aristotle never considers the question and the later folk who do are working with a different system.  What A would have said if he had thought about it is an interesting question.  BTW, he can't have the out of {me'iro broda} = {su'o broda ... naku ...} either, which is more of a loss.

However, if we switch back to the traditional system, which covers almost all cases, then we get all familiar stuff, including all those odd critters involving changing order or fiddling with negations.  Impure as it is, it does seem to be the nearest thing to a satisfactory solution that will placate everybody most of the time.