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Re: [jboske] Quantifiers, Existential Import, and all that stuff

At 07:49 PM 3/1/02 -0500, pycyn@aol.com wrote:
Aristotle wisely always said "not all S is P" for this case, the "some" version is later, when the problem was misunderstood or forgotten.

But, whatever Aristotle did, what does Lojban do? {su'o da broda naku brode} has the same conflict as "Some S is not P" -- the variable says there doesn't have to be an S (even without the buried conditional, say), the {su'o} says there does, and pushing the negation through says "No" again. There are just two possibilities before we push on to a more complex solution. We can say that {su'o da} does not mean the same think when something inside it is negative, so that it does not have existential import then. Or we can invent a new quantifier (only one is needed, as opposed to every other solution I have thought of, which take more) which is always existentially free, whether before a variable or not (and make {su'o} always existential). The second alternative seem the wiser one, although it complicates the rules just used quite a bit.

Nothing new is needed, if Aristotle satisfies. I believe that {me'iro da broda cu brode} is a literal translation of the Aristotle approach.

(Of course we could get into philosophical hot water if we debate whether "not all" = "less than all" if "all" refers to something that does not exist, but I'll leave that to someone else %^).

lojbab lojbab@lojban.org
Bob LeChevalier, President, The Logical Language Group, Inc.
2904 Beau Lane, Fairfax VA 22031-1303 USA 703-385-0273
Artificial language Loglan/Lojban: http://www.lojban.org