From Pycyn@aol.com Mon Jan 31 02:20:13 2000 X-Digest-Num: 349 Message-ID: <44114.349.1892.959273825@eGroups.com> Date: Mon, 31 Jan 2000 05:20:13 EST From: Pycyn@aol.com Subject: Restricted quantification (ex: Subjunctives) I don't know exactly why nobody else likes restricted quantification, but since it tends to get shot down in the context of unicorns and the like, I suspect it is that many like it that statements about the member of the empty class are always true in standard (20th century) logic and people want to be able to say true things about unicorns (I suggested a different way to deal with that a while back, using another favorite bugbear, intentional context and/or subject raising). The present situation in fact evolved in a complex way from restricting all restricted quantifiers (the original sort) to the universe of discourse and then doing the sorting (restricted quantifiers are also called sortl quantifiers) by conditionals in the predicate place. This left the universal quantifers with residual existential import, which bugs some logicians still (who want empty universe logics of one sort or another -- what happens when there is nothing in the world to which quantifiers and terms generally allude). Restricted quantifiers are the original (i.e., Aristotelian and, covertly, Akshapadan) version, realized in modern form with each bound variable restricted to members of a given set, which is assumed to be non-empty. (There is a version with empty sets permitted, but it reduces on the one hand to the usual system and on the other to an empty-universe mishmash, which no one likes.) Restricted quantifiers also seem to be underlie quantifier ((and determiner generally) structures in natural languages, so that the usual quantifiers really are as artifical as they often feel. So, given that we have lebbenty-lebben ways to do quantifiers, I always thought it made sense to allow at least one of them to be this natural and ancient logical sort, most conveniently the da poi format. This suggestion always gets pooh-poohed, though I conveniently forget why each time. (Oh yes, it allows for the differences between each & every against any & all in English). Universals take the Aristotelian A form seriously, rather than degenerately (the empty-class version uses the obverse No S is non-P, which under the best version of A's system lacks existential import). The particular forms don't usually make much difference in interpretation, and the other determiners are dealt with in all the weird ways Lojban has. pc