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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