1. a quantifier that is a universal on its face (ex. every)
2. a quantifier that is not universal on its face, but is logically equivalent to a universal quantifier (ex. no)
3. a non-quantificational construction that can nonetheless assert a universal (ex. the tallest)
4. a construction that admits of a presupposed partition, with (implied) universal quantification over the partition's elements.
the first category is mostly obvious. what i take it to include which may be not obvious is generics, which are arguably not universal on their face because they have no face - i.e. they are invisible. i am talking about sentences like the following:
bears are godless killing machinesi take these to be universal statements over typical instances of bears, in the first example, and mary's mornings, in the second. i won't defend this view here; i may defend it elsewhere.
mary takes aspirin in the morning
the second category - of quantifiers logically equivalent to universals - is mostly there to capture negation. negative quantifiers are usually translated as negated existential quantifiers, but they are logically equivalent to universally negated sentences. for example, nobody loves you is typically translated as it is not the case that for some x, x loves you. but it can also be translated as for every x, it is not the case that x loves you. given this translation, we have a universal for the exceptive to leech off of.
sentential negation also admits exceptives, as in mary hasn't kissed john, except last new year's. in davidsonian semantics and its neo- and semi- varieties, sentential negation can be seen as negative quantification over the sentence's event argument. so the last sentence can be translated for every past event e, e is not an event of mary kissing john, except event e' last new year's. so sentential negation falls in this category too. negative polarity any falls in this category as well. free choice any can fall in this category or the last one, depending on how you look at it - you can consider it facially a universal or just translatable as one, as you fancy.
the third category consists of non-quantificational structures that can carry quantificational meanings, like the five, the tallest, and the only. i will suggest that this is where zamparelli's analysis starts to become relevant. it's also where i start to go out on a limb. what i'm going to claim here is that unlike ordinary the, the in these cases includes a universal component. zamparelli's analysis makes this somewhat plausible, because it allows us to associate universal quantification with the strong DP syntax rather than making it a purely lexical phenomenon. what i'll suppose is that inherently quantificational determiners like every are necessarily found in SDP, the strong determiner phrase; some determiners, like some, can never be universal for semantic reasons, and they must appear in the predicative determiner phrase, PDP; and others, like the and perhaps few and many, can appear either in SDP or PDP, and receive an interpretation accordingly.
zamparelli noted that the possessive can be predicative or non-predicative, depending on whether it is followed by a cardinal or not:
these are my toys. those are my toys too.in the first sentence, the possessor my is in PDP, which allows an empty SDP (or allows SDP not to project), so there is no uniqueness requirement on the possessive. in the second sentence, the possessor is forced to SDP by the presence of the cardinal, which imposes the uniqueness requirement, shown by the unacceptability of adding the second sentence. the same would be true if "three" was replaced by "only" or any superlative.
*these are my three toys. those are my three toys too.
i'm suggesting that the same happens with the. it is located in PDP unless there is something like a cardinal, a superlative or only to force it into SDP. as a consequence, the is not universal in the boys, but is universal in the three boys or the tallest boys, allowing these phrases to license exceptives.
two problems arise: first, what is the if not universal? presumably it is a group. the collective/distributive analysis of definites is well known. i suggest that when the is in PDP, it has a collective, group, interpretation, which does not require asserting something of all the members of the group. in PDP, the has a distributive, universal, interpretation. i wish i could say i have independent evidence for this analysis. maybe i'll get some for christmas.
second, there's the fact that the in SDP is not downward entailing in its first argument, casting doubt on the analysis that it is universal.
the five high schoolers helped outthis might be rescued by a von fintel-style strawsonian condition on entailment; or maybe we'll have to refine how we talk about universals and entailment in order to make this work.
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the five tenth graders helped out
what about few and many? if we follow partee's 1986 paper many quantifiers, these are ambiguous between a cardinal interpretation and a quantificational one. maybe the cardinals are in PDP and the quantifiers in SDP; or maybe paolo acquaviva's breakdown of quantifiers like few into negation + many engages the SDP layer through negation. it seems like i'm grasping at straws here, but ultimately i don't think these analyses are as implausible as they seem from my presentation. i'm a little ill and i've been writing all day, so give me a break.
the last category is of quantifiers that admit of presupposed partitions with implied universal quantification over the partition's elements. if you don't know what i'm talking about, refer to my previous posts here and here. what i suggest is that SDP licenses such presuppositions, so that quantifiers that appear in SDP can admit of these interpretations, and license exceptives, even though their semantics are not universal. this applies to most, as well as many and few when these are interpreted with non-cardinal meaning. cardinals, some, and a(n) can't appear in SDP so they never admit the presupposition interpretation.
this approach predicts that many and few can only allow the presupposed meaning on their proportional interpretations and not the cardinal ones. i contend this is true. care to contradict me?
many scandinavians have won the nobel prize, except finnsthis should mean that for every scandinavian country, relatively many, but not necessarily absolutely many, nationals of that country won the nobel prize.
this approach raises the question of why the presupposition interpretation is not available with universals. i claim that it is, but you'd never notice it because it's logically entailed by the universal interpretation. for example, every high schooler helped out logically entails [presupposing a partition P of the set of high schoolers, for every element Q of P,] every x, x an element of Q, helped out. this is true for every partition P, so the presupposition is always utterly redundant, hence undetectable.
actually, i wonder if the universal interpretation of the can be brought in under this category, thereby eliminating the problems mentioned above. maybe the best interpretation of the tallest boys helped out is [given a partition P on the tallest boys, for every element Q of P] the boys x, x an element of Q, helped out. this seems to get the semantics right.
also, now that i think of it, aren't exceptives pretty okay with the when the sentence's predicate is highly distributive, but not when when it tends to admit of a collective reading?
the boys have blue eyes, except jimmy
*the boys lifted the table, except jimmy
having blue eyes is very individual, which highly favors the distributive reading which i'm arguing is associated with the universal interpretation and SDP, while lifting the table strongly suggests a collective reading, which is associated with a non-universal interpretation and PDP. maybe this whole analysis can be made plausible yet.
now what accounts for the Det friend that i have pattern? i hope it's not restrictions on movement, cause goddamn, i don't understand that stuff.
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