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### 5. Theory of Logic / G. Quantification / 6. Plural Quantification

#### [quantifiers pick out collections, not just 'one+' or 'all']

24 ideas
 14236 Each horse doesn't fall under the concept 'horse that draws the carriage', because all four are needed [Oliver/Smiley on Frege]
 12798 Plurals can in principle be paraphrased away altogether [Quine]
 14235 Saying 'they can become a set' is a tautology, because reference to 'they' implies a collection [Cargile]
 10267 We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro]
 10698 Plural forms have no more ontological commitment than to first-order objects [Boolos]
 15731 Quantification sometimes commits to 'sets', but sometimes just to pluralities (or 'classes') [Lewis]
 15518 I like plural quantification, but am not convinced of its connection with second-order logic [Lewis]
 15525 Plural quantification lacks a complete axiom system [Lewis]
 10268 Maybe plural quantifiers should be understood in terms of classes or sets [Shapiro]
 12845 Some natural languages don't distinguish between singular and plural [Simons]
 10635 Second-order quantification and plural quantification are different [Linnebo]
 10636 Plural plurals are unnatural and need a first-level ontology [Linnebo]
 10639 Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo]
 10640 Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo]
 10641 Traditionally we eliminate plurals by quantifying over sets [Linnebo]
 10778 Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo]
 10783 Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo]
 14234 If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
 14237 We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley]
 12794 Plurals are semantical but not ontological [Laycock]
 10666 Plural reference will refer to complex facts without postulating complex things [Hossack]
 10669 Plural reference is just an abbreviation when properties are distributive, but not otherwise [Hossack]
 10675 A plural comprehension principle says there are some things one of which meets some condition [Hossack]
 14232 We normally formalise 'There are Fs' with singular quantification and predication, but this may be wrong [Liggins]