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Single Idea 15731

[filed under theme 5. Theory of Logic / G. Quantification / 6. Plural Quantification ]

Full Idea

I consider some apparent quantification over sets or classes of whatnots to carry genuine ontological commitment to 'sets' of them, but sometimes it is innocent plural quantification committed only to whatnots, for which I use 'class'.

Gist of Idea

Quantification sometimes commits to 'sets', but sometimes just to pluralities (or 'classes')

Source

David Lewis (On the Plurality of Worlds [1986], 1.5 n37)

Book Ref

Lewis,David: 'On the Plurality of Worlds' [Blackwell 2001], p.51

A Reaction

How do you tell whether you are committed to a set or not? Can I claim an innocent plurality each time, while you accuse me of a guilty set? Can I firmly commit to a set, to be told that I can never manage more than a plurality?

The 24 ideas with the same theme [quantifiers pick out collections, not just 'one+' or 'all']:

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]