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Single Idea 10636

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

Full Idea

Higher-order plural quantification (plural plurals) is often rejected because plural quantification is supposedly ontological innocent, with no plural things to be plural, and because it is not found in ordinary English.

Gist of Idea

Plural plurals are unnatural and need a first-level ontology

Source

Øystein Linnebo (Plural Quantification [2008], 2.4)

Book Ref

'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.8

A Reaction

[Summary; he cites Boolos as a notable rejector] Linnebo observes that Icelandic contains a word 'tvennir' which means 'two pairs of'.

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]