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Single Idea 12798
[filed under theme 5. Theory of Logic / G. Quantification / 6. Plural Quantification
]
Full Idea
By certain standardizations of phrasing the contexts that call for plurals can in principle be paraphrased away altogether.
Gist of Idea
Plurals can in principle be paraphrased away altogether
Source
Willard Quine (Word and Object [1960], §19)
Book Ref
Quine,Willard: 'Word and Object' [MIT 1969], p.90
A Reaction
Laycock, who quotes this, calls it 'unduly optimistic', but I presume that it was the standard view of plural reference until Boolos raised the subject.
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]
|