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Single Idea 15525
[filed under theme 5. Theory of Logic / G. Quantification / 6. Plural Quantification
]
Full Idea
There is an irremediable lack of a complete axiom system for plural quantification.
Gist of Idea
Plural quantification lacks a complete axiom system
Source
David Lewis (Parts of Classes [1991], 4.7)
Book Ref
Lewis,David: 'Parts of Classes' [Blackwell 1991], p.120
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]
|