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Quantifiers (part 1)

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Quantifiers denote relations between sets rather than individuals. Words like "all", "some", and "none" are quantifiers. Quantifier statements claim a relation between two sets and make statements about the world, unlike lexical relations which are about word meanings. Quantifiers can denote set relations like a subset relation between sets.

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Quantifiers Part 1We have been talking about a predicate denoting a relation between individuals.But look at the examples:(1) Nobody loves Mary.
(2) Somebody loves Mary.
(3) Everybody loves Mary.
The denotations of everybody and nobody cannot be treated as individuals.Quantifiers (1)Words like all, some and none are called quantifiers.Previously, we said that hyponym relations are defined in terms of superordinate and co-hyponyms.If duck is a hyponym ofbird then the set of ducks is a subset of the set of birds.Also, an antonym relation was represented by disjoint sets (smoker vs. non-smoker)
Quantifiers (1)Something similar applies when studying quantifiers.The previous lexical relations could be expressed as all ducks are birds and no smokers are non-smokersBecause these are lexical relations, they dont make very informative statements about the world.
QUANTIFIERSA more interesting claim isall Australians are sportspeopleThey are not statements about the meaning of words but claims about the situation in the world.However, they are like the lexical relations in claiming a particular relation between two sets.
QUANTIFIERSThe first step is to treat quantifiers as denoting a relation between two sets.All denotes the subset relation between two sets.
Some Australians are sportspeople. Australians Sportspeople

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Quantifiers (part 1)

  • 1. Quantifiers Part 1We have been talking about a predicate denoting a relation between individuals.But look at the examples:(1) Nobody loves Mary.
  • 4. The denotations of everybody and nobody cannot be treated as individuals.Quantifiers (1)Words like all, some and none are called quantifiers.Previously, we said that hyponym relations are defined in terms of superordinate and co-hyponyms.If duck is a hyponym ofbird then the set of ducks is a subset of the set of birds.Also, an antonym relation was represented by disjoint sets (smoker vs. non-smoker)
  • 5. Quantifiers (1)Something similar applies when studying quantifiers.The previous lexical relations could be expressed as all ducks are birds and no smokers are non-smokersBecause these are lexical relations, they dont make very informative statements about the world.
  • 6. QUANTIFIERSA more interesting claim isall Australians are sportspeopleThey are not statements about the meaning of words but claims about the situation in the world.However, they are like the lexical relations in claiming a particular relation between two sets.
  • 7. QUANTIFIERSThe first step is to treat quantifiers as denoting a relation between two sets.All denotes the subset relation between two sets.
  • 8. Some Australians are sportspeople. Australians Sportspeople
  • 9. quantifiersNo Australians are sportspeople. Australians Sportspeople
  • 11. Lexical relations dont make very informative statements about the world.Quantifiers:Like lexical relations claiming a relation between two sets.
  • 12. Not statements about the meaning of words but claims about the situation in the world.