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5. Theory of Logic / G. Quantification / 3. Objectual Quantification

[universal and existential quantifiers picking objects]

9 ideas
Aristotelian logic has two quantifiers of the subject ('all' and 'some') [Devlin on Aristotle]
Frege reduced most quantifiers to 'everything' combined with 'not' [McCullogh on Frege]
Frege introduced quantifiers for generality [Weiner on Frege]
Existence is entirely expressed by the existential quantifier [McGinn on Russell]
'Partial quantifier' would be a better name than 'existential quantifier', as no existence would be implied [McGinn]
'All horses' either picks out the horses, or the things which are horses [Jubien]
Philosophers reduce complex English kind-quantifiers to the simplistic first-order quantifier [Jubien]
The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD]
It is better if the existential quantifier refers to 'something', rather than a 'thing' which needs individuation [Lowe]