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5. Theory of Logic / G. Quantification / 1. Quantification

[general ideas about expressing quantities of objects]

21 ideas
Affirming/denying sentences are universal, particular, or indeterminate [Aristotle]
The word 'every' only signifies when added to a term such as 'man', referring to all men [William of Ockham]
A quantifier is a second-level predicate (which explains how it contributes to truth-conditions) [George/Velleman on Frege]
'Any' is better than 'all' where infinite classes are concerned [Russell]
Objects are the values of variables, so a referentially opaque context cannot be quantified into [Quine]
Universal quantification is widespread, but it is definable in terms of existential quantification [Quine]
Quantifying into referentially opaque contexts often produces nonsense [Quine]
No sense can be made of quantification into opaque contexts [Hale on Quine]
Finite quantification can be eliminated in favour of disjunction and conjunction [Dummett on Quine]
Nominalists should quantify existentially at first-order, and substitutionally when higher [Marcus (Barcan)]
Traditional quantifiers combine ordinary language generality and ontology assumptions [Harré]
Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances [Dummett]
'Prenex normal form' is all quantifiers at the beginning, out of the scope of truth-functors [Bostock]
The quantifier is overrated as an analytical tool [McGinn]
Existential quantifiers just express the quantity of things, leaving existence to the predicate 'exists' [McGinn]
Wittgenstein tried unsuccessfully to reduce quantifiers to conjunctions and disjunctions [Jacquette]
Quantifiers turn an open sentence into one to which a truth-value can be assigned [Mautner]
Not all quantification is either objectual or substitutional [Williamson]
Quantifiers are second-order predicates [Read]
Traditionally, universal sentences had existential import, but were later treated as conditional claims [Orenstein]
The quantifier in logic is not like the ordinary English one (which has empty names, non-denoting terms etc) [Hofweber]