structure for 'Theory of Logic'    |     alphabetical list of themes    |     expand these ideas

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

#### [general ideas about expressing quantities of objects]

22 ideas
 11149 Affirming/denying sentences are universal, particular, or indeterminate [Aristotle]
 9106 The word 'every' only signifies when added to a term such as 'man', referring to all men [William of Ockham]
 9950 A quantifier is a second-level predicate (which explains how it contributes to truth-conditions) [Frege, by George/Velleman]
 14137 'Any' is better than 'all' where infinite classes are concerned [Russell]
 9467 Wittgenstein tried unsuccessfully to reduce quantifiers to conjunctions and disjunctions [Wittgenstein, by Jacquette]
 10922 Objects are the values of variables, so a referentially opaque context cannot be quantified into [Quine]
 9015 Universal quantification is widespread, but it is definable in terms of existential quantification [Quine]
 10926 Quantifying into referentially opaque contexts often produces nonsense [Quine]
 10311 No sense can be made of quantification into opaque contexts [Quine, by Hale]
 10538 Finite quantification can be eliminated in favour of disjunction and conjunction [Quine, by Dummett]
 10799 Nominalists should quantify existentially at first-order, and substitutionally when higher [Marcus (Barcan)]
 15891 Traditional quantifiers combine ordinary language generality and ontology assumptions [Harré]
 19057 Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances [Dummett]
 13438 'Prenex normal form' is all quantifiers at the beginning, out of the scope of truth-functors [Bostock]
 6042 The quantifier is overrated as an analytical tool [McGinn]
 6067 Existential quantifiers just express the quantity of things, leaving existence to the predicate 'exists' [McGinn]
 6890 Quantifiers turn an open sentence into one to which a truth-value can be assigned [Mautner]
 18492 Not all quantification is either objectual or substitutional [Williamson]
 11007 Quantifiers are second-order predicates [Read]
 8452 Traditionally, universal sentences had existential import, but were later treated as conditional claims [Orenstein]
 16416 The quantifier in logic is not like the ordinary English one (which has empty names, non-denoting terms etc) [Hofweber]
 21643 The inferential quantifier focuses on truth; the domain quantifier focuses on reality [Hofweber]