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Single Idea 14137

[filed under theme 5. Theory of Logic / G. Quantification / 1. Quantification ]

Full Idea

The word 'any' is preferable to the word 'all' where infinite classes are concerned.

Gist of Idea

'Any' is better than 'all' where infinite classes are concerned

Source

Bertrand Russell (The Principles of Mathematics [1903], §284)

Book Ref

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.305

A Reaction

The reason must be that it is hard to quantify over 'all' of the infinite members, but it is easier to say what is true of any one of them.

The 23 ideas with the same theme [general ideas about expressing quantities of objects]:

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]
23494 Conjunctive and disjunctive quantifiers are too specific, and are confined to the finite [Morris,M]