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Single Idea 10538

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

Full Idea

Quine even asserts that where we have no infinite domains, quantification can be eliminated in favour of finite disjunction and conjunction.

Gist of Idea

Finite quantification can be eliminated in favour of disjunction and conjunction

Source

report of Willard Quine (works [1961]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14

Book Ref

Dummett,Michael: 'Frege Philosophy of Language' [Duckworth 1981], p.478

A Reaction

Thus ∃x is expressed as 'this or this or this...', and ∀ is expressed as 'this and this and this...' Dummett raises an eyebrow, but it sounds OK to me.

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]