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Single Idea 10142

[filed under theme 2. Reason / D. Definition / 7. Contextual Definition ]

Full Idea

Frege gave up on the attempt to introduce natural numbers by contextual definition, but the project has been revived by neo-logicists.

Gist of Idea

The attempt to define numbers by contextual definition has been revived

Source

report of Crispin Wright (Frege's Concept of Numbers as Objects [1983]) by Kit Fine - The Limits of Abstraction II

Book Ref

Fine,Kit: 'The Limits of Abstraction' [OUP 2008], p.55

The 14 ideas with the same theme [definition relying wholly on facts about context]:

9845 We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege]
9844 Originally Frege liked contextual definitions, but later preferred them fully explicit [Frege, by Dummett]
9822 Nothing should be defined in terms of that to which it is conceptually prior [Frege, by Dummett]
21560 Any linguistic expression may lack meaning when taken out of context [Russell]
19047 Bentham's contextual definitions preserved terms after their denotation became doubtful [Quine]
19048 Contextual definition shifted the emphasis from words to whole sentences [Quine]
8995 Definition by words is determinate but relative; fixing contexts could make it absolute [Quine]
9847 A contextual definition permits the elimination of the expression by a substitution [Dummett]
10476 The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W]
10142 The attempt to define numbers by contextual definition has been revived [Wright,C, by Fine,K]
9961 'Contextual definitions' replace whole statements, not just expressions [Mautner]
10204 An 'implicit definition' gives a direct description of the relations of an entity [Shapiro]
18776 Contextual definitions eliminate descriptions from contexts [Linsky,B]
9955 Contextual definitions replace a complete sentence containing the expression [George/Velleman]