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Single Idea 10204

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

Full Idea

An 'implicit definition' characterizes a structure or class of structures by giving a direct description of the relations that hold among the places of the structure.

Gist of Idea

An 'implicit definition' gives a direct description of the relations of an entity

Source

Stewart Shapiro (Philosophy of Mathematics [1997], Intro)

Book Ref

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.13

A Reaction

This might also be thought of as a 'functional definition', since it seems to say what the structure or entity does, rather than give the intrinsic characteristics that make its relations and actions possible.

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]