Combining Texts

Ideas for 'Thinking About Mathematics', 'Philosophy of Mathematics' and 'The Sophist'

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2. Reason / D. Definition / 7. Contextual Definition
An 'implicit definition' gives a direct description of the relations of an entity [Shapiro]
     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.
     From: Stewart Shapiro (Philosophy of Mathematics [1997], Intro)
     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.