display all the ideas for this combination of texts
3 ideas
| 9844 | Originally Frege liked contextual definitions, but later preferred them fully explicit [Frege, by Dummett] |
| Full Idea: In his middle period, Frege became hostile to contextual definitions, and any definition other than an explicit one, ..but at the time of the 'Grundlagen' he conceived of his context principle as licensing contextual definitions. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.11 | |
| A reaction: His context principle says words only have a meaning in a context. Intuitively, I would say that there is no correct answer to how something should be defined. Totally circularity is hopeless, but presuppositions just weaken a definition. |
| 9822 | Nothing should be defined in terms of that to which it is conceptually prior [Frege, by Dummett] |
| Full Idea: Frege appeals to a general principle that nothing should be defined in terms of that to which it is conceptually prior. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §64) by Michael Dummett - Frege philosophy of mathematics Ch.3 | |
| A reaction: The point is that the terms of the definition would depend on the thing being defined. But of all the elusive concepts, that of 'conceptual priority' is one of the slipperiest. An example is the question of precedence between 'parallel' and 'direction'. |
| 10204 | 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. |