display all the ideas for this combination of philosophers
9 ideas
| 9821 | A definition need not capture the sense of an expression - just get the reference right [Frege, by Dummett] |
| Full Idea: Frege expressly denies that a correct definition need capture the sense of the expression it defines: it need only get the reference right. | |
| From: report of Gottlob Frege (Review of Husserl's 'Phil of Arithmetic' [1894]) by Michael Dummett - Frege philosophy of mathematics Ch.3 | |
| A reaction: This might hit up against the renate/cordate problem, of two co-extensive concepts, where the definition gets the extension right, but the intension wrong. |
| 13886 | Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C] |
| Full Idea: Frege later became fastidious about definitions, and demanded that they must provide for every possible case, and that no function is properly determined unless its value is fixed for every conceivable object as argument. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Crispin Wright - Frege's Concept of Numbers as Objects 3.xiv | |
| A reaction: Presumably definitions come in degrees of completeness, but it seems harsh to describe a desire for the perfect definition as 'fastidious', especially if we are talking about mathematics, rather than defining 'happiness'. |
| 16877 | A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege] |
| Full Idea: We construct a sense out of its constituents and introduce an entirely new sign to express this sense. This may be called a 'constructive definition', but we prefer to call it a 'definition' tout court. It contrasts with an 'analytic' definition. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.210) | |
| A reaction: An analytic definition is evidently a deconstruction of a past constructive definition. Fregean definition is a creative activity. |
| 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'. |
| 9845 | We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege] |
| Full Idea: Given the reference (bedeutung) of an expression and a part of it, obviously the reference of the remaining part is not always determined. So we may not define a symbol or word by defining an expression in which it occurs, whose remaining parts are known | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §66) | |
| A reaction: Dummett cites this as Frege's rejection of contextual definitions, which he had employed in the Grundlagen. I take it not so much that they are wrong, as that Frege decided to set the bar a bit higher. |
| 11219 | Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta] |
| Full Idea: Frege has defended the austere view that, in mathematics at least, only stipulative definitions should be countenanced. | |
| From: report of Gottlob Frege (Logic in Mathematics [1914]) by Anil Gupta - Definitions 1.3 | |
| A reaction: This sounds intriguingly at odds with Frege's well-known platonism about numbers (as sets of equinumerous sets). It makes sense for other mathematical concepts. |
| 10019 | Only what is logically complex can be defined; what is simple must be pointed to [Frege] |
| Full Idea: Only what is logically complex can be defined; what is simple can only be pointed to. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §180), quoted by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.137 | |
| A reaction: Frege presumably has in mind his treasured abstract objects, such as cardinal numbers. It is hard to see how you could 'point to' anything in the phenomenal world that had atomic simplicity. Hodes calls this a 'desperate Kantian move'. |
| 602 | Some fools think you cannot define anything, but only say what it is like [Antisthenes (I), by Aristotle] |
| Full Idea: There is an application of that old chestnut of the cynic Antisthenes' followers (and other buffoons of that kind). Their claim was that a definition of what something is is impossible. You cannot define silver, though you can say it is like tin. | |
| From: report of Antisthenes (Ath) (fragments/reports [c.405 BCE]) by Aristotle - Metaphysics 1043b |