display all the ideas for this combination of philosophers
16 ideas
| 10804 | Thoughts have a natural order, to which human thinking is drawn [Frege, by Yablo] |
| Full Idea: Burge has argued that Frege's rationalism runs very deep. Frege holds that there is a natural order of thoughts to which human thinking is naturally drawn. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Stephen Yablo - Carving Content at the Joints § 8 | |
| A reaction: [Yablo cites Burge 1984,1992,1998] What an intriguing idea. I always start from empiricist beginnings, but some aspects of rationalism just sieze you by the throat. |
| 9832 | Frege sees no 'intersubjective' category, between objective and subjective [Dummett on Frege] |
| Full Idea: Frege left no place for a category of the intersubjective, intermediate between the wholly objective and the radically subjective. | |
| From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.7 | |
| A reaction: Interesting. More sophisticated accounts of language (with the Private Language Argument as background) hold out possibilities of objectivity arising from an articulate community. See Idea 95. |
| 8414 | Keep the psychological and subjective separate from the logical and objective [Frege] |
| Full Idea: Always separate sharply the psychological from the logical, the subjective from the objective. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], Intro p.x) | |
| A reaction: This (with Ideas 7732 and 8415) is said to be the foundation of modern analytical philosophy. It contrasts with Husserl's 'Logical Investigations', which are the foundations of phenomenology. I think it is time someone challenged Frege here. |
| 7740 | There exists a realm, beyond objects and ideas, of non-spatio-temporal thoughts [Frege, by Weiner] |
| Full Idea: There is, in addition to the external world of physical objects and the internal world of ideas, a third realm of non-spatio-temporal objective objects, among which are thoughts. | |
| From: report of Gottlob Frege (The Thought: a Logical Enquiry [1918]) by Joan Weiner - Frege Ch.7 | |
| A reaction: This seems to be Platonism, and, in particular, to give a Platonic existent status to propositions. Personally I believe in propositions, but as glimpses of how our brains actually work, not as mystical objects. |
| 8939 | We should not describe human laws of thought, but how to correctly track truth [Frege, by Fisher] |
| Full Idea: Frege disagree that logic should merely describe the laws of thought - how people actually did reason. Logic is essentially normative, not descriptive. We want the one logic which successfully tracks the truth. | |
| From: report of Gottlob Frege (Begriffsschrift [1879]) by Jennifer Fisher - On the Philosophy of Logic 1.III | |
| A reaction: This explains Frege's sustained attack on psychologism, and it also explains we he ended up as a platonist about logic - because he wanted its laws to be valid independently of human thinking. A step too far, perhaps. Brains are truth machines. |
| 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'. |
| 17495 | Proof aims to remove doubts, but also to show the interdependence of truths [Frege] |
| Full Idea: Proof has as its goal not only to raise the truth of a proposition above all doubts, but additionally to provide insight into the interdependence of truths. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §02) | |
| A reaction: This is a major idea in Frege's thinking, and a reason why he is the father of modern metaphysics as well as the father of modern logic. You study the framework of truths by studying the logic that connects them. |
| 16878 | We must be clear about every premise and every law used in a proof [Frege] |
| Full Idea: It is so important, if we are to have a clear insight into what is going on, for us to be able to recognise the premises of every inference which occurs in a proof and the law of inference in accordance with which it takes place. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.212) | |
| A reaction: Teachers of logic like natural deduction, because it reduces everything to a few clear laws, which can be stated at each step. |
| 8632 | You can't transfer external properties unchanged to apply to ideas [Frege] |
| Full Idea: It would be remarkable if a property abstracted from external things could be transferred without any change of sense to events, to ideas and to concepts, like speaking of 'blue ideas' or 'salty concepts'. | |
| From: Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §24) | |
| A reaction: Since those phrases make perfectly good metaphorical sense, I presume the Frege was a fairly literal sort of chap. Is this the earliest emergence of the idea of a category mistake? |