13 ideas
13733 | Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn] |
Full Idea: Frege (1893) considered a definite description to be a genuine singular term (as we do), so that a sentence like 'The present King of France is bald' would have the same logical form as 'Harry Truman is bald'. | |
From: report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by M Fitting/R Mendelsohn - First-Order Modal Logic | |
A reaction: The difficulty is what the term refers to, and they embrace a degree of Meinongianism - that is that non-existent objects can still have properties attributed to them, and so can be allowed some sort of 'existence'. |
9874 | Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege] |
Full Idea: The contradiction in Frege's system is due to the presence of second-order quantification, ..and Frege's explanation of the second-order quantifier, unlike that which he provides for the first-order one, appears to be substitutional rather than objectual. | |
From: comment on Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], §25) by Michael Dummett - Frege philosophy of mathematics Ch.17 | |
A reaction: In Idea 9871 Dummett adds the further point that Frege lacks a clear notion of the domain of quantification. At this stage I don't fully understand this idea, but it is clearly of significance, so I will return to it. |
18252 | Real numbers are ratios of quantities, such as lengths or masses [Frege] |
Full Idea: If 'number' is the referent of a numerical symbol, a real number is the same as a ratio of quantities. ...A length can have to another length the same ratio as a mass to another mass. | |
From: Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], III.1.73), quoted by Michael Dummett - Frege philosophy of mathematics 21 'Frege's' | |
A reaction: This is part of a critique of Cantor and the Cauchy series approach. Interesting that Frege, who is in the platonist camp, is keen to connect the real numbers with natural phenomena. He is always keen to keep touch with the application of mathematics. |
18271 | We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege] |
Full Idea: It cannot be demanded that everything be proved, because that is impossible; but we can require that all propositions used without proof be expressly declared as such, so that we can see distinctly what the whole structure rests upon. | |
From: Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], p.2), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 7 'What' |
10623 | Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright] |
Full Idea: Frege opts for his famous definition of numbers in terms of extensions of the concept 'equal to the concept F', but he then (in 'Grundgesetze') needs a theory of extensions or classes, which he provided by means of Basic Law V. | |
From: report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by B Hale / C Wright - Intro to 'The Reason's Proper Study' §1 |
9975 | Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege] |
Full Idea: Cantor pointed out explicitly to Frege that it is a mistake to take the notion of a set (i.e. of that which has a cardinal number) to simply mean the extension of a concept. ...Frege's later assumption of this was an act of recklessness. | |
From: comment on Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by William W. Tait - Frege versus Cantor and Dedekind III | |
A reaction: ['recklessness' is on p.61] Tait has no sympathy with the image of Frege as an intellectual martyr. Frege had insufficient respect for a great genius. Cantor, crucially, understood infinity much better than Frege. |
18165 | My Basic Law V is a law of pure logic [Frege] |
Full Idea: I hold that my Basic Law V is a law of pure logic. | |
From: Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], p.4), quoted by Penelope Maddy - Naturalism in Mathematics I.1 | |
A reaction: This is, of course, the notorious law which fell foul of Russell's Paradox. It is said to be pure logic, even though it refers to things that are F and things that are G. |
12742 | A whole is just its parts, but there are no smallest parts, so only minds and perceptions exist [Leibniz] |
Full Idea: The whole, if it is assumed to be body or matter, is nothing other than all of its parts; but this is absurd, since there aren't any smallest parts. Therefore there really exist only minds and their perceptions. | |
From: Gottfried Leibniz (Calculus Ratiocinator [1679], A6.4.279), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 7 | |
A reaction: Leibniz is sometimes labelled as an 'idealist', but this text is unusual in being so explicit, and he was mainly concerned to explain the reality of individual bodies. Monads were his final attempt to do this, not an attempt to escape into pure minds. |
9190 | A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett] |
Full Idea: In later Frege, a concept could be taken as a particular case of a function, mapping every object on to one of the truth-values (T or F), according as to whether, as we should ordinarily say, that object fell under the concept or not. | |
From: report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by Michael Dummett - The Philosophy of Mathematics 3.5 | |
A reaction: As so often in these attempts at explanation, this sounds circular. You can't decide whether an object truly falls under a concept, if you haven't already got the concept. His troubles all arise (I say) because he scorns abstractionist accounts. |
13665 | Frege took the study of concepts to be part of logic [Frege, by Shapiro] |
Full Idea: Frege took the study of concepts and their extensions to be within logic. | |
From: report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by Stewart Shapiro - Foundations without Foundationalism 7.1 | |
A reaction: This is part of the plan to make logic a universal language (see Idea 13664). I disagree with this, and with the general logicist view of the position of logic. The logical approach thins concepts out. See Deleuze/Guattari's horror at this. |
23104 | Dworkin believed we should promote equality, to increase autonomy [Dworkin, by Kekes] |
Full Idea: Egalitarians believe that most often it is by promoting equality that autonomy is increased; this is the egalitarianism of such liberals as Ronald Dworkin. | |
From: report of Ronald Dworkin (Taking Rights Seriously [1977]) by John Kekes - Against Liberalism 05.1 | |
A reaction: Not my idea of equality. The whole point is to ascribe reasonable equality to everyone, including those with a limited capacity for autonomy. Equality is a consequence of universal respect. |
23257 | We can treat people as equals, or actually treat them equally [Dworkin, by Grayling] |
Full Idea: Dworkin distinguishes between treating people as equals, that is, 'with equal concern and respect', and treating them equally. This latter can be unjust. | |
From: report of Ronald Dworkin (Taking Rights Seriously [1977]) by A.C. Grayling - The Good State 2 | |
A reaction: The big difference I see between them is that the first is mere words, and the second is actions. Cf. 'thoughts and prayers' after US school shootings. How about equal entitlements, all things being equal? |
18621 | Treating people as equals is the one basic value of all plausible political theories [Dworkin, by Kymlicka] |
Full Idea: Dworkin suggests that every plausible political theory has the same ultimate value, which is equality - in the more abstract and fundamental sense of treating people 'as equals'. | |
From: report of Ronald Dworkin (Taking Rights Seriously [1977], 179-83) by Will Kymlicka - Contemporary Political Philosophy (1st edn) | |
A reaction: I associate this idea with Kant (who says they are equal by virtue of their rationality), so that's a pretty influential idea. I would associate the main challenge to this with Nietzsche. |