19 ideas
| 4424 | A warlike philosopher challenges problems to single combat [Nietzsche] |
| Full Idea: A warlike philosopher challenges problems to single combat. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], Wise §7) | |
| A reaction: And what do pacifist philosophers do? It is a moot point whether philosophy is even possible without a streak of aggression. Otherwise you circle the problem, but don't confront it. |
| 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. |
| 16616 | Substances 'substand' (beneath accidents), or 'subsist' (independently) [Eustachius] |
| Full Idea: It is proper to substance both to stretch out or exist beneath accidents, which is to substand, and to exist per se and not in another, which is to subsist. | |
| From: Eustachius a Sancto Paulo (Summa [1609], I.1.3b.1.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 06.2 | |
| A reaction: This reflects Aristotle wavering between 'ousia' being the whole of a thing, or the substrate of a thing. In current discussion, 'substance' still wavers between a thing which 'is' a substance, and substance being the essence. |
| 16585 | Prime matter is free of all forms, but has the potential for all forms [Eustachius] |
| Full Idea: Everyone says that prime matter, considered in itself, is free of all forms and at the same time is open to all forms - or, that matter is in potentiality to all forms. | |
| From: Eustachius a Sancto Paulo (Summa [1609], III.1.1.2.3), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 03.1 | |
| A reaction: This is the notorious doctrine developed to support the hylomorphic picture derived from Aristotle. No one could quite figure out what prime matter was, so it faded away. |
| 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. |
| 2886 | The distinction between egoistic and non-egoistic acts is absurd [Nietzsche] |
| Full Idea: There are neither egoistic nor unegoistic actions: both concepts are psychologically nonsense. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], 4.5) | |
| A reaction: Not quite true, but I like this observation. The idea that you could divide everyone's actions into these two groups is certainly nonsense. But some people are more altruistic than others! |
| 4426 | A bad result distorts one's judgement about the virtue of what one has done [Nietzsche] |
| Full Idea: I should prefer to exclude the bad result, the consequences, from the question of value as a matter of principle. Faced with a bad result, one loses all too easily the right perspective for what one has done. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], Clever §1) | |
| A reaction: If the perspective is easily lost, we should make more effort, not ignore consequences. The question is whether you could have foreseen or controlled the consequences. |
| 4425 | The overcoming of pity I count among the noble virtues [Nietzsche] |
| Full Idea: The overcoming of pity I count among the noble virtues. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], Wise §4) | |
| A reaction: Hm. I can just about see that there might be more important things than compassion for suffering, but I can't see any human activity that makes it worthwhile to trample on pity. |
| 20132 | To become what you are you must have no self-awareness [Nietzsche] |
| Full Idea: To become what one is, one must not have the faintest notion of what one is. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], II.9), quoted by Brian Leiter - Nietzsche On Morality 3 'fatalism' | |
| A reaction: [Don't understand 'II.9'] Enigmatic but striking. As I understand it, Nietzsche thought that knowing what you are is virtually impossible, though he spent a lifetime studying himself. Would you recognise someone who had become what they are? |
| 20144 | Eternal recurrence is the highest attainable affirmation [Nietzsche] |
| Full Idea: Eternal recurrence is the highest formula of affirmation that is at all attainable. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], III.Z-1?), quoted by Brian Leiter - Nietzsche On Morality | |
| A reaction: Did Nietzsche have in mind an even higher formulation that was unattainable? The aim of eternal recurrence is to offer the highest possible ideal that remains rooted in the nature of ordinary life. It is a cut-down version of the Form of the Good. |
| 2889 | One repays a teacher badly if one remains only a pupil [Nietzsche] |
| Full Idea: One repays a teacher badly if one remains only a pupil. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], Fore) |
| 2887 | I am not an atheist because of reasoning or evidence, but because of instinct [Nietzsche] |
| Full Idea: I have absolutely no knowledge of atheism as an outcome of reasoning, still less an event: with me it is obvious by instinct. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], 3.1) |