15 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. |
| 16705 | Whiteness isn't created in an alteration, because it is just this-being-white [Oresme] |
| Full Idea: If it is said that whiteness begins to be through alteration, this does not hold, because whiteness is nothing other than this-being-white. | |
| From: Nicole Oresme (On 'Generation and Corruption' [1349], I.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 19.3 | |
| A reaction: This innocent-looking remark is dynamite, because it rejects the separability of qualities, which threatens the doctrine of Transubstantiation. |
| 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. |
| 23061 | Free atheism should start by questioning its faith in humanity [Gray] |
| Full Idea: A free-thinking atheism would begin by questioning the prevailing faith in humanity. But there is little prospect of contemporary atheists giving up their reverence for this phantom. | |
| From: John Gray (Seven Types of Atheism [2018], Conc) | |
| A reaction: He seems to be referring to 'humanism', which I take to be quite different from atheism. I take it as obvious that simple atheism is entirely neutral on the question of whether we should have 'faith' in humanity (which presumably mean optimism). |
| 23057 | Gnosticism has a supreme creator God, giving way to a possibly hostile Demiurge [Gray] |
| Full Idea: Gnostic traditions envisage a supreme God that created the universe and then withdrew into itself, leaving the world to be ruled by a lesser god, or Demiurge, which might be indifferent or hostile to mankind. | |
| From: John Gray (Seven Types of Atheism [2018], Intro) | |
| A reaction: It doesn't seem to solve any problems, given that the first God is 'supreme', and is therefore responsible for the introduction and actions of the later Demiurge. |
| 23056 | Judaism only became monotheistic around 550 BCE [Gray] |
| Full Idea: It was only sometime around the sixth century BC, during the period when the Israelites returned to Jerusalem, that the idea that there is only one God emerged in Jewish religion. | |
| From: John Gray (Seven Types of Atheism [2018], Intro) | |
| A reaction: There seems to be a parallel move among the Greeks to elevate Zeus to special status. |
| 23055 | Christians introduced the idea that a religion needs a creed [Gray] |
| Full Idea: The notion that religions are creeds - lists of propositions or doctrines that everyone must accept or reject - emerged only with Christianity. | |
| From: John Gray (Seven Types of Atheism [2018], Intro) | |
| A reaction: With a creed comes the possibility of heresy. I''m not happy with children being taught to recite something which begins 'I believe…', but which they have never thought about and barely understand. |
| 23058 | Buddhism has no divinity or souls, and the aim is to lose the illusion of a self [Gray] |
| Full Idea: Buddhism says nothing of any divine mind and rejects any idea of the soul. The world consists of processes and events. The human sense of self is an illusion; freedom is found in ridding oneself of this illusion. | |
| From: John Gray (Seven Types of Atheism [2018], Intro) | |
| A reaction: I'm not clear why shaking off the illusion of a self is a superior state. Freedom to do what? Presumably nothing at all, since there is no self to desire anything. |