4 ideas
| 18256 | Quantity is inconceivable without the idea of addition [Frege] |
| Full Idea: There is so intimate a connection between the concepts of addition and of quantity that one cannot begin to grasp the latter without the former. | |
| From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], p.2), quoted by Michael Dummett - Frege philosophy of mathematics 22 'Quantit' | |
| A reaction: Frege offers good reasons for making cardinals prior to ordinals, though plenty of people disagree. |
| 9831 | Geometry appeals to intuition as the source of its axioms [Frege] |
| Full Idea: The elements of all geometrical constructions are intuitions, and geometry appeals to intuition as the source of its axioms. | |
| From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], Ch.6), quoted by Michael Dummett - Frege philosophy of mathematics | |
| A reaction: Very early Frege, but he stuck to this view, while firmly rejecting intuition as a source of arithmetic. Frege would have known well that Euclid's assumption about parallels had been challenged. |
| 7439 | The qualities involved in sensations are entirely intentional [Anscombe, by Armstrong] |
| Full Idea: Anscombe argued that the qualities involved in sensations are one and all intentional only (and I think this holds even for the bodily sensations). | |
| From: report of G.E.M. Anscombe (The Intentionality of Sensation [1965]) by David M. Armstrong - Pref to new 'Materialist Theory' p.xxii | |
| A reaction: Compare Harry Gildersleve's exactly opposite proposal in Idea 7272. I think I am coming round to the Anscombe view, which builds the more mysterious up from the less mysterious. Gildersleve must explain how atomic qualia arise. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |