4 ideas
| 15585 | Later Heidegger sees philosophy as more like poetry than like science [Heidegger, by Polt] |
| Full Idea: In his later work Heidegger came to view philosophy as closer to poetry than to science. | |
| From: report of Martin Heidegger (The Origin of the Work of Art [1935], p.178) by Richard Polt - Heidegger: an introduction 5 'Signs' |
| 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. |
| 21570 | Numbers are just verbal conveniences, which can be analysed away [Russell] |
| Full Idea: Numbers are nothing but a verbal convenience, and disappear when the propositions that seem to contain them are fully written out. | |
| From: Bertrand Russell (Is Mathematics purely Linguistic? [1952], p.301) | |
| A reaction: This is the culmination of the process which began with his 1905 theory of definite descriptions. The intervening step was Wittgenstein's purely formal account of the logical connectives. |