5 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. |
| 14289 | There are some assertable conditionals one would reject if one learned the antecedent [Jackson, by Edgington] |
| Full Idea: Jackson came to realise that there are assertable conditionals which one would not continue to believe if one learned the antecedent, such as Lewis's "If Reagan worked for the KGB, I'll never find out". | |
| From: report of Frank Jackson (Conditionals [1987]) by Dorothy Edgington - Conditionals (Stanf) 4.2 | |
| A reaction: That pesky David Lewis made trouble for everybody. Edgington agrees that his earlier formulation (Idea 14288) holds good for nearly all cases. There is a self-referential element in Lewis's example. |
| 12156 | Aesthetics has risen and fallen with Romanticism [Scruton] |
| Full Idea: The rise and fall (as we presently perceive them) of aesthetics have been contemporaneous with the rise and fall of Romanticism. | |
| From: Roger Scruton (Recent Aesthetics in England and America [1980], p.3) | |
| A reaction: Maybe it started a little before Romanticism, as part of the Englightenment aim of being rational about everything, and maybe it survives Romanticism because we want to be scientific about everything. |
| 12158 | Aesthetic experience informs the world with the values of the observer [Scruton] |
| Full Idea: It is possible to conclude that aesthetic experience has a peculiar practical significance: it represents the world as informed by the values of the observer. | |
| From: Roger Scruton (Recent Aesthetics in England and America [1980], p.13) | |
| A reaction: An excellent remark. If you look at, or listen to, anything, you can make a conscious effort to drain away your personal values (objectivity; science?), or you can consciously flood them with values. But moral and aesthetic vision must differ... |