6 ideas
| 17809 | Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel] |
| Full Idea: Usually Gödel's incompleteness theorems are taken as showing a limitation on the syntactic approach to an understanding of the concept of infinity. | |
| From: Georg Kreisel (Hilbert's Programme [1958], 05) |
| 17810 | The study of mathematical foundations needs new non-mathematical concepts [Kreisel] |
| Full Idea: It is necessary to use non-mathematical concepts, i.e. concepts lacking the precision which permit mathematical manipulation, for a significant approach to foundations. We currently have no concepts of this kind which we can take seriously. | |
| From: Georg Kreisel (Hilbert's Programme [1958], 06) | |
| A reaction: Music to the ears of any philosopher of mathematics, because it means they are not yet out of a job. |
| 16597 | Quantity is the capacity to be divided [Digby] |
| Full Idea: Quantity …is divisibility, or a capacity to be divided into parts. | |
| From: Kenelm Digby (Two treatises [1644], I.2.8), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 04.1 | |
| A reaction: 'Quantity' is scholastic philosophy is a concept we no longer possess. Without quantity, a thing might potentially exist at a spaceless point. Quantity is what spreads things out. See Pasnau Ch. 4. |
| 16731 | Colours arise from the rarity, density and mixture of matter [Digby] |
| Full Idea: The origin of all colours in bodies is plainly deduced out of the various degrees of rarity and density, variously mixed and compounded. | |
| From: Kenelm Digby (Two treatises [1644], I.29.4), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 22.5 | |
| A reaction: We are still struggling with this question, though I think the picture is gradually become clear, once you get the hang of the brain. Easy! See Idea 17396. |
| 17811 | The natural conception of points ducks the problem of naming or constructing each point [Kreisel] |
| Full Idea: In analysis, the most natural conception of a point ignores the matter of naming the point, i.e. how the real number is represented or by what constructions the point is reached from given points. | |
| From: Georg Kreisel (Hilbert's Programme [1958], 13) | |
| A reaction: This problem has bothered me. There are formal ways of constructing real numbers, but they don't seem to result in a name for each one. |
| 3029 | Stilpo said if Athena is a daughter of Zeus, then a statue is only the child of a sculptor, and so is not a god [Stilpo, by Diog. Laertius] |
| Full Idea: Stilpo asked a man whether Athena is the daughter of Zeus, and when he said yes, said,"But this statue of Athena by Phidias is the child of Phidias, so it is not a god." | |
| From: report of Stilpo (fragments/reports [c.330 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.10.5 |