7 ideas
| 17423 | The essence of natural numbers must reflect all the functions they perform [Sicha] |
| Full Idea: What is really essential to being a natural number is what is common to the natural numbers in all the functions they perform. | |
| From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 2) | |
| A reaction: I could try using natural numbers as insults. 'You despicable seven!' 'How dare you!' I actually agree. The question about functions is always 'what is it about this thing that enables it to perform this function'. |
| 17425 | To know how many, you need a numerical quantifier, as well as equinumerosity [Sicha] |
| Full Idea: A knowledge of 'how many' cannot be inferred from the equinumerosity of two collections; a numerical quantifier statement is needed. | |
| From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 3) |
| 17424 | Counting puts an initial segment of a serial ordering 1-1 with some other entities [Sicha] |
| Full Idea: Counting is the activity of putting an initial segment of a serially ordered string in 1-1 correspondence with some other collection of entities. | |
| From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 2) |
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points. | |
| From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13 | |
| A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry. |
| 7276 | All art is quite useless [Wilde] |
| Full Idea: All art is quite useless. | |
| From: Oscar Wilde (Preface to 'Dorian Gray' [1891]) | |
| A reaction: Echoes Kant's thought that art is 'purposive without purpose'. Although I find Wilde's claims that morality has nothing to do with art to be naïve, I find this remark sympathetic. Art may play with moral feelings, but is unlikely to affect actions. |
| 7274 | Books are only well or badly written, not moral or immoral [Wilde] |
| Full Idea: There is no such thing as a moral or an immoral book. Books are well written, or badly written. That is all. | |
| From: Oscar Wilde (Preface to 'Dorian Gray' [1891]) | |
| A reaction: This is simply false. Novels that are viciously (or subtly) racist, sexist, homophobic, or egotistical can obviously be immoral. I could write a nasty story about Oscar Wilde. It might, though, be very well written. If life is moral, so are novels. |
| 7275 | Having ethical sympathies is a bad mannerism of style in an artist [Wilde] |
| Full Idea: No artist has ethical sympathies. An ethical sympathy in an artist is an unpardonable mannerism of style. | |
| From: Oscar Wilde (Preface to 'Dorian Gray' [1891]) | |
| A reaction: This has a Nietzschean suggestion that the artist is 'beyond good and evil', and operates on some higher level of values, which in Wilde's case seem to be purely aesthetic. You can't justify a callous murder by executing it beautifully. |