6 ideas
| 9548 | A mathematical object exists if there is no contradiction in its definition [Waterfield] |
| Full Idea: A mathematical object exists provided there is no contradiction implied in its definition. | |
| From: Robin Waterfield (Introduction to 'Hippias Minor' [1987], p.44), quoted by Charles Chihara - A Structural Account of Mathematics 1.4 | |
| A reaction: A rather bizarre criterion for existence. Not one, for example, that you would consider applying to the existence of physical objects! But then Poincaré is the father of 'conventionalism', rather than being a platonist. |
| 12167 | Reference without predication is the characteristic of expression [Scruton] |
| Full Idea: Characteristic of expression is the presence of 'reference' without predication. | |
| From: Roger Scruton (Representation in Music [1976], p.71) | |
| A reaction: This echoes (in linguistic terms) Kant's thought that art is 'purposive without purpose'. The remark is comfortable in an essay on music, but it gets more tricky when the topic is literature, or even representational painting. |
| 12166 | If music refers to love, it contains no predication, so it is expression, not language [Scruton] |
| Full Idea: If a passage carries a reference to love, we are not told what it says about love. And to speak of language with 'reference' but no predication is simply to misuse the word. We leave the realm of representation and enter that of expression. | |
| From: Roger Scruton (Representation in Music [1976], p.63-4) | |
| A reaction: This is a beautifully simple objection to the idea (associated with Nelson Goodman) that art is a language. Though what an 'expression' of something amounts to I am not quite sure. |
| 12168 | Music is not representational, since thoughts about a subject are never essential to it [Scruton] |
| Full Idea: Music is not representational, since thoughts about a subject are never essential to the understanding of music. | |
| From: Roger Scruton (Representation in Music [1976], p.74) | |
| A reaction: I would not have thought that many people thought music was representational, but Scruton particularly mentions passages in opera that seem to pick up aspects of the story. Do even bell sounds not represent bells? |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |