3 ideas
| 9138 | An infinite series of sentences asserting falsehood produces the paradox without self-reference [Yablo, by Sorensen] |
| Full Idea: Banning self-reference is too narrow to avoid the liar paradox. With 1) all the subsequent sentences are false, 2) all the subsequent sentences are false, 3) all the subsequent... the paradox still arises. Self-reference is a special case of this. | |
| From: report of Stephen Yablo (Paradox without Self-Reference [1993]) by Roy Sorensen - Vagueness and Contradiction 11.1 | |
| A reaction: [Idea 9137 pointed out that the ban was too narrow. Sorensen p.168 explains why this one is paradoxical] This is a nice example of progress in philosophy, since the Greeks would have been thrilled with this idea (unless they knew it, but it was lost). |
| 8628 | I hold that algebra and number are developments of logic [Jevons] |
| Full Idea: I hold that algebra is a highly developed logic, and number but logical discrimination. | |
| From: William S. Jevons (The Principles of Science [1879], p.156), quoted by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §15 | |
| A reaction: Thus Frege shows that logicism was an idea that was in the air before he started writing. Riemann's geometry and Boole's logic presumably had some influence here. |
| 8113 | Art is like understanding a natural language, and needs a grasp of a symbol system [Goodman, by Gardner] |
| Full Idea: In Goodman's account, knowing what a painting represents is logically like understanding a sentence in a natural language. It requires a grasp of the 'symbol system' to which the painting belongs. | |
| From: report of Nelson Goodman (The Languages of Art [1976]) by Sebastian Gardner - Aesthetics 2.3.2 | |
| A reaction: This may fit some pictures well (e.g. early Flemish painting, with its complex iconography), but others hardly at all. You can enjoy a first experience of (say) ballet long before you get the hang of the 'symbol system' involved. |