3 ideas
| 9220 | Lewis must specify that all possibilities are in his worlds, making the whole thing circular [Shalkowski, by Sider] |
| Full Idea: If purple cows are simply absent from Lewis's multiverse, then certain correct propositions turn out to be impossible. Lewis must require a world for every possibility. But then it is circular, as the multiverse needs modal notions to characterize it. | |
| From: report of Scott Shalkowski (Ontological Ground of Alethic Modality [1994], 3.9) by Theodore Sider - Reductive Theories of Modality 3.9 | |
| A reaction: [Inversely, a world containing a round square would make that possible] This sounds very nice, though Sider rejects it (p.197). I've never seen how you could define possibility using the concept of 'possible' worlds. |
| 9145 | We form the image of a cardinal number by a double abstraction, from the elements and from their order [Cantor] |
| Full Idea: We call 'cardinal number' the general concept which, by means of our active faculty of thought, arises when we make abstraction from an aggregate of its various elements, and of their order. From this double abstraction the number is an image in our mind. | |
| From: George Cantor (Beitrage [1915], §1), quoted by Kit Fine - Cantorian Abstraction: Recon. and Defence Intro | |
| A reaction: [compressed] This is the great Cantor, creator of set theory, endorsing the traditional abstractionism which Frege and his followers so despise. Fine offers a defence of it. The Frege view is platonist, because it refuses to connect numbers to the world. |
| 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. |