7 ideas
| 18200 | Very large sets should be studied in an 'if-then' spirit [Putnam] |
| Full Idea: Sets of a very high type or very high cardinality (higher than the continuum, for example), should today be investigated in an 'if-then' spirit. | |
| From: Hilary Putnam (The Philosophy of Logic [1971], p.347), quoted by Penelope Maddy - Naturalism in Mathematics | |
| A reaction: Quine says the large sets should be regarded as 'uninterpreted'. |
| 18199 | Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam] |
| Full Idea: We may say that indispensability is a pretty strong argument for the existence of at least predicative sets, and a pretty strong, but not as strong, argument for the existence of impredicative sets. | |
| From: Hilary Putnam (The Philosophy of Logic [1971], p.346), quoted by Penelope Maddy - Naturalism in Mathematics II.2 |
| 8857 | We must quantify over numbers for science; but that commits us to their existence [Putnam] |
| Full Idea: Quantification over mathematical entities is indispensable for science..., therefore we should accept such quantification; but this commits us to accepting the existence of the mathematical entities in question. | |
| From: Hilary Putnam (The Philosophy of Logic [1971], p.57), quoted by Stephen Yablo - Apriority and Existence | |
| A reaction: I'm not surprised that Hartry Field launched his Fictionalist view of mathematics in response to such a counterintuitive claim. I take it we use numbers to slice up reality the way we use latitude to slice up the globe. No commitment to lines! |
| 1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
| Full Idea: I regard you all as relatives - by nature, not by convention. By nature like is akin to like, but convention is a tyrant over humankind and often constrains people to act contrary to nature. | |
| From: Hippias (fragments/reports [c.430 BCE]), quoted by Plato - Protagoras 337c8 |
| 2427 | Maybe understanding doesn't need consciousness, despite what Searle seems to think [Searle, by Chalmers] |
| Full Idea: Searle originally directed the Chinese Room against machine intentionality rather than consciousness, arguing that it is "understanding" that the room lacks,….but on Searle's view intentionality requires consciousness. | |
| From: report of John Searle (Minds, Brains and Science [1984]) by David J.Chalmers - The Conscious Mind 4.9.4 | |
| A reaction: I doubt whether 'understanding' is a sufficiently clear and distinct concept to support Searle's claim. Understanding comes in degrees, and we often think and act with minimal understanding. |
| 7389 | A program won't contain understanding if it is small enough to imagine [Dennett on Searle] |
| Full Idea: There is nothing remotely like genuine understanding in any hunk of programming small enough to imagine readily. | |
| From: comment on John Searle (Minds, Brains and Science [1984]) by Daniel C. Dennett - Consciousness Explained 14.1 | |
| A reaction: We mustn't hide behind 'complexity', but I think Dennett is right. It is important to think of speed as well as complexity. Searle gives the impression that he knows exactly what 'understanding' is, but I doubt if anyone else does. |
| 7390 | If bigger and bigger brain parts can't understand, how can a whole brain? [Dennett on Searle] |
| Full Idea: The argument that begins "this little bit of brain activity doesn't understand Chinese, and neither does this bigger bit..." is headed for the unwanted conclusion that even the activity of the whole brain won't account for understanding Chinese. | |
| From: comment on John Searle (Minds, Brains and Science [1984]) by Daniel C. Dennett - Consciousness Explained 14.1 | |
| A reaction: In other words, Searle is guilty of a fallacy of composition (in negative form - parts don't have it, so whole can't have it). Dennett is right. The whole shebang of the full brain will obviously do wonderful (and commonplace) things brain bits can't. |