8 ideas
| 17879 | Axiomatising set theory makes it all relative [Skolem] |
| Full Idea: Axiomatising set theory leads to a relativity of set-theoretic notions, and this relativity is inseparably bound up with every thoroughgoing axiomatisation. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.296) |
| 17878 | If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem] |
| Full Idea: Löwenheim's theorem reads as follows: If a first-order proposition is satisfied in any domain at all, it is already satisfied in a denumerably infinite domain. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.293) |
| 17880 | Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem] |
| Full Idea: The initial foundations should be immediately clear, natural and not open to question. This is satisfied by the notion of integer and by inductive inference, by it is not satisfied by the axioms of Zermelo, or anything else of that kind. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.299) | |
| A reaction: This is a plea (endorsed by Almog) that the integers themselves should be taken as primitive and foundational. I would say that the idea of successor is more primitive than the integers. |
| 17881 | Mathematician want performable operations, not propositions about objects [Skolem] |
| Full Idea: Most mathematicians want mathematics to deal, ultimately, with performable computing operations, and not to consist of formal propositions about objects called this or that. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.300) |
| 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. |