8 ideas
| 18189 | ZFC could contain a contradiction, and it can never prove its own consistency [MacLane] |
| Full Idea: We have at hand no proof that the axioms of ZFC for set theory will never yield a contradiction, while Gödel's second theorem tells us that such a consistency proof cannot be conducted within ZFC. | |
| From: Saunders MacLane (Mathematics: Form and Function [1986], p.406), quoted by Penelope Maddy - Naturalism in Mathematics | |
| A reaction: Maddy quotes this, while defending set theory as the foundation of mathematics, but it clearly isn't the most secure foundation that could be devised. She says the benefits of set theory do not need guaranteed consistency (p.30). |
| 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. |
| 2986 | Belief is the most important propositional attitude [Lyons] |
| Full Idea: Belief might be accorded the status of core or chief propositional attitude. | |
| From: William Lyons (Approaches to Intentionality [1995], p.126) |
| 2978 | Consciousness no longer seems essential to intentionality [Lyons] |
| Full Idea: In contrast with Brentano and Husserl, consciousness or attention are no longer seen as essential to intentionality. | |
| From: William Lyons (Approaches to Intentionality [1995], Intro) | |
| A reaction: This strikes me as being correct, although there seem to be plenty of current philosophers who do not accept it (e.g. Searle). I think philosophy of mind may be stuck in the dark ages if thinkers don't accept this proposal. |
| 2984 | Perceptions could give us information without symbolic representation [Lyons] |
| Full Idea: It is possible to give an account of concept-formation without a language of thought or representation, based on perception, which in the brain seems to involve information without representation. | |
| From: William Lyons (Approaches to Intentionality [1995], p.66) | |
| A reaction: This claim strikes me as being a little too confident. One might say that a concept IS a representation. However, the perception of several horses might 'blur' together to form a generalised horse. |
| 2979 | Propositional attitudes require representation [Lyons] |
| Full Idea: How else, other than via some form of representational system, could a human organism contain information as a content over which it could operate or 'attitudinise'? | |
| From: William Lyons (Approaches to Intentionality [1995], Intro) | |
| A reaction: Depends what you mean by 'representational'. In its vaguest sense, this is just a tautology - content must be held in the mind in some form or other, but that tells us nothing. |
| 2987 | Folk psychology works badly for alien cultures [Lyons] |
| Full Idea: It is not easy to employ our folk psychology in the understanding of persons in a very different culture. | |
| From: William Lyons (Approaches to Intentionality [1995], p.241) | |
| A reaction: This strikes me as a highly significant problem for the friends of folk psychology. It also breaks down in extreme situations, or with mental illness. It seems closer to culture than to brain structure. |
| 2977 | All thinking has content [Lyons] |
| Full Idea: I cannot say I am simply thinking but not thinking about anything. | |
| From: William Lyons (Approaches to Intentionality [1995], Intro) | |
| A reaction: Hard to disagree. However, I can plausibly reply to 'What are you thinking?' with 'Nothing', if my consciousness is freewheeling. Utterly disconnected content isn't really what we call 'thinking'. |