5 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). |
| 3979 | The Turing Machine is the best idea yet about how the mind works [Fodor on Turing] |
| Full Idea: Alan Turing had (in his theory of the 'Turing Machine') what I suppose is the best thought about how the mind works that anyone has had so far. | |
| From: comment on Alan Turing (Computing Machinery and Intelligence [1950]) by Jerry A. Fodor - Jerry A. Fodor on himself p.296 | |
| A reaction: I am not convinced, because I don't think rationality is possible without consciousness. The brain may bypass the representations used by a computer. |
| 5321 | In 50 years computers will successfully imitate humans with a 70% success rate [Turing] |
| Full Idea: In about fifty years' time it will be possible to program computers to play the imitation game so well that an average interrogator will not have more than 70% chance of making the right identification after five minutes of questioning. | |
| From: Alan Turing (Computing Machinery and Intelligence [1950], p.57), quoted by Robert Kirk - Mind and Body §5.9 | |
| A reaction: This is the famous prophecy called 'The Turing Test'. The current state (2004) seems to be that the figure of 70% is very near, but no one sees much prospect of advancing much further in the next 100 years. Dennett sees jokes as a big problem. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |