6 ideas
| 21554 | Sets always exceed terms, so all the sets must exceed all the sets [Lackey] |
| Full Idea: Cantor proved that the number of sets in a collection of terms is larger than the number of terms. Hence Cantor's Paradox says the number of sets in the collection of all sets must be larger than the number of sets in the collection of all sets. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: The sets must count as terms in the next iteration, but that is a normal application of the Power Set axiom. |
| 21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
| Full Idea: The ordinal series is well-ordered and thus has an ordinal number, and a series of ordinals to a given ordinal exceeds that ordinal by 1. So the series of all ordinals has an ordinal number that exceeds its own ordinal number by 1. | |
| From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127) | |
| A reaction: Formulated by Burali-Forti in 1897. |
| 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. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |