9 ideas
| 17809 | Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel] |
| Full Idea: Usually Gödel's incompleteness theorems are taken as showing a limitation on the syntactic approach to an understanding of the concept of infinity. | |
| From: Georg Kreisel (Hilbert's Programme [1958], 05) |
| 17810 | The study of mathematical foundations needs new non-mathematical concepts [Kreisel] |
| Full Idea: It is necessary to use non-mathematical concepts, i.e. concepts lacking the precision which permit mathematical manipulation, for a significant approach to foundations. We currently have no concepts of this kind which we can take seriously. | |
| From: Georg Kreisel (Hilbert's Programme [1958], 06) | |
| A reaction: Music to the ears of any philosopher of mathematics, because it means they are not yet out of a job. |
| 23395 | Mohists desire wealth, population and social order as the best consequences [Mozi, by Norden] |
| Full Idea: The consequentialist Mohists give a fairly objective characterisation of benefits as wealth, populousness, and social order, and harm as poverty, depopulation, and social chaos. | |
| From: report of Mozi (The Mozi [c.440 BCE]) by Bryan van Norden - Intro to Classical Chinese Philosophy 4.I | |
| A reaction: That is a formula favoured by many authoritarian leaders in modern times. |
| 23394 | If people regarded other states as they did their own, they would never attack them [Mozi] |
| Full Idea: If people regarded other people's states in the same way that they regard their own, who then would incite their own state to attack that of another? | |
| From: Mozi (The Mozi [c.440 BCE], 16), quoted by Bryan van Norden - Intro to Classical Chinese Philosophy 4.I | |
| A reaction: A nice case of the application of golden rule thinking to states, instead of to individuals. I can't see Putin (in 2022) being impressed by 'how would you like it if another country invaded Russia?'. The Golden Rule is an analogy argument. |
| 23396 | Mozi condemns partiality, which is the cause of all the great harms in the world [Mozi] |
| Full Idea: It is those who are partial in their dealings with others who are the real cause of all the great harms in the world. That is why our teacher Mozi says 'I condemn partiality'. | |
| From: Mozi (The Mozi [c.440 BCE], 16), quoted by Bryan van Norden - Intro to Classical Chinese Philosophy 4.II | |
| A reaction: This is morality as the rule of law, rather than as the result of human affections. He is on the same wavelength as Kant. Mozi was criticising Confucius, who favoured family over strangers. |
| 23397 | Those who are against impartiality still prefer impartial protectors [Mozi] |
| Full Idea: Even though one may not advocate impartiality, one would certainly want to entrust one's family to the person who is impartial. | |
| From: Mozi (The Mozi [c.440 BCE], 16), quoted by Bryan van Norden - Intro to Classical Chinese Philosophy 4.II | |
| A reaction: In the modern world his example would be the police, so he effectively he wants the impartiality of the law. But who wants legal impartiality within the affairs of a family? |
| 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 |
| 17811 | The natural conception of points ducks the problem of naming or constructing each point [Kreisel] |
| Full Idea: In analysis, the most natural conception of a point ignores the matter of naming the point, i.e. how the real number is represented or by what constructions the point is reached from given points. | |
| From: Georg Kreisel (Hilbert's Programme [1958], 13) | |
| A reaction: This problem has bothered me. There are formal ways of constructing real numbers, but they don't seem to result in a name for each one. |
| 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. |