8 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. |
| 4692 | It is not true that killing and allowing to die (or acts and omissions) are morally indistinguishable [Foot] |
| Full Idea: Many philosophers (e.g. Rachels) have argued that there is no morally relevant distinction between killing and allowing to die (or the related 'acts and omissions'),..as in not sending food, or sending poisoned food. I disagree. | |
| From: Philippa Foot (Killing and Letting Die [1985], p.78) | |
| A reaction: It appears that some omissions are worse than acts. It is more honest to just shoot an injured person, than to walk away and leave them to die. A range of cases. |
| 4694 | Making a runaway tram kill one person instead of five is diverting a fatal sequence, not initiating one [Foot] |
| Full Idea: If a runaway tram is heading towards a track on which five people are standing, and there is someone who can switch the points, diverting it onto a track where there is one person,...this is diverting a fatal sequence, not starting a new one. | |
| From: Philippa Foot (Killing and Letting Die [1985], p.85) | |
| A reaction: Suppose the one person was of immense community value, or someone you personally hated? Clearly she is interested in the agent's virtue, rather than the actual consequences. |
| 4693 | The right of non-interference (with a 'negative duty'), and the right to goods/services ('positive') [Foot] |
| Full Idea: There are rights to non-interference (and their corresponding "negative duties"), and the rights to goods and services (with corresponding "positive duties"). Interference usually needs more justification than withholding goods. | |
| From: Philippa Foot (Killing and Letting Die [1985], p.82) | |
| A reaction: This invites the question of which is the stronger, and whether paternalism can overrule non-interference, or an expectation of self-sufficiency overrule the positive rights. |
| 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. |