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. |
| 23111 | If we say that freedom depends on rationality, the irrational actions are not free [Sidgwick] |
| Full Idea: If we say that a man is a free agent in proportion as he acts rationally, we cannot also say that it is by free choice that he acts irrationally. | |
| From: Henry Sidgwick (The Methods of Ethics (7th edn) [1874], p.511), quoted by John Kekes - Against Liberalism 7.4 | |
| A reaction: A very nice riposte. Clearly people can rationally choose to act irrationally, e.g. at a wild party. |
| 23059 | Self-interest is not rational, if the self is just a succession of memories and behaviour [Sidgwick, by Gray] |
| Full Idea: Sidgwick said self-interest is not self-evidently rational. Unless we invoke a religious idea of the soul, human personality is no more than a succession of continuities in memory and behaviour. In that case, why should anyone favour their future self? | |
| From: report of Henry Sidgwick (The Methods of Ethics (7th edn) [1874]) by John Gray - Seven Types of Atheism 2 | |
| A reaction: This sounds like Locke's account of the self, as psychological continuity. We can say that our continuous self is a fiction, the hero of our own narrative. Personally I think of the self as a sustained set of brains structures which change very little. |
| 4129 | It is self-evident (from the point of view of the Universe) that no individual has more importance than another [Sidgwick] |
| Full Idea: It is a self-evident principle that the good of one individual is of no more importance, from the point of view of the Universe, than the good of any other, ..and as a rational being I am bound to aim at good generally, not merely at a particular part. | |
| From: Henry Sidgwick (The Methods of Ethics (7th edn) [1874], III.XIII.3) | |
| A reaction: Showing that even a very empirical theory like utilitarianism has an a priori basis. Of course, the principle is false. What about animals, the senile, criminals, androids? What bestows 'importance'? |
| 20588 | Sidwick argues for utilitarian institutions, rather than actions [Sidgwick, by Tuckness/Wolf] |
| Full Idea: Sidgwick's complex version of utilitarianism urges that institutions should be set in place to maximise utility, but that individual actions people undertake might not appear to be justifiable on utilitarian terms. | |
| From: report of Henry Sidgwick (The Methods of Ethics (7th edn) [1874]) by Tuckness,A/Wolf,C - This is Political Philosophy 1 Refs | |
| A reaction: This seems to be a specifically political version of utilitarianism, but isn't cited much by political philosophers who discuss utilitarianism. |
| 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. |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |
| Full Idea: The Egyptians were the first to claim that the soul of a human being is immortal, and that each time the body dies the soul enters another creature just as it is being born. | |
| From: Herodotus (The Histories [c.435 BCE], 2.123.2) |