11 ideas
| 9198 | It is no longer possible to be a sage, but we can practice the exercise of wisdom [Hadot] |
| Full Idea: Personally I firmly believe, perhaps naively, that it is possible for modern man to live, not as a sage (sophos) - most of the ancients did not hold this to be possible - but as a practitioner of the ever-fragile exercise of wisdom. | |
| From: Pierre Hadot (Philosophy as a way of life [1987], 7) | |
| A reaction: It seems to me quite plausible that the philosophical life might yet become a widespread ideal, even though philosophers seem to still be sheltering from storms two thousand years after Plato gave us that image. |
| 9197 | The logos represents a demand for universal rationality [Hadot] |
| Full Idea: The logos represents a demand for universal rationality. | |
| From: Pierre Hadot (Philosophy as a way of life [1987], 3.3) | |
| A reaction: That is at one end of the spectrum. At the other, in parts of 'Theaetetus', it is just a polite request to be given a few reasons, instead of a splattering of hopes and prejudices. |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 9196 | The pleasure of existing is the only genuine pleasure [Hadot] |
| Full Idea: For epicureans, the only genuine pleasure there is is the pleasure of existing. | |
| From: Pierre Hadot (Philosophy as a way of life [1987], 3.1) | |
| A reaction: I don't know Hadot's source for this claim, but it is a nice idea, which I shall endeavour to incorporate into my own attitude to daily living. I'm not quite clear, though, why the pleasure of music is not a 'genuine' one. |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| Full Idea: Philosophers are the forefathers of heretics. | |
| From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2 |
| 6610 | I believe because it is absurd [Tertullian] |
| Full Idea: I believe because it is absurd ('Credo quia absurdum est'). | |
| From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2 | |
| A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though. |