15 ideas
| 4424 | A warlike philosopher challenges problems to single combat [Nietzsche] |
| Full Idea: A warlike philosopher challenges problems to single combat. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], Wise §7) | |
| A reaction: And what do pacifist philosophers do? It is a moot point whether philosophy is even possible without a streak of aggression. Otherwise you circle the problem, but don't confront it. |
| 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) |
| 22244 | 'Partial reference' is when the subject thinks two objects are one object [Field,H, by Recanati] |
| Full Idea: A subject's thought is about A, but, unbeknownst to the subject, B is substituted for A. Then there is Field's 'partial reference', because the subject's thought is still partially about A, even though they are following B. | |
| From: report of Hartry Field (Theory Change and the Indeterminacy of Reference [1973]) by François Recanati - Mental Files in Flux 2 | |
| A reaction: Used to interpret a well-known case: Wally says of Udo 'he needs a haircut'; Zach looks at someone else and says 'he sure does'. Recanati explains it by mental files. |
| 2886 | The distinction between egoistic and non-egoistic acts is absurd [Nietzsche] |
| Full Idea: There are neither egoistic nor unegoistic actions: both concepts are psychologically nonsense. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], 4.5) | |
| A reaction: Not quite true, but I like this observation. The idea that you could divide everyone's actions into these two groups is certainly nonsense. But some people are more altruistic than others! |
| 4426 | A bad result distorts one's judgement about the virtue of what one has done [Nietzsche] |
| Full Idea: I should prefer to exclude the bad result, the consequences, from the question of value as a matter of principle. Faced with a bad result, one loses all too easily the right perspective for what one has done. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], Clever §1) | |
| A reaction: If the perspective is easily lost, we should make more effort, not ignore consequences. The question is whether you could have foreseen or controlled the consequences. |
| 4425 | The overcoming of pity I count among the noble virtues [Nietzsche] |
| Full Idea: The overcoming of pity I count among the noble virtues. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], Wise §4) | |
| A reaction: Hm. I can just about see that there might be more important things than compassion for suffering, but I can't see any human activity that makes it worthwhile to trample on pity. |
| 20132 | To become what you are you must have no self-awareness [Nietzsche] |
| Full Idea: To become what one is, one must not have the faintest notion of what one is. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], II.9), quoted by Brian Leiter - Nietzsche On Morality 3 'fatalism' | |
| A reaction: [Don't understand 'II.9'] Enigmatic but striking. As I understand it, Nietzsche thought that knowing what you are is virtually impossible, though he spent a lifetime studying himself. Would you recognise someone who had become what they are? |
| 20144 | Eternal recurrence is the highest attainable affirmation [Nietzsche] |
| Full Idea: Eternal recurrence is the highest formula of affirmation that is at all attainable. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], III.Z-1?), quoted by Brian Leiter - Nietzsche On Morality | |
| A reaction: Did Nietzsche have in mind an even higher formulation that was unattainable? The aim of eternal recurrence is to offer the highest possible ideal that remains rooted in the nature of ordinary life. It is a cut-down version of the Form of the Good. |
| 2889 | One repays a teacher badly if one remains only a pupil [Nietzsche] |
| Full Idea: One repays a teacher badly if one remains only a pupil. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], Fore) |
| 2887 | I am not an atheist because of reasoning or evidence, but because of instinct [Nietzsche] |
| Full Idea: I have absolutely no knowledge of atheism as an outcome of reasoning, still less an event: with me it is obvious by instinct. | |
| From: Friedrich Nietzsche (Ecce Homo [1889], 3.1) |