19 ideas
| 17892 | For clear questions posed by reason, reason can also find clear answers [Gödel] |
| Full Idea: I uphold the belief that for clear questions posed by reason, reason can also find clear answers. | |
| From: Kurt Gödel (works [1930]), quoted by Peter Koellner - On the Question of Absolute Undecidability 1.5 | |
| A reaction: [written in 1961] This contradicts the implication normally taken from his much earlier Incompleteness Theorems. |
| 9188 | Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett] |
| Full Idea: Gödel proved the completeness of standard formalizations of first-order logic, including Frege's original one. However, an implication of his famous theorem on the incompleteness of arithmetic is that second-order logic is incomplete. | |
| From: report of Kurt Gödel (works [1930]) by Michael Dummett - The Philosophy of Mathematics 3.1 | |
| A reaction: This must mean that it is impossible to characterise arithmetic fully in terms of first-order logic. In which case we can only characterize the features of abstract reality in general if we employ an incomplete system. We're doomed. |
| 10620 | Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel] |
| Full Idea: At that time (c.1930) a concept of objective mathematical truth as opposed to demonstrability was viewed with greatest suspicion and widely rejected as meaningless. | |
| From: Kurt Gödel (works [1930]), quoted by Peter Smith - Intro to Gödel's Theorems 28.2 | |
| A reaction: [quoted from a letter] This is the time of Ramsey's redundancy account, and before Tarski's famous paper of 1933. It is also the high point of Formalism, associated with Hilbert. |
| 17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
| Full Idea: Gödel was quick to point out that his original incompleteness theorems did not produce instances of absolute undecidability and hence did not undermine Hilbert's conviction that for every precise mathematical question there is a discoverable answer. | |
| From: report of Kurt Gödel (works [1930]) by Peter Koellner - On the Question of Absolute Undecidability Intro | |
| A reaction: The normal simplistic view among philosophes is that Gödel did indeed decisively refute the optimistic claims of Hilbert. Roughly, whether Hilbert is right depends on which axioms of set theory you adopt. |
| 17885 | Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner] |
| Full Idea: Eventually Gödel ...expressed the hope that there might be a generalised completeness theorem according to which there are no absolutely undecidable sentences. | |
| From: report of Kurt Gödel (works [1930]) by Peter Koellner - On the Question of Absolute Undecidability Intro | |
| A reaction: This comes as a bit of a shock to those who associate him with the inherent undecidability of reality. |
| 10614 | The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel] |
| Full Idea: The concept of truth of sentences in a language cannot be defined in the language. This is the true reason for the existence of undecidable propositions in the formal systems containing arithmetic. | |
| From: Kurt Gödel (works [1930]), quoted by Peter Smith - Intro to Gödel's Theorems 21.6 | |
| A reaction: [from a letter by Gödel] So they key to Incompleteness is Tarski's observations about truth. Highly significant, as I take it. |
| 8239 | If the King likes music then there is hope for the state [Mengzi (Mencius)] |
| Full Idea: If the King has a great fondness for music, then perhaps there is hope for the state of Ch'i. | |
| From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 1.B.1) | |
| A reaction: This seems to be Shakespeare's attitude to music as well. The general idea must be that love of music requires a selfless state of mind, where the mind revels in the beauty of something outside of itself. Respect is the desirable result. |
| 23398 | Human nature is naturally compassionate and good (as a 'sprout'), but people may not be good [Mengzi (Mencius), by Norden] |
| Full Idea: Mengzi does not claim that humans are innately good; he claims that human nature is innately good. …He says that 'the heart of compassion' (manifested when anyone sees a child about to fall into a well) is the 'sprout of benevolence'. | |
| From: report of Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE]) by Bryan van Norden - Intro to Classical Chinese Philosophy 6.II | |
| A reaction: There is a nice distinction here between the 'sprout' of human nature and the finished product. Seeds have the potential to produce tall healthy plants, but circumstances can warp them. |
| 23400 | Righteousness is extending the unthinkable, to reveal what must be done [Mengzi (Mencius)] |
| Full Idea: People all have things they will not do. To extend this reaction to that which they will do is righteousness. | |
| From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 7B31), quoted by Bryan van Norden - Intro to Classical Chinese Philosophy 6.IV | |
| A reaction: Very nice! Kekes points out the enormous importance of unthinkable deeds. Depravity is when the unthinkable gradually begins to look possible, which is probably a social phenomenon, a creeping cancer in a culture. |
| 23399 | Each correct feeling relies on an underlying virtue [Mengzi (Mencius)] |
| Full Idea: The heart of compassion is benevolence. The heart of disdain is righteousness. The heart of respect is propriety. The heart of approval and disapproval is wisdom. | |
| From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 6A6), quoted by Bryan van Norden - Intro to Classical Chinese Philosophy 6.III | |
| A reaction: 'Disdain' seems to be the response to anyone who is disrespectful. Note that wisdom concerns judgements. Respect seems to be more of a social convention than an actual concern for others. |
| 8235 | Should a coward who ran fifty paces from a battle laugh at another who ran a hundred? [Mengzi (Mencius)] |
| Full Idea: If two soldiers were fleeing from a battle, and one stopped after a hundred paces and the other stopped after a fifty paces, what would you think if the latter, as one who only ran fifty paces, were to laugh at the former who ran a hundred? | |
| From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 1.A.3) | |
| A reaction: A nice illustration, in my view, of the universality of truths about human virtue. In no culture would this laughter be appropriate. Nevertheless, there must be degrees of dishonour. Better to flee than join in with the likely winners. |
| 8240 | A true king shares his pleasure with the people [Mengzi (Mencius)] |
| Full Idea: If you shared your enjoyment of music or of hunting with the people, you would be a true King. | |
| From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 1.B.1) | |
| A reaction: I suspect that this is a great truth for dictators and traditional monarchs. One pictures the successful ones attending public entertainments, and allowing the public to see their own. Tyrants keep entertainment private. Nero is a counterexample! |
| 23104 | Dworkin believed we should promote equality, to increase autonomy [Dworkin, by Kekes] |
| Full Idea: Egalitarians believe that most often it is by promoting equality that autonomy is increased; this is the egalitarianism of such liberals as Ronald Dworkin. | |
| From: report of Ronald Dworkin (Taking Rights Seriously [1977]) by John Kekes - Against Liberalism 05.1 | |
| A reaction: Not my idea of equality. The whole point is to ascribe reasonable equality to everyone, including those with a limited capacity for autonomy. Equality is a consequence of universal respect. |
| 8237 | Extend the treatment of the old and young in your family to the rest of society [Mengzi (Mencius)] |
| Full Idea: Treat the aged of your own family in a manner befitting their venerable age and extend this treatment to the aged of other families. Treat your own young in a manner befitting their tender age, and extend this to the young of other families. | |
| From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 1.A.7) | |
| A reaction: This seems to me to articulate the ideal of communitarianism very nicely. Morality is not just about healthy adults in war and peace. It must include the children and the old. The values of the family are above the values of contracts and calculations. |
| 23257 | We can treat people as equals, or actually treat them equally [Dworkin, by Grayling] |
| Full Idea: Dworkin distinguishes between treating people as equals, that is, 'with equal concern and respect', and treating them equally. This latter can be unjust. | |
| From: report of Ronald Dworkin (Taking Rights Seriously [1977]) by A.C. Grayling - The Good State 2 | |
| A reaction: The big difference I see between them is that the first is mere words, and the second is actions. Cf. 'thoughts and prayers' after US school shootings. How about equal entitlements, all things being equal? |
| 18621 | Treating people as equals is the one basic value of all plausible political theories [Dworkin, by Kymlicka] |
| Full Idea: Dworkin suggests that every plausible political theory has the same ultimate value, which is equality - in the more abstract and fundamental sense of treating people 'as equals'. | |
| From: report of Ronald Dworkin (Taking Rights Seriously [1977], 179-83) by Will Kymlicka - Contemporary Political Philosophy (1st edn) | |
| A reaction: I associate this idea with Kant (who says they are equal by virtue of their rationality), so that's a pretty influential idea. I would associate the main challenge to this with Nietzsche. |
| 8241 | Only put someone to death if the whole population believes it is deserved [Mengzi (Mencius)] |
| Full Idea: When close attendants say a man deserves death, do not listen; when all the councillors say so, do not listen; when everyone says so, have the case investigated. If he is guilty, put him to death; he was put to death by the whole country. | |
| From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 1.B.7) | |
| A reaction: The jury system is a gesture in this direction. Compare Idea 95. In Mencius's time, no doubt, everyone believed that capital punishment was sometimes right. Nowadays, when many people (e.g. me) reject it, the procedure won't work. |
| 8238 | Seeking peace through war is like looking for fish up a tree [Mengzi (Mencius)] |
| Full Idea: Your desire to extend your territory by war, in order to bring peace, is like looking for fish by climbing a tree. | |
| From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 1.A.7) | |
| A reaction: Mencius had a flair for analogies. Just occasionally I suppose he might be wrong on this point, but I would think that experiments in the laboratory of history have shown that he is right in nearly all cases. |
| 8236 | Avoid the animals you are going to eat, as it is hard once you have got to know them [Mengzi (Mencius)] |
| Full Idea: Once a gentleman has seen animals alive, he cannot bear to see them die, and once having heard their cry, he cannot bear to eat their flesh. That is why the gentleman keeps his distance from the kitchen. | |
| From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 1.A.7) | |
| A reaction: If you applied this to a Gestapo officer and his victims, it would obviously be the epitome of wickedness. But it is complex. Compassion is expected when we encounter suffering, but we are not obliged to seek out suffering. Or are we? |