39 ideas
| 501 | Reason is a more powerful persuader than gold [Democritus (attr)] |
| Full Idea: In power of persuasion, reasoning is far stronger than gold. | |
| From: Democritus (attrib) (reports [c.250 BCE], B051), quoted by John Stobaeus - Anthology 2.04.12 |
| 13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
| Full Idea: A 'linear ordering' (or 'total ordering') on A is a binary relation R meeting two conditions: R is transitive (of xRy and yRz, the xRz), and R satisfies trichotomy (either xRy or x=y or yRx). | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:62) |
| 13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
| Full Idea: To know if A ∈ B, we look at the set A as a single object, and check if it is among B's members. But if we want to know whether A ⊆ B then we must open up set A and check whether its various members are among the members of B. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:04) | |
| A reaction: This idea is one of the key ideas to grasp if you are going to get the hang of set theory. John ∈ USA ∈ UN, but John is not a member of the UN, because he isn't a country. See Idea 12337 for a special case. |
| 13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
| Full Idea: The 'ordered pair' <x,y> is defined to be {{x}, {x,y}}; hence it can be proved that <u,v> = <x,y> iff u = x and v = y (given by Kuratowski in 1921). ...The definition is somewhat arbitrary, and others could be used. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:36) | |
| A reaction: This looks to me like one of those regular cases where the formal definitions capture all the logical behaviour of the concept that are required for inference, while failing to fully capture the concept for ordinary conversation. |
| 13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
| Full Idea: Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ. A man with an empty container is better off than a man with nothing. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1.03) |
| 13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
| Full Idea: It might be thought at first that the empty set would be a rather useless or even frivolous set to mention, but from the empty set by various set-theoretic operations a surprising array of sets will be constructed. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:02) | |
| A reaction: This nicely sums up the ontological commitments of mathematics - that we will accept absolutely anything, as long as we can have some fun with it. Sets are an abstraction from reality, and the empty set is the very idea of that abstraction. |
| 13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
| Full Idea: Given any x we have the singleton {x}, which is defined by the pairing axiom to be {x,x}. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 2:19) | |
| A reaction: An interesting contrivance which is obviously aimed at keeping the axioms to a minimum. If you can do it intuitively with a new axiom, or unintuitively with an existing axiom - prefer the latter! |
| 13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
| Full Idea: It was observed by several people that for a satisfactory theory of ordinal numbers, Zermelo's axioms required strengthening. The Axiom of Replacement was proposed by Fraenkel and others, giving rise to the Zermelo-Fraenkel (ZF) axioms. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 1:15) |
| 13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
| Full Idea: For functions, we know that for any y there exists an appropriate x, but we can't yet form a function H, as we have no way of defining one particular choice of x. Hence we need the axiom of choice. | |
| From: Herbert B. Enderton (Elements of Set Theory [1977], 3:48) |
| 21833 | Research suggest that we overrate conscious experience [Flanagan] |
| Full Idea: The emerging consensus is that we probably overrate the power of conscious experience in our lives. Freud, of course, said the same thing for different reasons. | |
| From: Owen Flanagan (The Really Hard Problem [2007], 3 'Ontology') | |
| A reaction: [He cites Pockett, Banks and Gallagher 2006]. Freud was concerned with big deep secrets, but the modern view concerns ordinary decisions and perceptions. An important idea, which should incline us all to become Nietzscheans. |
| 21834 | Sensations may be identical to brain events, but complex mental events don't seem to be [Flanagan] |
| Full Idea: There is still some hope for something like identity theory for sensations. But almost no one believes that strict identity theory will work for more complex mental states. Strict identity is stronger than type neurophysicalism. | |
| From: Owen Flanagan (The Really Hard Problem [2007], 3 'Ontology') | |
| A reaction: It is so hard to express the problem. What needs to be explained? How can one bunch of neurons represent many different things? It's not like computing. That just transfers the data to brains, where the puzzling stuff happens. |
| 514 | Beauty is merely animal without intelligence [Democritus (attr)] |
| Full Idea: Physical beauty is merely animal unless intelligence be present. | |
| From: Democritus (attrib) (reports [c.250 BCE], B105) |
| 525 | Behave well when alone, and feel shame in you own eyes [Democritus (attr)] |
| Full Idea: Do not say or do what is base, even when you are alone. Learn to feel shame in your own eyes much more than before others. | |
| From: Democritus (attrib) (reports [c.250 BCE], B244), quoted by John Stobaeus - Anthology 3.31.7 | |
| A reaction: I like this. How you think and behave when unobserved is the true test of who you are. Feeling shame at a very private failing is an interesting phenomenon. |
| 21837 | Morality is normative because it identifies best practices among the normal practices [Flanagan] |
| Full Idea: Morality is 'normative' in the sense that it consists of the extraction of 'good' or 'excellent' practices from common practices. | |
| From: Owen Flanagan (The Really Hard Problem [2007], 4 'Naturalism') | |
| A reaction: I take normativity not be the mere labelling of certain things as 'good', but as a way of responding to that fact, with some sort of motivation. |
| 502 | Good breeding in men means having a good character [Democritus (attr)] |
| Full Idea: Good breeding in cattle depends on physical health, but in men on a well-formed character. | |
| From: Democritus (attrib) (reports [c.250 BCE], B057), quoted by John Stobaeus - Anthology 4.29.18 | |
| A reaction: In our ultra-democratic age (supposedly) it is heresy to talk about good breeding, or some people being superior to others. But surely people should aim to improve their characters? |
| 21830 | For Darwinians, altruism is either contracts or genetics [Flanagan] |
| Full Idea: Two explanations came forward in the neo-Darwinian synthesis. Altruism is either 1) person-based reciprocal altruism, or 2) gene-based kin altruism. | |
| From: Owen Flanagan (The Really Hard Problem [2007], 2 'Darwin') | |
| A reaction: Flanagan obviously thinks there is also 'genuine psychological atruism'. Presumably we don't explain mathematics or music or the desire to travel as either contracts or genetics, so we have other explanations available. |
| 507 | Virtuous love consists of decorous desire for the beautiful [Democritus (attr)] |
| Full Idea: Virtuous love consists of decorous desire for the beautiful. | |
| From: Democritus (attrib) (reports [c.250 BCE], B073), quoted by John Stobaeus - Anthology 3.5.23 | |
| A reaction: Is it possible to love something without seeing it as beautiful? A badly crippled dog, for example. If not, that seems to reveal something about beauty. |
| 21835 | We need Eudaimonics - the empirical study of how we should flourish [Flanagan] |
| Full Idea: It would be nice if I could advance the case for Eudaimonics - empirical enquiry into the nature, causes, and constituents of flourishing, …and the case for some ways of living and being as better than others. | |
| From: Owen Flanagan (The Really Hard Problem [2007], 4 'Normative') | |
| A reaction: Things seem to be moving in that direction. Lots of statistics about happiness have been appearing. |
| 505 | Good and true are the same for everyone, but pleasures differ [Democritus (attr)] |
| Full Idea: For all men, good and true are the same; but pleasant differs for different men. | |
| From: Democritus (attrib) (reports [c.250 BCE], B069) | |
| A reaction: Truth is not 'for' anyone, but there's good-in-itself, and good-for-me. Are there some pleasures we should all enjoy (such as watching our children flourish)? |
| 521 | We should only choose pleasures which are concerned with the beautiful [Democritus (attr)] |
| Full Idea: One should choose not every pleasure, but only that concerned with the beautiful. | |
| From: Democritus (attrib) (reports [c.250 BCE], B207), quoted by John Stobaeus - Anthology 3.05.22 | |
| A reaction: The pleasures we should prefer are those which involve the whole person, rather than the mere stimulation of one sense. Sez me. |
| 508 | Only accept beneficial pleasures [Democritus (attr)] |
| Full Idea: Accept no pleasure unless it is beneficial. | |
| From: Democritus (attrib) (reports [c.250 BCE], B074) | |
| A reaction: Maybe all pleasures bestow some benefit - even if they are linked to harm. I struggle to see what is wrong with a harmless and non-beneficial pleasure, and I doubt if anyone could explain it to me. |
| 520 | The great pleasures come from the contemplation of noble works [Democritus (attr)] |
| Full Idea: The great pleasures come from the contemplation of noble works. | |
| From: Democritus (attrib) (reports [c.250 BCE], B194), quoted by John Stobaeus - Anthology 3.03.46 | |
| A reaction: Only, of course, for those able to perceive the nobility. In what does the 'nobility' consist, other than in the morally acceptable pleasure? Hard to explain 'noble'. Just 'wow!'? |
| 522 | Moderation brings more pleasures, and so increases pleasure [Democritus (attr)] |
| Full Idea: Moderation multiplies pleasures, and increases pleasure. | |
| From: Democritus (attrib) (reports [c.250 BCE], B211), quoted by John Stobaeus - Anthology 3.05.27 | |
| A reaction: So moderation is a sneaky trick to avoid moderation? I presume the most intense pleasures are mostly unfamiliar, and so add novelty to the mix. Apart from eating chocolate, of course. |
| 506 | Immoderate desire is the mark of a child, not an adult [Democritus (attr)] |
| Full Idea: Immoderate desire is the mark of a child, not a man. | |
| From: Democritus (attrib) (reports [c.250 BCE], B070) | |
| A reaction: Not factually correct, since the world is full of adults who have immoderate desires (notably for money). However, there are plenty of grown ups who don't seem very adult. |
| 523 | It is as brave to master pleasure as to overcome the enemy [Democritus (attr)] |
| Full Idea: The brave man is not only he who overcomes the enemy, but he who is stronger than pleasures. Some men are masters of cities, but are enslaved by women. | |
| From: Democritus (attrib) (reports [c.250 BCE], B214), quoted by John Stobaeus - Anthology 3.07.25 | |
| A reaction: I'm not sure if 'bravery' is the relevant virtue here.Sounds like self-control or temperance. I suspect that mastering a city is quite pleasurable, if that's your thing. |
| 503 | Virtue doesn't just avoid evil, but also doesn't desire it [Democritus (attr)] |
| Full Idea: Virtue consists, not in avoiding wrong-doing, but in having no wish thereto. | |
| From: Democritus (attrib) (reports [c.250 BCE], B062), quoted by John Stobaeus - Anthology 3.17.37 |
| 497 | Be virtuous from duty, not from fear [Democritus (attr)] |
| Full Idea: Refrain from crimes not through fear but through duty [deon]. | |
| From: Democritus (attrib) (reports [c.250 BCE], B041), quoted by John Stobaeus - Anthology 3.01.95 | |
| A reaction: [not sure about the translation here] |
| 518 | A bad life is just a drawn-out death [Democritus (attr)] |
| Full Idea: To live badly is not just to live badly, but to spend a long time dying. | |
| From: Democritus (attrib) (reports [c.250 BCE], B160), quoted by (who?) - where? |
| 499 | Repentance of shameful deeds is salvation [Democritus (attr)] |
| Full Idea: Repentance for shameful deeds is salvation in life. | |
| From: Democritus (attrib) (reports [c.250 BCE], B043) |
| 524 | Virtue comes more from practice than from nature [Democritus (attr)] |
| Full Idea: More men become good through practice than by nature. | |
| From: Democritus (attrib) (reports [c.250 BCE], B242), quoted by John Stobaeus - Anthology 3.29.66 |
| 519 | One must avoid even speaking of evil deeds [Democritus (attr)] |
| Full Idea: One must avoid even speaking of evil deeds. | |
| From: Democritus (attrib) (reports [c.250 BCE], B190), quoted by John Stobaeus - Anthology 3.01.91 |
| 500 | The wrongdoer is more unfortunate than the person wronged [Democritus (attr)] |
| Full Idea: The wrongdoer is more unfortunate than the man wronged. | |
| From: Democritus (attrib) (reports [c.250 BCE], B045) |
| 1539 | The endless desire for money is a crueller slavery than poverty [Democritus (attr)] |
| Full Idea: Unless a point of satiety is reached, the desire for money is far more cruel than the utmost poverty, because the greater the desire, the greater the need | |
| From: Democritus (attrib) (reports [c.250 BCE], B219), quoted by John Stobaeus - Anthology 3.10.43 |
| 526 | Small appetite makes poverty equal to wealth [Democritus (attr)] |
| Full Idea: Small appetite makes poverty equivalent to wealth. | |
| From: Democritus (attrib) (reports [c.250 BCE], B284), quoted by John Stobaeus - Anthology 4.33.24 |
| 511 | It is better to have one intelligent friend than many unintelligent [Democritus (attr)] |
| Full Idea: The friendship of one intelligent man is better than that of all the unintelligent. | |
| From: Democritus (attrib) (reports [c.250 BCE], B098) |
| 498 | It is a great thing, when one is in adversity, to think of duty [Democritus (attr)] |
| Full Idea: It is a great thing, when one is in adversity, to think of duty. | |
| From: Democritus (attrib) (reports [c.250 BCE], B042), quoted by John Stobaeus - Anthology 4.44.68 | |
| A reaction: Something wrong with the translation here, if there is no Greek word for 'duty'. |
| 1541 | It is better to be poor in a democracy than be rich without freedom [Democritus (attr)] |
| Full Idea: Poverty in a democracy is as preferable to what is called prosperity under autocracy as freedom is to slavery. | |
| From: Democritus (attrib) (reports [c.250 BCE], B251), quoted by John Stobaeus - Anthology 3.40.42 |
| 21831 | Alienation is not finding what one wants, or being unable to achieve it [Flanagan] |
| Full Idea: What Marx called 'alienation' is the widespread condition of not being able to discover what one wants, or not being remotely positioned to achieve. | |
| From: Owen Flanagan (The Really Hard Problem [2007], 2 'Expanding') | |
| A reaction: I took alienation to concern people's relationship to the means of production in their trade. On Flanagan's definition I would expect almost everyone aged under 20 to count as alienated. |
| 21832 | Buddhists reject God and the self, and accept suffering as key, and liberation through wisdom [Flanagan] |
| Full Idea: Buddhism rejected the idea of a creator God, and the unchanging self [atman]. They accept the appearance-reality distinction, reward for virtue [karma], suffering defining our predicament, and that liberation [nirvana] is possible through wisdom. | |
| From: Owen Flanagan (The Really Hard Problem [2007], 3 'Buddhism') | |
| A reaction: [Compressed] Flanagan is an analytic philosopher and a practising Buddhist. Looking at a happiness map today which shows Europeans largely happy, and Africans largely miserable, I can see why they thought suffering was basic. |