39 ideas
| 10571 | Concern for rigour can get in the way of understanding phenomena [Fine,K] |
| Full Idea: It is often the case that the concern for rigor gets in the way of a true understanding of the phenomena to be explained. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) | |
| A reaction: This is a counter to Timothy Williamson's love affair with rigour in philosophy. It strikes me as the big current question for analytical philosophy - of whether the intense pursuit of 'rigour' will actually deliver the wisdom we all seek. |
| 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 |
| 10565 | There is no stage at which we can take all the sets to have been generated [Fine,K] |
| Full Idea: There is no stage at which we can take all the sets to have been generated, since the set of all those sets which have been generated at a given stage will itself give us something new. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10564 | We might combine the axioms of set theory with the axioms of mereology [Fine,K] |
| Full Idea: We might combine the standard axioms of set theory with the standard axioms of mereology. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10569 | If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K] |
| Full Idea: We are tempted to ask of second-order quantifiers 'what are you quantifying over?', or 'when you say "for some F" then what is the F?', but these questions already presuppose that the quantifiers are first-order. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005]) |
| 10570 | Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K] |
| Full Idea: In doing semantics we normally assign some appropriate entity to each predicate, but this is largely for technical convenience. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10573 | Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K] |
| Full Idea: Because of Dedekind's definition of reals by cuts, there is a bizarre modern doctrine that there are many 1's - the natural number 1, the rational number 1, the real number 1, and even the complex number 1. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) | |
| A reaction: See Idea 10572. |
| 10575 | Why should a Dedekind cut correspond to a number? [Fine,K] |
| Full Idea: By what right can Dedekind suppose that there is a number corresponding to any pair of irrationals that constitute an irrational cut? | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10574 | Unless we know whether 0 is identical with the null set, we create confusions [Fine,K] |
| Full Idea: What is the union of the singleton {0}, of zero, and the singleton {φ}, of the null set? Is it the one-element set {0}, or the two-element set {0, φ}? Unless the question of identity between 0 and φ is resolved, we cannot say. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10560 | Set-theoretic imperialists think sets can represent every mathematical object [Fine,K] |
| Full Idea: Set-theoretic imperialists think that it must be possible to represent every mathematical object as a set. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10568 | Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K] |
| Full Idea: Logicists traditionally claim that the theorems of mathematics can be derived by logical means from the relevant definitions of the terms, and that these theorems are epistemically innocent (knowable without Kantian intuition or empirical confirmation). | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 2) |
| 10563 | A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K] |
| Full Idea: It is natural to have a generative conception of abstracts (like the iterative conception of sets). The abstracts are formed at stages, with the abstracts formed at any given stage being the abstracts of those concepts of objects formed at prior stages. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) | |
| A reaction: See 10567 for Fine's later modification. This may not guarantee 'levels', but it implies some sort of conceptual priority between abstract entities. |
| 10561 | Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K] |
| Full Idea: Abstraction-theoretic imperialists think that it must be possible to represent every mathematical object as a Fregean abstract. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10562 | We can combine ZF sets with abstracts as urelements [Fine,K] |
| Full Idea: I propose a unified theory which is a version of ZF or ZFC with urelements, where the urelements are taken to be the abstracts. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) |
| 10567 | We can create objects from conditions, rather than from concepts [Fine,K] |
| Full Idea: Instead of viewing the abstracts (or sums) as being generated from objects, via the concepts from which they are defined, we can take them to be generated from conditions. The number of the universe ∞ is the number of self-identical objects. | |
| From: Kit Fine (Replies on 'Limits of Abstraction' [2005], 1) | |
| A reaction: The point is that no particular object is now required to make the abstraction. |
| 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. |
| 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? |
| 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. |
| 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. |
| 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)? |
| 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 |
| 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? |
| 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] |
| 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 |
| 19945 | Jew and Greeks, bond and free, male and female, are all one in Christ [Paul] |
| Full Idea: There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female; for ye are all one in Christ Jesus. | |
| From: St Paul (09: Galatians [c.55], 3.28) | |
| A reaction: No wonder women and slaves were enthusiastic about Christianity. This verse is powerful and influential, even if it was largely ignored by Christian rulers. Consider the relative positions of women in Islam and Christendom. |