48 ideas
| 13310 | Wisdom does not lie in books, and unread people can also become wise [Seneca] |
| Full Idea: What grounds could I possibly have for supposing that a person who has no acquaintance with books will never be a wise man? For wisdom does not lie in books. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 088) | |
| A reaction: A useful warning to the likes of me, who may have retreated from the hurly-burly of the agora (see Callicles in Plato's 'Gorgias'), under the illusion that detachment is needed for wisdom. Maybe involvement is needed for wisdom. |
| 13295 | Wise people escape necessity by willing it [Seneca] |
| Full Idea: There is nothing a wise man does reluctantly; he escapes necessity because he wills what necessity is going to force on him. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 054) | |
| A reaction: He is discussing death in this letter. The difficulty here is sliding into fatalism. For instance, if you are informed that you have cancer, it is tempting to become 'wise' and will your own death, but lots of people fight it, and win. |
| 13317 | Philosophy aims at happiness [Seneca] |
| Full Idea: Philosophy takes as her aim the state of happiness. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 090) | |
| A reaction: A startlingly forthright view. It seems to neglect what I take to be the main aim of philosophy, which is to achieve understanding. I presume true happiness would follow from that. Seneca must now explain why soporific pleasure is wrong. |
| 13293 | What philosophy offers humanity is guidance [Seneca] |
| Full Idea: Shall I tell you what philosophy holds out for humanity? Counsel. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 048) | |
| A reaction: See Quine for a flat modern denial of this claim (Idea 9764). There is a modern tendency to see ethics and political thought operating at a meta- or metameta- level. I take the main ethical theories to be very illuminating of real life. |
| 13309 | That something is a necessary condition of something else doesn't mean it caused it [Seneca] |
| Full Idea: There's no reason for you to assume that, X being something without which Y could never have come about, Y came about as a result of the assistance of X. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 088) | |
| A reaction: This thought originates with Carneades, reported by Cicero. This is a clear message to the likes of Mackie, who are in danger of thinking that giving the preconditions of something is sufficient to give its causes. |
| 13313 | Even philosophers have got bogged down in analysing tiny bits of language [Seneca] |
| Full Idea: Even the philosophers have descended to the level of drawing distinctions between the uses of different syllables and discussing the proper meanings of prepositions and conjunctions. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 088) | |
| A reaction: How wonderfully prescient! The vast industry of modern philosophy of language exactly fits Seneca's description. I don't quite share his contempt, of course, and I think Seneca would have a bit of sympathy with modern analysis (just a bit!). |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| Full Idea: Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle. |
| 10245 | One geometry cannot be more true than another [Poincaré] |
| Full Idea: One geometry cannot be more true than another; it can only be more convenient. | |
| From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics | |
| A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate. |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| Full Idea: It is surely wise to identify the positions in the natural numbers structure with their counterparts in the integer, rational, real and complex number structures. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2) | |
| A reaction: The point is that this might be denied, since 3, 3/1, 3.00.., and -3*i^2 are all arrived at by different methods of construction. Natural 3 has a predecessor, but real 3 doesn't. I agree, intuitively, with Shapiro. Russell (1919) disagreed. |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| Full Idea: A sequence a1,a2,... of rational numbers is 'Cauchy' if for each rational number ε>0 there is a natural number N such that for all natural numbers m, n, if m>N and n>N then -ε < am - an < ε. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 7.2 n4) | |
| A reaction: The sequence is 'Cauchy' if N exists. |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| Full Idea: There is a dedicated contingent who hold that the category of 'categories' is the proper foundation for mathematics. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.3 n7) | |
| A reaction: He cites Lawvere (1966) and McLarty (1993), the latter presenting the view as a form of structuralism. I would say that the concept of a category will need further explication, and probably reduce to either sets or relations or properties. |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| Full Idea: Zermelo said that for each number n, its successor is the singleton of n, so 3 is {{{null}}}, and 1 is not a member of 3. Von Neumann said each number n is the set of numbers less than n, so 3 is {null,{null},{null,{null}}}, and 1 is a member of 3. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2) | |
| A reaction: See Idea 645 - Zermelo could save Plato from the criticisms of Aristotle! These two accounts are cited by opponents of the set-theoretical account of numbers, because it seems impossible to arbitrate between them. |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| Full Idea: The structuralist vigorously rejects any sort of ontological independence among the natural numbers; the essence of a natural number is its relations to other natural numbers. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1) | |
| A reaction: This seems to place the emphasis on ordinals (what order?) rather than on cardinality (how many?). I am strongly inclined to think that this is the correct view, though you can't really have relations if there is nothing to relate. |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| Full Idea: A 'system' is a collection of objects with certain relations among them; a 'pattern' or 'structure' is the abstract form of a system, highlighting the interrelationships and ignoring any features they do not affect how they relate to other objects. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1) | |
| A reaction: Note that 'ignoring' features is a psychological account of abstraction, which (thanks to Frege and Geach) is supposed to be taboo - but which I suspect is actually indispensable in any proper account of thought and concepts. |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| Full Idea: The thesis that principles of arithmetic are derivable from the laws of logic runs against a now common view that logic itself has no ontology. There are no particular logical objects. From this perspective logicism is a non-starter. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 5.1) | |
| A reaction: This criticism strikes me as utterly devastating. There are two routes to go: prove that logic does have an ontology of objects (what would they be?), or - better - deny that arithmetic contains any 'objects'. Or give up logicism. |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| Full Idea: Term Formalism is the view that mathematics is just about characters or symbols - the systems of numerals and other linguistic forms. ...This will cover integers and rational numbers, but what are real numbers supposed to be, if they lack names? | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.1) | |
| A reaction: Real numbers (such as pi and root-2) have infinite decimal expansions, so we can start naming those. We could also start giving names like 'Harry' to other reals, though it might take a while. OK, I give up. |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| Full Idea: Game Formalism likens mathematics to chess, where the 'content' of mathematics is exhausted by the rules of operating with its language. ...This, however, leaves the problem of why the mathematical games are so useful to the sciences. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.2) | |
| A reaction: This thought pushes us towards structuralism. It could still be a game, but one we learned from observing nature, which plays its own games. Chess is, after all, modelled on warfare. |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| Full Idea: The Deductivist version of formalism (sometimes called 'if-thenism') says that the practice of mathematics consists of determining logical consequences of otherwise uninterpreted axioms. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.2) | |
| A reaction: [Hilbert is the source] More plausible than Term or Game Formalism (qv). It still leaves the question of why it seems applicable to nature, and why those particular axioms might be chosen. In some sense, though, it is obviously right. |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| Full Idea: Critics commonly complain that the intuitionist restrictions cripple the mathematician. On the other hand, intuitionist mathematics allows for many potentially important distinctions not available in classical mathematics, and is often more subtle. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 7.1) | |
| A reaction: The main way in which it cripples is its restriction on talk of infinity ('Cantor's heaven'), which was resented by Hilbert. Since high-level infinities are interesting, it would be odd if we were not allowed to discuss them. |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| Full Idea: I classify conceptualists according to what they say about properties or concepts. If someone classified properties as existing independent of language I would classify her as a realist in ontology of mathematics. Or they may be idealists or nominalists. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 2.2.1) | |
| A reaction: In other words, Shapiro wants to eliminate 'conceptualist' as a useful label in philosophy of mathematics. He's probably right. All thought involves concepts, but that doesn't produce a conceptualist theory of, say, football. |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| Full Idea: A definition of a mathematical entity is 'impredicative' if it refers to a collection that contains the defined entity. The definition of 'least upper bound' is impredicative as it refers to upper bounds and characterizes a member of this set. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: The big question is whether mathematics can live with impredicative definitions, or whether they threaten to be viciously circular, and undermine the whole enterprise. |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| Full Idea: Rationalism is a long-standing school that can be characterized as an attempt to extend the perceived methodology of mathematics to all of knowledge. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.1) | |
| A reaction: Sometimes called 'Descartes's Dream', or the 'Enlightenment Project', the dream of proving everything. Within maths, Hilbert's Programme aimed for the same certainty. Idea 22 is the motto for the opposition to this approach. |
| 13297 | To the four causes Plato adds a fifth, the idea which guided the event [Seneca] |
| Full Idea: To the four Aristotelian causes Plato adds a fifth in the model - what he himself calls the 'idea' - this being what the sculptor had constantly before his eyes as he executed the intended work. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 065) | |
| A reaction: A very interesting interpretation. I take the four 'causes' to be primarily the four 'explanations', and it exactly fits how we should understand Plato, as offer a crucial underlying explanation. The statue is Aristotle's example. |
| 13307 | If everything can be measured, try measuring the size of a man's soul [Seneca] |
| Full Idea: Nothing's outside your scope when it comes to measurement. Well, if you're such an expert, measure a man's soul; tell me how large or how small that is. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 088) | |
| A reaction: This is Descartes's non-spatial argument, which I take to be one of the four main props to his mind-body dualism. As always, it is expressed with beautiful concision by Seneca. |
| 21399 | Referring to a person, and speaking about him, are very different [Seneca] |
| Full Idea: It makes a very great difference whether you refer to the person directly, or speak about him. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 117.13), quoted by A.A. Long - Hellenistic Philosophy 4.3.2 | |
| A reaction: We seem to think that the distinctiveness of reference was first spotted by Frege. Not so. |
| 13325 | Trouble in life comes from copying other people, which is following convention instead of reason [Seneca] |
| Full Idea: One of the causes of the troubles that beset us is the way our lives are guided by the example of others; instead of being set to rights by reason we're seduced by convention. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 123) | |
| A reaction: An interesting practical spin and critique of the standard metaethical idea that morality is just convention. If you think morality is convention, presumably your moral duty is to imitate your neighbours. Nice deconstruction. |
| 22239 | Humans acquired the concept of virtue from an analogy with bodily health and strength [Seneca, by Allen] |
| Full Idea: Seneca held that human beings owe the original acquisition of the concept of virtue to an analogy with bodily health and strength | |
| From: report of Seneca the Younger (Letters from a Stoic [c.60], 120.5) by James Allen - Soul's Virtue and the Health of the Body p.76 | |
| A reaction: This is an unusual view, even for a stoic, but shows how close the concepts of health and virtue were. Notice that it is strength as well as health. Plato just emphasises mental and physical harmony. |
| 13294 | We know death, which is like before birth; ceasing to be and never beginning are the same [Seneca] |
| Full Idea: I already know what death is like - it will be the same after me as it was before me. ..Only an utter idiot would think a lamp was worse off when it was put out than before it was lit. ..What does it matter whether you cease to be or never begin? | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 054) | |
| A reaction: These sentiments are, interestingly, derived from the epicureans, rather than from the stoic tradition, but to us they probably look close together, where they looked like opponents at the time. |
| 13299 | Living is nothing wonderful; what matters is to die well [Seneca] |
| Full Idea: There's nothing so very great about living - all your slaves and all the animals do it. What is, however, a great thing is to die in a manner which is honourable, enlightened and courageous. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 077) | |
| A reaction: You get the feeling that Seneca actually thought suicide was better than a natural death. Did he actually seek his own death? It is an odd interpretation of his own stoic injunction to 'live according to nature'. |
| 13300 | It is as silly to lament ceasing to be as to lament not having lived in the remote past [Seneca] |
| Full Idea: Wouldn't you think a man a prize fool if he burst into tears because he didn't live a thousand years ago? A man is such a fool for shedding tears because he isn't going to be alive a thousand years from now. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 077) | |
| A reaction: These thoughts are traditional, dating back to Epicurus, but Seneca is exceptionally going at finding new variations and examples to reinforce the basic thought. |
| 13321 | Is anything sweeter than valuing yourself more when you find you are loved? [Seneca] |
| Full Idea: Can anything be sweeter than to find that you are so dear to your wife that this makes you dearer to yourself? | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 104) | |
| A reaction: Another lovely penetrating remark from Seneca. I suppose a symptom of low self-esteem might be 'why does she love someone as worthless as me?', but that would be unusual. |
| 13292 | Selfishness does not produce happiness; to live for yourself, live for others [Seneca] |
| Full Idea: No one can lead a happy life if he thinks only of himself and turns everything to his own purposes. You should live for the other person if you wish to live for yourself. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 048) | |
| A reaction: It is important to see this as a key aspect of the ancient aspiration to virtue. The end result is not far from Christianity. It is simplistic to see the quest for virtue as a crass self-obsessed quest for self-improvement. We are social. |
| 13303 | A man is as unhappy as he has convinced himself he is [Seneca] |
| Full Idea: A man is as unhappy as he has convinced himself he is. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 078) | |
| A reaction: Seneca is a very penetrating thinker about ordinary life - an aspect of philosophy which is nowadays totally neglected by the most eminent philosophers. |
| 13302 | Life is like a play - it is the quality that matters, not the length [Seneca] |
| Full Idea: As it is with a play, so it is with life - what matters is not how long the acting lasts, but how good it is. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 077) | |
| A reaction: A very nice epigram, culminating the wonderful Letter 77 on the subject of death. A play needs to be a decent length if it is to exhibit its qualities. It would be heartbreaking if all of Shakespeare's plays were just 20-minute sketches. |
| 13301 | We are scared of death - except when we are immersed in pleasure! [Seneca] |
| Full Idea: You are scared of death - but how heedless of it you are while you are dealing with a dish of choice mushrooms! | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 077) | |
| A reaction: A beautifully simple observation, from the greatest philosopher of death. Maybe hospices should concentrate on sex, drugs and rock and roll. |
| 13323 | The whole point of pleasure-seeking is novelty, and abandoning established ways [Seneca] |
| Full Idea: The whole object of luxurious living is the delight it takes in irregular ways and in not merely departing from the correct course but going to the farthest point away from it, and in eventually even taking a stand diametrically opposed to it. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 122) | |
| A reaction: A rather conservative and puritanical remark, but worthy of contemplation even for committed hedonists. It is just a sad facts that most pleasures diminish with familiarity. Small children make delightful remarks. Imagine if they repeated them. |
| 13318 | Nature doesn't give us virtue; we must unremittingly pursue it, as a training and an art [Seneca] |
| Full Idea: Nature does not give a man virtue; the process of becoming a good man is an art. ...Virtue only comes to a character which has been thoroughly schooled and trained and brought to a pitch of perfection by unremitting practice. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 090) | |
| A reaction: This is an important gloss from a leading stoic on the slogan of 'live according to nature'. One might say that the natural life must be 'tracked' (as Philip Larkin says we track happiness). The natural life is, above all, the rational life, for stoics. |
| 13324 | Living contrary to nature is like rowing against the stream [Seneca] |
| Full Idea: For those who follow nature everything is easy and straightforward, whereas for those who fight against her life is just like rowing against the stream. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 102) | |
| A reaction: A classic statement of the well-known stoic slogan, but expressed with Seneca's characteristic elegance. There is always a slight hidden of dubious fatalism in the slogan. 'Rage, rage, against the dying of the light!' - Dylan Thomas. |
| 13305 | Character is ruined by not looking back over our pasts, since the future rests on the past [Seneca] |
| Full Idea: What really ruins our characters is the fact that none of us looks back over his life. We think a little about what we are going to do, and fail to think about what we have done, yet plans for the future depend on the past. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 083) | |
| A reaction: One always assumes that writings about the wisdom of daily life will be one mass of clichés, but Seneca proves otherwise. With a pang I realise that I may be too guilty of not thinking about the past. I've even been proud of it. |
| 13312 | Excessive curiosity is a form of intemperance [Seneca] |
| Full Idea: To want to know more than is sufficient is a form of intemperance. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 088) | |
| A reaction: This comes as a bit of a surprise, given the high value that philosophers place on knowledge. I'm reminded of Auberon Waugh's criticism of the Scots as a 'wildly over-educated people'. I think the problem is what you could have been doing instead. |
| 13308 | It's no good winning lots of fights, if you are then conquered by your own temper [Seneca] |
| Full Idea: What's the use of overcoming opponent after opponent in the wrestling or boxing rings if you can be overcome by your temper? | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 088) | |
| A reaction: He has such a nice way of presenting what might be traditional and commonplace ideas. If you see life as a battle, then you should think very carefully about who the opponents are - because they may be hiding within. |
| 13315 | To govern used to mean to serve, not to rule; rulers did not test their powers over those who bestowed it [Seneca] |
| Full Idea: In the Golden Age, to govern was to serve, not to rule. No one used to try out the extent of his power over those to whom he owed that power in the first place. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 090) | |
| A reaction: I spent my professional career trying to persuade people that management should be a subjection to the managed. Wake up! The second half of this idea is the interesting bit - the temptation to just 'try out' your powers gets to them all. |
| 13290 | One joy of learning is making teaching possible [Seneca] |
| Full Idea: Part of my joy in learning is that it puts me in a position to teach. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 006) | |
| A reaction: This doesn't quite distinguish between bad learning and good learning, but I take a commitment to wanting to teach what you know as an essential part of wanting to know. |
| 13322 | Both teachers and pupils should aim at one thing - the improvement of the pupil [Seneca] |
| Full Idea: A person teaching and a person learning should have the same end in view: the improvement of the latter. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 108) | |
| A reaction: [He cites a philospher called Attalus for this remark] This is worthy to be up in the hall of every educational institution in the world, and especially in the staff rooms. |
| 13298 | Suicide may be appropriate even when it is not urgent, if there are few reasons against it [Seneca] |
| Full Idea: There are many occasions on which a man should leave life not only bravely but for reasons which are not as pressing as they might be - the reasons which restrain us being not so pressing either. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 077) | |
| A reaction: This is an interesting and startling claim from the great champion of suicide, who nobly and memorably committed suicide himself. But we all dread a loved one miscalculating Seneca's dialectic, and dying when living would have been better. |
| 13320 | Sometimes we have a duty not to commit suicide, for those we love [Seneca] |
| Full Idea: There are times when, however pressing one's reasons to the contrary, one's dying breath must be held back as it is passing one's lips, even if this is torture, simply out of consideration for one's dear ones. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 104) | |
| A reaction: This is, of course, a highly significant counterbalance to his normal acceptance of suicide. I wish anyone who is planning suicide would heed it. They have no idea how much suffering will usually result from their action. |
| 13319 | If we control our own death, no one has power over us [Seneca] |
| Full Idea: No one has power over us when death is in our own power. | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 091) | |
| A reaction: A classic slogan for the stoic view of suicide, an idea that crops up in Shakespeare's 'Julius Caesar'. He doesn't seem to have understood that they can take away your shoelaces. |
| 13311 | Does time exist on its own? Did anything precede it? Did it pre-exist the cosmos? [Seneca] |
| Full Idea: Look how many questions there are on time. Does it have an existence of its own? Does anything exist prior to time, independently of it? Did it begin with the universe, or did it exist even before then? | |
| From: Seneca the Younger (Letters from a Stoic [c.60], 088) | |
| A reaction: I'm not sure that the questions have shifted or become any clearer after two thousand years, despite Einstein and co. Note that discussions of time were not initiated by Augustine. |