26 ideas
| 6319 | Wise people choose inaction and silence [Laozi (Lao Tzu)] |
| Full Idea: The sage keeps to the deed that consists in taking no action and practises the teaching that uses no words. | |
| From: Laozi (Lao Tzu) (Daodejing (Tao Te Ching) [c.530 BCE], I.II.6) | |
| A reaction: Notice that this is an active 'deed', and a positive 'practice'. He is not just recommending indifference and lethargy. Personally I don't find the advice very appealing, but it might be good if you live in 'interesting times'. |
| 6325 | One who knows does not speak; one who speaks does not know [Laozi (Lao Tzu)] |
| Full Idea: One who knows does not speak; one who speaks does not know. | |
| From: Laozi (Lao Tzu) (Daodejing (Tao Te Ching) [c.530 BCE], II.LVI.128) | |
| A reaction: A famous remark, which my western mind finds simply perplexing. It strikes me as wicked selfishness to keep your wisdom to yourself, and not try to persuade others to follow it. We are all in this together, I say. |
| 6321 | Vulgar people are alert; I alone am muddled [Laozi (Lao Tzu)] |
| Full Idea: Vulgar people are alert; I alone am muddled. | |
| From: Laozi (Lao Tzu) (Daodejing (Tao Te Ching) [c.530 BCE], I.XX.47) | |
| A reaction: Personally I think all human beings are deeply perplexed when they actually address their situation, but most people never spend more than a few minutes a year worrying about it. |
| 9193 | ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett] |
| Full Idea: ZF set theory is a first-order axiomatization. Variables range over sets, there are no second-order variables, and primitive predicates are just 'equals' and 'member of'. The axiom of extensionality says sets with the same members are identical. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 7) | |
| A reaction: If the eleven members of the cricket team are the same as the eleven members of the hockey team, is the cricket team the same as the hockey team? Our cricket team is better than our hockey team, so different predicates apply to them. |
| 9194 | The main alternative to ZF is one which includes looser classes as well as sets [Dummett] |
| Full Idea: The main alternative to ZF is two-sorted theories, with some variables ranging over classes. Classes have more generous existence assumptions: there is a universal class, containing all sets, and a class containing all ordinals. Classes are not members. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 7.1.1) | |
| A reaction: My intuition is to prefer strict systems when it comes to logical theories. The whole point is precision. Otherwise we could just think about things, and skip all this difficult symbolic stuff. |
| 9195 | Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett] |
| Full Idea: It must not be concluded from the rejection of excluded middle that intuitionistic logic operates with three values: true, false, and neither true nor false. It does not make use of true and false, but only with a construction being a proof. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 8.1) | |
| A reaction: This just sounds like verificationism to me, with all its problems. It seems to make speculative statements meaningless, which can't be right. Realism has lots of propositions which are assumed to be true or false, but also unknowable. |
| 9186 | First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett] |
| Full Idea: First-order logic is distinguished by generalizations (quantification) only over objects: second-order logic admits generalizations or quantification over properties or kinds of objects, and over relations between them, and functions defined over them. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 3.1) | |
| A reaction: Second-order logic was introduced by Frege, but is (interestingly) rejected by Quine, because of the ontological commitments involved. I remain unconvinced that quantification entails ontological commitment, so I'm happy. |
| 9187 | Logical truths and inference are characterized either syntactically or semantically [Dummett] |
| Full Idea: There are two ways of characterizing logical truths and correct inference. Proof-theoretic or syntactic characterizations, if the formalization admits of proof or derivation; and model-theoretic or semantic versions, being true in all interpretations. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 3.1) | |
| A reaction: Dummett calls this distinction 'fundamental'. The second one involves truth, and hence meaning, where the first one just responds to rules. ..But how can you have a notion of correctly following a rule, without a notion of truth? |
| 9191 | Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett] |
| Full Idea: It can be argued that the notion of ordinal numbers is more fundamental than that of cardinals. To count objects, we must count them in sequence. ..The theory of ordinals forms the substratum of Cantor's theory of cardinals. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 5) | |
| A reaction: Depends what you mean by 'fundamental'. I would take cardinality to be psychologically prior ('that is a lot of sheep'). You can't order people by height without first acquiring some people with differing heights. I vote for cardinals. |
| 9192 | The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett] |
| Full Idea: The number 4 cannot be characterized solely by its position in a system, because it has different positions in the system of natural numbers and that of the positive whole numbers, whereas these systems have the very same structure. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 6.1) | |
| A reaction: Dummett seems to think this is fairly decisive against structuralism. There is also the structure of the real numbers. We will solve this by saying that the wholes are abstracted from the naturals, which are abstracted from the reals. Job done. |
| 23647 | Objects have an essential constitution, producing its qualities, which we are too ignorant to define [Reid] |
| Full Idea: Individuals and objects have a real essence, or constitution of nature, from which all their qualities flow: but this essence our faculties do not comprehend. They are therefore incapable of definition. | |
| From: Thomas Reid (Essays on Intellectual Powers 4: Conception [1785], 1) | |
| A reaction: Aha - he's one of us! I prefer the phrase 'essential nature' of an object, which is understood, I think, by everyone. I especially like the last bit, directed at those who mistakenly think that Aristotle identified the essence with the definition. |
| 11958 | Impossibilites are easily conceived in mathematics and geometry [Reid, by Molnar] |
| Full Idea: Reid pointed out how easily conceivable mathematical and geometric impossibilities are. | |
| From: report of Thomas Reid (Essays on Intellectual Powers 4: Conception [1785], IV.III) by George Molnar - Powers 11.3 | |
| A reaction: The defence would be that you have to really really conceive them, and the only way the impossible can be conceived is by blurring it at the crucial point, or by claiming to conceive more than you actually can |
| 6328 | To know yet to think that one does not know is best [Laozi (Lao Tzu)] |
| Full Idea: To know yet to think that one does not know is best. | |
| From: Laozi (Lao Tzu) (Daodejing (Tao Te Ching) [c.530 BCE], II.LXXI.173) | |
| A reaction: Tricky. Self-deception doesn't sound like a virtue to me. There are epistemic virtues, and caution about one's own knowledge has to be one of them, but a totally false assessment sounds counter-productive. |
| 6323 | Pursuit of learning increases activity; the Way decreases it [Laozi (Lao Tzu)] |
| Full Idea: In the pursuit of learning one knows more every day; in the pursuit of the Way one does less every day. | |
| From: Laozi (Lao Tzu) (Daodejing (Tao Te Ching) [c.530 BCE], II.XLVII.108) | |
| A reaction: Everything in my culture has raised the status of the pursuit of learning, so that I can hardly comprehend what is proposed by the Way. I don't believe that the Way can be achieved without great learning, but one might move beyond learning. |
| 23646 | Reference is by name, or a term-plus-circumstance, or ostensively, or by description [Reid] |
| Full Idea: An individual is expressed by a proper name, or by a general word joined to distinguishing circumstances; if unknown, it may be pointed out to the senses; when beyond the reach of the senses it may be picked out by an imperfect but true description. | |
| From: Thomas Reid (Essays on Intellectual Powers 4: Conception [1785], 1) | |
| A reaction: [compressed] If Putnam, Kripke and Donnellan had read this paragraph they could have save themselves a lot of work! I take reference to be the activity of speakers and writers, and these are the main tools of the trade. |
| 23645 | A word's meaning is the thing conceived, as fixed by linguistic experts [Reid] |
| Full Idea: The meaning of a word (such as 'felony') is the thing conceived; and that meaning is the conception affixed to it by those who best understand the language. | |
| From: Thomas Reid (Essays on Intellectual Powers 4: Conception [1785], 1) | |
| A reaction: He means legal experts. This is precisely that same as Putnam's account of the meaning of 'elm tree'. His discussion here of reference is the earliest I have encountered, and it is good common sense (for which Reid is famous). |
| 6331 | Truth is not beautiful; beautiful speech is not truthful [Laozi (Lao Tzu)] |
| Full Idea: Truthful words are not beautiful; beautiful words are not truthful. | |
| From: Laozi (Lao Tzu) (Daodejing (Tao Te Ching) [c.530 BCE], II.LXXXI.194) | |
| A reaction: A sharp disagreement with Keats ('Ode to a Grecian Urn'). A deep and important question, especially in relation to Plato's discussion of rhetoric (where he is very ambivalent). Great mathematics is beautiful. Truth can harsh. On the whole, I disagree. |
| 6330 | One with no use for life is wiser than one who values it [Laozi (Lao Tzu)] |
| Full Idea: It is just because one has no use for life that one is wiser than the man who values life. | |
| From: Laozi (Lao Tzu) (Daodejing (Tao Te Ching) [c.530 BCE], II.LXXV.181a) | |
| A reaction: To have no use for life certainly seems to put a person into a position of superiority, especially when the 'Titanic' is sinking. However, if our lives have no value, I don't know what does. A balance must clearly be struck. |
| 6327 | Do good to him who has done you an injury [Laozi (Lao Tzu)] |
| Full Idea: Do good to him who has done you an injury. | |
| From: Laozi (Lao Tzu) (Daodejing (Tao Te Ching) [c.530 BCE], II.LXIII.148) | |
| A reaction: Compare Idea 6288 (Jesus). People like this really mess up the social contract theory of morality. If they are going to return good for your evil, there doesn't seem much point in helping them, given how much effort is involved. Most peculiar… |
| 23402 | The highest virtue is achieved without effort [Laozi (Lao Tzu)] |
| Full Idea: Those of highest virtue do not strive for virtue, and so they have it. | |
| From: Laozi (Lao Tzu) (Daodejing (Tao Te Ching) [c.530 BCE], 38), quoted by Bryan van Norden - Intro to Classical Chinese Philosophy 8.II.2 | |
| A reaction: Every moralist's dream is the person to whom virtue comes so naturally that no thought is required. This says they don't even notice it; Aristotle says they simply enjoying behaving virtuously. |
| 6324 | To gain in goodness, treat as good those who are good, and those who are not [Laozi (Lao Tzu)] |
| Full Idea: Those who are good I treat as good; those who are not good I also treat as good; in doing so I gain in goodness. | |
| From: Laozi (Lao Tzu) (Daodejing (Tao Te Ching) [c.530 BCE], II.XLIX.111) | |
| A reaction: Socrates (idea 346) and Jesus (Idea 6288) had similar ideas. Who, though, is going to administer justice, and where is the idea that people 'deserve' good or ill treatment? Schoolteachers should treat all children as if they were good. |
| 6322 | There is no crime greater than having too many desires [Laozi (Lao Tzu)] |
| Full Idea: There is no crime greater than having too many desires. | |
| From: Laozi (Lao Tzu) (Daodejing (Tao Te Ching) [c.530 BCE], II.XLVI.104) | |
| A reaction: It seems harsh to call this a 'crime', given that no one is likely to choose to have 'too many' desires. The crime is in deciding to stimulate desire to excess, or deciding to show no sensible restraint. |
| 6320 | The best rulers are invisible, the next admired, the next feared, and the worst are exploited [Laozi (Lao Tzu)] |
| Full Idea: The best of all rulers is but a shadowy presence to his subjects; next comes the ruler they love and praise; next comes one they fear; next comes one with whom they take liberties. | |
| From: Laozi (Lao Tzu) (Daodejing (Tao Te Ching) [c.530 BCE], I.XVII.39) | |
| A reaction: This fits our understanding of football referees to perfection. It might apply to anyone doing a vital adminstrative job, such as compiling a school timetable. It is hard, though, to accept anonymity as a mark of success. |
| 6329 | People are hard to govern because authorities love to do things [Laozi (Lao Tzu)] |
| Full Idea: It is because those in authority are too fond of action that the people are difficult to govern. | |
| From: Laozi (Lao Tzu) (Daodejing (Tao Te Ching) [c.530 BCE], II.LXXV.181) | |
| A reaction: I love this. It should be on the wall of every human institution in our civilization. How the heart sinks at the prospect of a 'new initiative'. Not that I am against action; it is just important to recognise that inaction is sometimes the best option. |
| 6326 | The better known the law, the more criminals there are [Laozi (Lao Tzu)] |
| Full Idea: The better known the laws and edicts, the more thieves and robbers there are. | |
| From: Laozi (Lao Tzu) (Daodejing (Tao Te Ching) [c.530 BCE], II.LVII.132) | |
| A reaction: Nice. I link this with my favourite moral maxim from Democritus (Idea 519). The idea is that continual emphasis on what you should not do fills the mind with evil possibilities. Moral perfection must start by taking goodness for granted. |
| 23401 | A military victory is not a thing of beauty [Laozi (Lao Tzu)] |
| Full Idea: A military victory is not a thing of beauty. | |
| From: Laozi (Lao Tzu) (Daodejing (Tao Te Ching) [c.530 BCE], 31), quoted by Bryan van Norden - Intro to Classical Chinese Philosophy 8.II.1 | |
| A reaction: Should be written on the wall of every military academy and barracks. |