25 ideas
| 7278 | Words of wisdom are precise and clear [Zhuangzi (Chuang Tzu)] |
| Full Idea: Words of wisdom are precise and clear. | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.2) | |
| A reaction: I can only approve of this. The issue of clarity is much discussed amongs philosophers, especially in the analytic v continental debate. Note, therefore, the additional requirement to be 'precise'. Should we be less clear in order to be precise? |
| 7281 | Don't even start, let's just stay put [Zhuangzi (Chuang Tzu)] |
| Full Idea: Don't even start, let's just stay put. | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.2) | |
| A reaction: What a remarkable proposal! He seems frightened to make an omelette, because he will have to break an egg, or he might burn himself. I can't relate to this idea, but it's existence must be noted, like other scepticisms. |
| 7282 | Disagreement means you do not understand at all [Zhuangzi (Chuang Tzu)] |
| Full Idea: The sage encompasses everything, while ordinary people just argue about things. Disagreement means you do not understand at all. | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.2) | |
| A reaction: This is why democracy and western analytical philosophy come as a package. We can't assume that our government is always right, and we can't assume that a 'sage' has managed to encompass everything. Criticism is essential! |
| 7284 | If you beat me in argument, does that mean you are right? [Zhuangzi (Chuang Tzu)] |
| Full Idea: If you get the better of me in a disagreement, rather than me getting the better of you, does this mean that you are automatically right and I am automatically wrong? | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.2) | |
| A reaction: Very nice. I don't, though, think that this invalidates the process of argument. What matters about such an exchange is the resulting reflection by the two parties. Only a fool thinks that he is right because he won, or wrong because he lost. |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| Full Idea: One feature of the Axiom of Choice that troubled many mathematicians was the so-called Banach-Tarski paradox: using the Axiom, a sphere can be decomposed into finitely many parts and those parts reassembled into two spheres the same size as the original. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) | |
| A reaction: (The key is that the parts are non-measurable). To an outsider it is puzzling that the Axiom has been universally accepted, even though it produces such a result. Someone can explain that, I'm sure. |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.3) | |
| A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics. |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth. | |
| From: Penelope Maddy (Defending the Axioms [2011], 5.3ii) |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40) |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| Full Idea: Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.4) | |
| A reaction: This seems to make it more like a map of mathematics than the actual essence of mathematics. |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.3) | |
| A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor. |
| 8508 | A 'trope' is an abstract particular, the occurrence of an essence [Williams,DC] |
| Full Idea: I shall divert the word 'trope' to stand for the abstract particular which is, so to speak, the occurrence of an essence. | |
| From: Donald C. Williams (On the Elements of Being: I [1953], p.115) | |
| A reaction: Thus tropes entered philosophical discussion. Presumably the precedent for an 'abstract particular' would be a particular occurrence of the number 7. |
| 8509 | A world is completely constituted by its tropes and their connections [Williams,DC] |
| Full Idea: Any possible world, and hence, of course, this one, is completely constituted by its tropes and connections of location and similarity. | |
| From: Donald C. Williams (On the Elements of Being: I [1953], p.116) | |
| A reaction: Note that Williams regularly referred to possible worlds in 1953. This is a full-blooded trope theory, which asserts that objects are bundles of tropes, so that both particulars and universals are ontologically taken care of. |
| 8510 | 'Socrates is wise' means a concurrence sum contains a member of a similarity set [Williams,DC] |
| Full Idea: 'Socrates is wise' means that the concurrence sum (Socrates) includes a trope which is a member of the similarity set (Wisdom). | |
| From: Donald C. Williams (On the Elements of Being: I [1953], p.119) | |
| A reaction: Resemblance has to be taken as a basic (and presumably unanalysable) concept, which invites Russell's objection (Idea 4441). |
| 7289 | Do not try to do things, or to master knowledge; just be empty [Zhuangzi (Chuang Tzu)] |
| Full Idea: Do not try to do things. Do not try to master knowledge. ...Just be empty. | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.7) | |
| A reaction: Stands as a nice challenge to the assumption that knowledge is a good thing. Aristotle's views make a nice contrast (Ideas 548 and 549). Personally I totally agree with Aristotle, and with the western tradition. |
| 23403 | You know you were dreaming when you wake, but there might then be a greater awakening from that [Zhuangzi (Chuang Tzu)] |
| Full Idea: Often after waking do you know that your dream was a dream. Still, there may be an even greater awakening after which you will know that this, too, was just a greater dream. | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], 02), quoted by Bryan van Norden - Intro to Classical Chinese Philosophy 9.2 | |
| A reaction: This is the key to the full horror of dream scepticism (as dramatised in the film 'The Matrix'). We can never know whether there is yet another awakening about to occur. |
| 7285 | Did Chuang Tzu dream he was a butterfly, or a butterfly dream he was Chuang Tzu? [Zhuangzi (Chuang Tzu)] |
| Full Idea: Once I, Chuang Tzu, dreamt that I was a butterfly, flitting around and enjoying myself. Suddenly I woke and was Chuang Tzu again. But had I been Chuang Tzu dreaming I was a butterfly, or a butterfly dreaming I was now Chuang Tzu? | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.2) | |
| A reaction: Plato (Idea 2047) also spotted this problem, later made famous by Descartes (Idea 2250). Given the size of a butterfly's brain, this suggests that Chuang Tzu was a dualist. What can't I take the idea seriously, when reason says I should? |
| 7277 | The perfect man has no self [Zhuangzi (Chuang Tzu)] |
| Full Idea: As the saying goes, 'The perfect man has no self' | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.1) | |
| A reaction: This seems to be quoted with approval. This is interesting because it implies that lesser beings do have a self, and that having a self is a moral issue, and one which can be controlled. One could, I suppose, concentrate on externals. |
| 7286 | To see with true clarity, your self must be irrelevant [Zhuangzi (Chuang Tzu)] |
| Full Idea: When a man discerns his own self as irrelevant, he sees with true clarity. | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.6) | |
| A reaction: Seeing 'with clarity' is only one of the ways of seeing, and one mustn't unquestioningly assume that it is the best. Wisdom should contemplate vision with and without the self, and then rise higher and compare the two views. Compare Parfit (Idea 5518). |
| 7279 | If words can't be defined, they may just be the chirruping of chicks [Zhuangzi (Chuang Tzu)] |
| Full Idea: Our words are not just hot air. Words work because they are something, but the problem is that, if we cannot define a word's meaning, it doesn't really say anything. Can we make a case for it being anything different from the chirruping of chicks? | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.2) | |
| A reaction: This obviously points us towards Quine's challenge to analyticity, and hence the value of definitions (Ideas 1622 and 1624). Even for Chuang Tzu, it seems naïve to think that you cannot use a word well if you cannot define it. |
| 23404 | Words are for meaning, and once you have that you can forget the words [Zhuangzi (Chuang Tzu)] |
| Full Idea: Words are for meaning: when you've gotten the meaning, you can forget the words. | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], 26), quoted by Bryan van Norden - Intro to Classical Chinese Philosophy 9.VI | |
| A reaction: 'What exactly did this person say?' 'Don't know, but I've given you the accurate gist'. This is such an obvious phenomenon that I amazed by modern philosophers who deny propositions, or deny meaning entirely. |
| 7283 | Great courage is not violent [Zhuangzi (Chuang Tzu)] |
| Full Idea: Great courage is not violent. | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.2) | |
| A reaction: A very nice remark. This, I think, is what the Greeks were struggling to say about courage, but they never quite pinned it down as Chuang Tzu does. |
| 7280 | As all life is one, what need is there for words? [Zhuangzi (Chuang Tzu)] |
| Full Idea: As all life is one, what need is there for words? | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.2) | |
| A reaction: In a sense this is nonsense, but it has an appeal. I presume that God would not need words, any more than he would need arithmetic. Life is obviously a complex one, with parts which can be discussed. |
| 7288 | Go with the flow, and be one with the void of Heaven [Zhuangzi (Chuang Tzu)] |
| Full Idea: Don't struggle, go with the flow, and you will find yourself at one with the vastness of the void of Heaven. | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.6) | |
| A reaction: Ugh. I've got all eternity to do that. The underlying assumption of Taoism seems to be that it is better not to have been born, and if you are thus unfortunate, you should try to pretend that it never happened. Much too negative for my taste. |
| 7287 | Fish forget about each other in the pond and forget each other in the Tao [Zhuangzi (Chuang Tzu)] |
| Full Idea: Fish forget about each other in the pond and forget each other in the Tao. | |
| From: Zhuangzi (Chuang Tzu) (The Book of Chuang Tzu [c.329 BCE], Ch.6) | |
| A reaction: Strikingly different from Christianity. No wonder Europeans used to describe orientals as 'enigmatic'; the faces of Taoists presumably express indifference. Not for me, I'm afraid. I identify with my fellow humans, because of our shared predicaments. |