13 ideas
| 18086 | Weierstrass eliminated talk of infinitesimals [Weierstrass, by Kitcher] |
| Full Idea: Weierstrass effectively eliminated the infinitesimalist language of his predecessors. | |
| From: report of Karl Weierstrass (works [1855]) by Philip Kitcher - The Nature of Mathematical Knowledge 10.6 |
| 18092 | Weierstrass made limits central, but the existence of limits still needed to be proved [Weierstrass, by Bostock] |
| Full Idea: After Weierstrass had stressed the importance of limits, one now needed to be able to prove the existence of such limits. | |
| From: report of Karl Weierstrass (works [1855]) by David Bostock - Philosophy of Mathematics 4.4 | |
| A reaction: The solution to this is found in work on series (going back to Cauchy), and on Dedekind's cuts. |
| 16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
| Full Idea: It seems unavoidable that the facts about logically necessary relations between levels of facts are themselves logically distinct further facts, irreducible to the microphysical facts. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], C) | |
| A reaction: I'm beginning to think that rejecting every theory of reality that is proposed by carefully exposing some infinite regress hidden in it is a rather lazy way to do philosophy. Almost as bad as rejecting anything if it can't be defined. |
| 16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
| Full Idea: Logical supervenience, restricted to individuals, seems to imply strong reduction. It is said that where the B-facts logically supervene on the A-facts, the B-facts simply re-describe what the A-facts describe, and the B-facts come along 'for free'. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], C) | |
| A reaction: This seems to be taking 'logically' to mean 'analytically'. Presumably an entailment is logically supervenient on its premisses, and may therefore be very revealing, even if some people think such things are analytic. |
| 16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
| Full Idea: The root intuition behind nonreductive materialism is that reality is composed of ontologically distinct layers or levels. …The upper levels depend on the physical without reducing to it. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], B) | |
| A reaction: A nice clear statement of a view which I take to be false. This relationship is the sort of thing that drives people fishing for an account of it to use the word 'supervenience', which just says two things seem to hang out together. Fluffy materialism. |
| 16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
| Full Idea: Jessica Wilson (1999) says what makes physicalist accounts different from emergentism etc. is that each individual causal power associated with a supervenient property is numerically identical with a causal power associated with its base property. | |
| From: Lynch,MP/Glasgow,JM (The Impossibility of Superdupervenience [2003], n 11) | |
| A reaction: Hence the key thought in so-called (serious, rather than self-evident) 'emergentism' is so-called 'downward causation', which I take to be an idle daydream. |
| 7544 | Many people imagine that to experience is to understand [Goethe] |
| Full Idea: There are many people who imagine that what they experience they also understand. | |
| From: Wolfgang von Goethe (Maxims and Reflections [1825], 889) | |
| A reaction: This should be posted over the arrivals gate of every international airport, for returning holiday-makers. It seems to place Goethe on the rationalist side of the debate with empiricism. It is hard to explain 'understanding' in Humean terms. |
| 7541 | Man never understands how anthropomorphic he is [Goethe] |
| Full Idea: Man never understands how anthropomorphic he is. | |
| From: Wolfgang von Goethe (Maxims and Reflections [1825], 203) | |
| A reaction: Nice. It is true, even when it is pointed out to us. No matter how hard we try to realise how very different animals are from us, we can't help identifying with them. Religious people even do it with inanimate creation. |
| 7543 | We gain self-knowledge through action, not thought - especially when doing our duty [Goethe] |
| Full Idea: How can we learn self-knowledge? Never by taking thought, but rather by action. Try to do your duty and you'll soon discover what you're like. | |
| From: Wolfgang von Goethe (Maxims and Reflections [1825], 442) | |
| A reaction: Good! I even like the unfashionable bit about duty. If you just do what you want, you will discover your interests, but not so much about your capacities. However, when you have to do something less comfortable, it is very revealing. |
| 7540 | Beauty is a manifestation of secret natural laws [Goethe] |
| Full Idea: Beauty is a manifestation of secret natural laws which without this appearance would have remained eternally hidden from us. | |
| From: Wolfgang von Goethe (Maxims and Reflections [1825], 183) | |
| A reaction: An interesting defence of beauty as an objective feature of the world. I'm not sure. Much beauty is indeed the result of growth or erosion expressing underlying laws, but then I have always thought there was a sexual component to visual beauty. |
| 7538 | The happiest people link the beginning and end of life [Goethe] |
| Full Idea: The happiest man is one who can link the end of his life with its beginning. | |
| From: Wolfgang von Goethe (Maxims and Reflections [1825], 140) | |
| A reaction: [from 'Art and Antiquity']. A nice thought, which chimes in with the idea that a good life is like a complete story or a work of art (Idea 7501), or that it is 'eudaimon'. |
| 7542 | The best form of government teaches us to govern ourselves [Goethe] |
| Full Idea: You ask which form of government is the best? Whichever teaches us to govern ourselves. | |
| From: Wolfgang von Goethe (Maxims and Reflections [1825], 353) | |
| A reaction: Not a fashionable view, since the rise of freedom as the highest political ideal, but I identify with the idea that a good government should educate, and should try to facilitate virtue as well as pleasure. |
| 7539 | To get duties from people without rights, you must pay them well [Goethe] |
| Full Idea: If you demand duties from people and will not concede them rights, you have to pay them well. | |
| From: Wolfgang von Goethe (Maxims and Reflections [1825], 180) | |
| A reaction: [from 'Art and Antiquity']. ...or have great power over them. Goethe gives the optimistic liberal view, rather than the Marxist view. |