16 ideas
17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert] |
Full Idea: The standpoint of pure experience seems to me to be refuted by the objection that the existence, possible or actual, of an arbitrarily large number can never be derived through experience, that is, through experiment. | |
From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.130) | |
A reaction: Alternatively, empiricism refutes infinite numbers! No modern mathematician will accept that, but you wonder in what sense the proposed entities qualify as 'numbers'. |
17698 | Logic already contains some arithmetic, so the two must be developed together [Hilbert] |
Full Idea: In the traditional exposition of the laws of logic certain fundamental arithmetic notions are already used, for example in the notion of set, and to some extent also of number. Thus we turn in a circle, and a partly simultaneous development is required. | |
From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.131) | |
A reaction: If the Axiom of Infinity is meant, it may be possible to purge the arithmetic from the logic. Then the challenge to derive arithmetic from it becomes rather tougher. |
22049 | Transcendental idealism aims to explain objectivity through subjectivity [Bowie] |
Full Idea: The aim of transcendental idealism is to give a basis for objectivity in terms of subjectivity. | |
From: Andrew Bowie (German Philosophy: a very short introduction [2010], 1) | |
A reaction: Hume used subjectivity to undermine the findings of objectivity. There was then no return to naive objectivity. Kant's aim then was to thwart global scepticism. Post-Kantians feared that he had failed. |
22055 | The Idealists saw the same unexplained spontaneity in Kant's judgements and choices [Bowie] |
Full Idea: The Idealist saw in Kant that knowledge, which depends on the spontaneity of judgement, and self-determined spontaneous action, can be seen as sharing the same source, which is not accessible to scientific investigation. | |
From: Andrew Bowie (German Philosophy: a very short introduction [2010]) | |
A reaction: This is the 'spontaneity' of judgements and choices which was seen as the main idea in Kant. It inspired romantic individualism. The judgements are the rule-based application of concepts. |
22054 | German Idealism tried to stop oppositions of appearances/things and receptivity/spontaneity [Bowie] |
Full Idea: A central aim of German Idealism is to overcome Kant's oppositions between appearances and thing in themselves, and between receptivity and spontaneity. | |
From: Andrew Bowie (German Philosophy: a very short introduction [2010], 2) | |
A reaction: I have the impression that there were two strategies: break down the opposition within the self (Fichte), or break down the opposition in the world (Spinozism). |
22056 | Crucial to Idealism is the idea of continuity between receptivity and spontaneous judgement [Bowie] |
Full Idea: A crucial idea for German Idealism (from Hamann) is that apparently passive receptivity and active spontaneity are in fact different degrees of the same 'activity, and the gap between subject and world can be closed. | |
From: Andrew Bowie (German Philosophy: a very short introduction [2010], 3) | |
A reaction: The 'passive' bit seems to be Hume's 'impressions', which are Kant's 'intuitions', which need 'spontaneous' interpretation to become experiences. Critics of Kant said this implied a dualism. |
8239 | If the King likes music then there is hope for the state [Mengzi (Mencius)] |
Full Idea: If the King has a great fondness for music, then perhaps there is hope for the state of Ch'i. | |
From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 1.B.1) | |
A reaction: This seems to be Shakespeare's attitude to music as well. The general idea must be that love of music requires a selfless state of mind, where the mind revels in the beauty of something outside of itself. Respect is the desirable result. |
23398 | Human nature is naturally compassionate and good (as a 'sprout'), but people may not be good [Mengzi (Mencius), by Norden] |
Full Idea: Mengzi does not claim that humans are innately good; he claims that human nature is innately good. …He says that 'the heart of compassion' (manifested when anyone sees a child about to fall into a well) is the 'sprout of benevolence'. | |
From: report of Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE]) by Bryan van Norden - Intro to Classical Chinese Philosophy 6.II | |
A reaction: There is a nice distinction here between the 'sprout' of human nature and the finished product. Seeds have the potential to produce tall healthy plants, but circumstances can warp them. |
23400 | Righteousness is extending the unthinkable, to reveal what must be done [Mengzi (Mencius)] |
Full Idea: People all have things they will not do. To extend this reaction to that which they will do is righteousness. | |
From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 7B31), quoted by Bryan van Norden - Intro to Classical Chinese Philosophy 6.IV | |
A reaction: Very nice! Kekes points out the enormous importance of unthinkable deeds. Depravity is when the unthinkable gradually begins to look possible, which is probably a social phenomenon, a creeping cancer in a culture. |
23399 | Each correct feeling relies on an underlying virtue [Mengzi (Mencius)] |
Full Idea: The heart of compassion is benevolence. The heart of disdain is righteousness. The heart of respect is propriety. The heart of approval and disapproval is wisdom. | |
From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 6A6), quoted by Bryan van Norden - Intro to Classical Chinese Philosophy 6.III | |
A reaction: 'Disdain' seems to be the response to anyone who is disrespectful. Note that wisdom concerns judgements. Respect seems to be more of a social convention than an actual concern for others. |
8235 | Should a coward who ran fifty paces from a battle laugh at another who ran a hundred? [Mengzi (Mencius)] |
Full Idea: If two soldiers were fleeing from a battle, and one stopped after a hundred paces and the other stopped after a fifty paces, what would you think if the latter, as one who only ran fifty paces, were to laugh at the former who ran a hundred? | |
From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 1.A.3) | |
A reaction: A nice illustration, in my view, of the universality of truths about human virtue. In no culture would this laughter be appropriate. Nevertheless, there must be degrees of dishonour. Better to flee than join in with the likely winners. |
8240 | A true king shares his pleasure with the people [Mengzi (Mencius)] |
Full Idea: If you shared your enjoyment of music or of hunting with the people, you would be a true King. | |
From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 1.B.1) | |
A reaction: I suspect that this is a great truth for dictators and traditional monarchs. One pictures the successful ones attending public entertainments, and allowing the public to see their own. Tyrants keep entertainment private. Nero is a counterexample! |
8237 | Extend the treatment of the old and young in your family to the rest of society [Mengzi (Mencius)] |
Full Idea: Treat the aged of your own family in a manner befitting their venerable age and extend this treatment to the aged of other families. Treat your own young in a manner befitting their tender age, and extend this to the young of other families. | |
From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 1.A.7) | |
A reaction: This seems to me to articulate the ideal of communitarianism very nicely. Morality is not just about healthy adults in war and peace. It must include the children and the old. The values of the family are above the values of contracts and calculations. |
8241 | Only put someone to death if the whole population believes it is deserved [Mengzi (Mencius)] |
Full Idea: When close attendants say a man deserves death, do not listen; when all the councillors say so, do not listen; when everyone says so, have the case investigated. If he is guilty, put him to death; he was put to death by the whole country. | |
From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 1.B.7) | |
A reaction: The jury system is a gesture in this direction. Compare Idea 95. In Mencius's time, no doubt, everyone believed that capital punishment was sometimes right. Nowadays, when many people (e.g. me) reject it, the procedure won't work. |
8238 | Seeking peace through war is like looking for fish up a tree [Mengzi (Mencius)] |
Full Idea: Your desire to extend your territory by war, in order to bring peace, is like looking for fish by climbing a tree. | |
From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 1.A.7) | |
A reaction: Mencius had a flair for analogies. Just occasionally I suppose he might be wrong on this point, but I would think that experiments in the laboratory of history have shown that he is right in nearly all cases. |
8236 | Avoid the animals you are going to eat, as it is hard once you have got to know them [Mengzi (Mencius)] |
Full Idea: Once a gentleman has seen animals alive, he cannot bear to see them die, and once having heard their cry, he cannot bear to eat their flesh. That is why the gentleman keeps his distance from the kitchen. | |
From: Mengzi (Mencius) (The Mengzi (Mencius) [c.332 BCE], 1.A.7) | |
A reaction: If you applied this to a Gestapo officer and his victims, it would obviously be the epitome of wickedness. But it is complex. Compassion is expected when we encounter suffering, but we are not obliged to seek out suffering. Or are we? |