20 ideas
| 22462 | We should speak the truth, but also preserve and pursue it [Foot] |
| Full Idea: There belongs to truthfulness not only the avoidance of lying but also that other kind of attachment to truth which has to do with its preservation and pursuit. | |
| From: Philippa Foot (Utilitarianism and the Virtues [1985], p.74) | |
| A reaction: This is truth as a value, rather than as a mere phenomenon of accurate thought and speech. The importance of 'preserving' the truth is the less common part of this idea. |
| 10807 | Mathematics reduces to set theory, which reduces, with some mereology, to the singleton function [Lewis] |
| Full Idea: It is generally accepted that mathematics reduces to set theory, and I argue that set theory in turn reduces, with some aid of mereology, to the theory of the singleton function. | |
| From: David Lewis (Mathematics is Megethology [1993], p.03) |
| 10809 | We can accept the null set, but not a null class, a class lacking members [Lewis] |
| Full Idea: In my usage of 'class', there is no such things as the null class. I don't mind calling some memberless thing - some individual - the null set. But that doesn't make it a memberless class. Rather, that makes it a 'set' that is not a class. | |
| From: David Lewis (Mathematics is Megethology [1993], p.05) | |
| A reaction: Lewis calls this usage 'idiosyncratic', but it strikes me as excellent. Set theorists can have their vital null class, and sensible people can be left to say, with Lewis, that classes of things must have members. |
| 10811 | The null set plays the role of last resort, for class abstracts and for existence [Lewis] |
| Full Idea: The null set serves two useful purposes. It is a denotation of last resort for class abstracts that denote no nonempty class. And it is an individual of last resort: we can count on its existence, and fearlessly build the hierarchy of sets from it. | |
| From: David Lewis (Mathematics is Megethology [1993], p.09) | |
| A reaction: This passage assuages my major reservation about the existence of the null set, but at the expense of confirming that it must be taken as an entirely fictional entity. |
| 10812 | The null set is not a little speck of sheer nothingness, a black hole in Reality [Lewis] |
| Full Idea: Should we accept the null set as a most extraordinary individual, a little speck of sheer nothingness, a sort of black hole in the fabric of Reality itself? Not that either, I think. | |
| From: David Lewis (Mathematics is Megethology [1993], p.09) | |
| A reaction: Correct! |
| 10813 | What on earth is the relationship between a singleton and an element? [Lewis] |
| Full Idea: A new student of set theory has just one thing, the element, and he has another single thing, the singleton, and not the slightest guidance about what one thing has to do with the other. | |
| From: David Lewis (Mathematics is Megethology [1993], p.12) |
| 10814 | Are all singletons exact intrinsic duplicates? [Lewis] |
| Full Idea: Are all singletons exact intrinsic duplicates? | |
| From: David Lewis (Mathematics is Megethology [1993], p.13) |
| 10806 | Megethology is the result of adding plural quantification to mereology [Lewis] |
| Full Idea: Megethology is the result of adding plural quantification, as advocated by George Boolos, to the language of mereology. | |
| From: David Lewis (Mathematics is Megethology [1993], p.03) |
| 10816 | We can use mereology to simulate quantification over relations [Lewis] |
| Full Idea: We can simulate quantification over relations using megethology. Roughly, a quantifier over relations is a plural quantifier over things that encode ordered pairs by mereological means. | |
| From: David Lewis (Mathematics is Megethology [1993], p.18) | |
| A reaction: [He credits this idea to Burgess and Haven] The point is to avoid second-order logic, which quantifies over relations as ordered n-tuple sets. |
| 10808 | Mathematics is generalisations about singleton functions [Lewis] |
| Full Idea: We can take the theory of singleton functions, and hence set theory, and hence mathematics, to consist of generalisations about all singleton functions. | |
| From: David Lewis (Mathematics is Megethology [1993], p.03) | |
| A reaction: At first glance this sounds like a fancy version of the somewhat discredited Greek idea that mathematics is built on the concept of a 'unit'. |
| 10815 | We don't need 'abstract structures' to have structural truths about successor functions [Lewis] |
| Full Idea: We needn't believe in 'abstract structures' to have general structural truths about all successor functions. | |
| From: David Lewis (Mathematics is Megethology [1993], p.16) |
| 10810 | I say that absolutely any things can have a mereological fusion [Lewis] |
| Full Idea: I accept the principle of Unrestricted Composition: whenever there are some things, no matter how many or how unrelated or how disparate in character they may be, they have a mereological fusion. ...The trout-turkey is part fish and part fowl. | |
| From: David Lewis (Mathematics is Megethology [1993], p.07) | |
| A reaction: This nicely ducks the question of when things form natural wholes and when they don't, but I would have thought that that might be one of the central issues of metaphysicals, so I think I'll give Lewis's principle a miss. |
| 22458 | Consequentialists can hurt the innocent in order to prevent further wickedness [Foot] |
| Full Idea: For consequentialists there will be nothing that it will not be right to do to a perfectly innocent individual, if that is the only way of preventing another agent from doing more things of the same kind. | |
| From: Philippa Foot (Utilitarianism and the Virtues [1985], p.61) | |
| A reaction: This is her generalised version that Williams dramatised as Jim and the Indians. Roughly, if you achieve a good outcome, it matters little how it is achieved. Foot sees consequentialism as the main problem with utilitarianism. |
| 22460 | Why might we think that a state of affairs can be morally good or bad? [Foot] |
| Full Idea: We should ask why we think that it makes sense to talk about morally good and bad states of affairs. | |
| From: Philippa Foot (Utilitarianism and the Virtues [1985], p.68) | |
| A reaction: This is the key question in her attack on consequentialism. There is nothing 'morally' good about my football team winning a great victory. |
| 22461 | Good outcomes are not external guides to morality, but a part of virtuous actions [Foot] |
| Full Idea: It is not that maximum welfare or 'the best outcome' stands outside morality as it foundation and arbiter, but rather that it appears within morality as the end of one of the virtues. | |
| From: Philippa Foot (Utilitarianism and the Virtues [1985], p.73) | |
| A reaction: She cites justice and benevolence as aiming at different (and even conflicting) outcomes. I'm not sure about her distinction between 'outside' and 'within' morality. I suppose a virtuously created end is a moral end, unlike mere good states of affairs. |
| 22464 | The idea of a good state of affairs has no role in the thought of Aristotle, Rawls or Scanlon [Foot] |
| Full Idea: The idea of the goodness of total states of affairs played no part in Aristotle's moral philosophy, and in modern times plays not part either in Rawls's account of justice or in the theories of more thoroughgoing contractualists such as Scanlon. | |
| From: Philippa Foot (Utilitarianism and the Virtues [1985], p.76) | |
| A reaction: We can add Kant to that. But if the supremely good state of affairs were permanently achieved, would that make morality irrelevant? A community of the exceptionally virtuous would not need the veil of ignorance, or contracts. |
| 22463 | Morality is seen as tacit legislation by the community [Foot] |
| Full Idea: Morality is thought of as a kind of tacit legislation by the community. | |
| From: Philippa Foot (Utilitarianism and the Virtues [1985], p.75) | |
| A reaction: Foot presents this as a utilitarian doctrine, because the tacit legislation is felt to produce the best outcomes. This is Nietzsche's good and evil, beyond which he wished to go (presumably following other values). |
| 22459 | For consequentialism, it is irrational to follow a rule which in this instance ends badly [Foot] |
| Full Idea: It would be irrational to obey even the most useful rule if in a particular instance we clearly see that such obedience will not have the best results. | |
| From: Philippa Foot (Utilitarianism and the Virtues [1985], p.62) | |
| A reaction: This is the simple reason why attempts at rule utilitarianism always lead back to act utilitarianism. Another way of putting it is that a good rule can only be assessed by the outcomes of individual acts that follow it. |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |