44 ideas
| 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. |
| 20589 | Maybe a person's true self is their second-order desires [Tuckness/Wolf] |
| Full Idea: A second-order desire is a desire about what kind of desires you want to have. ....Some philosophers have argued that we should associate a person's second-order desires with her 'true self'. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 2 'What is') | |
| A reaction: Presumably the buck stops at these second-order desires, though we might request an account of their origin. 'What sort of person do I want to be?' looks like a third-order question. I don't even want to be a saint. Self is nothing to do with desires? |
| 20583 | If maximising pleasure needs measurement, so does fulfilling desires [Tuckness/Wolf] |
| Full Idea: Just as hedonists need a way to compare pleasures, so desire fulfilment theorists need a way to compare the fulfilment of desires. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 1 'Is happiness') | |
| A reaction: A nice point. We picture desire fulfilment as just ticking it off when it is achieved, but if your desire is for a really nice house, the achievement of that can be pretty vague. |
| 20584 | Desire satisfaction as the ideal is confused, because we desire what we judge to be good [Tuckness/Wolf] |
| Full Idea: Critics of desire satisfaction theory argue that it gets things backward. We desire things because we already think they are good in some way. Desire theory puts it the other way round. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 1 'Is happiness') | |
| A reaction: Not persuasive. It looks to me as if skiing is a spendid pastime, but I have no desire to do it. More exercise would even be a good for me, but I don't desire that either. Indeed, right now I desire more cake, which is very naughty. |
| 20598 | In a democracy, which 'people' are included in the decision process? [Tuckness/Wolf] |
| Full Idea: In any democratic state, who are 'the people' who get to rule themselves? That is, who gets to participate in the public decision process, and who is excluded? | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'What is') | |
| A reaction: In the modern world this may be clear-cut when a democracy gets started, but people move around so much more that every democracy is faced with new types of residents. Then there is age, criminality, mental health... |
| 20614 | People often have greater attachment to ethnic or tribal groups than to the state [Tuckness/Wolf] |
| Full Idea: Some states have a number of different ethnic or tribal groups. Often these attachments are much stronger than the attachment people feel towards the state. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 6 'Membership') | |
| A reaction: In Britain I fine people torn between attachments to the UK and to England or Wales or Scotland or NI. Attachments to football clubs are much stronger than most patriotism. Or attachment to a particular locality. Does it matter? |
| 20596 | For global justice, adopt rules without knowing which country you will inhabit [Tuckness/Wolf] |
| Full Idea: Imagine a new original position where we adopted rules for global justice without knowing which country we would inhabit. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 4 'Cosmopolitan') | |
| A reaction: Nice question. North Korea!! Rawls says it is only within a nation, because there is a co-operative enterprise going on. That is, I presume, that the choosers involved are a 'people'. See Kant's 'Perpetual Peace' for an alternative. |
| 20593 | The veil of ignorance ensures both fairness and unanimity [Tuckness/Wolf] |
| Full Idea: The veil of ignorance ensures that the original position is fair, but it also guarantees that agreement will be unanimous (which would be impossible if each person insisted that justice should match her own conception). | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 4 'Original') | |
| A reaction: Not clear about this. If I choose very cautiously, but others choose very riskily, and they win, why I should I fall in with their unanimity? That can only be if we agree to be unanimous in backing the result. Like a democratic election? |
| 20608 | Unjust institutions may be seen as just; are they legitimate if just but seen as unjust? [Tuckness/Wolf] |
| Full Idea: Legitimacy and perceived legitimacy do not always go together: people can believe that their institutions are just, but they may be wrong. Is the reverse also possible? Can institutions be legitimate if people believe they are not? | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'What are') | |
| A reaction: Nice thoughts. An institution cannot be just merely because it is seen that way (if someone gets away with rigging an election). If they are just but seen as unjust, I presume they are legitimate (which is objective), but disfunctional. |
| 20597 | If winning elections depends on wealth, we have plutocracy instead of democracy [Tuckness/Wolf] |
| Full Idea: If we let people's influence on election outcomes depend on their wealth, then we don't have a democracy any more. We have a plutocracy, where the people who have all the wealth have all the political power too. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'Intro') | |
| A reaction: [see Michael Walzer on 'complex equality'] This is startling true in the United States, but still somewhat true elsewhere. Being wealthy enough to control the media is the key in modern democracies. |
| 20606 | Epistemic theories defend democracy as more likely to produce the right answer [Tuckness/Wolf] |
| Full Idea: According to epistemic theories of democracy, democratic outcomes are justified because they are more likely to be true or right than the choice of the individual. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'Do the people') | |
| A reaction: Bear in mind Condorcet's proof that this claim is only correct if individuals have a better than 50% chance of being right, which may be so on obvious things, but is implausible for decisions like going to war. |
| 20600 | Which areas of public concern should be decided democratically, and which not? [Tuckness/Wolf] |
| Full Idea: Are there areas which are excluded from democratic decision making? Or should all issues of public concern be decided through a democratic process? | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'What is') | |
| A reaction: Crucially, are we discussing direct democracy, or representative democracy? In Britain all major decisions are made by the cabinet. Our representatives appoint leaders, who then appoint the decision makers. Judiciary is non-democratic. |
| 20609 | If several losing groups would win if they combine, a runoff seems called for [Tuckness/Wolf] |
| Full Idea: It is possible that the people who supported several losing candidates might have joined forces and had a majority. For that reason, many countries have a runoff election. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'Does democracy') | |
| A reaction: The problem is that there is no rationale as to who stands in an election. If their views are evenly spread, the first result seems OK. If there are five left-wingers and one right-winger, a runoff seems to be produce a more just result. |
| 20605 | Rights as interests (unlike rights as autonomy) supports mandatory voting [Tuckness/Wolf] |
| Full Idea: If rights concern people's interests, that might support mandatory voting, but if rights rely on protecting autonomy that might oppose it. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'Interest') | |
| A reaction: I approach it from the other end, and am inclined to support mandatory voting, which suggests I am more concerned about interests than about autonomy. |
| 20599 | How should democratic votes be aggregated? Can some person's votes count for more? [Tuckness/Wolf] |
| Full Idea: A major question for democracy is how are the contributions of different people aggregated into a collective decision? Must votes have equal weight and consideration, or is it permissible for different people's votes to count differently? | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'What is') | |
| A reaction: Mill hoped that wise and knowledgeable people would have a strong influence over the others, but we have recently moved into the post-truth era, where we are swamped by bogus facts. Does that strengthen the case for elite voting? |
| 20601 | Discussion before voting should be an essential part of democracy [Tuckness/Wolf] |
| Full Idea: According to advocates of deliberative democracy, people should have an opportunity to talk and reason with one another before votes are cast. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'Who gets') | |
| A reaction: This is now done on Facebook and Twitter, but no one thinks that is sufficient. We will never again persuade most people to actually meet up and discuss issues. |
| 20613 | We have obligations to our family, even though we didn't choose its members [Tuckness/Wolf] |
| Full Idea: Many of our most important obligations are things we did not consent to. If you think you have obligations to your family, did you choose to have them as family members? | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 6 'Gratitude') | |
| A reaction: A question that gets close to the heart of the communitarian ideal, I think. We choose to have children, and we bring them up, but even then we don't choose who our children are. |
| 20586 | Free speech does not include the right to shout 'Fire!' in a crowded theatre [Tuckness/Wolf] |
| Full Idea: Oliver Wendell Holmes (in 1919) noted that freedom of speech does not include the right to shout 'Fire!' in a crowded theatre. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 1 'Conflict') | |
| A reaction: The point here is that such irresponsible free speech does not even require legislation, and there is probably already some law under which the perpetrator could be prosecuted. |
| 20587 | Most people want equality because they want a flourishing life [Tuckness/Wolf] |
| Full Idea: If we want equality so much, we find that it is often because they think of equality as a prerequisite for a certain kind of flourishing life. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 1 'Happiness') | |
| A reaction: Most writers seem to agree that we don't want equality for its own sake. In what respects do we want to be equal? Why not equal in hair colour? Hence it looks as if equality drops out. I would aim to derive it from the social virtue of respect. |
| 20591 | If there is no suffering, wealth inequalities don't matter much [Tuckness/Wolf] |
| Full Idea: It is hard to get worked up over wealth inequalities if no one is suffering from them! | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 3 'Deprivation') | |
| A reaction: The more the poorer group resent the inequality, the more they suffer. When is resenting huge inequalities in wealth justified? It depends how the big wealth was obtained. |
| 20602 | Some rights are 'claims' that other people should act in a certain way [Tuckness/Wolf] |
| Full Idea: A 'claim right' is one in which the person asserting the right makes a claim on others to act or not act in a certain way. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'Claim') | |
| A reaction: There seems to be a crucial distinction between rights which entail obligations on some individual or institution, and those which don't. Contracts (including employment contracts) generate duties on the parties. |
| 20604 | Choice theory says protecting individual autonomy is basic (but needs to cover infants and animals) [Tuckness/Wolf] |
| Full Idea: Choice theorists hold that rights protect our rights to make autonomous judgements, because our basic right to autonomy must be protected, The theory has a problem with people unable to exercise autonomy (such as infants and animals). | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'Interest') | |
| A reaction: The problem of infants and animals looks like a decisive objection to me. We obviously don't protect dangerous or hostile autonomous judgements, and it is not clear why protecting stupid autonomy should be basic. |
| 20603 | One theory (fairly utilitarian) says rights protect interests (but it needs to cover trivial interests) [Tuckness/Wolf] |
| Full Idea: Interest theorists hold that rights serve to protect people's important interests. This is closely allied with utilitarian values. The theory has difficulty accounting for relatively trivial interests (like owning a lemonade you bought). | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'Interest') | |
| A reaction: This sounds more plausible than choice theory (Idea 20604). It is obvious that infants must have rights. The lemonade problem seems to demand some sort of rule utilitarianism. Sidgwick looks promising. Rights can also be moral claims. |
| 20607 | Having a right does not entail further rights needed to implement it [Tuckness/Wolf] |
| Full Idea: Possession of a right (such as self-defence) does not always imply that one has additional rights to whatever they need (such as a handgun) in order to exercise the first right. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'Is there') | |
| A reaction: The right to life entails a right to food (but not to a banquet), so it is a stronger right than self-defence. I have no obligation to let you defend yourself against me, but I may have an obligation to feed you if you are starving. (Distinction here?) |
| 20612 | If being subject to the law resembles a promise, we are morally obliged to obey it [Tuckness/Wolf] |
| Full Idea: One of the more common reasons people will give for having a moral obligation to obey the law is consent. ...It rests on the intuitively appealing idea of an analogy with a promise. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 6 'Consent') | |
| A reaction: [They cite Locke and Jefferson] In Locke's case it has to be a 'tacit' promise, which is more realistic. In real life we have problems with people who 'said' they would do something. They are often accused of promising, when they didn't. |
| 20611 | If others must obey laws that we like, we must obey laws that they like? [Tuckness/Wolf] |
| Full Idea: If we expect others to obey the laws we think just, do we have an obligation to obey the laws that other people think just? | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 6 'What should') | |
| A reaction: Depends whether you have to be consistent about everything. I'm picky about which laws I obey, but I'm not going to tell you that, in case you get the same idea. Free riders. |
| 20610 | Instead of against natural law, we might assess unjust laws against the values of the culture [Tuckness/Wolf] |
| Full Idea: Do we need natural law theory in order to make sense of the idea that laws can be unjust? Perhaps not: we might consider whether laws are consistent with the values of the culture or society where they apply. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 5 'Unjust') | |
| A reaction: So were the wicked laws passed by the Nazis consistent with 1930s German culture? Impossible to say. |
| 20617 | How should the punishment fit the crime (for stealing chickens?) [Tuckness/Wolf] |
| Full Idea: One criticism of the retributive theory of punishment is that it is hard to know how to fit the punishment to the crime. What punishment should correspond to stealing chickens? | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 7 'Rationales') | |
| A reaction: The ancient world was more keen on restitution for such crimes, which makes much better sense. Buy them some chickens, plus twenty percent. |
| 20615 | Just wars: resist aggression, done on just cause, proportionate, last resort, not futile, legal [Tuckness/Wolf] |
| Full Idea: Classical just war theory: resist aggression; just cause must be the real reason; must be proportionate; last resort; not futile; made by a nation's authority. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 9 'Ius ad') | |
| A reaction: [My squashed summary of Tuckness and Wolf] A very helpful list, from Cicero, Augustine and Aquinas. So where is the sticking point for pacifists? Presumably it is never the last resort, and aggression should not answer aggression. |
| 20616 | During wars: proportional force, fair targets, fair weapons, safe prisoners, no reprisals [Tuckness/Wolf] |
| Full Idea: Classical just war theory during a war: force must be proportional; only legitimate targets; avoid prohibited weapons; safety for prisoners of war; no reprisals. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 9 'In the conduct') | |
| A reaction: What of massacre if a besieged city refuses to surrender? It was commonplace, and sometimes the only way to achieve victory. What if the enemy breaks all the rules? Nice rules though. At the heart of civilisation. |
| 20620 | If minority views are accepted in debate, then religious views must be accepted [Tuckness/Wolf] |
| Full Idea: It is unfair to exclude religious arguments from the public square because they are not accepted by everyone, unless other views that are not accepted by everyone are also excluded. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 9 'fairly') | |
| A reaction: Raises the obvious problems of a huge group in the grips of a fairly crazy view, and a tiny group (e.g. specialist scientists) in possession of a correct view. You can't just assess it on the size of the group. You can be wrong but reasonable. |
| 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. |
| 20619 | Is abortion the ending of a life, or a decision not to start one? [Tuckness/Wolf] |
| Full Idea: One group may consider abortion as a decision to end a life, while another may regard it as the decision not to start one. | |
| From: Tuckness,A/Wolf,C (This is Political Philosophy [2017], 8 'Hard I') | |
| A reaction: An early foetus is 'life', but is it 'a life'? Is a blade of grass 'a life'? Is a cell in a body 'a life'? |
| 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. |