42 ideas
| 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. |
| 6866 | It is disturbing if we become unreal when we die, but if time is unreal, then we remain real after death [Le Poidevin] |
| Full Idea: For the A-theorists called 'presentists' the past is as unreal as the future, and reality leaves us behind once we die, which is disturbing; but B-theorists, who see time as unreal, say we are just as real after our deaths as we were beforehand. | |
| From: Robin Le Poidevin (Interview with Baggini and Stangroom [2001], p.174) | |
| A reaction: See Idea 6865 for A and B theories. I wonder if this problem is only superficially 'disturbing'. Becoming unreal may sound more drastic than becoming dead, but they both sound pretty terminal to me. |
| 6867 | Existentialism focuses on freedom and self-making, and insertion into the world [Le Poidevin] |
| Full Idea: I take existentialism to be the focus on the freedom and self-making of the human being, and his or her insertion into the world. | |
| From: Robin Le Poidevin (Interview with Baggini and Stangroom [2001], p.222) | |
| A reaction: I take 'self-making' to be the key here. If neuroscientists somehow 'proved' that there was no free will, I don't see that making any difference to existentialism. 'Insertion' seems odd, unless it refers to growing up. |
| 20489 | Human beings can never really flourish in a long-term state of nature [Wolff,J] |
| Full Idea: We must agree with Hobbes, Locke and Rousseau that nothing genuinely worthy of being called a state of nature will, at least in the long term, be a condition in which human beings can flourish. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 1 'Conc') | |
| A reaction: Given our highly encultured concept of modern flourishing, that is obviously right. There may be another reality where hom sap flourishes in a quite different and much simpler way. Education as personal, not institutional? |
| 20483 | Collective rationality is individuals doing their best, assuming others all do the same [Wolff,J] |
| Full Idea: We need to distinguish between individual and collective rationality. Collective rationality is what is best for each individual, on the assumption that everyone else will act the same way. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 1 'Hobbes') | |
| A reaction: Wolff is surmising what lies behind Hobbes's Laws of Nature (which concern collective rationality). The Prisoner's Dilemma is the dramatisation of this distinction. I would making the teaching of the distinction compulsory in schools. |
| 20532 | Should love be the first virtue of a society, as it is of the family? [Wolff,J] |
| Full Idea: Love, or at least affection, not justice, is the first virtue of the family. Should mutual affection also be the first virtue of social and political institutions? | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 6 'Transcending') | |
| A reaction: Surely this ideal should be at the heart of any society, no matter how far away from the ideal it is pushed by events and failures of character? I take 'respect' to be the form of love we feel for strangers. |
| 20490 | For utilitarians, consent to the state is irrelevant, if it produces more happiness [Wolff,J] |
| Full Idea: On the utilitarian account the state is justified if and only if it produces more happiness than any alternative. Whether we consent to the state is irrelevant. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 2 'Intro') | |
| A reaction: The paternalistic character of utilitarianism is a familiar problem. I quite like this approach, even though liberals will find it a bit naughty. We make children go to school, for their own good. Experts endorse society, even when citizens don't. |
| 20493 | Social contract theory has the attracton of including everyone, and being voluntary [Wolff,J] |
| Full Idea: Social contract theory ...satisfies the twin demands of universalism - every person must be obligated - and voluntarism - political obligations can come into existence only through consent. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 2 'Voluntaristic') | |
| A reaction: I'm going off the idea that being a member of large society is voluntary. It can't possibly be so for most people, and it shouldn't be. I'm British, and society expects me to remain so (though they might release me, if convenient). |
| 20494 | Maybe voting in elections is a grant of legitimacy to the winners [Wolff,J] |
| Full Idea: One thought is that consent to government is communicated via the ballot-box. In voting for the government we give it our consent. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 2 'Voluntaristic') | |
| A reaction: Hm. This may be a strong positive reason why some people refuse to vote. We shouldn't load voting with such heavy commitments. It's just 'given the current situation, who will be temporarily in charge'. |
| 20500 | We can see the 'general will' as what is in the general interest [Wolff,J] |
| Full Idea: The general will demands the policy which is equally in everyone's interests. Thus we can think of the general will as the general interest. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 3 'Rousseau') | |
| A reaction: That seems to assume that the people know what is in their interests. Rousseau's General Will mainly concerns who governs, and their mode of government, but not details of actual policy. |
| 20497 | How can dictators advance the interests of the people, if they don't consult them about interests? [Wolff,J] |
| Full Idea: Even if a dictator wants to advance the interests of the people, how are those interests to be known? In a democracy people show their interests, it seems, by voting: they vote for what they want. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 3 'Knowledge') | |
| A reaction: I suppose a wise and kind despot could observe very carefully, and understand the interests of the people better than they do themselves. Indeed, I very much doubt, in 2017, whether the people know what is good for them. |
| 20506 | 'Separation of powers' allows legislative, executive and judicial functions to monitor one another [Wolff,J] |
| Full Idea: The Federalists took the idea of 'separation of powers' from Locke and Montesquieu. This places the legislative, executive and judicial functions in independent hands, so that in theory any branch of government would be checked by the other two. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 3 'Representative') | |
| A reaction: [The American Federalist writers of 1787-8 were Madison, Hamilton and Jay] This is a brilliant idea. An interesting further element that has been added to it is the monitoring by a free press, presumably because the other three were negligent. |
| 20530 | Political choice can be by utility, or maximin, or maximax [Wolff,J] |
| Full Idea: Political choices can be made by the utility principles (maximising total utility), or maximin (maximising for the worst off, a view for pessimists), or maximax (not serious, but one for optimists, being unequal, and aiming for a high maximum). | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 5 'Choosing') | |
| A reaction: [my summary of a page of Wolff] Rawls embodies the maximin view. Wolff implies that we must choose between utilitarianism and Rawls. Would Marxists endorse maximin? He also adds 'constrained maximisation', with a safety net. |
| 20487 | A realistic and less utopian anarchism looks increasingly like liberal democracy [Wolff,J] |
| Full Idea: As the anarchist picture of society becomes increasingly realistic and less utopian, it also becomes increasingly difficult to tell it apart from a liberal democratic state. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 1 'Anarchism') | |
| A reaction: Nice challenge to anarchism, which is clear in what it opposes, but isn't much of a political philosophy if it doesn't have positive aspirations. Anarchists may hope that people will beautifully co-operate, but what if they re-form the state to do it? |
| 20488 | It is hard for anarchists to deny that we need experts [Wolff,J] |
| Full Idea: Many anarchists have accepted the need for the authority of experts within society | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 1 'Anarchism') | |
| A reaction: The status of experts may be the hottest topic in contemporary politics, given the contempt for experts shown by Trump, and by the Brexit campaign of 2016. It is a nice point that even anarchists can't duck the problem. |
| 20529 | Utilitarianism probably implies a free market plus welfare [Wolff,J] |
| Full Idea: A utilitarian political philosophy would probably be a free market with a welfare state. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 5 'Choosing') | |
| A reaction: This is roughly how Britain became, after the welfare state was added to Millian liberalism. What's missing from this formula is some degree of control of the free market, to permit welfare. |
| 20510 | A system of democracy which includes both freedom and equality is almost impossible [Wolff,J] |
| Full Idea: We are very unlikely to be able to find an instrumental defence of democracy which also builds the values of freedom and equality into a feasible system. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 3 'Conc') | |
| A reaction: I increasingly think that freedom is the most overrated political virtue (though it is certainly a virtue). Total freedom is ridiculous, but the aim of sacrificing many other social goods in order to maximise freedom also looks wrong. |
| 20511 | Democracy expresses equal respect (which explains why criminals forfeit the vote) [Wolff,J] |
| Full Idea: Democracy is a way of expressing equal respect for all, which is perhaps why we withdraw the vote from criminals: by their behaviour they forfeit the right to equal respect. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 3 'Conc') | |
| A reaction: I disagree, and he has converted me to franchise for criminals. One-off criminals do not forfeit my respect for them as people, though their action may merit a controlling response on our part. Bad character, not a bad action, forfeits respect. |
| 20502 | Democracy has been seen as consistent with many types of inequality [Wolff,J] |
| Full Idea: Greeks assumed democracy was consistent with slavery, Rousseau that it was consistent with sexual inequality, and Wollstonecraft that it was consistent with disenfranchisement of the poor. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 3 'Freedom') | |
| A reaction: If you are allowed to restrict the franchise in some way, then a narrow oligarchy can qualify as a democracy, with half a dozen voters. |
| 20496 | A true democracy could not tolerate slavery, exploitation or colonialism [Wolff,J] |
| Full Idea: A democratic state has power only over the people who make up the electorate. Ruling over a subservient class, or territory, is claimed to be antithetical to the true ideals of democracy. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 3 'Intro') | |
| A reaction: Is making trade deals very favourable to yourself (i.e. good capitalism) antithetical to democracy? |
| 20498 | We should decide whether voting is for self-interests, or for the common good [Wolff,J] |
| Full Idea: To avoid mixed-motivation voting, we must choose between one model of people voting in accordance with their preferences, and another of voting for their estimate of the common good. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 3 'Voting') | |
| A reaction: Personally I always voted for the common good, and only slowly realised that most people were voting for their own interests. A rational society would at least bring this dichotomy into the open. Voting for self-interest isn't wicked. |
| 20499 | Condorcet proved that sensible voting leads to an emphatically right answer [Wolff,J] |
| Full Idea: Condorcet proved that provided people have a better than even chance of getting the right answer, and that they vote for their idea of the common good, then majority decisions are an excellent way to get the right result. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 3 'Voting') | |
| A reaction: [compressed] The point is that collective voting magnifies the result. If they tend to be right, the collective view is super-right. But if they tend towards the wrong, the collective view goes very wrong indeed. History is full of the latter. |
| 20509 | Occasional defeat is acceptable, but a minority that is continually defeated is a problem [Wolff,J] |
| Full Idea: Most of us can accept losing from time to time, but sometimes an entrenched majority will win vote after vote, leaving the minority group permanently outvoted and ignored. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 3 'Protecting') | |
| A reaction: This is the key problem of the treatment of minorities in a democracy. Personally I have only once been on the winning side in voting for my MP, and he changed party a couple of years later. |
| 20524 | Market prices indicate shortages and gluts, and where the profits are to be made [Wolff,J] |
| Full Idea: The price system is a way of signalling and transmitting information. The fact that the price of a good rises shows that the good is in short supply. And if prices rise in a sector because of increasing demand, then new producers rush in for the profits. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 5 'Free') | |
| A reaction: [Woff is discussing Hayek] Why do we have a shortage of decent housing in the UK? Centralised economies lack this direct way of discovering where their efforts should be directed. |
| 20518 | Liberty principles can't justify laws against duelling, incest between siblings and euthanasia [Wolff,J] |
| Full Idea: Many laws of contemporary society are very hard to defend in terms of Mill's Liberty Principle, such as laws against duelling, incest between siblings, and euthanasia. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 4 'Poison') | |
| A reaction: [He cites Chief Justice Lord Devlin for this] Being killed in a duel can cause widespread misery. Fear of inbreeding is behind the second one, and fear of murdering the old behind the third one. No man is an island. |
| 20531 | Either Difference allows unequal liberty, or Liberty makes implementing Difference impossible [Wolff,J] |
| Full Idea: Critics say that the Difference Principle allows inequality of liberty ...and (more often) that liberty means we cannot impose any restriction on individual property holdings. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 5 'Nozick') | |
| A reaction: The second objection is associated with Robert Nozick. The point is that you can implement the Difference Principle without restricting liberty. The standard right-wing objection of social welfare. |
| 20526 | Utilitarians argue for equal distribution because of diminishing utility of repetition [Wolff,J] |
| Full Idea: The utilitarian argument for equality assumes that people have 'diminishing marginal returns' for goods. If there are two people and two nice chocolate biscuits, then utilitarianism is likely to recommend one each. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 5 'Arguments') | |
| A reaction: The point is that the second biscuit provides slightly diminished pleasure. This is why you can buy boxes of assorted biscuits, which you are then not required to share. |
| 20528 | Difference Principle: all inequalities should be in favour of the disadvantaged [Wolff,J] |
| Full Idea: Difference Principle: Social and economic inequalities are to be arranged so that they are to the greatest benefit of the least advantaged. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 5 'Choosing') | |
| A reaction: Rivals would say that inequalities should go to those who have earned them. |
| 20503 | Political equality is not much use without social equality [Wolff,J] |
| Full Idea: As Marx observed, and as women have learnt to their cost, equal political rights are worth fighting for, but they are of little value if one is still treated unequally in day-to-day life. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 3 'Participatory') | |
| A reaction: In fact social equality comes first, because that will imply political equality and financial justice. I think it is all covered under the virtue of 'respect', which should have pre-eminence in both public and private life. |
| 20512 | Standard rights: life, free speech, assembly, movement, vote, stand (plus shelter, food, health?) [Wolff,J] |
| Full Idea: The normal liberal basic rights are right to life, free speech, free assembly and freedom of movement, plus the rights to vote and stand for office. Some theorists add the right to a decent living standard (shelter, food and health care). | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 4 'Liberty') | |
| A reaction: I think he has forgotten to add education. In Britain Beatrice Webb seems to have single-handedly added the living standard group to the list. |
| 20513 | If natural rights are axiomatic, there is then no way we can defend them [Wolff,J] |
| Full Idea: The theory of basic natural rights is problematic, because although the theory is rigorous and principled, the disadvantage is that we are left with nothing more fundamental to say in defence of these rights. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 4 'Liberty') | |
| A reaction: This is a nice point about anything which is treated as axiomatic - even Euclid's geometry. Presumably rights can only be justified by the needs of our shared human nature. |
| 20514 | If rights are natural, rather than inferred, how do we know which rights we have? [Wolff,J] |
| Full Idea: If natural rights have a fundamental status, and so are not arrived at on the basis of some other argument, how do we know what rights we have? | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 4 'Liberty') | |
| A reaction: He cites Bentham as using this point. Utilitarianism at least provides a grounding for the identification of possible basic rights. Start from what we want, or what we more objectively need? Human needs, or needs in our present culture? |
| 20522 | Utilitarians might say property ownership encourages the best use of the land [Wolff,J] |
| Full Idea: A utilitarian justification of property rights says allowing people to appropriate property, trade in it, and leave it to their descendants will encourage them to make the most productive use of their resources. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 5 'Locke') | |
| A reaction: This obviously has a point, but equally justifies confiscation of land from people who are not making best use of it. In Sicily many landowners refused to allow the peasants to make any use at all of the land. |
| 20534 | Rights and justice are only the last resorts of a society, something to fall back on [Wolff,J] |
| Full Idea: Justice is the last virtue of society, or at least the last resort. Rights, or considerations of justice, are like an insurance policy: something offering security to fall back on. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 6 'Transcending') | |
| A reaction: I like this. He points out that a good family doesn't talk of rights and justice. We want a friendly harmonious society, with safety nets. |
| 20492 | Following some laws is not a moral matter; trivial traffic rules, for example [Wolff,J] |
| Full Idea: Some laws have little grounding in morality. You may believe you have a moral obligation to stop at a red light at a deserted crossroads, but only because that is what the law tells you to do. | |
| From: Jonathan Wolff (An Introduction to Political Philosophy (Rev) [2006], 2 'Goal') | |
| A reaction: I would have thought such a law was wholly grounded in the morality of teamwork. It is the problem of rule utilitarianism, and also a problem about virtuous character. The puzzle is not the law, but the strict obedience to it. |
| 6865 | A-theory says past, present, future and flow exist; B-theory says this just reports our perspective [Le Poidevin] |
| Full Idea: The A-theory regards our intuitive distinction of time into past, present and future as objective, and takes seriously the idea that time flows; the B-theory says this just reflects our perspective, like the spatial distinction between here and there. | |
| From: Robin Le Poidevin (Interview with Baggini and Stangroom [2001], p.174) | |
| A reaction: The distinction comes from McTaggart. Physics seems to be built on an objective view of time, and yet Einstein makes time relative. What possible evidence could decide between the two theories? |