27 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. |
| 6386 | In no important way can psychology be reduced to the physical sciences [Davidson] |
| Full Idea: There is no important sense in which psychology can be reduced to the physical sciences. | |
| From: Donald Davidson (The Material Mind [1973], p.259) | |
| A reaction: In no 'important' way can the beauty of the Lake District be reduced to geology - but it is geology. 'Important' to whom? To a metaphysician, I would say psychology does reduce to physics, and that is important, but it is not important to a psychologist. |
| 23125 | Most good social changes are incremental, rather than revolutionary [Gopnik] |
| Full Idea: More permanent positive social change is made incrementally rather than by revolutionary transformation. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 1) | |
| A reaction: This is the standard liberal response to revolution. Revolutionaries obviously consider such a claim to be very naïve, and a failure to grasp how deep the changes need to go. |
| 23126 | Conservatives often want peace, prosperity and tolerance, but not social fairness [Gopnik] |
| Full Idea: Many conservatives want their world to be peaceful, properous, and pluralist, just as liberals do, but they don't particularly care that it be fair. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 1) | |
| A reaction: Every conservative will have a sense of what is fair (such as appropriate punishments, and keeping of contracts), but they are more inclined to think that fairness must be fought for by individuals, not imposed by governments. |
| 23132 | Conservatives believe obedience and rank are essential to social order [Gopnik] |
| Full Idea: The idea that the appearance of submission and obedience and rank are essential to order is at the heart of the conservative ideal. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 2) | |
| A reaction: [He has just quoted Edmund Burke writing of Marie Antoinette] I once heard Richard Hare say that he thought social order would be best modelled on the army. A colleague once told me that obedience is a prime duty of a school teacher. |
| 23128 | The opposite of liberalism is dogmatism [Gopnik] |
| Full Idea: The opposite of liberalism is not conservatism but dogmatism. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 1) | |
| A reaction: Nice. It pinpoints the liberal opposition to both extremes of normal politics. It might make anarchists their allies, though! |
| 23142 | People are fallible, so liberalism tries to distribute power [Gopnik] |
| Full Idea: Liberalism makes the idea of fallibility into a political practice by trying not to have too much power concentrated in one place or part of the system. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 3) | |
| A reaction: There is a potential inefficiency and failure to focus on key goals implicit in this aim. It may be a good idea for a peacetime democracy, but a terrible idea for a wartime army. To stop corruption, don't let anyone do anything? |
| 23143 | Liberals have tried very hard to build a conscience into their institutions [Gopnik] |
| Full Idea: What liberalism can say on its own behalf is that no system of power in human history has tried harder to insert a corrective conscience into its institutions. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 3) | |
| A reaction: What we are learning in recent years is that wonderful liberal institutions can be quietly eroded by the forces of darkness, once those forces have sufficient control of the media to hide what they are doing. The 'rule of law' is wobbling. |
| 23141 | Left-wingers are inconsistent in their essentialist descriptions of social groups [Gopnik] |
| Full Idea: A criticism of the left is that it is essentialist at some moments, and wildly anti-essentialist at others. We can call this opportunistic essentialism. Gender is fluid - except for transgender kids. Race is a construction - except for white races. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 3) | |
| A reaction: [compressed] Interesting. Gopnik's solution seems to be to abandon all social essentialism as wicked. In this context he is probably right, but I am firmly committed to the idea that many entities in the world have essential natures. 'Bourgeois'. |
| 23124 | Liberal community is not blood ties or tradition, but shared choices, and sympathy for the losers [Gopnik] |
| Full Idea: The liberal idea of community is not one, as it is for many conservatives, of blood ties or traditional authority. It rest on the idea of shared choices …including even a sense of sympathy for those caught on the losing side of the argument. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 1) | |
| A reaction: The key point is that most liberals (other than extreme libertarians) have a strong sense of community, contrary to the standard criticisms offered by communitarians. |
| 23127 | Liberal community includes flight from the family, into energetic reforming groups [Gopnik] |
| Full Idea: Where conservatives believe in the renewal of traditional community, liberals believe as well in the flight from family and tradition into new kinds of communal order. …It is an idea of assembling confidence and energies for reform. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 1) | |
| A reaction: He cites Greenwich Village as an example. This suggests that his vision is a little narrow. His communities are for radicals who flee to join like minds in big cities. Politics must care about community for those left behind. Pubs, sport and pets. |
| 23138 | Modern left-wingers criticise liberalism's control of culture [Gopnik] |
| Full Idea: Most left-wing critiques of liberalism now turn more often on its cultural power and its cultural illusions. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 3) | |
| A reaction: As opposed to older Marxists critiques of the exploitation of workers. This is certainly fertile ground for interesting studies of our culture. It is very hard to grasp the influence had by the endless stories we expose ourselves to. |
| 23129 | Right-wingers attack liberal faith in reason, left-wingers attack its faith in reform [Gopnik] |
| Full Idea: The right-wing critique of liberalism is largely an attack on its overreliance on reason; the left-wing one, mostly an attack on its false faith in reform. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 2) | |
| A reaction: I doubt whether sensible liberals do rely too much on reason, though they do rely of scientific evidence (after peer review!). No one can doubt that lots of reforms have occurred, so it must be frustration with the very slow process. |
| 23133 | Cosmopolitan liberals lack national loyalty, and welcome excessive immigration [Gopnik] |
| Full Idea: Critics say liberal cosmopolitanism is indifference to national loyalty, making them easily contemplate going elsewhere and, worse still, welcoming in the world through unsifted immigration. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 2) | |
| A reaction: There is certainly some truth in this. Not all liberals are so cosmopolitan, though. It is interesting to observe whether people who retire stay in their old community or move to somewhere quite new. |
| 23139 | Liberalism's attempt to be neutral and colour-blind erases cultural identities [Gopnik] |
| Full Idea: The 'colour-blind' universe of 'neutral' liberalism is actually an attempt to erase cultural identity and history. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 3) | |
| A reaction: This is the modern critique of liberalism [centred on the Intersectionality of Bell Hooks or Kimberlé Crenshaw], which analyses alienated minorities, and their emphasis on their difference in response. It can lead to 'identity politics'. |
| 23135 | Classic Marxists see liberalism as the ideology of the bourgeoisie [Gopnik] |
| Full Idea: The classic Marxist account shows liberalism as merely the ideology of the bourgeoisie. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 3) | |
| A reaction: The word 'merely' does an awful lot of work in philosohy! I suspect that 'bourgeoisie' is self-defining here - as the believers in liberalism - given that lots of Marxists emerge from the middle classes. |
| 23140 | Environmental disasters result not from capitalism, but from a general drive for growth [Gopnik] |
| Full Idea: It is the drive for growth, not capitalism in particular, that makes environmental disasters happen. Those caused by the command economics of Eastern Europe were far greater than even the worst known in Western Europe. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 3) | |
| A reaction: So the next question is whether you can have capitalism without a drive for growth. I would have thought not, given the role recycled profit plays in driving capitalism. Command economies are more easily swept away. |
| 23130 | Popular imperialism gives the poor the belief that their acts have world historical meaning [Gopnik] |
| Full Idea: Popular imperialism is the cosmopolitanism of the poor, the lever by which the small and impotent come to believe that their acts have world historical meaning. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 2) | |
| A reaction: It is not only the poor who like imperialism. The focus of this popular attitude is the armed forces, and especially the army, where personal bravery is most obvious. The army gets strong support, no matter how dubious are its activities. |
| 23131 | Patriots love their place, but nationalists have a paranoid ethnic hostility [Gopnik] |
| Full Idea: The patriot loves his place and its cheeses; …the nationalist has not particular affection for the place, but employs his obsessive sense of encirclement and grievance on behalf of acts of ethnic vengeance. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 2) | |
| A reaction: 'Vengeance' seems a bit strong. John Le Carré said nationalists are distinguished by the need to have enemies. Russia is particularly obsessed with 'encirclement'. |
| 23136 | Liberal free speech is actually paid speech [Gopnik] |
| Full Idea: What liberals call free speech or a free press is invariably paid speech. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 3) | |
| A reaction: He give this as the left-wing view of liberalism. The much-hated social media are a substantial breech in this tendency. Sales of newspapers are declining everywhere, so the battle is for television channels. |
| 23134 | A 'free' society implies a free market, which always produces predatory capitalism and inequalities [Gopnik] |
| Full Idea: 'Free societies', as a matter of practical fact, always mean free-market societies - and free markets will never sponsor more than predatory capitalism. Inequalities always emerge. | |
| From: Adam Gopnik (A Thousand Small Sanities [2019], 3) | |
| A reaction: This is part of his account of left-wing objections to liberalism. The crux of the liberal view is a conviction that the worst of capitalism can be restrained. This began to look doubtful once huge multinational companies emerged. What to do? |