34 ideas
| 12452 | Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer] |
| Full Idea: Not to the mathematician, but to the psychologist, belongs the task of explaining why ...we are averse to so-called contradictory systems in which the negative as well as the positive of certain propositions are valid. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.79) | |
| A reaction: Was the turning point of Graham Priest's life the day he read this sentence? I don't agree. I take the principle of non-contradiction to be a highly generalised observation of how the world works (and Russell agrees with me). |
| 15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |
| Full Idea: From the intuitionist standpoint the dogma of the universal validity of the principle of excluded third in mathematics can only be considered as a phenomenon of history of civilization, like the rationality of pi or rotation of the sky about the earth. | |
| From: Luitzen E.J. Brouwer (works [1930]), quoted by Shaughan Lavine - Understanding the Infinite VI.2 | |
| A reaction: [Brouwer 1952:510-11] |
| 9455 | Maybe proper names have the content of fixing a thing's category [Bealer] |
| Full Idea: Some say that proper names have no descriptive content, but others think that although a name does not have the right sort of descriptive content which fixes a unique referent, it has a content which fixes the sort or category to which it belongs. | |
| From: George Bealer (Propositions [1998], §7) | |
| A reaction: Presumably 'Mary', and 'Felix', and 'Rover', and 'Smallville' are cases in point. There is a well known journalist called 'Manchester', a famous man called 'Hilary', a village in Hertfordshire called 'Matching Tie'... Interesting, though. |
| 9454 | The four leading theories of definite descriptions are Frege's, Russell's, Evans's, and Prior's [Bealer] |
| Full Idea: The four leading theories of definite descriptions are Frege's, Russell's, Evans's, and Prior's, ...of which to many Frege's is the most intuitive of the four. Frege says they refer to the unique item (if it exists) which satisfies the predicate. | |
| From: George Bealer (Propositions [1998], §5) | |
| A reaction: He doesn't expound the other three, but I record this a corrective to the view that Russell has the only game in town. |
| 18119 | Mathematics is a mental activity which does not use language [Brouwer, by Bostock] |
| Full Idea: Brouwer made the rather extraordinary claim that mathematics is a mental activity which uses no language. | |
| From: report of Luitzen E.J. Brouwer (Mathematics, Science and Language [1928]) by David Bostock - Philosophy of Mathematics 7.1 | |
| A reaction: Since I take language to have far less of a role in thought than is commonly believed, I don't think this idea is absurd. I would say that we don't use language much when we are talking! |
| 18247 | Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro] |
| Full Idea: In his early writing, Brouwer took a real number to be a Cauchy sequence determined by a rule. Later he augmented rule-governed sequences with free-choice sequences, but even then the attitude is that Cauchy sequences are potential, not actual infinities. | |
| From: report of Luitzen E.J. Brouwer (works [1930]) by Stewart Shapiro - Philosophy of Mathematics 6.6 | |
| A reaction: This is the 'constructivist' view of numbers, as espoused by intuitionists like Brouwer. |
| 12451 | Scientific laws largely rest on the results of counting and measuring [Brouwer] |
| Full Idea: A large part of the natural laws introduced by science treat only of the mutual relations between the results of counting and measuring. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.77) | |
| A reaction: His point, I take it, is that the higher reaches of numbers have lost touch with the original point of the system. I now see the whole issue as just depending on conventions about the agreed extension of the word 'number'. |
| 18118 | Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock] |
| Full Idea: Brouwer regards as somehow 'wicked' the idea that mathematics can be applied to a non-mental subject matter, the physical world, and that it might develop in response to the needs which that application reveals. | |
| From: report of Luitzen E.J. Brouwer (Mathematics, Science and Language [1928]) by David Bostock - Philosophy of Mathematics 7.1 | |
| A reaction: The idea is that mathematics only concerns creations of the human mind. It presumably has no more application than, say, noughts-and-crosses. |
| 12454 | Intuitionists only accept denumerable sets [Brouwer] |
| Full Idea: The intuitionist recognises only the existence of denumerable sets. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80) | |
| A reaction: That takes you up to omega, but not beyond, presumably because it then loses sight of the original intuition of 'bare two-oneness' (Idea 12453). I sympathise, but the word 'number' has shifted its meaning a lot these days. |
| 12453 | Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer] |
| Full Idea: Neo-intuitionism sees the falling apart of moments, reunited while remaining separated in time, as the fundamental phenomenon of human intellect, passing by abstracting to mathematical thinking, the intuition of bare two-oneness. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80) | |
| A reaction: [compressed] A famous and somewhat obscure idea. He goes on to say that this creates one and two, and all the finite ordinals. |
| 8728 | Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer] |
| Full Idea: Mathematics rigorously treated from the point of view of deducing theorems exclusively by means of introspective construction, is called intuitionistic mathematics. It deviates from classical mathematics, which believes in unknown truths. | |
| From: Luitzen E.J. Brouwer (Consciousness, Philosophy and Mathematics [1948]), quoted by Stewart Shapiro - Thinking About Mathematics 1.2 | |
| A reaction: Clearly intuitionist mathematics is a close cousin of logical positivism and the verification principle. This view would be anathema to Frege, because it is psychological. Personally I believe in the existence of unknown truths, big time! |
| 10117 | Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman] |
| Full Idea: The concern of mathematical intuitionists was that the use of certain forms of inference generates, not contradiction, but unjustified assertions. | |
| From: report of Luitzen E.J. Brouwer (Intuitionism and Formalism [1912]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: This seems to be the real origin of the verificationist idea in the theory of meaning. It is a hugely revolutionary idea - that ideas are not only ruled out of court by contradiction, but that there are other criteria which should also be met. |
| 9453 | Sentences saying the same with the same rigid designators may still express different propositions [Bealer] |
| Full Idea: The propositions behind 'Cicero is emulated more than Tully' seems to differ somehow from 'Tully is emulated more than Cicero', despite the proper names being rigid designators. | |
| From: George Bealer (Propositions [1998], §1) | |
| A reaction: Interesting, because this isn't a directly propositional attitude situation like 'believes', though it depends on such things. Bealer says this is a key modern difficulty with propositions. |
| 9452 | Propositions might be reduced to functions (worlds to truth values), or ordered sets of properties and relations [Bealer] |
| Full Idea: The reductionist view of propositions sees them as either extensional functions from possible worlds to truth values, or as ordered sets of properties, relations, and perhaps particulars. | |
| From: George Bealer (Propositions [1998], §1) | |
| A reaction: The usual problem of all functional accounts is 'what is it about x that enables it to have that function?' And if they are sets, where does the ordering come in? A proposition isn't just a list of items in some particular order. Both wrong. |
| 9451 | Modal logic and brain science have reaffirmed traditional belief in propositions [Bealer] |
| Full Idea: Philosophers have been skeptical about abstract objects, and so have been skeptical about propositions,..but with the rise of modal logic and metaphysics, and cognitive science's realism about intentional states, traditional propositions are now dominant. | |
| From: George Bealer (Propositions [1998], §1) | |
| A reaction: I personally strongly favour belief in propositions as brain states, which don't need a bizarre ontological status, but are essential to explain language, reasoning and communication. |
| 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. |
| 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. |
| 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. |
| 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? |