36 ideas
| 15585 | Later Heidegger sees philosophy as more like poetry than like science [Heidegger, by Polt] |
| Full Idea: In his later work Heidegger came to view philosophy as closer to poetry than to science. | |
| From: report of Martin Heidegger (The Origin of the Work of Art [1935], p.178) by Richard Polt - Heidegger: an introduction 5 'Signs' |
| 17453 | The meaning of a number isn't just the numerals leading up to it [Heck] |
| Full Idea: My knowing what the number '33' denotes cannot consist in my knowing that it denotes the number of decimal numbers between '1' and '33', because I would know that even if it were in hexadecimal (which I don't know well). | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: Obviously you wouldn't understand '33' if you didn't understand what '33 things' meant. |
| 17457 | A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck] |
| Full Idea: An appreciation of the connection between sameness of number and equinumerosity that it reports is essential to even the most primitive grasp of the concept of cardinal number. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 6) |
| 17448 | In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck] |
| Full Idea: One need not conceive of the numerals as objects in their own right in order to count. The numerals are not mentioned in counting (as objects to be correlated with baseball players), but are used. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 3) | |
| A reaction: He observes that when you name the team, you aren't correlating a list of names with the players. I could correlate any old tags with some objects, and you could tell me the cardinality denoted by the last tag. I do ordinals, you do cardinals. |
| 17455 | Is counting basically mindless, and independent of the cardinality involved? [Heck] |
| Full Idea: I am not denying that counting can be done mindlessly, without making judgments of cardinality along the way. ...But the question is whether counting is, as it were, fundamentally a mindless exercise. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: He says no. It seems to me like going on a journey, where you can forget where you are going and where you have got to so far, but those underlying facts are always there. If you just tag things with unknown foreign numbers, you aren't really counting. |
| 17456 | Counting is the assignment of successively larger cardinal numbers to collections [Heck] |
| Full Idea: Counting is not mere tagging: it is the successive assignment of cardinal numbers to increasingly large collections of objects. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: That the cardinals are 'successive' seems to mean that they are ordinals as well. If you don't know that 'seven' means a cardinality, as well as 'successor of six', you haven't understood it. Days of the week have successors. Does PA capture cardinality? |
| 17450 | Understanding 'just as many' needn't involve grasping one-one correspondence [Heck] |
| Full Idea: It is far from obvious that knowing what 'just as many' means requires knowing what a one-one correspondence is. The notion of a one-one correspondence is very sophisticated, and it is far from clear that five-year-olds have any grasp of it. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 4) | |
| A reaction: The point is that children decide 'just as many' by counting each group and arriving at the same numeral, not by matching up. He cites psychological research by Gelman and Galistel. |
| 17451 | We can know 'just as many' without the concepts of equinumerosity or numbers [Heck] |
| Full Idea: 'Just as many' is independent of the ability to count, and we shouldn't characterise equinumerosity through counting. It is also independent of the concept of number. Enough cookies to go round doesn't need how many cookies. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 4) | |
| A reaction: [compressed] He talks of children having an 'operational' ability which is independent of these more sophisticated concepts. Interesting. You see how early man could relate 'how many' prior to the development of numbers. |
| 17459 | Frege's Theorem explains why the numbers satisfy the Peano axioms [Heck] |
| Full Idea: The interest of Frege's Theorem is that it offers us an explanation of the fact that the numbers satisfy the Dedekind-Peano axioms. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 6) | |
| A reaction: He says 'explaining' does not make it more fundamental, since all proofs explain why their conclusions hold. |
| 17454 | Children can use numbers, without a concept of them as countable objects [Heck] |
| Full Idea: For a long time my daughter had no understanding of the question of how many numerals or numbers there are between 'one' and 'five'. I think she lacked the concept of numerals as objects which can themselves be counted. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 5) | |
| A reaction: I can't make any sense of numbers actually being objects, though clearly treating all sorts of things as objects helps thinking (as in 'the victory is all that matters'). |
| 17458 | Equinumerosity is not the same concept as one-one correspondence [Heck] |
| Full Idea: Equinumerosity is not the same concept as being in one-one correspondence with. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 6) | |
| A reaction: He says this is the case, even if they are coextensive, like renate and cordate. You can see that five loaves are equinumerous with five fishes, without doing a one-one matchup. |
| 17449 | We can understand cardinality without the idea of one-one correspondence [Heck] |
| Full Idea: One can have a perfectly serviceable concept of cardinality without so much as having the concept of one-one correspondence. | |
| From: Richard G. Heck (Cardinality, Counting and Equinumerosity [2000], 3) | |
| A reaction: This is the culmination of a lengthy discussion. It includes citations about the psychology of children's counting. Cardinality needs one group of things, and 1-1 needs two groups. |
| 20547 | We should respect the right of people to live in their own way, even if it is irrational [Swift] |
| Full Idea: Forcing people to do what is rational involves a lack of respect, a failure to respect the value of her living her life in her own (irrational) way. | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 2 'Resisting' 6) | |
| A reaction: Up to a point. Irrationally eccentric is one thing, and irrationally self-destructive is another. You can sit back and watch your children embrace a life less happy than the one you wanted for them - but not a life of utter misery. |
| 20564 | Anti-colonial movements usually invoke the right of their 'people' to self-determination [Swift] |
| Full Idea: Nationalist movements seeking to throw off the yoke of colonial rule are often motivated by a sense that their 'people' have the right to self-determination. | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 5 'Intrinsic 1') | |
| A reaction: In 2017, Basques, Catalans and Kurds come to mind. The whole of Africa was an example of this c.1950-80, but there was uncertainty about states, tribes and language groups. |
| 20535 | Isn't it more rational to maximise the average position, but with a safety net? [Swift] |
| Full Idea: Wouldn't it be more rational to choose principles that would maximize the average position, perhaps subject to some 'floor' level beneath which they would not want to take the risk of sinking? | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 1 'Rawls') | |
| A reaction: The criticism is that Rawls's prediction is over-cautious, and that people will take mild risks in what they choose, as long as there is no danger of disaster. (Just as you should allow small children to risk injury, but not death). |
| 20537 | Hypothetical contracts have no binding force [Swift] |
| Full Idea: A common objection to Rawls is that hypothetical contracts, unlike real ones, have no binding force. | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 1 'Rawls') | |
| A reaction: [I think Dworkin made this point] 'Contract' may be metaphorical. Perhaps it is just an 'initial agreement' or a 'working arrangement', |
| 20542 | Cosmopolitans reject the right of different states to distribute resources in different ways [Swift] |
| Full Idea: Cosmopolitans who claim that the same distributive principles should apply to all human beings seem to be denying that different states may make different judgements about how they want to allocate resources among their members. | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 1 'Social') | |
| A reaction: If you want to be a citizen of the world, you have to face up to the pluralistic character of cultures. Do you thereby want to be a citizen of both California and Saudi Arabia? Or are you actually just becoming a citizen of nowhere? |
| 20559 | Democracy is bad, but the other systems are worse [Swift] |
| Full Idea: During WW2 Winston Churchill famously said that democracy is the worst form of government, except for all the others that have been tried. | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 5 'Procedures') | |
| A reaction: [Actually a speech in 1947, which began 'it has been said that....'] Aristotle thought an intelligent and benevolent dictatorship was the best form, but held little hope of achieving it. Getting rid of bad rulers is the big virtue. |
| 20561 | Since all opinions are treated as equal in democracy, it implies there are no right answers [Swift] |
| Full Idea: If there were moral knowledge about political matters, democracy would be a very strange way of reaching it. Democratic law-making means treating each person's view as equally good, which only makes sense if there is nothing to be right or wrong about. | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 5 'Subjectivism') | |
| A reaction: Ah, I suddenly grasp that the modern fad for a rather gormless blanket relativism is rooted in the modern desire to take democracy really seriously. Important to remember Condorcet's point here. |
| 20562 | Design your democracy to treat citizens equally, or to produce better citizens? [Swift] |
| Full Idea: If your main reason for being a democrat is that democratic procedures respect citizens equally, then you may want a different kind of democracy from those who favour it because they think it tends to produce better citizens? | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 5 'Values') | |
| A reaction: [Combine this with Idea 20563] |
| 20563 | Design your democracy to yield political stability, or good decisions? [Swift] |
| Full Idea: If you value democracy because it yields political stability, then you will probably worry about different aspects of the procedure from those who care about its producing good decisions. | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 5 'Values') | |
| A reaction: [Combine this with Idea 20562] Surely the primary aim must be good decisions? The other three options are the result of pessimism about any method achieving that. Instability, inequality and dud citizens are bars to good decisions. |
| 20560 | Teledemocracy omits debate and deliberation, which are important parts of good decisions [Swift] |
| Full Idea: We are averse to teledemocracy because it misses out some important parts of a good decision-making procedure, such as debate and deliberation. | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 5 'Procedures') | |
| A reaction: Perhaps you should be sent a short info pack, and only allowed to vote when you have passed a factual multiple choice test about the topic. Or one pack from each political party. Maybe compulsory online discussion as well. |
| 20554 | Multiculturalism is a barrier to the whole state being a community [Swift] |
| Full Idea: For those wanting to regard the state itself as a community, multiculturalism can be a problem. | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 4 'Liberalism') | |
| A reaction: A very important idea. A certain type of aggressive patriot passionately wants the whole country to be a close-bound community, and becomes deeply frustrated by the impossibility of this in a complex and fluid modern world. |
| 20553 | Liberals mistakenly think individuals choose their values, without reference to the community [Swift] |
| Full Idea: The two core liberal mistakes (according to communitarians) are that people choose their values, and that they do so in some way detached from their communities. | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 4 'Correcting') | |
| A reaction: I think I might be a communitarian liberal, meaning that extreme individualism is both incorrect and pernicious, but that communities should only exist to promote the varied lives of individuals within them. |
| 20556 | The best way to build a cohesive community is to be involved in a war [Swift] |
| Full Idea: There is nothing like a war to build a sense of common purpose, of being in the same boat, and to generate the kind of interaction between people that breaks down divisive social boundaries. | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014]) | |
| A reaction: A nice warning to those who over-do or simplify communitarianism. Alternatively, the greatest sign of health in a community is that citizens have almost no interest in one another? |
| 20557 | Membership and inclusion in a community implies non-membership and exclusion [Swift] |
| Full Idea: Community is about membership and inclusion. But that means it is also about non-membership and exclusion. | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 4 'Conc') | |
| A reaction: I'm a fan of communitarianism (focused on Aristotle's life of individual virtue for each citizen), but I'm beginning to see that it has a poisonous cousin travelling under the same name. The cousin's rallying cries focus on aliens and enemies. |
| 20555 | Liberals are concerned to protect individuals from too much community [Swift] |
| Full Idea: Liberals are concerned to protect individuals from too much community - from practices that stifle the individual's freedom to choose for herself how she lives her life. | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 4 'Liberalism') | |
| A reaction: The phrase 'too much community' is an excellent warning to communitarians. I'm happy to be enmeshed in a community, as long as it is composed of highly liberal and easy-going individuals. Avoid too much bad community. |
| 20540 | Redistributing wealth treats some people as means, rather than as ends [Swift] |
| Full Idea: Treating people as means seems like a fairly accurate description of what is involved when the state coercively redistributes resources from some to others. | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 1 'Nozick') | |
| A reaction: The objection comes from Nozick, and alludes to Kant's desire to treat everyone as an end in themselves. Personally I don't mind at all being treated as a means, when my wife asks me to make her a cup of tea. Or paying my taxes to help the community. |
| 20551 | Men have had the power to structure all of our social institutions [Swift] |
| Full Idea: The problem for feminists is that men have had the power to structure all our social institutions - family, economy, polity - in ways that suit them. | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 3 'Gender') | |
| A reaction: An interesting question is whether masculine domination runs even deeper than that, into our value system, our metaphysics, our science, our epistemology, our language. How do you tell? If women take over half the masculine roles, does that solve it? |
| 20545 | Maybe a freedom is from a restraint, and also in order to do something [Swift] |
| Full Idea: Maybe freedom is a triadic relation, involving an agent, freedom from a contraint, and in order to act towards some goal. | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 2 'Two') | |
| A reaction: [He cites Gerald MacCallum for this thought] The point is that this makes freedom both negative and positive, contrary to Isaiah Berlin's claim. But on the first day of the school holidays you are 'free', with nothing in particular in mind. |
| 20550 | Opportunity should ignore extraneous factors, or foster competence, or ignore all disadvantages [Swift] |
| Full Idea: The minimal conception of equality of opportunity is that race or gender or religion should not affect chances of a good job or education. The conventional conception needs equality in acquiring competences. Radical views ignore inborn disadvantages. | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 3 'Equality') | |
| A reaction: [my summary of Swift] The strong version only says the less talented should have access to large rewards. The whole idea has strong capitalist assumptions. |
| 20536 | Inequalities are needed, as incentives to do the most important jobs [Swift] |
| Full Idea: Without inequalities, people will have no incentive to do one job rather than another - to do the kind of work which is most useful. | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 1 'Rawls') | |
| A reaction: The reality is that the lowest pay goes to the jobs that no one wants to do, and all the really nice jobs are usually well paid. Which is a conspiracy, because all the salaries are set by the people with the nice jobs. |
| 20548 | A person can desire redistibution of wealth, without it being for reasons of equality [Swift] |
| Full Idea: Someone who rejects equality can care passionately that resources should be transferred from the rich to the poor. They are just rejecting a particular reason that might be offered to justify the redistribution. | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 3 'Intro') | |
| A reaction: For example, it might be for utilitarian reasons, which usually only seek maximised happiness, not equal happiness. And one may love many forms of equality, without economic equality being one of them. |
| 20541 | You can't necessarily sell your legitimate right to something, even if you produced it [Swift] |
| Full Idea: Ownership is a complicated idea. I have a right to the office photocopier, but I can's sell the right to others. If people have absolute rights over what they produce, why can't parents sell their children into slavery? | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 1 'Nozick') | |
| A reaction: If I make a car from stolen parts, does constructing it make it mine? Etc. Do birds own their nests? Swift goes on to ask if we 'own' our bodies. |
| 20546 | Libertarians about property ignore the fact that private property is a denial of freedoms [Swift] |
| Full Idea: Libertarians say that they care about freedom, and argue for private property rights on freedom grounds. But they don't sem to care about, or even notice, the unfreedom implied by the existence of private property rights. | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 2 'Freedom') | |
| A reaction: When I pass some vast country estate totally surrounded by a high wall, I certainly don't think how wonderful it is that someone has the right to own this property as private land. On the contrary.... |
| 20533 | Justice can be seen as fairness or entitlement or desert [Swift] |
| Full Idea: The three influential conceptions of justice are as fairness (Rawls), as entitlement (Nozick), and as desert. | |
| From: Adam Swift (Political Philosophy (3rd ed) [2014], 1 'Concept') |