47 ideas
| 9572 | Realists about sets say there exists a null set in the real world, with no members [Chihara] |
| Full Idea: In the Gödelian realistic view of set theory the statement that there is a null set as the assertion of the existence in the real world of a set that has no members. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 11.6) | |
| A reaction: It seems to me obvious that such a claim is nonsense on stilts. 'In the beginning there was the null set'? |
| 9550 | We only know relational facts about the empty set, but nothing intrinsic [Chihara] |
| Full Idea: Everything we know about the empty set is relational; we know that nothing is the membership relation to it. But what do we know about its 'intrinsic properties'? | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.5) | |
| A reaction: Set theory seems to depend on the concept of the empty set. Modern theorists seem over-influenced by the Quine-Putnam view, that if science needs it, we must commit ourselves to its existence. |
| 9562 | In simple type theory there is a hierarchy of null sets [Chihara] |
| Full Idea: In simple type theory, there is a null set of type 1, a null set of type 2, a null set of type 3..... (Quine has expressed his distaste for this). | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 07.4) | |
| A reaction: It is bad enough trying to individuate the unique null set, without whole gangs of them drifting indistinguishably through the logical fog. All rational beings should share Quine's distaste, even if Quine is wrong. |
| 9573 | The null set is a structural position which has no other position in membership relation [Chihara] |
| Full Idea: In the structuralist view of sets, in structures of a certain sort the null set is taken to be a position (or point) that will be such that no other position (or point) will be in the membership relation to it. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 11.6) | |
| A reaction: It would be hard to conceive of something having a place in a structure if nothing had a relation to it, so is the null set related to singeton sets but not there members. It will be hard to avoid Platonism here. Set theory needs the null set. |
| 9551 | What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara] |
| Full Idea: What is it about the intrinsic properties of just that one unit set in virtue of which Bill Clinton is related to just it and not to any other unit sets in the set-theoretical universe? | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.5) | |
| A reaction: If we all kept pet woodlice, we had better not hold a wood louse rally, or we might go home with the wrong one. My singleton seems seems remarkably like yours. Could we, perhaps, swap, just for a change? |
| 9549 | The set theorist cannot tell us what 'membership' is [Chihara] |
| Full Idea: The set theorist cannot tell us anything about the true relationship of membership. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.5) | |
| A reaction: If three unrelated objects suddenly became members of a set, it is hard to see how the world would have changed, except in the minds of those thinking about it. |
| 9571 | ZFU refers to the physical world, when it talks of 'urelements' [Chihara] |
| Full Idea: ZFU set theory talks about physical objects (the urelements), and hence is in some way about the physical world. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 11.5) | |
| A reaction: This sounds a bit surprising, given that the whole theory would appear to be quite unaffected if God announced that idealism is true and there are no physical objects. |
| 9563 | A pack of wolves doesn't cease when one member dies [Chihara] |
| Full Idea: A pack of wolves is not thought to go out of existence just because some member of the pack is killed. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 07.5) | |
| A reaction: The point is that the formal extensional notion of a set doesn't correspond to our common sense notion of a group or class. Even a highly scientific theory about wolves needs a loose notion of a wolf pack. |
| 9561 | The mathematics of relations is entirely covered by ordered pairs [Chihara] |
| Full Idea: Everything one needs to do with relations in mathematics can be done by taking a relation to be a set of ordered pairs. (Ordered triples etc. can be defined as order pairs, so that <x,y,z> is <x,<y,z>>). | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 07.2) | |
| A reaction: How do we distinguish 'I own my cat' from 'I love my cat'? Or 'I quite like my cat' from 'I adore my cat'? Nevertheless, this is an interesting starting point for a discussion of relations. |
| 9552 | Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara] |
| Full Idea: In first-order logic a set of sentences is 'consistent' iff there is an interpretation (or structure) in which the set of sentences is true. ..For Frege, though, a set of sentences is consistent if it is not possible to deduce a contradiction from it. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 02.1) | |
| A reaction: The first approach seems positive, the second negative. Frege seems to have a higher standard, which is appealing, but the first one seems intuitively right. There is a possible world where this could work. |
| 9553 | Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara] |
| Full Idea: With the invention of analytic geometry (by Fermat and then Descartes) physical space could be represented as having a mathematical structure, which could eventually lead to its axiomatization (by Hilbert). | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 02.3) | |
| A reaction: The idea that space might have axioms seems to be pythagoreanism run riot. I wonder if there is some flaw at the heart of Einstein's General Theory because of this? |
| 10192 | We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride] |
| Full Idea: Chihara's 'constructability theory' is nominalist - mathematics is reducible to a simple theory of types. Instead of talk of sets {x:x is F}, we talk of open sentences Fx defining them. Existence claims become constructability of sentence tokens. | |
| From: report of Charles Chihara (A Structural Account of Mathematics [2004]) by Fraser MacBride - Review of Chihara's 'Structural Acc of Maths' p.81 | |
| A reaction: This seems to be approaching the problem in a Fregean way, by giving an account of the semantics. Chihara is trying to evade the Quinean idea that assertion is ontological commitment. But has Chihara retreated too far? How does he assert existence? |
| 9559 | If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara] |
| Full Idea: If mathematics shares whatever confirmation accrues to the theories using it, would it not be reasonable to suppose that mathematics shares whatever disconfirmation accrues to the theories using it? | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 05.8) | |
| A reaction: Presumably Quine would bite the bullet here, although maths is much closer to the centre of his web of belief, and so far less likely to require adjustment. In practice, though, mathematics is not challenged whenever an experiment fails. |
| 9566 | No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara] |
| Full Idea: Evidently, no scientific explanations of specific phenomena would collapse as a result of any hypothetical discovery that no mathematical objects exist. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 09.1) | |
| A reaction: It is inconceivable that anyone would challenge this claim. A good model seems to be drama; a play needs commitment from actors and audience, even when we know it is fiction. The point is that mathematics doesn't collapse either. |
| 18658 | The 'Kantian' self steps back from commitment to its social situation [Kymlicka] |
| Full Idea: The 'Kantian' view of the self strongly defends the view that the self is prior to its socially given roles and relationships, and is free only if it is capable of holding these features of its social situation at a distance, and judging them by reason. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 6.3) | |
| A reaction: There is no correct answer here, because I am capable of Kantian distancing, and also capable of submersing myself in the social constructions around me. If society fosters rebellion (1810s, 1960s) then we become more Kantian. |
| 9568 | I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara] |
| Full Idea: What I refer to as an 'equivalence class' (of line segments of a particular length) is an open sentence in my Constructibility Theory. I just use this terminology of the Platonist for didactic purposes. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 09.10) | |
| A reaction: This is because 'equivalence classes' is committed to the existence of classes, which is Quinean Platonism. I am with Chihara in wanting a story that avoids such things. Kit Fine is investigating similar notions of rules of construction. |
| 9547 | Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara] |
| Full Idea: Causal theories of reference seem doomed to failure for the case of reference to mathematical entities, since such entities are evidently causally inert. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], 01.3) | |
| A reaction: Presumably you could baptise a fictional entity such as 'Polonius', and initiate a social causal chain, with a tradition of reference. You could baptise a baby in absentia. |
| 19216 | Propositions (such as 'that dog is barking') only exist if their items exist [Williamson] |
| Full Idea: A proposition about an item exists only if that item exists... how could something be the proposition that that dog is barking in circumstances in which that dog does not exist? | |
| From: Timothy Williamson (Necessary Existents [2002], p.240), quoted by Trenton Merricks - Propositions | |
| A reaction: This is a view of propositions I can't make sense of. If I'm under an illusion that there is a dog barking nearby, when there isn't one, can I not say 'that dog is barking'? If I haven't expressed a proposition, what have I done? |
| 18650 | Teleological theories give the good priority over concern for people [Kymlicka] |
| Full Idea: Teleological theories take concern for the good (e.g. freedom or utility) as fundamental, and concern for people as derivative. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 2.4.a.ii) | |
| A reaction: There's a nice fundamental question with which to begin a discussion of value: which matters most - abstract values, or individual people? Placing a collective of people first (Stalinism?) seems to fall between them. |
| 18664 | Maybe the particularist moral thought of women is better than the impartial public thinking of men [Kymlicka] |
| Full Idea: There is a significant strand of contemporary feminism which argues that we should take seriously women's different morality. ...The particularistic thought women employ is a better morality than the impartial thought men employ in the public sphere. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 7.3) | |
| A reaction: I had taken Particularism to be an offshoot of virtue theory, as promulgated by Jonathan Dancy. Evidently the influence of feminism is strong. Personally I think the world would be a better place if it was run by women. |
| 18624 | Utilitarianism is not a decision-procedure; choice of the best procedure is an open question [Kymlicka] |
| Full Idea: Utilitarianism is essentially a 'standard of rightness', not a 'decision-procedure'. ...It is an open question whether we should employ a utilitarian decision-procedure - indeed, this question itself is to be answered by examining its consequences. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 2.3.b) | |
| A reaction: The point is that the aim is to maximise happiness, and you might do that by just maximising baked bean consumption, and not even thinking about happiness. This idea is labelled 'indirect utilitarianism'. Happiness does seem to be a by-product. |
| 18626 | One view says start with equality, and infer equal weight to interests, and hence maximum utility [Kymlicka] |
| Full Idea: The first main argument for utilitarianism is that people matter equally, and hence each person's interests should be given equal weight, and hence morally right acts will maximise utility. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 2.4.a) | |
| A reaction: The point is that this starts from the aim of equality, and infers maximum utility as its consequence. Equality has a primitive value. Whenever you dig down to a primitive value in a theory, I just find myself puzzled. What can justify basic equality? |
| 18627 | A second view says start with maximising the good, implying aggregation, and hence equality [Kymlicka] |
| Full Idea: The second main argument for utilitarianism defines the right in terms of maximising the good, which leads to the utilitarian aggregation standard, which as a mere consequence treats people's interests equally. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 2.4.b) | |
| A reaction: This takes maximum good as a primitive, and arrives at equality as the way to achieve it. So which is more morally fundamental, a maximum of goodness, or human equality? Kymlicka says this idea is too impersonal. |
| 18625 | To maximise utility should we double the population, even if life somewhat deteriorates? [Kymlicka] |
| Full Idea: Morally, should we double the population, even if it means reducing each person's welfare by almost half (since that will still increase overall utility)? | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 2.4.b) | |
| A reaction: [He cites Derek Parfit for this] The key word is 'almost', which ensures a small increase in overall utility. I think this is a particularly good objection to utilitarianism, which aims to maximise an abstraction called 'utility'. |
| 18638 | The difference principles says we must subsidise the costs of other people's choices [Kymlicka] |
| Full Idea: The difference principle does not make any distinction between chosen and unchosen inequalities, ....but the difference principle requires that some people subsidise the costs of other people's choices. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 3.3.b.2) | |
| A reaction: We do this in education, allowing people to study things in which we can see little point. We subsidise public ceremonies which strike us as ridiculous. |
| 18635 | Social contract theories are usually rejected because there never was such a contract [Kymlicka] |
| Full Idea: Social contract theories have all been subjected to the same criticism - that there never was such a state of nature, or such a contract. Hence neither citizens nor government are bound by it. Contracts only create obligations if they are actually agreed. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 3.3) | |
| A reaction: Even if they have been agreed in the past, why should subsequent generations be bound to them? Modern Germans aren't bound by their grandparents' oaths of allegiance to fascism. |
| 18630 | Utilitarianism is no longer a distinctive political position [Kymlicka] |
| Full Idea: Modern utilitarianism, despite its radical heritage, no longer defines a distinctive political position. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 2.6) | |
| A reaction: This is his final sentence on the topic. I suppose utilitarianism exists as a moral theory at too high a level of generality to count as a political theory. |
| 18623 | The quest of the general good is partly undermined by people's past entitlements [Kymlicka] |
| Full Idea: The existence of past entitlements on the part of particular people partially pre-empts, or constrains, the utilitarian quest to maximise the general good. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 2.3.a) | |
| A reaction: In other words, there is never a clean slate in politics (except in some hideously violent revolution). You might be able to justify to someone a withdrawal of their past entitlements. E.g. confiscating a stolen painting that was bought in ignorance. |
| 18628 | We shouldn't endorse preferences which reject equality, and show prejudice and selfishness [Kymlicka] |
| Full Idea: Equality should enter into the very formation of our preferences. ....Prejudiced and selfish preferences should be excluded from the start, for they already reflect a failure to show equal consideration. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 2.5.b) | |
| A reaction: This is meant to block utilitarian summing of preferences like racism, but it feels like a rather desperate attempt to get righteous liberal values in at the beginning, where they can't be questioned. How can you justify equal respect and treatment? |
| 18629 | Using utilitarian principles to make decisions encourages cold detachment from people [Kymlicka] |
| Full Idea: Acting directly on utilitarian grounds is counter-productive, for it encourages a contingent and detached attitude towards what should be whole-hearted personal and political commitments. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 2.7) | |
| A reaction: I've always seen this as an objection to utilitarianism, but I now see that it is only an objection to the decision procedure. We should be warm-hearted and committed, in the knowledge that this will increase benefits to all. Hm. A bit schizoid. |
| 18637 | Utilitarianism is irrational if it tells you to trade in your rights and resources just for benefits [Kymlicka] |
| Full Idea: Utilitarianism is an irrational choice, for it is rational to ensure your basic rights and resources are protected, even if you thereby lessen your chance of receiving benefits above and beyond the basic goods that you seek to protect. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 3.3) | |
| A reaction: [He's discussing Rawls] Utilitarians would obviously respond to this by saying that the rights and resources are needed to protect future benefits, so it would be short-termism to trade them in now. |
| 18663 | Modern liberalism has added personal privacy to our personal social lives [Kymlicka] |
| Full Idea: Modern liberalism is concerned not only to protect the private sphere of social life, but also to carve out a realm within the private sphere where individuals can have privacy. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 7.2.b) | |
| A reaction: Interestingly, he associates this development with the romantic movement, which designated social interaction as public and political, creating a need for true privacy. Privacy is the blessing and blight of the modern world. |
| 18632 | Liberalism tends to give priority to basic liberties [Kymlicka] |
| Full Idea: One way of differentiating liberalism is that it gives priority to the basic liberties. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 3.1.b) | |
| A reaction: [He is citing Rawls for this] This is not the same as extreme libertarianism, which makes liberty the only priority. The issue would be over which liberties count as 'basic'. Taxation would be a good test case. |
| 18656 | Marxists say liberalism is unjust, because it allows exploitation in the sale of labour [Kymlicka] |
| Full Idea: The fundamental flaw of liberal justice, Marxists claim, is that it licences the continuation of the worker by the capitalist, since it licences the buying and selling labour. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 5.2.a) | |
| A reaction: I can't see that all sale of labour is exploitation, if (for example) the wage paid was extremely high (maybe even higher than the employer's wage, which is possible). So exploitation involves something more. |
| 18659 | The 'Kantian' view of the self misses the way it is embedded or situated in society [Kymlicka] |
| Full Idea: Communitarians believe that the 'Kantian' view of the self is false, because it ignores the fact that the self is 'embedded' or 'situated' in existing social practices, so that we cannot always stand back and opt out of them. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 6.3) | |
| A reaction: [Hegel and Charles Taylor 1979 seem to be the sources for this] I have several times been told that I am so typical of the culture I arose in that it is almost comical. This was quite disconcerting, but I got used to it, and now I love it. |
| 18660 | Communitarians say we should pay more attention to our history [Kymlicka] |
| Full Idea: Communitarians like to say that political theory should pay more attention to the history of each culture. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 6.4.c) | |
| A reaction: I like this. Kylicka says communitarians tend not to do this, partly because history might reveal an unpleasant basis for present society (such as English country house life benefiting from slavery). The ignorance of history among politicians appals me. |
| 18657 | Communitarian states only encourage fairly orthodox ideas of the good life [Kymlicka] |
| Full Idea: A communitarian state can and should encourage people to adopt conceptions of the good that conform to the community's way of life, while discouraging conceptions of the good that conflict with it. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 6.2) | |
| A reaction: This is the conservative aspect of communitarianism which many people (notably liberals) find uncongenial. This conservatism is implicit in Aristotle's account of virtue. I have become more conservative to accommodate it. |
| 18649 | If everyone owned himself, that would prevent slavery [Kymlicka] |
| Full Idea: The best way to prevent enslavement of one person to another is to give each person ownership over himself. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 4.2.c) | |
| A reaction: [The idea comes from Nozick, but Kymlicka is assessing how it should be understood] The best way to block any social evil like slavery is to make it unthinkable. Legislation is second best. Presumably I could sell myself into slavery (like Faust)? |
| 18640 | Libertarians like the free market, but they also think that the free market is just [Kymlicka] |
| Full Idea: Not everyone who favours the free market is a libertarian, for they do not all share the libertarian view that the free market is inherently just. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 4.1.a) | |
| A reaction: Illuminating. It would appear that exploitation is possible within a strictly free market, so it seems unlikely that free markets are inherently just (unless you don't acknowledge that 'exploitation' is wrong). |
| 18651 | The most valuable liberties to us need not be the ones with the most freedom [Kymlicka] |
| Full Idea: Different liberties promote different interests for many different reasons, and there is no reason to assume that the liberties which are most valuable to us are the ones with the most freedom. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 2.4.a.iii) | |
| A reaction: As I grow older I come more and more to think that freedom is overvalued. But have you tried the other thing? We complacently take huge freedoms for granted. Be passionate about fundamental freedoms, and relaxed about the rest. |
| 18661 | Ancient freedom was free participation in politics, not private independence of life [Kymlicka] |
| Full Idea: The liberty of the ancients was their active participation in the exercise of political power, not the peaceful enjoyment of personal independence. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 7.2.a) | |
| A reaction: Interesting. It takes a feat of imagination to grasp a world where the desire for freedom to sit at home and compile a database of philosophical ideas never even crossed anyone's mind. |
| 18633 | Equal opportunities seems fair, because your fate is from your choices, not your circumstances [Kymlicka] |
| Full Idea: The ideology of equal opportunity seems fair to many people in our society because it ensures that people's fate is determined by their choices, rather than their circumstances. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 3.2) | |
| A reaction: Is it that we surmise that people have 'free will', and then engineer a situation where it can be exercised? Is it that the rest of us don't want to feel guilty when someone else's life goes awry (because it was 'their fault')? |
| 18634 | Equal opportunity arbitrarily worries about social circumstances, but ignores talents [Kymlicka] |
| Full Idea: The prevailing view [of equal opportunity] only recognises differences in social circumstances, while ignoring differences in natural talents (or treating them as if they were a choice). This is an arbitrary limit on the theory's central intuition. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 3.2) | |
| A reaction: Of course we (society) can do a lot about your social circumstances, but very little about your talents, other than to develop them or thwart them. Talented children need more than mere 'opportunity'. |
| 18654 | Marxists say justice is unneeded in the truly good community [Kymlicka] |
| Full Idea: Marxists believe that justice, far from being the first virtue of social institutions, is something that the truly good community has no need for. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 5.1) | |
| A reaction: This seems to imply that in the truly good community there are nothing but truly good individuals, which is taking social determinism to its limits. Are all the citizens of a bad community inherently bad? |
| 18652 | The Lockean view of freedom depends on whether you had a right to what is restricted [Kymlicka] |
| Full Idea: The Lockean camp defines freedom in terms of the exercise of our rights. Whether or not a restriction decreases our freedom depends on whether or not we had a right to do the restricted thing. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 2.4.a.iii) | |
| A reaction: My first instinct is to be sympathetic to this, since a detached and general notion of 'freedom' strikes me as suspect. He offers the rival 'Spenserian' view of freedom as just having the choice. |
| 18655 | Justice corrects social faults, but also expresses respect to individuals as ends [Kymlicka] |
| Full Idea: Justice is more than a remedial virtue. It does remedy defects in social co-ordination, ...but it also expresses the respect individuals are owed as ends in themselves, not as mean's to someone's good, or even to the common good. | |
| From: Will Kymlicka (Contemporary Political Philosophy (1st edn) [1990], 5.1) | |
| A reaction: That is, I take it, that justice operates at two different levels in our theoretical social thinking. |
| 9574 | 'Gunk' is an individual possessing no parts that are atoms [Chihara] |
| Full Idea: An 'atomless gunk' is defined to be an individual possessing no parts that are atoms. | |
| From: Charles Chihara (A Structural Account of Mathematics [2004], App A) | |
| A reaction: [Lewis coined it] If you ask what are a-toms made of and what are ideas made of, the only answer we can offer is that the a-toms are made of gunk, and the ideas aren't made of anything, which is still bad news for the existence of ideas. |