46 ideas
| 20981 | What justifies reliance on reason? Is it just a tool? Why is it better than blind belief? [Sen] |
| Full Idea: What is the ultimate justification for relying on reason? Is reason cherished as a good tool, and if so, how does it differ from blind and unquestioning belief? | |
| From: Amartya Sen (The Idea of Justice [2009], 01 'Critique') | |
| A reaction: And can it answer the romantic charge of stunting a rich life? NIetzsche started this one, by asking the value of truth. Proposal: treat others rationally, and treat yourself intuitively. |
| 20982 | In politics and ethics, scrutiny from different perspectives is essential for objectivity [Sen] |
| Full Idea: I take reasoned scrutiny from different perspectives to be an essential part of the demands of objectivity for ethical and political convictions. | |
| From: Amartya Sen (The Idea of Justice [2009], 01 'Adam') | |
| A reaction: We should distinguish the nature of objectivity from ways of achieving it. Multiple perspectives don't guarantee objectivity. This is peer review in science, and publisher's readers of philosophy texts. What is objectivity? The same as truth? |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| Full Idea: Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle. |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| Full Idea: It is surely wise to identify the positions in the natural numbers structure with their counterparts in the integer, rational, real and complex number structures. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2) | |
| A reaction: The point is that this might be denied, since 3, 3/1, 3.00.., and -3*i^2 are all arrived at by different methods of construction. Natural 3 has a predecessor, but real 3 doesn't. I agree, intuitively, with Shapiro. Russell (1919) disagreed. |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| Full Idea: A sequence a1,a2,... of rational numbers is 'Cauchy' if for each rational number ε>0 there is a natural number N such that for all natural numbers m, n, if m>N and n>N then -ε < am - an < ε. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 7.2 n4) | |
| A reaction: The sequence is 'Cauchy' if N exists. |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| Full Idea: There is a dedicated contingent who hold that the category of 'categories' is the proper foundation for mathematics. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.3 n7) | |
| A reaction: He cites Lawvere (1966) and McLarty (1993), the latter presenting the view as a form of structuralism. I would say that the concept of a category will need further explication, and probably reduce to either sets or relations or properties. |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| Full Idea: Zermelo said that for each number n, its successor is the singleton of n, so 3 is {{{null}}}, and 1 is not a member of 3. Von Neumann said each number n is the set of numbers less than n, so 3 is {null,{null},{null,{null}}}, and 1 is a member of 3. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2) | |
| A reaction: See Idea 645 - Zermelo could save Plato from the criticisms of Aristotle! These two accounts are cited by opponents of the set-theoretical account of numbers, because it seems impossible to arbitrate between them. |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| Full Idea: The structuralist vigorously rejects any sort of ontological independence among the natural numbers; the essence of a natural number is its relations to other natural numbers. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1) | |
| A reaction: This seems to place the emphasis on ordinals (what order?) rather than on cardinality (how many?). I am strongly inclined to think that this is the correct view, though you can't really have relations if there is nothing to relate. |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| Full Idea: A 'system' is a collection of objects with certain relations among them; a 'pattern' or 'structure' is the abstract form of a system, highlighting the interrelationships and ignoring any features they do not affect how they relate to other objects. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1) | |
| A reaction: Note that 'ignoring' features is a psychological account of abstraction, which (thanks to Frege and Geach) is supposed to be taboo - but which I suspect is actually indispensable in any proper account of thought and concepts. |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| Full Idea: The thesis that principles of arithmetic are derivable from the laws of logic runs against a now common view that logic itself has no ontology. There are no particular logical objects. From this perspective logicism is a non-starter. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 5.1) | |
| A reaction: This criticism strikes me as utterly devastating. There are two routes to go: prove that logic does have an ontology of objects (what would they be?), or - better - deny that arithmetic contains any 'objects'. Or give up logicism. |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| Full Idea: Term Formalism is the view that mathematics is just about characters or symbols - the systems of numerals and other linguistic forms. ...This will cover integers and rational numbers, but what are real numbers supposed to be, if they lack names? | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.1) | |
| A reaction: Real numbers (such as pi and root-2) have infinite decimal expansions, so we can start naming those. We could also start giving names like 'Harry' to other reals, though it might take a while. OK, I give up. |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| Full Idea: Game Formalism likens mathematics to chess, where the 'content' of mathematics is exhausted by the rules of operating with its language. ...This, however, leaves the problem of why the mathematical games are so useful to the sciences. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.2) | |
| A reaction: This thought pushes us towards structuralism. It could still be a game, but one we learned from observing nature, which plays its own games. Chess is, after all, modelled on warfare. |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| Full Idea: The Deductivist version of formalism (sometimes called 'if-thenism') says that the practice of mathematics consists of determining logical consequences of otherwise uninterpreted axioms. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.2) | |
| A reaction: [Hilbert is the source] More plausible than Term or Game Formalism (qv). It still leaves the question of why it seems applicable to nature, and why those particular axioms might be chosen. In some sense, though, it is obviously right. |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| Full Idea: Critics commonly complain that the intuitionist restrictions cripple the mathematician. On the other hand, intuitionist mathematics allows for many potentially important distinctions not available in classical mathematics, and is often more subtle. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 7.1) | |
| A reaction: The main way in which it cripples is its restriction on talk of infinity ('Cantor's heaven'), which was resented by Hilbert. Since high-level infinities are interesting, it would be odd if we were not allowed to discuss them. |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| Full Idea: I classify conceptualists according to what they say about properties or concepts. If someone classified properties as existing independent of language I would classify her as a realist in ontology of mathematics. Or they may be idealists or nominalists. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 2.2.1) | |
| A reaction: In other words, Shapiro wants to eliminate 'conceptualist' as a useful label in philosophy of mathematics. He's probably right. All thought involves concepts, but that doesn't produce a conceptualist theory of, say, football. |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| Full Idea: A definition of a mathematical entity is 'impredicative' if it refers to a collection that contains the defined entity. The definition of 'least upper bound' is impredicative as it refers to upper bounds and characterizes a member of this set. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: The big question is whether mathematics can live with impredicative definitions, or whether they threaten to be viciously circular, and undermine the whole enterprise. |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| Full Idea: Rationalism is a long-standing school that can be characterized as an attempt to extend the perceived methodology of mathematics to all of knowledge. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.1) | |
| A reaction: Sometimes called 'Descartes's Dream', or the 'Enlightenment Project', the dream of proving everything. Within maths, Hilbert's Programme aimed for the same certainty. Idea 22 is the motto for the opposition to this approach. |
| 20990 | Rationality is conformity to reasons that can be sustained even after scrutiny [Sen] |
| Full Idea: My main argument can be fairly easily understood in terms of seeing rationality as conformity with reasons that one can sustain, even after scrutiny, and not just at first sight. | |
| From: Amartya Sen (The Idea of Justice [2009], 08 'Rational' n) | |
| A reaction: We would need to say more about the 'scrutiny' before we had a really good account of rationality here. In Idea 20982 he emphasises the need for scrutiny by other people, and not mere self-criticism. The key may to be invite outside criticism. |
| 21005 | A human right is not plausible if public scrutiny might reject it [Sen] |
| Full Idea: The force of a claim for a human right would indeed be seriously undermined if it were possible to show that it is unlikely to survive open public scrutiny. | |
| From: Amartya Sen (The Idea of Justice [2009], 17 'Scrutiny') | |
| A reaction: This is a public aspect of Scanlon's 'contractualist' approach to ethics. You can hardly disagree with the idea, though anti-racist legislation in a strongly racist society might be a good test case. |
| 20983 | The original position insures that the agreements reached are fair [Sen] |
| Full Idea: The original position is the appropriate initial status quo which insures that the fundamental agreements reached in it are fair. This fact yields the name 'justice as fairness'. | |
| From: Amartya Sen (The Idea of Justice [2009], 01.4) | |
| A reaction: I suppose it insures fairness on day one of the new society, but that might have all been wiped out in the next fortnight, when you find you are the least advantaged as a result of racism. |
| 20987 | The veil of ignorance encourages neutral interests, but not a wider view of values [Sen] |
| Full Idea: The veil of ignorance is very effective for making people see beyond their vested interests and goals. And yet it does little to ensure an open scrutiny of local and possibly parochial values. | |
| From: Amartya Sen (The Idea of Justice [2009], 06 'Original') | |
| A reaction: Communitarians also make a similar criticism of Rawls - that people in the initial position simplify themselves into pure rational agents looking for 'basic goods'. |
| 20984 | A social contract limits the pursuit of justice to members of a single society [Sen] |
| Full Idea: The use of the social contract in the Rawlsian form inescapably limits the involvement of participants in the pursuit of justice to the members of a given polity, or 'people'. | |
| From: Amartya Sen (The Idea of Justice [2009], 02 'Relevance') | |
| A reaction: This relates to the criticism of contractarian ethics - that the weak have nothing to bargain with. One can either add international contracts, or appeal to natural human rights. Or we could just be nice to one another? Nah! |
| 20986 | A person's voice may count because of their interests, or because of their good sense [Sen] |
| Full Idea: A person's voice may count either because her interests are involved, or because he reasoning and judgement can enlighten a discussion. | |
| From: Amartya Sen (The Idea of Justice [2009], 04 'Diversity') | |
| A reaction: Good. Inarticulate people may have strong interests, and articulate and helpful people may be wholly disinterested. But people may have unworthy interests, and may be articulate but not sensible. |
| 21001 | Famines tend to be caused by authoritarian rule [Sen] |
| Full Idea: The history of famines has had a peculiarly close connection with authoritarian rules. | |
| From: Amartya Sen (The Idea of Justice [2009], 16 'Famine') | |
| A reaction: He cites the British Empire, the Soviet Union, China and Cambodia. There is unlikely to be a local famine if there is free movement of food supplies.342 |
| 21002 | Effective democracy needs tolerant values [Sen] |
| Full Idea: The formation of tolerant values is quite central to the smooth functioning of a democratic system. | |
| From: Amartya Sen (The Idea of Justice [2009], 16 'Minority') | |
| A reaction: There is presumably a brutal sort of democracy, if the majority in a polarised society agree to crush a minority. |
| 20999 | Democracy as 'government by discussion' now has wide support [Sen] |
| Full Idea: In contemporary political philosophy the view that democracy is best seen as 'government by discussion' has gained widespread support. | |
| From: Amartya Sen (The Idea of Justice [2009], 15 'Content') | |
| A reaction: The obvious worry about this is inefficiency in decision-making. Also the dominance of noisy stupidity. But citizens need to feel involved, and committed to the decisions. |
| 20979 | Democracy needs more than some institutions; diverse sections of the people must be heard [Sen] |
| Full Idea: Democracy has to be judged not just by the institutions that formally exist but by the extent to which different voices from diverse sections of the people can actually be heard. | |
| From: Amartya Sen (The Idea of Justice [2009], Pref 'Public') | |
| A reaction: Depends what you mean by 'democracy'. Should the workplace and the school and the family be democratic, or just the choice of leaders? What can oblige leaders to listen to the people? Listen to, and then ignore? |
| 20993 | Eradicating smallpox does not impoverish nature [Sen] |
| Full Idea: The eradication of smallpox is not viewed as an impoverishment of nature. | |
| From: Amartya Sen (The Idea of Justice [2009], 11 'Sustainable') | |
| A reaction: You'd have to be a pretty 'deep' ecologist to defend the carrier of smallpox, or Dutch Elm disease. The idea is included for balance. |
| 20995 | Capabilities are part of freedom, involving real opportunities [Sen] |
| Full Idea: Capability is an aspect of freedom, concentrating in particular on substantive opportunities. | |
| From: Amartya Sen (The Idea of Justice [2009], 13 'Well-being') | |
| A reaction: This is the 'capabilities approach' of Sen and Nussbaum. The key word is 'substantive' (as opposed to theoretical). We are all free to become astronauts, but.... |
| 20998 | Freedom can involve capabilities, independence and non-interference [Sen] |
| Full Idea: There is no embarrassment in accommodating several distinct features within the idea of freedom, focusing respectively on capability, lack of dependence and lack of interference. | |
| From: Amartya Sen (The Idea of Justice [2009], 14 'Capability') | |
| A reaction: This relates to Berlin's distinction between negative and positive rights. |
| 20997 | The need for equality among people arises from impartiality and objectivity [Sen] |
| Full Idea: The demand for seeing people as equals (in some important perspective) relates to the normative demand for impartiality, and the related claims of objectivity. | |
| From: Amartya Sen (The Idea of Justice [2009], 14 'Equality') | |
| A reaction: Either impartiality already contains (analytically) the concept of equality, or the principle of sufficient reason must be invoked. True impartiality removes any reason for preferring one person to another. But what if preference is 'to my taste'? |
| 20996 | All modern theories of justice demand equality of something [Sen] |
| Full Idea: Every normative theory of social justice that has received support and advocacy in recent times seems to demand equality of something. | |
| From: Amartya Sen (The Idea of Justice [2009], 14 Intro) | |
| A reaction: He mentions liberties, income, rights and utilities. |
| 20988 | Freedom from torture or terrorist attacks is independent of citizenship [Sen] |
| Full Idea: The human right of a person not to be tortured or subjected to terrorist attacks is affirmed independently of the country of which this person is a citizen. | |
| From: Amartya Sen (The Idea of Justice [2009], 06 'Exclusionary') | |
| A reaction: If rights can only be enshrined in a legal system, then I presume all systems of legal rights should ensure rights like these, irrespective of their nation. A universal charter of rights for tourists and alien residents? |
| 20980 | You don't need a complete theory of justice to see that slavery is wrong [Sen] |
| Full Idea: It was the diagnosis of an intolerable injustice in slavery that made abolition an overwhelming priority, and this did not require a search for a consensus on what a perfectly just society would look like. | |
| From: Amartya Sen (The Idea of Justice [2009], Intro 'Classical') | |
| A reaction: This illustrates Sen's key points, that we should focus on injustices, which are obvious, and that designing a totally just society has little relevance to justice in practice (which is what matters). Well said. |
| 20978 | Practical justice concerns not only ideals, but ways to achieve them [Sen] |
| Full Idea: A theory of justice that can serve as the basis of practical reason must include ways of judging how to reduce injustice and advance justice, rather than aiming only at the characterisation of perfectly just societies. | |
| From: Amartya Sen (The Idea of Justice [2009], Pref 'What') | |
| A reaction: Sounds simple, but this is Amartya Sen's revolutionary new idea - that justice is not just ideals and opportunities, but what sort of life people actually end up with. |
| 20985 | Our institutions should promote justice, rather than embodying it [Sen] |
| Full Idea: We have to seek institutions that promote justice, rather than treating the institutions as themselves manifestations of justice. | |
| From: Amartya Sen (The Idea of Justice [2009], 03 'Institutions') | |
| A reaction: The best quote I can find for summarising Sen's view. He criticises Rawls and others for trying to design institutions that embody justice. Our legal system promotes justice. Do our schools and hospitals? The Department for the Promotion of Justice? |
| 20994 | We must focus on removing manifest injustice, not just try to design a perfect society [Sen] |
| Full Idea: The demands of justice must give priority to the removal of manifest injustice, rather than concentrating on the long-distance search for the perfectly just society. | |
| From: Amartya Sen (The Idea of Justice [2009], 12 'Disability') | |
| A reaction: So the point is not to understand the world, but to change it? I'd want to put in a word for the theoretical and idealised project, which I see in terms of writing the perfect constitution. You can't just pick off injustices, perceived intuitively. |
| 21000 | If justice needs public reasoning, which needs democracy, then justice and democracy are linked [Sen] |
| Full Idea: If the demands of justice can be assessed only with the help of public reasoning, and that is constitutively related to the idea of democracy, then there is an intimate connection between justice and democracy. | |
| From: Amartya Sen (The Idea of Justice [2009], 15 'Content') | |
| A reaction: I suspect that he argued early on that rationality required many perspectives in order to later mount this defence of democracy. |
| 21332 | We don't get a love of 'order' from nature - which is thoroughly chaotic [Mill] |
| Full Idea: Even the love of 'order' which is thought to be a following of the ways of nature is in fact a contradiction of them. All which people are accustomed to deprecate as 'disorder' is precisely a counterpart of nature's ways. | |
| From: John Stuart Mill (Nature and Utility of Religion [1874], p.116) | |
| A reaction: The Greeks elevated the idea that the cosmos was orderly, but almost entirely based on the regular movement of the planets. They turned a blind eye to the messy bits of nature. As you magnify nature, order and chaos seem to alternate. |
| 21333 | Evil comes from good just as often as good comes from evil [Mill] |
| Full Idea: If good frequently comes out of evil, the converse fact, evil coming out of good, is equally common. | |
| From: John Stuart Mill (Nature and Utility of Religion [1874], p.117) | |
| A reaction: Mill surmises that on the whole good comes from good, and evil from evil, but the point is that the evidence doesn't favour the production of increased good. |
| 21335 | Belief that an afterlife is required for justice is an admission that this life is very unjust [Mill] |
| Full Idea: The necessity of redressing the balance [of injustice] is deemed one of the strongest arguments for another life after death, which amounts to an admission that the order of things in this life is often an example of injustice, not justice. | |
| From: John Stuart Mill (Nature and Utility of Religion [1874]) | |
| A reaction: It certainly seems that an omnipotent God could administer swift justice in this life. If the whole point is that we need freedom of will, then why is justice administered at a much later date? The freedom seems to be illusory. |
| 21334 | No necessity ties an omnipotent Creator, so he evidently wills human misery [Mill] |
| Full Idea: If a Creator is assumed to be omnipotent, if he bends to a supposed necessity, he himself makes the necessity which he bends to. If the maker of the world can all that he will, he wills misery, and there is no escape from the conclusion. | |
| From: John Stuart Mill (Nature and Utility of Religion [1874], p.119) | |
| A reaction: If you add that the Creator is supposed to be perfectly benevolent, you arrive at the paradox which Mackie spells out. Is the correct conclusion that God exists, and is malevolent? Mill doesn't take that option seriously. |
| 21329 | Nature dispenses cruelty with no concern for either mercy or justice [Mill] |
| Full Idea: All of this [cruel killing] nature does with the most supercilious disregard both of mercy and of justice, emptying her shafts upon the best and noblest indifferently with the meanest and worst | |
| From: John Stuart Mill (Nature and Utility of Religion [1874], p.115) | |
| A reaction: The existence of an afterlife at least offers an opportunity to rectify any injustice, but that hardly meets the question of why there was injustice in the first place. It would be odd if it actually is justice, but none of us can see why that is so. |
| 21328 | Killing is a human crime, but nature kills everyone, and often with great tortures [Mill] |
| Full Idea: Killing, the most criminal act recognised by human laws, nature does once to every being that lives, and frequently after protracted tortures such as the greatest know monsters purposely inflicted on their living fellow creatures | |
| From: John Stuart Mill (Nature and Utility of Religion [1874], p.115) | |
| A reaction: We certainly don't condemn lions for savaging gazelles, but the concept of a supreme mind controlling nature forces the question. Theology needs consistency between human and divine morality, and the supposed derivation of the former from the latter. |
| 21330 | Nature makes childbirth a miserable experience, often leading to the death of the mother [Mill] |
| Full Idea: In the clumsy provision which nature has made for the perpetual renewal of animal life, ...no human being ever comes into the world but another human being is literally stretched on the rack for hours or day, not unfrequently issuing in death. | |
| From: John Stuart Mill (Nature and Utility of Religion [1874], p.116) | |
| A reaction: This is a very powerful example, which is rarely cited in modern discussions. |
| 21331 | Hurricanes, locusts, floods and blight can starve a million people to death [Mill] |
| Full Idea: Nature often takes the means by which we live. A single hurricane, a flight of locusts, or an inundation, or a trifling chemical change in an edible root, starve a million people. | |
| From: John Stuart Mill (Nature and Utility of Religion [1874], p.116) | |
| A reaction: [second sentence compressed] The 'edible root' is an obvious reference to the Irish potato famine. Some desertification had human causes, but these are telling examples. |