42 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? |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| Full Idea: While truth can be defined in a relative way, as truth in one particular model, a non-relative notion of truth is implied, as truth in all models. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: [The article is actually discussing arithmetic] This idea strikes me as extremely important. True-in-all-models is usually taken to be tautological, but it does seem to give a more universal notion of truth. See semantic truth, Tarski, Davidson etc etc. |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| Full Idea: In standard ZFC ('Zermelo-Fraenkel with Choice') set theory we deal merely with pure sets, not with additional urelements. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: The 'urelements' would the actual objects that are members of the sets, be they physical or abstract. This idea is crucial to understanding philosophy of mathematics, and especially logicism. Must the sets exist, just as the urelements do? |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| Full Idea: In second-order logic there are three kinds of variables, for objects, for functions, and for predicates or sets. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: It is interesting that a predicate seems to be the same as a set, which begs rather a lot of questions. For those who dislike second-order logic, there seems nothing instrinsically wicked in having variables ranging over innumerable multi-order types. |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| Full Idea: 'Analysis' is the theory of the real numbers. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: 'Analysis' began with the infinitesimal calculus, which later built on the concept of 'limit'. A continuum of numbers seems to be required to make that work. |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| Full Idea: The difficulties for a nominalistic mereological approach to arithmetic is that an infinity of physical objects are needed (space-time points? strokes?), and it must define functions, such as 'successor'. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: Many ontologically austere accounts of arithmetic are faced with the problem of infinity. The obvious non-platonist response seems to be a modal or if-then approach. To postulate infinite abstract or physical entities so that we can add 3 and 2 is mad. |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| Full Idea: A common formulation of Peano Arithmetic uses 2nd-order logic, the constant '1', and a one-place function 's' ('successor'). Three axioms then give '1 is not a successor', 'different numbers have different successors', and induction. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: This is 'second-order' Peano Arithmetic, though it is at least as common to formulate in first-order terms (only quantifying over objects, not over properties - as is done here in the induction axiom). I like the use of '1' as basic instead of '0'! |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| Full Idea: The merits of basing an account of mathematics on set theory are that it allows for a comprehensive unified treatment of many otherwise separate branches of mathematics, and that all assumption, including existence, are explicit in the axioms. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I am forming the impression that set-theory provides one rather good model (maybe the best available) for mathematics, but that doesn't mean that mathematics is set-theory. The best map of a landscape isn't a landscape. |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| Full Idea: Structuralism has emerged from the development of abstract algebra (such as group theory), the creation of axiom systems, the introduction of set theory, and Bourbaki's encyclopaedic survey of set theoretic structures. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: In other words, mathematics has gradually risen from one level of abstraction to the next, so that mathematical entities like points and numbers receive less and less attention, with relationships becoming more prominent. |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| Full Idea: Relativist Structuralism simply picks one particular model of axiomatised arithmetic (i.e. one particular interpretation that satisfies the axioms), and then stipulates what the elements, functions and quantifiers refer to. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: The point is that a successful model can be offered, and it doesn't matter which one, like having any sort of aeroplane, as long as it flies. I don't find this approach congenial, though having a model is good. What is the essence of flight? |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| Full Idea: The term 'structure' has two uses in the literature, what can be called 'particular structures' (which are particular relational systems), but also what can be called 'universal structures' - what particular systems share, or what they instantiate. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §6) | |
| A reaction: This is a very helpful distinction, because it clarifies why (rather to my surprise) some structuralists turn out to be platonists in a new guise. Personal my interest in structuralism has been anti-platonist from the start. |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| Full Idea: According to 'pattern' structuralism, what we study are not the various particular isomorphic models of arithmetic, but something in addition to them: a corresponding pattern. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §7) | |
| A reaction: Put like that, we have to feel a temptation to wield Ockham's Razor. It's bad enough trying to give the structure of all the isomorphic models, without seeking an even more abstract account of underlying patterns. But patterns connect to minds.. |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| Full Idea: There are four main variants of structuralism in the philosophy of mathematics - formalist structuralism, relativist structuralism, universalist structuralism (with modal variants), and pattern structuralism. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §9) | |
| A reaction: I'm not sure where Chihara's later book fits into this, though it is at the nominalist end of the spectrum. Shapiro and Resnik do patterns (the latter more loosely); Hellman does modal universalism; Quine does the relativist version. Dedekind? |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| Full Idea: Formalist Structuralism endorses structural methodology in mathematics, but rejects semantic and metaphysical problems as either meaningless, or purely formal, or as inference relations. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §3) | |
| A reaction: [very compressed] I find the third option fairly congenial, certainly in preference to rather platonist accounts of structuralism. One still needs to distinguish the mathematical from the non-mathematical in the inference relations. |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| Full Idea: It is tempting to take a modal turn, and quantify over all possible objects, because if there are only a finite number of actual objects, then there are no models (of the right sort) for Peano Arithmetic, and arithmetic is vacuously true. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: [compressed; Geoffrey Hellman is the chief champion of this view] The article asks whether we are not still left with the puzzle of whether infinitely many objects are possible, instead of existent. |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| Full Idea: Universalist Structuralism is a semantic thesis, that an arithmetical statement asserts a universal if-then statement. We build an if-then statement (using quantifiers) into the structure, and we generalise away from any one particular model. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: There remains the question of what is distinctively mathematical about the highly generalised network of inferences that is being described. Presumable the axioms capture that, but why those particular axioms? Russell is cited as an originator. |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| Full Idea: Universalist Structuralism is eliminativist about abstract objects, in a distinctive form. Instead of treating the base element (say '1') as an ambiguous referring expression (the Relativist approach), it is a variable which is quantified out. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: I am a temperamental eliminativist on this front (and most others) so this is tempting. I am also in love with the concept of a 'variable', which I take to be utterly fundamental to all conceptual thought, even in animals, and not just a trick of algebra. |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| Full Idea: Relativist Structuralism must first assume the existence of an infinite set, otherwise there would be no model to pick, and arithmetical terms would have no reference. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: See Idea 10169 for Relativist Structuralism. They point out that ZFC has an Axiom of Infinity. |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| Full Idea: One way for a nominalist to reject appeal to all abstract objects, including sets, is to only appeal to nominalistically acceptable objects, including mereological sums. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I'm suddenly thinking that this looks very interesting and might be the way to go. The issue seems to be whether mereological sums should be seen as constrained by nature, or whether they are unrestricted. See Mereology in Ontology...|Intrinsic Identity. |
| 14367 | An explanation is a causal graph [Woodward,J, by Strevens] |
| Full Idea: On Woodward's manipulationist view, an explanation would take the form of a causal graph. | |
| From: report of James Woodward (Making Things Happen [2003]) by Michael Strevens - No Understanding without Explanation 1 | |
| A reaction: The idea is that causation is all to do with how nature responds when you try to manipulate it. I'm certainly in favour of tying explanation closely to causation. |
| 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. |