40 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? |
| 10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
| Full Idea: Late nineteenth century mathematicians said that, although plus, minus and 0 could not be precisely defined, they could be partially 'implicitly defined' as a group. This nonsense was rejected by Frege and others, as expressed in Russell 1903. | |
| From: Wilfrid Hodges (Model Theory [2005], 2) | |
| A reaction: [compressed] This is helpful in understanding what is going on in Frege's 'Grundlagen'. I won't challenge Hodges's claim that such definitions are nonsense, but there is a case for understanding groups of concepts together. |
| 10282 | Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W] |
| Full Idea: A logic is a collection of closely related artificial languages, and its older meaning is the study of the rules of sound argument. The languages can be used as a framework for studying rules of argument. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.1) | |
| A reaction: [Hodges then says he will stick to the languages] The suspicion is that one might confine the subject to the artificial languages simply because it is easier, and avoids the tricky philosophical questions. That approximates to computer programming. |
| 10478 | Since first-order languages are complete, |= and |- have the same meaning [Hodges,W] |
| Full Idea: In first-order languages the completeness theorem tells us that T |= φ holds if and only if there is a proof of φ from T (T |- φ). Since the two symbols express the same relationship, theorist often just use |- (but only for first-order!). | |
| From: Wilfrid Hodges (Model Theory [2005], 3) | |
| A reaction: [actually no spaces in the symbols] If you are going to study this kind of theory of logic, the first thing you need to do is sort out these symbols, which isn't easy! |
| 10477 | |= in model-theory means 'logical consequence' - it holds in all models [Hodges,W] |
| Full Idea: If every structure which is a model of a set of sentences T is also a model of one of its sentences φ, then this is known as the model-theoretic consequence relation, and is written T |= φ. Not to be confused with |= meaning 'satisfies'. | |
| From: Wilfrid Hodges (Model Theory [2005], 3) | |
| A reaction: See also Idea 10474, which gives the other meaning of |=, as 'satisfies'. The symbol is ALSO used in propositional logical, to mean 'tautologically implies'! Sort your act out, logicians. |
| 10670 | A 'singulariser' converts a plural like 'number of' to a syntactically neutral form [Cartwright,H, by Hossack] |
| Full Idea: Helen Cartwright calls 'a number of' a 'singulariser', an expression whose linguistic function is to convert to a syntactically neutral form an expression whose semantic value remains plural. It is a great convenience grammatically. | |
| From: report of Helen Cartwright (On Plural Reference and Set Theory [1993]) by Keith Hossack - Plurals and Complexes 2 | |
| A reaction: Compare Hofweber's Idea 10004, suggesting it is a crucial psychological convenience for reasoning, as well as a 'grammatical' convenience. |
| 10283 | A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W] |
| Full Idea: To have a truth-value, a first-order formula needs an 'interpretation' (I) of its constants, and a 'valuation' (ν) of its variables. Something in the world is attached to the constants; objects are attached to variables. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.3) |
| 10284 | There are three different standard presentations of semantics [Hodges,W] |
| Full Idea: Semantic rules can be presented in 'Tarski style', where the interpretation-plus-valuation is reduced to the same question for simpler formulas, or the 'Henkin-Hintikka style' in terms of games, or the 'Barwise-Etchemendy style' for computers. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.3) | |
| A reaction: I haven't yet got the hang of the latter two, but I note them to map the territory. |
| 10285 | I |= φ means that the formula φ is true in the interpretation I [Hodges,W] |
| Full Idea: I |= φ means that the formula φ is true in the interpretation I. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.5) | |
| A reaction: [There should be no space between the vertical and the two horizontals!] This contrasts with |-, which means 'is proved in'. That is a syntactic or proof-theoretic symbol, whereas |= is a semantic symbol (involving truth). |
| 10474 | |= should be read as 'is a model for' or 'satisfies' [Hodges,W] |
| Full Idea: The symbol in 'I |= S' reads that if the interpretation I (about word meaning) happens to make the sentence S state something true, then I 'is a model for' S, or I 'satisfies' S. | |
| From: Wilfrid Hodges (Model Theory [2005], 1) | |
| A reaction: Unfortunately this is not the only reading of the symbol |= [no space between | and =!], so care and familiarity are needed, but this is how to read it when dealing with models. See also Idea 10477. |
| 10473 | Model theory studies formal or natural language-interpretation using set-theory [Hodges,W] |
| Full Idea: Model theory is the study of the interpretation of any language, formal or natural, by means of set-theoretic structures, with Tarski's truth definition as a paradigm. | |
| From: Wilfrid Hodges (Model Theory [2005], Intro) | |
| A reaction: My attention is caught by the fact that natural languages are included. Might we say that science is model theory for English? That sounds like Quine's persistent message. |
| 10475 | A 'structure' is an interpretation specifying objects and classes of quantification [Hodges,W] |
| Full Idea: A 'structure' in model theory is an interpretation which explains what objects some expressions refer to, and what classes some quantifiers range over. | |
| From: Wilfrid Hodges (Model Theory [2005], 1) | |
| A reaction: He cites as examples 'first-order structures' used in mathematical model theory, and 'Kripke structures' used in model theory for modal logic. A structure is also called a 'universe'. |
| 10481 | Models in model theory are structures, not sets of descriptions [Hodges,W] |
| Full Idea: The models in model-theory are structures, but there is also a common use of 'model' to mean a formal theory which describes and explains a phenomenon, or plans to build it. | |
| From: Wilfrid Hodges (Model Theory [2005], 5) | |
| A reaction: Hodges is not at all clear here, but the idea seems to be that model-theory offers a set of objects and rules, where the common usage offers a set of descriptions. Model-theory needs homomorphisms to connect models to things, |
| 10288 | Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W] |
| Full Idea: Downward Löwenheim-Skolem (the weakest form): If L is a first-order language with at most countably many formulas, and T is a consistent theory in L. Then T has a model with at most countably many elements. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.10) |
| 10289 | Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W] |
| Full Idea: Upward Löwenheim-Skolem: every first-order theory with infinite models has arbitrarily large models. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.10) |
| 10287 | If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W] |
| Full Idea: Compactness Theorem: suppose T is a first-order theory, ψ is a first-order sentence, and T entails ψ. Then there is a finite subset U of T such that U entails ψ. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.10) | |
| A reaction: If entailment is possible, it can be done finitely. |
| 10480 | First-order logic can't discriminate between one infinite cardinal and another [Hodges,W] |
| Full Idea: First-order logic is hopeless for discriminating between one infinite cardinal and another. | |
| From: Wilfrid Hodges (Model Theory [2005], 4) | |
| A reaction: This seems rather significant, since mathematics largely relies on first-order logic for its metatheory. Personally I'm tempted to Ockham's Razor out all these super-infinities, but mathematicians seem to make use of them. |
| 10286 | A 'set' is a mathematically well-behaved class [Hodges,W] |
| Full Idea: A 'set' is a mathematically well-behaved class. | |
| From: Wilfrid Hodges (First-Order Logic [2001], 1.6) |
| 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. |