43 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? |
| 17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
| Full Idea: A proof of the consistency of propositional logic was given by Emil Post in 1921. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], History E.2.1) |
| 17765 | Propositional language can only relate statements as the same or as different [Walicki] |
| Full Idea: Propositional language is very rudimentary and has limited powers of expression. The only relation between various statements it can handle is that of identity and difference. As are all the same, but Bs can be different from As. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 7 Intro) | |
| A reaction: [second sentence a paraphrase] In predicate logic you could represent two statements as being the same except for one element (an object or predicate or relation or quantifier). |
| 17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
| Full Idea: Boolean connectives are interpreted as functions on the set {1,0}. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 5.1) | |
| A reaction: 1 and 0 are normally taken to be true (T) and false (F). Thus the functions output various combinations of true and false, which are truth tables. |
| 17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
| Full Idea: The empty set is mainly a mathematical convenience - defining a set by describing the properties of its members in an involved way, we may not know from the very beginning what its members are. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 1.1) |
| 17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
| Full Idea: Without the assumption of the empty set, one would often have to take special precautions for the case where a set happened to contain no elements. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 1.1) | |
| A reaction: Compare the introduction of the concept 'zero', where special precautions are therefore required. ...But other special precautions are needed without zero. Either he pays us, or we pay him, or ...er. Intersecting sets need the empty set. |
| 17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
| Full Idea: Ordinals play the central role in set theory, providing the paradigmatic well-orderings. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) | |
| A reaction: When you draw the big V of the iterative hierarchy of sets (built from successive power sets), the ordinals are marked as a single line up the middle, one ordinal for each level. |
| 17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
| Full Idea: In order to construct precise and valid patterns of arguments one has to determine their 'building blocks'. One has to identify the basic terms, their kinds and means of combination. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], History Intro) | |
| A reaction: A deceptively simple and important idea. All explanation requires patterns and levels, and it is the idea of building blocks which makes such things possible. It is right at the centre of our grasp of everything. |
| 17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
| Full Idea: A specification of a domain of objects, and of the rules for interpreting the symbols of a logical language in this domain such that all the theorems of the logical theory are true is said to be a 'model' of the theory. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], History E.1.3) | |
| A reaction: The basic ideas of this emerged 1915-30, but it needed Tarski's account of truth to really get it going. |
| 17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
| Full Idea: The L-S Theorem is ...a shocking result, since it implies that any consistent formal theory of everything - even about biology, physics, sets or the real numbers - can just as well be understood as being about natural numbers. It says nothing more. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], History E.2) | |
| A reaction: Illuminating. Particularly the point that no theory about the real numbers can say anything more than a theory about the natural numbers. So the natural numbers contain all the truths we can ever express? Eh????? |
| 17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
| Full Idea: Having such a compact [axiomatic] presentation of a complicated field [such as Euclid's], makes it possible to relate not only to particular theorems but also to the whole field as such. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 4.1) |
| 17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
| Full Idea: Axiomatic systems, their primitive terms and proofs, are purely syntactic, that is, do not presuppose any interpretation. ...[142] They never address the world directly, but address a possible semantic model which formally represents the world. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 4.1) |
| 17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
| Full Idea: Every member of an ordinal is itself an ordinal, and every ordinal is a transitive set (its members are also its subsets; a member of a member of an ordinal is also a member of the ordinal). | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) |
| 17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
| Full Idea: The collection of ordinals is defined inductively: Basis: the empty set is an ordinal; Ind: for an ordinal x, the union with its singleton is also an ordinal; and any arbitrary (possibly infinite) union of ordinals is an ordinal. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) | |
| A reaction: [symbolism translated into English] Walicki says they are called 'ordinal numbers', but are in fact a set. |
| 17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
| Full Idea: We can form infinite ordinals by taking unions of ordinals. We can thus form 'limit ordinals', which have no immediate predecessor. ω is the first (the union of all finite ordinals), ω + ω = sω is second, 3ω the third.... | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) |
| 17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
| Full Idea: There may be several ordinals for the same cardinality. ...Two ordinals can represent different ways of well-ordering the same number (aleph-0) of elements. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) | |
| A reaction: This only applies to infinite ordinals and cardinals. For the finite, the two coincide. In infinite arithmetic the rules are different. |
| 17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
| Full Idea: An ordinal can be defined as a transitive set of transitive sets, or else, as a transitive set totally ordered by set inclusion. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.3) |
| 17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
| Full Idea: Since non-Euclidean geometry preserves all Euclid's postulates except the fifth one, all the theorems derived without the use of the fifth postulate remain valid. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 4.1) |
| 17754 | Inductive proof depends on the choice of the ordering [Walicki] |
| Full Idea: Inductive proof is not guaranteed to work in all cases and, particularly, it depends heavily on the choice of the ordering. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], 2.1.1) | |
| A reaction: There has to be an well-founded ordering for inductive proofs to be possible. |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| Full Idea: The link between time and modality was severed by Duns Scotus, who proposed a notion of possibility based purely on the notion of semantic consistency. 'Possible' means for him logically possible, that is, not involving contradiction. | |
| From: Michal Walicki (Introduction to Mathematical Logic [2012], History B.4) |
| 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. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 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? |
| 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. |
| 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. |