38 ideas
| 7798 | There are three axiom schemas for propositional logic [Girle] |
| Full Idea: The axioms of propositional logic are: A→(B→A); A→(B→C)→(A→B)→(A→C) ; and (¬A→¬B)→(B→A). | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 6.5) |
| 7786 | Propositional logic handles negation, disjunction, conjunction; predicate logic adds quantifiers, predicates, relations [Girle] |
| Full Idea: Propositional logic can deal with negation, disjunction and conjunction of propositions, but predicate logic goes beyond it to deal with quantifiers, predicates and relations. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 1.1) | |
| A reaction: This is on the first page of an introduction to the next stage, which is to include modal notions like 'must' and 'possibly'. |
| 7799 | Proposition logic has definitions for its three operators: or, and, and identical [Girle] |
| Full Idea: The operators of propositional logic are defined as follows: 'or' (v) is not-A implies B; 'and' (ampersand) is not A-implies-not-B; and 'identity' (three line equals) is A-implies-B and B-implies-A. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 6.5) |
| 7797 | Axiom systems of logic contain axioms, inference rules, and definitions of proof and theorems [Girle] |
| Full Idea: An axiom system for a logic contains three elements: a set of axioms; a set of inference rules; and definitions for proofs and theorems. There are also definitions for the derivation of conclusions from sets of premises. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 6.5) |
| 7794 | There are seven modalities in S4, each with its negation [Girle] |
| Full Idea: In S4 there are fourteen modalities: no-operator; necessarily; possibly; necessarily-possibly; possibly-necessarily; necessarily-possibly-necessarily; and possibly-necessarily-possibly (each with its negation). | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 3.5) | |
| A reaction: This is said to be 'more complex' than S5, but also 'weaker'. |
| 7793 | ◊p → □◊p is the hallmark of S5 [Girle] |
| Full Idea: The critical formula that distinguishes S5 from all others is: ◊p → □◊p. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 3.3) | |
| A reaction: If it is possible that it is raining, then it is necessary that it is possible that it is raining. But if it is possible in this world, how can that possibility be necessary in all possible worlds? |
| 7795 | S5 has just six modalities, and all strings can be reduced to those [Girle] |
| Full Idea: In S5 there are six modalities: no-operator; necessarily; and possibly (and their negations). In any sequence of operators we may delete all but the last to gain an equivalent formula. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 3.5) | |
| A reaction: Such drastic simplification seems attractive. Is there really no difference, though, between 'necessarily-possibly', 'possibly-possibly' and just 'possibly'? Could p be contingently possible in this world, and necessarily possible in another? |
| 7796 | Modal logics were studied in terms of axioms, but now possible worlds semantics is added [Girle] |
| Full Idea: Modal logics were, for a long time, studied in terms of axiom systems. The advent of possible worlds semantics made it possible to study them in a semantic way as well. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 6.5) |
| 7787 | Possible worlds logics use true-in-a-world rather than true [Girle] |
| Full Idea: In possible worlds logics a statement is true-in-a-world rather than just true. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 1.1) | |
| A reaction: This sounds relativist, but I don't think it is. It is the facts which change, not the concept of truth. So 'donkeys can talk' may be true in a world, but not in the actual one. |
| 7788 | Modal logic has four basic modal negation equivalences [Girle] |
| Full Idea: The four important logical equivalences in modal logic (the Modal Negation equivalences) are: ¬◊p↔□¬p, ◊¬p↔¬□p, □p↔¬◊¬p, and ◊p↔¬□¬p. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 1.2) | |
| A reaction: [Possibly is written as a diamond, necessarily a square] These are parallel to a set of equivalences between quantifiers in predicate logic. They are called the four 'modal negation (MN) equivalences'. |
| 7789 | Necessary implication is called 'strict implication'; if successful, it is called 'entailment' [Girle] |
| Full Idea: Necessary implication is often called 'strict implication'. The sort of strict implication found in valid arguments, where the conjunction of the premises necessarily implies the conclusion, is often called 'entailment'. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 1.2) | |
| A reaction: These are basic concept for all logic. |
| 7790 | If an argument is invalid, a truth tree will indicate a counter-example [Girle] |
| Full Idea: The truth trees method for establishing the validity of arguments and formulas is easy to use, and has the advantage that if an argument or formula is not valid, then a counter-example can be retrieved from the tree. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 1.4) |
| 7800 | Analytic truths are divided into logically and conceptually necessary [Girle] |
| Full Idea: It has been customary to see analytic truths as dividing into the logically necessary and the conceptually necessary. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 7.3) | |
| A reaction: I suspect that this neglected distinction is important in discussions of Quine's elimination of the analytic/synthetic distinction. Was Quine too influenced by what is logically necessary, which might shift with a change of axioms? |
| 7801 | Possibilities can be logical, theoretical, physical, economic or human [Girle] |
| Full Idea: Qualified modalities seem to form a hierarchy, if we say that 'the possibility that there might be no hunger' is possible logically, theoretically, physically, economically, and humanly. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 7.3) | |
| A reaction: Girle also mentions conceptual possibility. I take 'physically' to be the same as 'naturally'. I would take 'metaphysically' possible to equate to 'theoretically' rather than 'logically'. Almost anything might be logically possible, with bizarre logic. |
| 7792 | A world has 'access' to a world it generates, which is important in possible worlds semantics [Girle] |
| Full Idea: When one world generates another then it has 'access' to the world it generated. The accessibility relation between worlds is very important in possible worlds semantics. | |
| From: Rod Girle (Modal Logics and Philosophy [2000], 3.2) | |
| A reaction: This invites the obvious question what is meant by 'generates'. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 23369 | Some liberals thinks checks and balances are enough, without virtuous citizens [Kymlicka] |
| Full Idea: Many classical liberals believed that a liberal democracy could function effectively even in the absence of an especially virtuous citizenry, by creating checks and balances. …One set of private interests would check another set of private interests. | |
| From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 7) | |
| A reaction: This seems to be the view of those who think a completely free market will evolve into a flourishing and just society. There is a basic debate about the importance of the character of the citizens in any polity. Marxists say they are entangled. |
| 23370 | Good citizens need civic virtues of loyalty, independence, diligence, respect, etc. [Kymlicka] |
| Full Idea: Galston says responsible citizenship requires four types of civic virtue: general (law-abiding, loyal), social (independent, open-minded), economic (diligent, restrained, adaptable), and political (respect, sensible, judgement, engagement). | |
| From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 7) | |
| A reaction: [Galston's 'Liberal Purposes' 1991] (compressed) This immediately seems to be asking too much, especially for those who know little, or are short of money. |
| 23373 | Liberals accept that people need society, but Aristotelians must show that they need political activity [Kymlicka] |
| Full Idea: To defend Aristotelian republicanism it is not enough to show that individual require society - liberals do not deny this. They must also show that individuals need to be politically active. | |
| From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 7) | |
| A reaction: Interesting. People are not just inactive because they have been rendered powerless. In any group of people there are some who are keen to have a voice, or lead, and others who are largely happy to follow. |
| 23375 | Minimal liberal citizenship needs common civility, as well as mere non-interference [Kymlicka] |
| Full Idea: Minimal citizenship is often seen as simply requiring non-interference with others, but that ignores a basic requirement of liberal citizenship, which is the social virtue of 'civility' or 'decency'. | |
| From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 7) | |
| A reaction: He makes the point that the minimal requirement has to be given up when there is a crisis, which needs much more involvement. This largely describes modern Britain, prior to the Brexit rift. |
| 23376 | Modern non-discrimination obliges modern citizens to treat each other as equals [Kymlicka] |
| Full Idea: The extension of non-discrimination from government to civil society …involves a radical extension of the obligations of liberal citizenship. The obligation to treat people as equal citizens now applies to everyday decisions. | |
| From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 7) | |
| A reaction: This is very difficult for an older generation who felt their 'entitlement' as leading citizens, or who routinely favoured their local traditional community. But they just have to 'get over it'! |
| 23377 | The right wing sees citizenship in terms of responsibility to earn a living, rather than rights [Kymlicka] |
| Full Idea: According to the New Right, to promote active citizenship-for-all or entitlements, we must focus instead on people's responsibility to earn a living. | |
| From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 7) | |
| A reaction: Every creature has to earn a living, but one method is to successfully sponge off others. A cushy job is a sort of sponging. An excessively well paid job is a sort of sponging. Citizenship must involve responsibilities of some sort. |
| 23371 | Modern democratic theory focuses on talk, not votes, because we need consensus or compromise [Kymlicka] |
| Full Idea: Modern discussion has shifted from 'vote-centric' (or 'aggregative') to 'talk-centric' democracy. The vote-centric model has no mechanism for developing a consensus, or shaping public opinion, or even formulating an honourable compromise. | |
| From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 7) | |
| A reaction: I'm struck by the fact that a person's preferences betweent these two is a reflection of character, or basic attitudes to morality. Some people think democratically about their relationships, and others very obviously don't. |
| 23390 | In a liberal democracy all subjects of authority have a right to determine the authority [Kymlicka] |
| Full Idea: A liberal-democratic system is one in which those people who are subject to political authority have a right to participate in determining that authority. | |
| From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8.4) | |
| A reaction: This applies to immigrants. The most anti-democratic move in recent democracies is the strategy of trying to make it more difficult to vote, perhaps by demanding identification documents, or creating huge queues. |
| 23374 | We have become attached to private life because that has become greatly enriched [Kymlicka] |
| Full Idea: Our attachment to private life, I believe, is the result not (or not only) of the impoverishment of public life, but the enrichment of private life. | |
| From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 7) | |
| A reaction: Interesting. Perhaps a sentiment expected more from a university lecturer than from a poorly-paid labourer. Does he mean watching innumerable TV shows instead of having sing-songs in the local pub? Increased leisure is indisputable. |
| 23387 | Liberals must avoid an official culture, as well as an official religion [Kymlicka] |
| Full Idea: Just as liberalism precludes the establishment of an official religion, so too there cannot be official cultures that have preferred status. | |
| From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8.3) | |
| A reaction: This becomes tricky in schools, where the old way of teaching national literature and particular types of music has been eroded in modern times. But once wide diversity is allowed there is no single story which can be taught. |
| 23388 | Liberals need more than freedom; they must build a nation, through a language and institutions [Kymlicka] |
| Full Idea: Liberals need to replace the idea of 'benign neglect', and recognise the central role of nation-building in a democracy. …This means promoting a common language, and equal access to institutions operating in that language. | |
| From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8.3) | |
| A reaction: 'Benign neglect' is non-interference with citizens' lives. Obviously the institutions include education, but is a state health service implied? Can equal access by guaranteed to private institutions? |
| 23380 | Some individuals can gain citizenship as part of a group, rather than as mere individuals [Kymlicka] |
| Full Idea: On the view of 'differentiated citizenship', members of certain groups would be incorporated into the community, not only as individuals, but also through the group, and their rights would depend in part on their group membership. | |
| From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8) | |
| A reaction: This is obviously a strategy to enable marginalised individuals to be fully included in society. The downside is that individuals gain their social identity through a label, rather than through themselves, which pure liberals dislike. 'Identity politics'. |
| 23381 | The status hierarchy is independent of the economic hierarchy [Kymlicka] |
| Full Idea: The evidence suggests that (contrary to the Marxist view) the status hierarchy is not reducible to the economic hierarchy. | |
| From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8) | |
| A reaction: Kymlicka is particularly thinking of racism, which lowers the status of certain groups, even if they are economically successful. I console myself for my modest economic status by getting lots of education. |
| 23383 | Some multiculturalists defended the rights of cohesive minorities against liberal individualism [Kymlicka] |
| Full Idea: Defending multiculturalism initially involved endorsing the communitarian critique of liberalism, and viewed minority rights as defending cohesive minority groups against the encroachment of liberal individualism. | |
| From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8.1) | |
| A reaction: Liberal individualists have to accept these criticisms from Marxists, communitarians and multiculturalists. The lone individual has no group that guarantees support, and individuals (especially the young) can easily sink. |
| 23384 | 'Culturalist' liberals say that even liberal individuals may need minority rights [Kymlicka] |
| Full Idea: The 'liberal culturalist' position is that minorities which share basic liberal principles nonetheless need minority rights. | |
| From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8.2) | |
| A reaction: Disabled liberals are an obvious example. This strikes me as a promising version of liberalism, which accepts the criticisms of extreme individualism. |
| 23385 | Multiculturalism may entail men dominating women in minority groups [Kymlicka] |
| Full Idea: Many feminists express concern that multiculturalism in practice typically means giving male members of the group the power to control the women in the group. | |
| From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8.2) | |
| A reaction: The way the young are treated might also be a problem. The underlying question is whether the minority group is more or less civilised than the central state. Liberalism always fights for the rights of the least powerful. |
| 23386 | Liberals must prefer minority right which are freedoms, not restrictions [Kymlicka] |
| Full Idea: Liberal defenders of multiculturalism must distinguish 'bad' minority rights which are restrictions from 'good' minority rights which supplement individual rights. | |
| From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8.2) | |
| A reaction: Presumably no sensible liberal wants to remove all restrictions, so deeper values must be invoked to justify the mode of approved minority rights. A list of human goods seems needed. |
| 23389 | Why shouldn't national minorities have their own right to nation-build? [Kymlicka] |
| Full Idea: Why should national minorities not have the same powers of nation-building as the majority? | |
| From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8.4) | |
| A reaction: A 'national minority' is marked by a different language, or a different religion, or both. No one doubts the majority's right to nation-build. Some further principle would be needed to deny that right to a minority. Maybe the minority was there first? |
| 23391 | Multiculturalism is liberal if it challenges inequality, conservative if it emphasises common good [Kymlicka] |
| Full Idea: Liberal multiculturalism challenges status inequalities while preserving individual freedom. …Conservative multiculturalism replaces liberal principles with a communitarian politics of the common good, at least at the local or group level. | |
| From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8.6) | |
| A reaction: [compressed] This sounds a bit simplistic. Recent emphasis on 'the common good', in the face of white supremacists etc., seems admirable, but surely challenging inequalities promotes the common good? Minority cultures are often conservative. |
| 23379 | Rights are a part of nation-building, to build a common national identity and culture [Kymlicka] |
| Full Idea: Extending citizenship to include common social rights was a tool of nation-building, intended in part to construct and consolidate a sense of common national identity and culture. | |
| From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8) | |
| A reaction: Kymlicka explains a lot of politics and society in terms of the desire of governments to 'build' their nation. You have to make people who are essentially powerless feel that they are at least in some way involved, and benefiting. |
| 23382 | Rights derived from group membership are opposed to the idea of state citizenship [Kymlicka] |
| Full Idea: The organisation of society on the basis of rights or claims that derive from group membership is sharply opposed to the concept of society based on citizenship. | |
| From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8) | |
| A reaction: [from John Porter 1987] Does this imply that you might have rights as part of a group which you don't have as a state citizen? Positive discrimination, for example. Differential rights sounds like potential trouble. |
| 23378 | The welfare state helps to integrate the working classes into a national culture [Kymlicka] |
| Full Idea: The development of the welfare state has been quite successful in integrating the working classes into national cultures throughout the Western democracies. | |
| From: Will Kymlicka (Contemporary Political Philosophy (2nd edn) [2002], 8) | |
| A reaction: Hard-line capitalists tend to hate the welfare state, as unfair to high earners, but it not only makes workers feel involved, but also provides a healthier, happier, more knowledgeable work force for employers. |