43 ideas
| 16877 | A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege] |
| Full Idea: We construct a sense out of its constituents and introduce an entirely new sign to express this sense. This may be called a 'constructive definition', but we prefer to call it a 'definition' tout court. It contrasts with an 'analytic' definition. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.210) | |
| A reaction: An analytic definition is evidently a deconstruction of a past constructive definition. Fregean definition is a creative activity. |
| 11219 | Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta] |
| Full Idea: Frege has defended the austere view that, in mathematics at least, only stipulative definitions should be countenanced. | |
| From: report of Gottlob Frege (Logic in Mathematics [1914]) by Anil Gupta - Definitions 1.3 | |
| A reaction: This sounds intriguingly at odds with Frege's well-known platonism about numbers (as sets of equinumerous sets). It makes sense for other mathematical concepts. |
| 16878 | We must be clear about every premise and every law used in a proof [Frege] |
| Full Idea: It is so important, if we are to have a clear insight into what is going on, for us to be able to recognise the premises of every inference which occurs in a proof and the law of inference in accordance with which it takes place. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.212) | |
| A reaction: Teachers of logic like natural deduction, because it reduces everything to a few clear laws, which can be stated at each step. |
| 16867 | Logic not only proves things, but also reveals logical relations between them [Frege] |
| Full Idea: A proof does not only serve to convince us of the truth of what is proved: it also serves to reveal logical relations between truths. Hence we find in Euclid proofs of truths that appear to stand in no need of proof because they are obvious without one. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.204) | |
| A reaction: This is a key idea in Frege's philosophy, and a reason why he is the founder of modern analytic philosophy, with logic placed at the centre of the subject. I take the value of proofs to be raising questions, more than giving answers. |
| 16863 | Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege] |
| Full Idea: Are there perhaps modes of inference peculiar to mathematics which …do not belong to logic? Here one may point to inference by mathematical induction from n to n+1. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.203) | |
| A reaction: He replies that it looks as if induction can be reduced to general laws, and those can be reduced to logic. |
| 16862 | The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege] |
| Full Idea: Mathematics has closer ties with logic than does almost any other discipline; for almost the entire activity of the mathematician consists in drawing inferences. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.203) | |
| A reaction: The interesting question is who is in charge - the mathematician or the logician? |
| 16865 | 'Theorems' are both proved, and used in proofs [Frege] |
| Full Idea: Usually a truth is only called a 'theorem' when it has not merely been obtained by inference, but is used in turn as a premise for a number of inferences in the science. ….Proofs use non-theorems, which only occur in that proof. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.204) |
| 16866 | Tracing inference backwards closes in on a small set of axioms and postulates [Frege] |
| Full Idea: We can trace the chains of inference backwards, …and the circle of theorems closes in more and more. ..We must eventually come to an end by arriving at truths can cannot be inferred, …which are the axioms and postulates. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.204) | |
| A reaction: The rival (more modern) view is that that all theorems are equal in status, and axioms are selected for convenience. |
| 16868 | The essence of mathematics is the kernel of primitive truths on which it rests [Frege] |
| Full Idea: Science must endeavour to make the circle of unprovable primitive truths as small as possible, for the whole of mathematics is contained in this kernel. The essence of mathematics has to be defined by this kernel of truths. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.204-5) | |
| A reaction: [compressed] I will make use of this thought, by arguing that mathematics may be 'explained' by this kernel. |
| 16871 | A truth can be an axiom in one system and not in another [Frege] |
| Full Idea: It is possible for a truth to be an axiom in one system and not in another. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.205) | |
| A reaction: Frege aspired to one huge single system, so this is a begrudging concession, one which modern thinkers would probably take for granted. |
| 16870 | Axioms are truths which cannot be doubted, and for which no proof is needed [Frege] |
| Full Idea: The axioms are theorems, but truths for which no proof can be given in our system, and no proof is needed. It follows from this that there are no false axioms, and we cannot accept a thought as an axiom if we are in doubt about its truth. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.205) | |
| A reaction: He struggles to be as objective as possible, but has to concede that whether we can 'doubt' the axiom is one of the criteria. |
| 16869 | To create order in mathematics we need a full system, guided by patterns of inference [Frege] |
| Full Idea: We cannot long remain content with the present fragmentation [of mathematics]. Order can be created only by a system. But to construct a system it is necessary that in any step forward we take we should be aware of the logical inferences involved. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.205) |
| 16864 | If principles are provable, they are theorems; if not, they are axioms [Frege] |
| Full Idea: If the law [of induction] can be proved, it will be included amongst the theorems of mathematics; if it cannot, it will be included amongst the axioms. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.203) | |
| A reaction: This links Frege with the traditional Euclidean view of axioms. The question, then, is how do we know them, given that we can't prove them. |
| 9388 | Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege] |
| Full Idea: Of any concept, we must require that it have a sharp boundary. Of any object it must hold either that it falls under the concept or it does not. We may not allow a third case in which it is somehow indeterminate whether an object falls under a concept. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.229), quoted by Ian Rumfitt - The Logic of Boundaryless Concepts p.1 n1 | |
| A reaction: This is the voice of the classical logician, which has echoed by Russell. I'm with them, I think, in the sense that logic can only work with precise concepts. The jury is still out. Maybe we can 'precisify', without achieving total precision. |
| 16876 | We need definitions to cram retrievable sense into a signed receptacle [Frege] |
| Full Idea: If we need such signs, we also need definitions so that we can cram this sense into the receptacle and also take it out again. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.209) | |
| A reaction: Has anyone noticed that Frege is the originator of the idea of the mental file? Has anyone noticed the role that definition plays in his account? |
| 16875 | We use signs to mark receptacles for complex senses [Frege] |
| Full Idea: We often need to use a sign with which we associate a very complex sense. Such a sign seems a receptacle for the sense, so that we can carry it with us, while being always aware that we can open this receptacle should we need what it contains. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.209) | |
| A reaction: This exactly the concept of a mental file, which I enthusiastically endorse. Frege even talks of 'opening the receptacle'. For Frege a definition (which he has been discussing) is the assigment of a label (the 'definiendum') to the file (the 'definiens'). |
| 19087 | The meaning or purport of a symbol is all the rational conduct it would lead to [Peirce] |
| Full Idea: The entire intellectual purport of any symbol consists in the total of all modes of rational conduct which, conditionally upon all the possible different circumstances and desires, would ensue upon the acceptance of the symbol. | |
| From: Charles Sanders Peirce (Issues of Pragmaticism [1905], EP ii.246), quoted by Danielle Macbeth - Pragmatism and Objective Truth p.169 n1 | |
| A reaction: Macbeth says pragmatism is founded on this theory of meaning, rather than on a theory of truth. I don't see why the causes of a symbol shouldn't be as much a part of its meaning as the consequences are. |
| 16879 | A sign won't gain sense just from being used in sentences with familiar components [Frege] |
| Full Idea: No sense accrues to a sign by the mere fact that it is used in one or more sentences, the other constituents of which are known. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.213) | |
| A reaction: Music to my ears. I've never grasped how meaning could be grasped entirely through use. |
| 16873 | Thoughts are not subjective or psychological, because some thoughts are the same for us all [Frege] |
| Full Idea: A thought is not something subjective, is not the product of any form of mental activity; for the thought that we have in Pythagoras's theorem is the same for everybody. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.206) | |
| A reaction: When such thoughts are treated as if the have objective (platonic) existence, I become bewildered. I take a thought (or proposition) to be entirely psychological, but that doesn't stop two people from having the same thought. |
| 16872 | A thought is the sense expressed by a sentence, and is what we prove [Frege] |
| Full Idea: The sentence is of value to us because of the sense that we grasp in it, which is recognisably the same in a translation. I call this sense the thought. What we prove is not a sentence, but a thought. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.206) | |
| A reaction: The 'sense' is presumably the German 'sinn', and a 'thought' in Frege is what we normally call a 'proposition'. So the sense of a sentence is a proposition, and logic proves propositions. I'm happy with that. |
| 16874 | The parts of a thought map onto the parts of a sentence [Frege] |
| Full Idea: A sentence is generally a complex sign, so the thought expressed by it is complex too: in fact it is put together in such a way that parts of a thought correspond to parts of the sentence. | |
| From: Gottlob Frege (Logic in Mathematics [1914], p.207) | |
| A reaction: This is the compositional view of propositions, as opposed to the holistic view. |
| 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. |