40 ideas
| 15717 | Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan] |
| Full Idea: The problem with the Axiom of Choice is that it allows an initiate (by an ingenious train of reasoning) to cut a golf ball into a finite number of pieces and put them together again to make a globe as big as the sun. | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 9) | |
| A reaction: I'm not sure how this works (and I think it was proposed by the young Tarski), but it sounds like a real problem to me, for all the modern assumptions that Choice is fine. |
| 15712 | 1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan] |
| Full Idea: You have 1 and 0, something and nothing. Adding gives us the naturals. Subtracting brings the negatives into light; dividing, the rationals; only with a new operation, taking of roots, do the irrationals show themselves. | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 1 'Mind') | |
| A reaction: The suggestion is constructivist, I suppose - that it is only operations that produce numbers. They go on to show that complex numbers don't quite fit the pattern. |
| 15711 | The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan] |
| Full Idea: The rationals are everywhere - the irrationals are everywhere else. | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 1 'Nameless') | |
| A reaction: Nice. That is, the rationals may be dense (you can always find another one in any gap), but the irrationals are continuous (no gaps). |
| 15714 | 'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan] |
| Full Idea: The 'commutative' laws say the order in which you add or multiply two numbers makes no difference; ...the 'associative' laws declare that regrouping couldn't change a sum or product (e.g. a+(b+c)=(a+b)+c ). | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 2 'Tablets') | |
| A reaction: This seem utterly self-evident, but in more complex systems they can break down, so it is worth being conscious of them. |
| 15715 | 'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan] |
| Full Idea: The 'distributive' law says you will get the same result if you first add two numbers, and then multiply them by a third, or first multiply each by the third and then add the results (i.e. a · (b+c) = a · b + a · c ). | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 2 'Tablets') | |
| A reaction: Obviously this will depend on getting the brackets right, to ensure you are indeed doing the same operations both ways. |
| 20475 | Maybe modal sentences cannot be true or false [Casullo] |
| Full Idea: Some people claim that modal sentences do not express truths or falsehoods. | |
| From: Albert Casullo (A Priori Knowledge [2002], 3.2) | |
| A reaction: I can only imagine this coming from a narrow hardline empiricist. It seems to me obvious that we make true or false statements about what is possible or impossible. |
| 20476 | If the necessary is a priori, so is the contingent, because the same evidence is involved [Casullo] |
| Full Idea: If one can only know a priori that a proposition is necessary, then one can know only a priori that a proposition is contingent. The evidence relevant to determining the latter is the same as that relevant to determining the former. | |
| From: Albert Casullo (A Priori Knowledge [2002], 3.2) | |
| A reaction: This seems a telling point, but I suppose it is obvious. If you see that the cat is on the mat, nothing in the situation tells you whether this is contingent or necessary. We assume it is contingent, but that may be an a priori assumption. |
| 20471 | Epistemic a priori conditions concern either the source, defeasibility or strength [Casullo] |
| Full Idea: There are three suggested epistemic conditions on a priori knowledge: the first regards the source of justification, the second regards the defeasibility of justification, and the third appeals to the strength of justification. | |
| From: Albert Casullo (A Priori Knowledge [2002], 2) | |
| A reaction: [compressed] He says these are all inspired by Kant. The non-epistemic suggested condition involve necessity or analyticity. The source would have to be entirely mental; the defeasibly could not be experiential; the strength would be certainty. |
| 20477 | The main claim of defenders of the a priori is that some justifications are non-experiential [Casullo] |
| Full Idea: The leading claim of proponents of the a priori is that sources of justification are of two significantly different types: experiential and nonexperiential. Initially this difference is marked at the phenomenological level. | |
| From: Albert Casullo (A Priori Knowledge [2002], 5) | |
| A reaction: He cites Plantinga and Bealer for the phenomenological starting point (that some knowledge just seems rationally obvious, certain, and perhaps necessary). |
| 20472 | Analysis of the a priori by necessity or analyticity addresses the proposition, not the justification [Casullo] |
| Full Idea: There is reason to view non-epistemic analyses of a priori knowledge (in terms of necessity or analyticity) with suspicion. The a priori concerns justification. Analysis by necessity or analyticity concerns the proposition rather than the justification. | |
| From: Albert Casullo (A Priori Knowledge [2002], 2.1) | |
| A reaction: [compressed] The fact that the a priori is entirely a mode of justification, rather than a type of truth, is the modern view, influenced by Kripke. Given that assumption, this is a good objection. |
| 3913 | Maybe imagination is the source of a priori justification [Casullo] |
| Full Idea: Some maintain that experiments in imagination are the source of a priori justification. | |
| From: Albert Casullo (A priori/A posteriori [1992], p.1) | |
| A reaction: What else could assessments of possibility and necessity be based on except imagination? |
| 20474 | 'Overriding' defeaters rule it out, and 'undermining' defeaters weaken in [Casullo] |
| Full Idea: A justified belief that a proposition is not true is an 'overriding' defeater, ...and the belief that a justification is inadequate or defective is an 'undermining' defeater. | |
| From: Albert Casullo (A Priori Knowledge [2002], n 40) | |
| A reaction: Sounds more like a sliding scale than a binary option. Quite useful, though. |
| 15713 | The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan] |
| Full Idea: The claim that no number is greater than a million is confirmed by the first million test cases. | |
| From: R Kaplan / E Kaplan (The Art of the Infinite [2003], 2 'Intro') | |
| A reaction: Extrapolate from this, and you can have as large a number of cases as you could possibly think of failing to do the inductive job. Love it! Induction isn't about accumulations of cases. It is about explanation, which is about essence. Yes! |
| 22849 | Rawls's theory cannot justify liberalism, since it presupposes free and equal participants [Charvet] |
| Full Idea: Rawls's theory presupposes that the contractors are conceived, and conceive themselves, to be free and equal persons. Consequently, the theory cannot be presented as a justificatory theory of liberalism. | |
| From: John Charvet (Liberalism: the basics [2019], 14) | |
| A reaction: Nice. If you imagine diverse groups with many strong beliefs coming together to form a society, Rawls is asking them all to become liberals before they all decide how to live together. |
| 22848 | People with strong prior beliefs would have nothing to do with a veil of ignorance [Charvet] |
| Full Idea: Why would a group of people with strong beliefs (e.g. religious beliefs) agree to debate the problem of what norms should govern their association from behind a veil of ignorance? …They would not accept the veil of ignorance as fair. | |
| From: John Charvet (Liberalism: the basics [2019], 14) | |
| A reaction: Nice. Rawls's experiment assumes liberal people with very few beliefs. No racial supremacist is going to enter a society in which they may be of a different race. Charvet says the entrants would all need to be pluralists about the good. |
| 22838 | Societies need shared values, so conservatism is right if rational discussion of values is impossible [Charvet] |
| Full Idea: Were it true that rational discussion of values is impossible, then a conservative attitude would seem to be the only viable position. Some set of common values is necessary to maintain the unity of a political society. | |
| From: John Charvet (Liberalism: the basics [2019], 07) | |
| A reaction: Better to say that the less values can be both discussed and changed the stronger is the case for a degree of conservatism. Conservatives tend to favour values asserted by authority, rather than by popular (undiscussed) consensus. |
| 22846 | The universalism of utilitarianism implies a world state [Charvet] |
| Full Idea: Utilitarianism is a universalist ethic, so the political realisation of this ethic would seem to be a world state seeking to maximise happiness for the world's population. | |
| From: John Charvet (Liberalism: the basics [2019], 12) | |
| A reaction: It certainly doesn't seem to favour the citizens of the state where it is implemented, since miserable people just across the border would have priority, and all miserable migrants must be welcomed. There is no loyalty to citizens. |
| 22835 | Liberals value freedom and equality, but the society itself must decide on its values [Charvet] |
| Full Idea: While freedom and equality are liberal values …they are fundamental regulative ideas of an independent society that is self-regulating …and decides what its own social and political arrangements should be. | |
| From: John Charvet (Liberalism: the basics [2019], 06) | |
| A reaction: So the central political activity is persuasion, not enforcement. Illiberal societies all contain liberal individuals. |
| 22831 | Modern libertarian societies still provide education and some housing [Charvet] |
| Full Idea: No society today is libertarian in the extreme sense. Even the freest economically, such as Singapore have their governments provide education services and public housing. | |
| From: John Charvet (Liberalism: the basics [2019], 05) | |
| A reaction: There is a good argument that many other services should be provided by a libertarian state, on the grounds that it is more efficient, and the services must otherwise paid for by much higher salaries. |
| 22839 | Liberalism needs people to either have equal autonomy, or everyone to have enough autonomy [Charvet] |
| Full Idea: To get a liberal society one would have to claim that either everyone possesses autonomy to an equal degree or that everyone possesses a threshold level of the capacity that entitles them to enjoy the full liberal rights. | |
| From: John Charvet (Liberalism: the basics [2019], 07) | |
| A reaction: This leaves out the more right-wing attitude that people can increase their capacity for autonomy if they are forced to stand on their own feet. A liberal society must decide how to treat persons incapable of proper autonomy. |
| 22847 | Kant places a higher value on the universal rational will than on the people asserting it [Charvet] |
| Full Idea: For Kant what is of absolute worth is the universal rational will which become an individual's actual will. Insofar as the individual fails to will the universal, they have no absolute worth, so whether or not they exist is unimportant. | |
| From: John Charvet (Liberalism: the basics [2019], 14) | |
| A reaction: A lovely demolition of the claims of Kant to be the patriarch of liberalism! Liberalism must place supreme value on each individual, not on some abstracted realm of pure reason and moral good. Liberals are motivated by love, not reason. |
| 22821 | Liberalism asserts maximum freedom, but that must be equal for all participants [Charvet] |
| Full Idea: Liberalism attaches fundamental value to leaving individuals as free as possible … - but there is another fundamental value implicit in this idea - the equal status of the participants in the practice. By this I mean that they all have the same rights. | |
| From: John Charvet (Liberalism: the basics [2019], Intro) | |
| A reaction: Libertarian liberalism (e.g. Nozick) only asserts the fundament principle of freedom, but such a society swiftly deprives most of its members of those very freedoms. Egalitarian Liberalism should be our default political ideology. |
| 22834 | Egalitarian liberals prefer equality (either of input or outcome) to liberty [Charvet] |
| Full Idea: Rather than libertarianism, egalitarian liberals promote equality, either of outcomes (of happiness or of well-being), or of inputs (such as opportunities, capacities or resources), which they favour ahead of freedom. | |
| From: John Charvet (Liberalism: the basics [2019], 06) | |
| A reaction: This is my team, I think. I think I'm a liberal who thinks liberty is a bit overrated. Equal outcome according to capacity (promoted by Nussbaum) seems attractive. |
| 22822 | Liberals promote community and well-being - because all good societies need them [Charvet] |
| Full Idea: Community and well-being are not specifically liberal values. They are values any independent political society must pursue whether it is a liberal society or not. | |
| From: John Charvet (Liberalism: the basics [2019], Intro) | |
| A reaction: This seems, at a stroke, to undermine the familiar debate between liberals and communitarians. I've switched to the former from the latter, because communitarians is potentially too paternalistic and conservative. Persuade individuals to be communal! |
| 22841 | Identity multiculturalism emerges from communitarianism, preferring community to humanity [Charvet] |
| Full Idea: Identity-based multiculturalism developed from communitarianism. …People come to consciousness of themselves as members of some community before they identify themselves as members of the human race. | |
| From: John Charvet (Liberalism: the basics [2019], 08) | |
| A reaction: This is 'identity politics', which Carvet sees as a problem from liberalism. Is it more important to be a woman or a Muslim or a Scot than to be a human being? It seems to create institutional antagonisms. |
| 22842 | For communitarians it seems that you must accept the culture you are born into [Charvet] |
| Full Idea: Communitarians have difficulty avoiding the relativist trap. It seems they must claim that if one is born into a liberal society one cannot but be a liberal, and if one is born into a communist society one cannot but be a communist. | |
| From: John Charvet (Liberalism: the basics [2019], 08) | |
| A reaction: Anyone who accepts the Hegelian view of history and culture seems doomed to such relativism, and Hegel is a communitarian precursor. This is a good reason for me to reject communitarianism, after a long flirtation. We can criticise our own culture. |
| 22830 | Give by ability and receive by need, rather than a free labour market [Charvet] |
| Full Idea: Only the most extreme collective socialism denies the freedom to sell one's labour power and buy that of others, under the communist slogan 'from each according to his ability, and to each according to his needs'. | |
| From: John Charvet (Liberalism: the basics [2019], 05) | |
| A reaction: [He cites Marx 'Critique of the Gotha Programme'] I would guess that this practice is not abnormal in old traditional villages, though a community would be tempted to reward highly a very successful member. |
| 22829 | Allowing defamatory speech is against society's interests, by blurring which people are trustworthy [Charvet] |
| Full Idea: The argument for restricting defamatory speech is that unrestricted speech makes it impossible, or too difficult, to distinguish between those who deserve a trustworthy reputation and those who don't - a distinction in society's best interests. | |
| From: John Charvet (Liberalism: the basics [2019], 03) | |
| A reaction: A nice example of appeal to the common good, in opposition to the normal freedoms of liberalism. An example of the Prisoner's Dilemma. Should assertion of the common good of a group be a prime value of liberalism? |
| 22836 | 'Freedom from' is an empty idea, if the freedom is not from impediments to my desires [Charvet] |
| Full Idea: Berlin's distinction of 'freedom from' and 'freedom to' is worthless …because to say that I want to be free from something for absolutely no reason makes no sense. Unfreedom is being blocked from what I want to do, which ceases if I no longer want it. | |
| From: John Charvet (Liberalism: the basics [2019], 07) | |
| A reaction: [compressed] The government could guarantee us against attacks by albatrosses, but we would hardly have a national holiday to celebrate the freedom. Still, there is freedom from incoming troubles, and freedom to output things. |
| 22837 | Positive freedom can lead to coercion, if you are forced to do what you chose to do [Charvet] |
| Full Idea: Berlin saw positive freedom as a justification for illiberal coercion. If I am positively free only in doing X, then if I am forced to do X, I will still be free. | |
| From: John Charvet (Liberalism: the basics [2019], 07) | |
| A reaction: I suppose Berlin is thinking of Russian farmers, who wanted to farm, but then found they were forced to do what they were going to do anyway. It's better than being forced to do what you didn't want to do. Forcing clearly isn't freedom. |
| 22844 | First level autonomy is application of personal values; second level is criticising them [Charvet] |
| Full Idea: First level autonomy is being able to apply one's scheme of values to one's actions and life; second level autonomy is being able to subject those values to critical evaluation. | |
| From: John Charvet (Liberalism: the basics [2019], 10) | |
| A reaction: Charvet sees this as a key issue for liberalism. How do you treat citizens who cannot advance beyond the first level? He mentions the elitism of Plato's Republic that results. |
| 22840 | Mere equality, as in two trees being the same height, has no value at all [Charvet] |
| Full Idea: That the relation of equality might be considered a value in itself is an absurdity. Would the equality of blinding the only sighted person in a blind society be good? Is it inherently good that two trees are the same height? This is nonsense. | |
| From: John Charvet (Liberalism: the basics [2019], 08) | |
| A reaction: He cites Temkin 1993 as defending the blinding example! Obviously equality is only possible in certain respects (though electrons might be equal in all respects). So the point is to identify the important respects. The rest is rhetoric. |
| 22843 | Inequalities are worse if they seem to be your fault, rather than social facts [Charvet] |
| Full Idea: Inequality is worse in a meritocracy than in a stratified society, because everyone enjoys a formal equality of status and your position in the social order is due to your merit or lack of merit, so you have only yourself to blame for being at the bottom. | |
| From: John Charvet (Liberalism: the basics [2019], 10) | |
| A reaction: This is the simple point that it is worse to lack some good if you might have possessed it, rather than it being entirely out of reach. It also makes the false assumption that people are largely responsible for their merit or lack of it (ignoring luck). |
| 22845 | Money allows unlimited inequalities, and we obviously all agree to money [Charvet] |
| Full Idea: The introduction of money allows people to accumulate wealth without limit. Since money only works through everyone's agreement …everyone can be taken to have agreed to the consequences of money in the unequal distribution of wealth. | |
| From: John Charvet (Liberalism: the basics [2019], 11) | |
| A reaction: [Locke] Presumably large inequalities of possessions and territory were possible before money, but there was at least an upper limit. The current owner of Amazon may end up with more wealth than the whole of the rest of humanity combined. |
| 22823 | The rule of law is mainly to restrict governments [Charvet] |
| Full Idea: The rule of law is directed at the restriction of the power of governments as much, if not more, then the power of private individuals. | |
| From: John Charvet (Liberalism: the basics [2019], 02) | |
| A reaction: The more powerful you are the more restricting is the rule of law. Every government is tempted to change the law to expand its powers. The UK government has just legislated to restrict public demonstrations. Law is the people's weapon against autocrats. |
| 22825 | The 1689 Bill of Rights denied the monarch new courts, or the right to sit as judge [Charvet] |
| Full Idea: The 1689 Bill of Rights said the monarch could not create new courts of law, or act as a judge at law. | |
| From: John Charvet (Liberalism: the basics [2019], 02) | |
| A reaction: The background was the abolition of the court of Star Chamber in 1641, which had been secret, severe, and controlled by the monarch. Is it possible to create a new type of court, or are we stuck with the current ones? |
| 22826 | From 1701 only parliament could remove judges, whose decisions could not be discussed [Charvet] |
| Full Idea: In 1701 UK judges were given secure tenure, being removable only by parliament which at the same time undertook to follow a convention not to discuss particular judicial decisions. | |
| From: John Charvet (Liberalism: the basics [2019], 02) | |
| A reaction: In recent years the UK Daily Mail published the pictures of three judges, and labelled them 'traitors' because of their verdict about leaving the European Union. |
| 22827 | Justice superior to the rule of law is claimed on behalf of the workers, or the will of the nation [Charvet] |
| Full Idea: Communist leaders justify themselves as the embodiment of the people's will as workers, and fascist leaders as expressing the will of the nation. Both believe their policies contain a superior justice on this basis. | |
| From: John Charvet (Liberalism: the basics [2019], 02) | |
| A reaction: [compressed] A neat summary of why the rule of law might be rejected (other than by simple tyrrany justified only by force). In modern democracies recent right-wing governments have pushed back the law and attacked justice on this basis. |
| 22828 | The rule of law mainly benefits those with property and liberties [Charvet] |
| Full Idea: A rule of law regime will primarily benefit those possessing property and liberty rights. | |
| From: John Charvet (Liberalism: the basics [2019], 02) | |
| A reaction: Important. It's no good fighting for the law if the law doesn't protect what you have got, or if you have got nothing to protect. Important steps must precede assertion of the rule of law. |
| 22832 | Welfare is needed if citizens are to accept the obligations of a liberal state [Charvet] |
| Full Idea: The welfare state provides the background conditions under which it is reasonable to expect one's fellow citizens to commit to liberal principles of interaction, even if those conditions can only be achieved through a degree of compulsion. | |
| From: John Charvet (Liberalism: the basics [2019], 05) | |
| A reaction: You cannot expect people to accept the role of 'free' citizen if that is likely to result in swift misery. A liberal state will only command loyalty if it has a safety net. Fully committed liberalism implies modest socialism. |