37 ideas
| 10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
| Full Idea: The logic of ZF Set Theory is classical first-order predicate logic with identity. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.121) | |
| A reaction: This logic seems to be unable to deal with very large cardinals, precisely those that are implied by set theory, so there is some sort of major problem hovering here. Boolos is fairly neutral. |
| 10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
| Full Idea: Maybe the axioms of extensionality and the pair set axiom 'force themselves on us' (Gödel's phrase), but I am not convinced about the axioms of infinity, union, power or replacement. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.130) | |
| A reaction: Boolos is perfectly happy with basic set theory, but rather dubious when very large cardinals come into the picture. |
| 10485 | Naďve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
| Full Idea: The naďve view of set theory (that any zero or more things form a set) is natural, but inconsistent: the things that do not belong to themselves are some things that do not form a set. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.127) | |
| A reaction: As clear a summary of Russell's Paradox as you could ever hope for. |
| 10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
| Full Idea: According to the iterative conception, every set is formed at some stage. There is a relation among stages, 'earlier than', which is transitive. A set is formed at a stage if and only if its members are all formed before that stage. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.126) | |
| A reaction: He gives examples of the early stages, and says the conception is supposed to 'justify' Zermelo set theory. It is also supposed to make the axioms 'natural', rather than just being selected for convenience. And it is consistent. |
| 10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
| Full Idea: The existence of infinitely many natural numbers seems to me no more troubling than that of infinitely many computer programs or sentences of English. There is, for example, no longest sentence, since any number of 'very's can be inserted. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.129) | |
| A reaction: If you really resisted an infinity of natural numbers, presumably you would also resist an actual infinity of 'very's. The fact that it is unclear what could ever stop a process doesn't guarantee that the process is actually endless. |
| 10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
| Full Idea: To the best of my knowledge nothing in mathematics or science requires the existence of very high orders of infinity. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.122) | |
| A reaction: He is referring to particular high orders of infinity implied by set theory. Personally I want to wield Ockham's Razor. Is being implied by set theory a sufficient reason to accept such outrageous entities into our ontology? |
| 10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
| Full Idea: It is no surprise that we should be able to reason mathematically about many of the things we experience, for they are already 'abstract'. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.129) | |
| A reaction: He has just given a list of exemplary abstract objects (Idea 10489), but I think there is a more interesting idea here - that our experience of actual physical objects is to some extent abstract, as soon as it is conceptualised. |
| 10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
| Full Idea: It's a kind of lunacy to think that sound scientific philosophy demands that we think that we see ink-tracks but not words, i.e. word-types. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.128) | |
| A reaction: This seems to link him with Armstrong's mockery of 'ostrich nominalism'. There seems to be some ambiguity with the word 'see' in this disagreement. When we look at very ancient scratches on stones, why don't we always 'see' if it is words? |
| 10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
| Full Idea: I am rather a fan of abstract objects, and confident of their existence. Smaller numbers, sets and functions don't offend my sense of reality. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.128) | |
| A reaction: The great Boolos is rather hard to disagree with, but I disagree. Logicians love abstract objects, indeed they would almost be out of a job without them. It seems to me they smuggle them into our ontology by redefining either 'object' or 'exists'. |
| 10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
| Full Idea: We twentieth century city dwellers deal with abstract objects all the time, such as bank balances, radio programs, software, newspaper articles, poems, mistakes, triangles. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.129) | |
| A reaction: I find this claim to be totally question-begging, and typical of a logician. The word 'object' gets horribly stretched in these discussions. We can create concepts which have all the logical properties of objects. Maybe they just 'subsist'? |
| 23590 | Criminal responsibility can be fully assigned to each member of a group [Walzer] |
| Full Idea: It is a feature of criminal responsibility that it can be distributed without being divided. We can, that is, blame more than one person for a particular act without splitting up the blame we assign. | |
| From: Michael Walzer (Just and Unjust Wars [1977], 19) | |
| A reaction: How far can this extend? To a large violent mob? To an entire nation? In court the responsibility is usually adjusted in the sentencing, rather than in the initial verdict. |
| 23578 | Double Effect needs a double intention - to achieve the good, and minimise the evil [Walzer] |
| Full Idea: Double effect is defensible, I want to argue, only when the two outcomes are the product of a double intention - that 'good' be achieved, and that the foreseeable evil be reduced as far as possible. | |
| From: Michael Walzer (Just and Unjust Wars [1977], 09) | |
| A reaction: A good proposal, I think. We have to accept evil side effects sometimes, but it is immoral to pursue some good 'whatever the cost'. |
| 23564 | Deep ethical theory is very controversial, but we have to live with higher ethical practice [Walzer] |
| Full Idea: The substructure of the ethical world is a matter of deep and unending controversy, Meanwhile, however, we are living in the superstructure. | |
| From: Michael Walzer (Just and Unjust Wars [1977], Pref) | |
| A reaction: This may be the best approach to ethics. Nearly all applied ethics takes the common sense consensus on values for granted. Personally I think that is because the substructure is the obvious success and failure of human functioning. |
| 23568 | If whole states possess rights, there can be social relations between states [Walzer] |
| Full Idea: If states possess rights more or less as individuals do, then it is possible to imagine a society among them more or less like the individuals. | |
| From: Michael Walzer (Just and Unjust Wars [1977], 04) | |
| A reaction: The state's rights must derive from the people. Plots of land don't have rights. In some states the people are in conflict. It can't just be the government which represents the rights of the state. |
| 23571 | States can rightly pre-empt real and serious threats [Walzer] |
| Full Idea: States can use force in the face of threats of war, if there is a serious risk to territory or independence. They are then forced to fight, and are the victims of aggression. | |
| From: Michael Walzer (Just and Unjust Wars [1977], 05) | |
| A reaction: [compressed] He uses this to justify Israeli pre-emptive strikes against Palestinians. I don't think his confident assertion of this principle is justified. It is open to massive abuse. There are, though, clearly situations where he is right. |
| 23572 | Just wars are self-defence, or a rightful intercession in another's troubles [Walzer] |
| Full Idea: Just wars may not be self-defence, if they are to help an independence struggle, or it is to save another country being invaded, or to prevent enslavement or massacre. | |
| From: Michael Walzer (Just and Unjust Wars [1977], 06) | |
| A reaction: [summary] Modern wars support some examples of these, but also suggest that without a long-term plan, or an understanding of the country they are entering, such intercessions may worsen the situation. |
| 23581 | The aim of reprisals is to enforce the rules of war [Walzer] |
| Full Idea: The purpose of reprisals is not to win the war or prevent defeat, but simply to enforce the rules [of war]. | |
| From: Michael Walzer (Just and Unjust Wars [1977], 13) | |
| A reaction: That may be wishful thinking, since reprisals are often vastly more ruthless than the original offence, and there is often injustice in the nature of the reprisals, since they cannot be precise. |
| 23582 | Reprisal is defensible, as an alternative to war [Walzer] |
| Full Idea: Reprisal is the first resort of force. It is an alternative to war, and that description is an important argument in its favour. | |
| From: Michael Walzer (Just and Unjust Wars [1977], 13) | |
| A reaction: Enduring wrongs with dignity might be another alternative. Successful reprisals may be acceptable, but how do you assess their prospects? |
| 23588 | With nuclear weapons we have a permanent supreme emergency (which is unstable) [Walzer] |
| Full Idea: With nuclear weapons, supreme emergency has become a permanent condition. …[283] But supreme emergency is never a stable position. | |
| From: Michael Walzer (Just and Unjust Wars [1977], 17) | |
| A reaction: The obvious instability of balanced mutual threat is a nuclear state which finds itself losing a war. |
| 23580 | States need not endure attacks passively, and successful reprisals are legitimate [Walzer] |
| Full Idea: Whenever there is some substantial chance of success, reprisals are the legitimate resort of a victim state; for no state can be required passively to endure attacks upon its citizens. | |
| From: Michael Walzer (Just and Unjust Wars [1977], 13) | |
| A reaction: My concern is whether the reprisals have any direct connection to the attacks. They killed some of ours, so we will kill some of theirs is immoral. E.g. bombing Tripoli as reprisal for crashing the Lockerbie plane. |
| 23587 | Nuclear bombs are not for normal war; they undermine the 'just war', with a new morality [Walzer] |
| Full Idea: Nuclear weapons are not designed for war at all. …They explode the idea of a just war. They are the first technological innovations that are simply not encompassable within the familiar moral world. | |
| From: Michael Walzer (Just and Unjust Wars [1977], 17) | |
| A reaction: A nuclear war can hardly lead to normal victory, if it destroys the thing you are trying to conquer. It is like bringing a machine gun to a boxing match. |
| 23567 | Even non-violent intrusive acts between states count as aggression, if they justify resistance [Walzer] |
| Full Idea: Every violation of an independent state is called aggression, which fails to differentiate between a seizure or imposition, and an actual conquest. …But what they have in common is that all aggressive acts justify forceful resistance. | |
| From: Michael Walzer (Just and Unjust Wars [1977], 04) | |
| A reaction: [compressed] Walzer concedes that this makes 'aggression' rather imprecise, and small acts can be used as an excuse for desired violent resistance. Each entrant in August 1914 seems to have had a slightly different motive. |
| 23570 | The only good reason for fighting is in defence of rights [Walzer] |
| Full Idea: The defence of rights is a reason for fighting. I want now to stress again, and finally, that it is the only reason. | |
| From: Michael Walzer (Just and Unjust Wars [1977], 04) | |
| A reaction: Walzer states at the beginning, without discussion, that his moral assumptions are based on the notion of rights. This is tricky because rights are assigned by some people to other people, and claims of rights can be challenged. |
| 23573 | For moral reasons, a just war must be a limited war [Walzer] |
| Full Idea: Just wars are limited wars; there are moral reasons for the statesmen and soldiers who fight them to be prudent and realistic. | |
| From: Michael Walzer (Just and Unjust Wars [1977], 07) | |
| A reaction: This is rather profound, I think. Watch closely the behaviour of the good guys when they are winning the war. In general, to know someone's moral principles, the best indicator is how they behave when they have power. |
| 23577 | Napoleon said 'I don't care about the deaths of a million men' [Walzer] |
| Full Idea: Napoleon said 'Soldiers are made to be killed. …I do not care a fig for the lives of a million men'. | |
| From: Michael Walzer (Just and Unjust Wars [1977], 08) | |
| A reaction: [Two separate remarks attributed to Napoleon] He apparently often said things like this this later in his career. It strikes me as despicable, and anyone who still tries to present Napoleon as admirable should be ashamed. |
| 23593 | Jus ad bellum and Jus in bello are independent; unjust wars can be fought in a just way [Walzer] |
| Full Idea: Justice of war [ad bellum] and justice in war [in bello] are logically independent. It is perfectly possible for a just war to be fought unjustly, and for an unjust war to be fought in strict accordance with the rules. | |
| From: Michael Walzer (Just and Unjust Wars [1977], 02) | |
| A reaction: The perfect decorum of an unjust firing squad might even make the crime worse. There is something chilling about an evil army conducting itself perfectly within the ethics of warfare. Better than the other thing, though. McMahan disagrees. |
| 23574 | The duties and moral status of loyal and obedient soldiers is the same in defence and aggression [Walzer] |
| Full Idea: The duties of individual soldiers …are precisely the same in wars of aggression and wars of defence. …The moral status of soldiers on both sides is very much the same; they are led to fight by their loyalty and their lawful obedience. | |
| From: Michael Walzer (Just and Unjust Wars [1977], 08) | |
| A reaction: He excludes war crimes. This is the thesis which Jeff McMahan objects to. It would be very odd to think that mafiosi and the legitimate police were morally equal, because the former are loyal. We should all try hard to avoid supporting unjust causes. |
| 23575 | We can't blame soldiers for anything they do which clearly promotes victory [Walzer] |
| Full Idea: It would be difficult to condemn soldiers for anything they did in the course of a battle or a war that they honestly believed, and had good reason to believe, was necessary, or important, or simply useful in determining the outcome. | |
| From: Michael Walzer (Just and Unjust Wars [1977], 08) | |
| A reaction: We can't blame unjust aggressors if their own lives are at stake, but what about in a surprise attack on the first day of the war (such as Pearl Harbour)? Or if they massacre the enemy with safe and overwhelming superiority? |
| 23584 | Rejecting Combatant Equality allows just soldiers to be harsher, even to the extreme [Walzer] |
| Full Idea: Objections to combatant equality appeal to a sliding scale of 'the more justice, the more right'. …It allows the justice of one's cause to make a difference in the way one fights. …The extreme says soldiers fightly justly can do anything that is useful. | |
| From: Michael Walzer (Just and Unjust Wars [1977], 14) | |
| A reaction: This slippery slope fear seems to be Walzer's main argument in favour of the moral equality of combatants. See Jeff McMahan for the opposing view. |
| 23589 | Kidnapped sailors and volunteers have different obligations to the passengers [Walzer] |
| Full Idea: Soldiers may stand to civilians like the crew of a liner to its passengers, for whom they must risk their lives. …But would they be so bound if the sailors had been kidnapped? | |
| From: Michael Walzer (Just and Unjust Wars [1977], 19) | |
| A reaction: The point, I assume, is that a conscripted army does not have the same obligations as volunteers. I can't imagine that principle being accepted in an army which is a mixture of the two. |
| 23614 | Even aggressor soldiers are not criminals, so they have equal rights with their opponents [Walzer] |
| Full Idea: Soldiers fighting for an aggressor state are not themselves criminals: hence their war rights are the same as those of their opponents. | |
| From: Michael Walzer (Just and Unjust Wars [1977], 08) | |
| A reaction: Walzer's main support for this is that opposing armies never regard one another as intrinsically criminal. It seems inevitable, though, that even the invaders themselves see that they are a bit more criminal than the defenders. |
| 23579 | Soldiers will only protect civilians if they feel safe from them [Walzer] |
| Full Idea: Soldiers must feel safe among civilians if civilians are ever to be safe from soldiers. | |
| From: Michael Walzer (Just and Unjust Wars [1977], 11) | |
| A reaction: This is the great dilemma of any resistance movement. It is very easy for the soldiers to abuse their power, even if they do feel safe. Then what? |
| 23586 | What matters in war is unacceptable targets, not unacceptable weapons [Walzer] |
| Full Idea: The crucial distinction in the theory and practice of war is not between prohibited and acceptable weapons but between prohibited and acceptable targets. | |
| From: Michael Walzer (Just and Unjust Wars [1977], 17) | |
| A reaction: Walzer presents this idea as arising out of discussions about nuclear deterrence. Gas attacks were accepted in WW1 trenches, but modern gas attacks on civilians are a crime. Are nuclear attacks on strictly military targets OK? E.g a fleet. |
| 23591 | If the oppressor is cruel, nonviolence is either surrender, or a mere gesture [Walzer] |
| Full Idea: When one cannot count on the moral code of the oppressor, nonviolence is either a disguised form of surrender or a minimalist way of upholding communal values after a military defeat. | |
| From: Michael Walzer (Just and Unjust Wars [1977], Afterword) | |
| A reaction: The point is that ruthless conquerors may just kill the nonviolent, so it would achieve nothing. Nonviolence is only a plausible strategy in a fairly civilised world. Hard to disagree. |
| 23592 | We can only lead war towards peace if we firmly enforce the rules of war [Walzer] |
| Full Idea: We must begin by insisting upon the rules of war and by holding soldiers rigidly to the norms they set. The restraint of war is the beginning of peace. | |
| From: Michael Walzer (Just and Unjust Wars [1977], Afterword) | |
| A reaction: Last sentence of his book. Some cultures have a much greater tradition of ruthless cruelty than others, it seems. Most war ethics seems to concern how the good guys should respond to the bad guys (since the latter hardly care). |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
| From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
| A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
| From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
| A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |