31 ideas
| 9193 | ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett] |
| Full Idea: ZF set theory is a first-order axiomatization. Variables range over sets, there are no second-order variables, and primitive predicates are just 'equals' and 'member of'. The axiom of extensionality says sets with the same members are identical. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 7) | |
| A reaction: If the eleven members of the cricket team are the same as the eleven members of the hockey team, is the cricket team the same as the hockey team? Our cricket team is better than our hockey team, so different predicates apply to them. |
| 9194 | The main alternative to ZF is one which includes looser classes as well as sets [Dummett] |
| Full Idea: The main alternative to ZF is two-sorted theories, with some variables ranging over classes. Classes have more generous existence assumptions: there is a universal class, containing all sets, and a class containing all ordinals. Classes are not members. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 7.1.1) | |
| A reaction: My intuition is to prefer strict systems when it comes to logical theories. The whole point is precision. Otherwise we could just think about things, and skip all this difficult symbolic stuff. |
| 9195 | Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett] |
| Full Idea: It must not be concluded from the rejection of excluded middle that intuitionistic logic operates with three values: true, false, and neither true nor false. It does not make use of true and false, but only with a construction being a proof. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 8.1) | |
| A reaction: This just sounds like verificationism to me, with all its problems. It seems to make speculative statements meaningless, which can't be right. Realism has lots of propositions which are assumed to be true or false, but also unknowable. |
| 9186 | First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett] |
| Full Idea: First-order logic is distinguished by generalizations (quantification) only over objects: second-order logic admits generalizations or quantification over properties or kinds of objects, and over relations between them, and functions defined over them. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 3.1) | |
| A reaction: Second-order logic was introduced by Frege, but is (interestingly) rejected by Quine, because of the ontological commitments involved. I remain unconvinced that quantification entails ontological commitment, so I'm happy. |
| 9187 | Logical truths and inference are characterized either syntactically or semantically [Dummett] |
| Full Idea: There are two ways of characterizing logical truths and correct inference. Proof-theoretic or syntactic characterizations, if the formalization admits of proof or derivation; and model-theoretic or semantic versions, being true in all interpretations. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 3.1) | |
| A reaction: Dummett calls this distinction 'fundamental'. The second one involves truth, and hence meaning, where the first one just responds to rules. ..But how can you have a notion of correctly following a rule, without a notion of truth? |
| 9191 | Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett] |
| Full Idea: It can be argued that the notion of ordinal numbers is more fundamental than that of cardinals. To count objects, we must count them in sequence. ..The theory of ordinals forms the substratum of Cantor's theory of cardinals. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 5) | |
| A reaction: Depends what you mean by 'fundamental'. I would take cardinality to be psychologically prior ('that is a lot of sheep'). You can't order people by height without first acquiring some people with differing heights. I vote for cardinals. |
| 9192 | The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett] |
| Full Idea: The number 4 cannot be characterized solely by its position in a system, because it has different positions in the system of natural numbers and that of the positive whole numbers, whereas these systems have the very same structure. | |
| From: Michael Dummett (The Philosophy of Mathematics [1998], 6.1) | |
| A reaction: Dummett seems to think this is fairly decisive against structuralism. There is also the structure of the real numbers. We will solve this by saying that the wholes are abstracted from the naturals, which are abstracted from the reals. Job done. |
| 3448 | Do new ideas increase the weight of the brain? [Dance] |
| Full Idea: If someone gives you a piece of information, does your brain suddenly become heavier? | |
| From: Adam Dance (works [2001]), quoted by PG - Db (ideas) | |
| A reaction: A beautifully simple question, which is a reductio of the idea that information is simply a physical object. The question points to a functionalist account of brain activity. |
| 23616 | Legal excuses are duress, ignorance, and diminished responsibility [McMahan] |
| Full Idea: The common legal practice is to distinguish three broad categories of excuse: duress, epistemic limitation, and diminished responsibility. | |
| From: Jeff McMahan (Killing in War [2009], 3.2.1) | |
| A reaction: McMahan cites these with reference to soldiers in wartime, but they have general application. The third one seems particularly open to very wide interpretation. Presumably I can't be excused by just being irresponsible. |
| 23606 | Liberty Rights are permissions, and Claim Rights are freedom from intervention [McMahan] |
| Full Idea: There are two types of right. A Liberty right is merely a permission, meaning it is not wrong to do it. But a Claim right is a right against intervention, meaning no one has a liberty right to prevent it. | |
| From: Jeff McMahan (Killing in War [2009], 2.3) | |
| A reaction: There must also be a third type of right, which requires other people to perform actions on your behalf. If you pay for a book in a shop, you must then be given the book. |
| 23595 | The worst unjustified wars have no aim at all [McMahan] |
| Full Idea: The most serious reason why a war might be unjustified is that it lacks any justifying aim at all. | |
| From: Jeff McMahan (Killing in War [2009], 1.1) | |
| A reaction: It seems that Louis XIV invaded the Netherlands in around 1674 purely to enhance his own glory. That strikes me as worse. I supposed Ghenghis Khan invaded places simply because he enjoyed fighting. |
| 23619 | A defensive war is unjust, if it is responding to a just war [McMahan] |
| Full Idea: It is possible for a defensive war to be unjust, when the defensive war to which it is a response is a just war. | |
| From: Jeff McMahan (Killing in War [2009], 3.3.3) | |
| A reaction: An example might be a state resisting an intervention from outside, when the state is in the process of exterminating some unwanted minority. Or perhaps the invaders are crossing the state's territory to achieve some admirable end. |
| 23620 | A person or state may be attacked if they are responsible for an unjustified threat [McMahan] |
| Full Idea: It is a necessary condition of liability to defensive attack that one be morally responsible for posing an objectively unjustified threat. | |
| From: Jeff McMahan (Killing in War [2009], 4.1.1) | |
| A reaction: This implies that one may not actually be doing the threatening (but merely ordering it, or enabling it). McMahan aims to have the same criteria for wartime as for peacetime. He denies Anscombe's claim that merely posing the threat is enough. |
| 23598 | You (e.g. a police officer) are not liable to attack just because you pose a threat [McMahan] |
| Full Idea: It is false that by posing a threat to another, one necessarily makes oneself liable to defensive action. A police officer who shoots an active murderer does not thereby by make herself liable to defensive action. | |
| From: Jeff McMahan (Killing in War [2009], 1.2) | |
| A reaction: This is one of his arguments against the moral equality of combatants. It is not morally OK to shoot all the local soldiers when you unjustly invade a territory. Sounds right to me. |
| 23594 | Wars can be unjust, despite a just cause, if they are unnecessary or excessive or of mixed cause [McMahan] |
| Full Idea: Wars can be unjust despite having a just cause, because they are not actually needed, or they will cause excessive harm, or they also pursue some unjust causes. | |
| From: Jeff McMahan (Killing in War [2009], 1.1) | |
| A reaction: [compressed] The point is that older writers often think that a 'just cause' is sufficient. He is obviously right. |
| 23597 | Just war theory says all and only persons posing a threat are liable to attack [McMahan] |
| Full Idea: In mainstream just war theory (Anscombe, Nagel, Walzer) the criterion of liability to attack is simply posing a threat. Since all combatants pose a threat to each other, they are morally liable to attack; because noncombatants do not, they are not liable. | |
| From: Jeff McMahan (Killing in War [2009], 1.2) | |
| A reaction: McMahan says that the distinction between legitimate and illegitimate targets rests mostly on this basis. The problem is that a huge range of unarmed people can also pose various degrees of threat. |
| 23600 | Proportionality in fighting can't be judged independently of the justice of each side [McMahan] |
| Full Idea: There is simply no satisfactory understanding of proportionality in war that can be applied independently of whether the acts that are evaluated support a just or an unjust cause. | |
| From: Jeff McMahan (Killing in War [2009], 1.3) | |
| A reaction: He rejects traditional just war theory, which sees both sides as morally equal in combat, and hence equally subject to the principles of proportional response. But the just can then be harsher, when their just principles should make them milder. |
| 23603 | Can an army start an unjust war, and then fight justly to defend their own civilians? [McMahan] |
| Full Idea: There is a paradox if the unjust are justified in fighting the just in order to protect their own civilians who have been endangered by the starting of an unjust war. | |
| From: Jeff McMahan (Killing in War [2009], 2.1) | |
| A reaction: [my summary of MacMahan pp.48-49] It suggests that in a war there may be local concepts of justice which are at odds with the general situation - which is the ad bellum/in bello distinction. But this is the justice of fighting, not how it is conducted. |
| 23611 | Soldiers cannot freely fight in unjust wars, just because they behave well when fighting [McMahan] |
| Full Idea: We must stop reassuring soldiers that they act permissibly when they fight in an unjust war, provided that they conduct themselve honorably on the battlefield by fighting in accordance with the rules of engagement. | |
| From: Jeff McMahan (Killing in War [2009], 2.8) | |
| A reaction: This culminates McMahan's arguments against the moral equality of combatants, and against the sharp division of justice of war from justice in war. How rare it is for philosophy to culminate in a policy recommendation! |
| 23612 | The law of war differs from criminal law; attacking just combatants is immoral, but legal [McMahan] |
| Full Idea: Unlike domestic criminal law, the law of war is designed not to protect moral rights but to prevent harm. …This means when unjust combatants attack just combatants they violate their moral rights, yet they act within their legal rights. | |
| From: Jeff McMahan (Killing in War [2009], 3.1.1) | |
| A reaction: He says we must bring the law of war much closer to the morality of war. If there is any hope of slowly eliminating war, it may lie in reforms such as these. |
| 23617 | If the unjust combatants are morally excused they are innocent, so how can they be killed? [McMahan] |
| Full Idea: If most unjust combatants are morally innocent because they are excused, and if it is wrong to intentionally kill morally innocent people, then a contingent form of pacificism may be inescapable. | |
| From: Jeff McMahan (Killing in War [2009], 3.3.1) | |
| A reaction: A very nice argument against the moral equality of combatants. If I think we are the good guys, and the opposing troops are no morally different from us, how can I possibly kill them? |
| 23599 | You don't become a legitimate target, just because you violently resist an unjust attack [McMahan] |
| Full Idea: It is hard to see how just combatants could become legitimate targets simply by offering violent resistance to unjust attacks by unjust coombatants. | |
| From: Jeff McMahan (Killing in War [2009], 1.3) | |
| A reaction: It is, however, hard to criticise a soldier who is dragged into fighting for an unjust cause, and then kills just defenders in the course of the fight. Once the bullets fly, normal morality seems to be suspended. Just survive. |
| 23596 | If all combatants are seen as morally equal, that facilitates starting unjust wars [McMahan] |
| Full Idea: It would be naïve to doubt that the widespread acceptance of the moral equality of combatants has facilitated the ability of governments to fight unjust wars. | |
| From: Jeff McMahan (Killing in War [2009], 1.1) | |
| A reaction: The point is that their armies are both compliant and seeing their actions as guiltless, which makes them perfect tools for evil. McMahan's ideal is an army which asks sharp questions about the justification of the war, before they fight it. |
| 23604 | Volunteer soldiers accept the risk of attack, but they don't agree to it, or to their deaths [McMahan] |
| Full Idea: When soldiers go to war, they undoubtedly assume a certain risk. They voluntarily expose themselves to a significant risk of being attacked. But this is entirely different from consenting to being attacked. | |
| From: Jeff McMahan (Killing in War [2009], 2.2.1) | |
| A reaction: This is his response to Walzer's thought that soldiers resemble people who volunteer for a boxing match. The sailors at Pearl Harbour obviously didn't consent to the attack, or accept the Japanese right to kill them. |
| 23608 | If being part of a big collective relieves soldiers of moral responsibility, why not the leaders too? [McMahan] |
| Full Idea: If acting as an agent of a political collective justifies the combatants fighting an unjust war, that should also release the leaders from responsibility for their role in the fighting of that war. No one ever explains why this is not so. | |
| From: Jeff McMahan (Killing in War [2009], 2.5) | |
| A reaction: At the very least there seems to be a problem of the cut off point between innocent soldiers and culpable leaders. Which rank in the army or executive triggers the blame? |
| 23610 | If soldiers can't refuse to fight in unjust wars, can they choose to fight in just wars? [McMahan] |
| Full Idea: There is a certain symmetry here. The permissibility of disobeying a command to fight in an unjust war suggests the permissibility of disobeying a command not to fight in a just war. | |
| From: Jeff McMahan (Killing in War [2009], 2.7) | |
| A reaction: The argument considered here is that since we could never allow soldiers to choose to fight in their own wars, we similarly cannot let them opt out of the official wars. Implying obedience is absolute. Soldiers don't get to 'choose' anything! |
| 23613 | Equality is both sides have permission, or both sides are justified, or one justified the other permitted [McMahan] |
| Full Idea: Moral equality means either 1) because just combatants are permitted to fight in a just way, so are the unjust , or 2) because the just are justified, so are the unjust, or 3) because the just are justified, the unjust are therefore permitted. | |
| From: Jeff McMahan (Killing in War [2009], 3.1.2) | |
| A reaction: [summary] McMahan calls 1) the weak version, and 2) the strong. He suggests that although 3) is unusual, it is what most people believe - that if the good are justified, the bad are permitted to fight back. He rejects them all. |
| 23615 | Fighting unjustly under duress does not justify it, or permit it, but it may excuse it [McMahan] |
| Full Idea: It is said that combatants are compelled to fight; they have no choice. But duress is not a justification; nor does it ground a permission - not even a subjective permission. It is, instead, an excusing condition. | |
| From: Jeff McMahan (Killing in War [2009], 3.1.2) | |
| A reaction: The 'subjective' permission is believing you are just, even if you aren't. A nice, accurate and true distinction made by McMahan, I think. It is roughly our postwar attitude to the Nazi army. |
| 23605 | Soldiers cannot know enough facts to evaluate the justice of their war [McMahan] |
| Full Idea: When soldiers are commanded to fight, they cannot reasonably be expected to have the factual knowledge necessary to evaluate the war as just or unjust. | |
| From: Jeff McMahan (Killing in War [2009], 2.3) | |
| A reaction: This is part of the 'epistemic' justification for a soldier to fight in an unjust war. Sometimes soldiers do have enoough knowledge, especially if they join up late on in a war, when they have studied and observed its progress. |
| 23602 | Innocence implies not being morally responsible, rather than merely being guiltless [McMahan] |
| Full Idea: My alternative conception is that one is 'innocent' if one is neither morally responsible for nor guilty of a wrong. Classical theory focused on guilt, but I think we should focus on moral responsibility (which is something less). | |
| From: Jeff McMahan (Killing in War [2009], 1.4) | |
| A reaction: This seems to make the supporters of evil equally liable to attack with its perpetrators. But you can observe perpetration a lot more easily than you can observe support. |
| 23618 | Unconditional surrender can't be demanded, since evil losers still have legitimate conditions [McMahan] |
| Full Idea: Achieving unconditional surrender can never be a justification for the continuation of war, since there are always conditions that a vanquished adversary, no matter how evil, can be justified in demanding. | |
| From: Jeff McMahan (Killing in War [2009], 3.3.1) | |
| A reaction: McMahan is particularly discussing Hiroshima, but this also applies to the European war in 1945. Presumably a civilised victor will grant the conditions which the losers would have demanded, and that probably happened in 1945. It's about power. |