53 ideas
| 15716 | If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert] |
| Full Idea: If the arbitrarily given axioms do not contradict each other with all their consequences, then they are true and the things defined by the axioms exist. For me this is the criterion of truth and existence. | |
| From: David Hilbert (Letter to Frege 29.12.1899 [1899]), quoted by R Kaplan / E Kaplan - The Art of the Infinite 2 'Mind' | |
| A reaction: If an axiom says something equivalent to 'fairies exist, but they are totally undetectable', this would seem to avoid contradiction with anything, and hence be true. Hilbert's idea sounds crazy to me. He developed full Formalism later. |
| 18844 | You would cripple mathematics if you denied Excluded Middle [Hilbert] |
| Full Idea: Taking the principle of Excluded Middle away from the mathematician would be the same, say, as prohibiting the astronomer from using the telescope or the boxer from using his fists. | |
| From: David Hilbert (The Foundations of Mathematics [1927], p.476), quoted by Ian Rumfitt - The Boundary Stones of Thought 9.4 | |
| A reaction: [p.476 in Van Heijenoort] |
| 17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
| Full Idea: The facts of geometry order themselves into a geometry, the facts of arithmetic into a theory of numbers, the facts of statics, electrodynamics into a theory of statics, electrodynamics, or the facts of the physics of gases into a theory of gases. | |
| From: David Hilbert (Axiomatic Thought [1918], [03]) | |
| A reaction: This is the confident (I would say 'essentialist') view of axioms, which received a bit of a setback with Gödel's Theorems. I certainly agree that the world proposes an order to us - we don't just randomly invent one that suits us. |
| 17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
| Full Idea: If a theory is to serve its purpose of orienting and ordering, it must first give us an overview of the independence and dependence of its propositions, and second give a guarantee of the consistency of all of the propositions. | |
| From: David Hilbert (Axiomatic Thought [1918], [09]) | |
| A reaction: Gödel's Second theorem showed that the theory can never prove its own consistency, which made the second Hilbert requirement more difficult. It is generally assumed that each of the axioms must be independent of the others. |
| 8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
| Full Idea: Hilbert wanted to derive ideal mathematics from the secure, paradox-free, finite mathematics (known as 'Hilbert's Programme'). ...Note that for the realist consistency is not something we need to prove; it is a precondition of thought. | |
| From: report of David Hilbert (works [1900], 6.7) by Michèle Friend - Introducing the Philosophy of Mathematics | |
| A reaction: I am an intuitive realist, though I am not so sure about that on cautious reflection. Compare the claims that there are reasons or causes for everything. Reality cannot contain contradicitions (can it?). Contradictions would be our fault. |
| 12456 | I aim to establish certainty for mathematical methods [Hilbert] |
| Full Idea: The goal of my theory is to establish once and for all the certitude of mathematical methods. | |
| From: David Hilbert (On the Infinite [1925], p.184) | |
| A reaction: This is the clearest statement of the famous Hilbert Programme, which is said to have been brought to an abrupt end by Gödel's Incompleteness Theorems. |
| 12461 | We believe all mathematical problems are solvable [Hilbert] |
| Full Idea: The thesis that every mathematical problem is solvable - we are all convinced that it really is so. | |
| From: David Hilbert (On the Infinite [1925], p.200) | |
| A reaction: This will include, for example, Goldbach's Conjecture (every even is the sum of two primes), which is utterly simple but with no proof anywhere in sight. |
| 13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
| Full Idea: One of Hilbert's aims in 'The Foundations of Geometry' was to eliminate number [as measure of lengths and angles] from geometry. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by William D. Hart - The Evolution of Logic 2 | |
| A reaction: Presumably this would particularly have to include the elimination of ratios (rather than actual specific lengths). |
| 9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
| Full Idea: No one shall drive us out of the paradise the Cantor has created for us. | |
| From: David Hilbert (On the Infinite [1925], p.191), quoted by James Robert Brown - Philosophy of Mathematics | |
| A reaction: This is Hilbert's famous refusal to accept any account of mathematics, such as Kant's, which excludes actual infinities. Cantor had laid out a whole glorious hierarchy of different infinities. |
| 12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
| Full Idea: To preserve the simple formal rules of ordinary Aristotelian logic, we must supplement the finitary statements with ideal statements. | |
| From: David Hilbert (On the Infinite [1925], p.195) | |
| A reaction: I find very appealing the picture of mathematics as rooted in the physical world, and then gradually extended by a series of 'idealisations', which should perhaps be thought of as fictions. |
| 12462 | Only the finite can bring certainty to the infinite [Hilbert] |
| Full Idea: Operating with the infinite can be made certain only by the finitary. | |
| From: David Hilbert (On the Infinite [1925], p.201) | |
| A reaction: See 'Compactness' for one aspect of this claim. I think Hilbert was fighting a rearguard action, and his idea now has few followers. |
| 12455 | The idea of an infinite totality is an illusion [Hilbert] |
| Full Idea: Just as in the limit processes of the infinitesimal calculus, the infinitely large and small proved to be a mere figure of speech, so too we must realise that the infinite in the sense of an infinite totality, used in deductive methods, is an illusion. | |
| From: David Hilbert (On the Infinite [1925], p.184) | |
| A reaction: This is a very authoritative rearguard action. I no longer think the dispute matters much, it being just a dispute over a proposed new meaning for the word 'number'. |
| 12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
| Full Idea: A homogeneous continuum which admits of the sort of divisibility needed to realise the infinitely small is nowhere to be found in reality. | |
| From: David Hilbert (On the Infinite [1925], p.186) | |
| A reaction: He makes this remark as a response to Planck's new quantum theory (the year before the big works of Heisenberg and Schrödinger). Personally I don't see why infinities should depend on the physical world, since they are imaginary. |
| 17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
| Full Idea: It is necessary to study the essence of mathematical proof itself if one wishes to answer such questions as the one about decidability in a finite number of operations. | |
| From: David Hilbert (Axiomatic Thought [1918], [53]) |
| 9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
| Full Idea: Hilbert's geometrical axioms were existential in character, asserting the existence of certain geometrical objects (points and lines). Euclid's postulates do not assert the existence of anything; they assert the possibility of certain constructions. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Charles Chihara - A Structural Account of Mathematics 01.1 | |
| A reaction: Chihara says geometry was originally understood modally, but came to be understood existentially. It seems extraordinary to me that philosophers of mathematics can have become more platonist over the centuries. |
| 18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
| Full Idea: In his formal investigation of Euclidean geometry, Hilbert uncovered congruence axioms that implicitly played a role in Euclid's proofs but were not explicitly recognised. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Horsten,L/Pettigrew,R - Mathematical Methods in Philosophy 2 | |
| A reaction: The writers are offering this as a good example of the benefits of a precise and formal approach to foundational questions. It's hard to disagree, but dispiriting if you need a PhD in maths before you can start doing philosophy. |
| 18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
| Full Idea: Hilbert's formulation of the Euclidean theory is of special interest because (besides being rigorously axiomatised) it does not employ the real numbers in the axioms. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Hartry Field - Science without Numbers 3 | |
| A reaction: Notice that this job was done by Hilbert, and not by the fictionalist Hartry Field. |
| 17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
| Full Idea: The linearity of the equation of the plane and of the orthogonal transformation of point-coordinates is completely adequate to produce the whole broad science of spatial Euclidean geometry purely by means of analysis. | |
| From: David Hilbert (Axiomatic Thought [1918], [05]) | |
| A reaction: This remark comes from the man who succeeded in producing modern axioms for geometry (in 1897), so he knows what he is talking about. We should not be wholly pessimistic about Hilbert's ambitious projects. He had to dig deeper than this idea... |
| 17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
| Full Idea: The laws of calculation and the rules of integers suffice for the construction of number theory. | |
| From: David Hilbert (Axiomatic Thought [1918], [05]) | |
| A reaction: This is the confident Hilbert view that the whole system can be fully spelled out. Gödel made this optimism more difficult. |
| 17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert] |
| Full Idea: The standpoint of pure experience seems to me to be refuted by the objection that the existence, possible or actual, of an arbitrarily large number can never be derived through experience, that is, through experiment. | |
| From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.130) | |
| A reaction: Alternatively, empiricism refutes infinite numbers! No modern mathematician will accept that, but you wonder in what sense the proposed entities qualify as 'numbers'. |
| 8628 | I hold that algebra and number are developments of logic [Jevons] |
| Full Idea: I hold that algebra is a highly developed logic, and number but logical discrimination. | |
| From: William S. Jevons (The Principles of Science [1879], p.156), quoted by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §15 | |
| A reaction: Thus Frege shows that logicism was an idea that was in the air before he started writing. Riemann's geometry and Boole's logic presumably had some influence here. |
| 17698 | Logic already contains some arithmetic, so the two must be developed together [Hilbert] |
| Full Idea: In the traditional exposition of the laws of logic certain fundamental arithmetic notions are already used, for example in the notion of set, and to some extent also of number. Thus we turn in a circle, and a partly simultaneous development is required. | |
| From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.131) | |
| A reaction: If the Axiom of Infinity is meant, it may be possible to purge the arithmetic from the logic. Then the challenge to derive arithmetic from it becomes rather tougher. |
| 10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
| Full Idea: The solid philosophical attitude that I think is required for the grounding of pure mathematics is this: In the beginning was the sign. | |
| From: David Hilbert (works [1900]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Why did people invent those particular signs? Presumably they were meant to designate something, in the world or in our experience. |
| 10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
| Full Idea: Hilbert replaced a semantic construal of inconsistency (that the theory entails a statement that is necessarily false) by a syntactic one (that the theory formally derives the statement (0 =1 ∧ 0 not-= 1). | |
| From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: Finding one particular clash will pinpoint the notion of inconsistency, but it doesn't seem to define what it means, since the concept has very wide application. |
| 22293 | Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter] |
| Full Idea: Hilbert proposed to circuvent the paradoxes by means of the doctrine (already proposed by Poincaré) that in mathematics consistency entails existence. | |
| From: report of David Hilbert (On the Concept of Number [1900], p.183) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 19 'Exist' | |
| A reaction: Interesting. Hilbert's idea has struck me as weird, but it makes sense if its main motive is to block the paradoxes. Roughly, the idea is 'it exists if it isn't paradoxical'. A low bar for existence (but then it is only in mathematics!). |
| 12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
| Full Idea: The subject matter of mathematics is the concrete symbols themselves whose structure is immediately clear and recognisable. | |
| From: David Hilbert (On the Infinite [1925], p.192) | |
| A reaction: I don't think many people will agree with Hilbert here. Does he mean token-symbols or type-symbols? You can do maths in your head, or with different symbols. If type-symbols, you have to explain what a type is. |
| 10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
| Full Idea: Hilbert's project was to establish the consistency of classical mathematics using just finitary means, to convince all parties that no contradictions will follow from employing the infinitary notions and reasoning. | |
| From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: This is the project which was badly torpedoed by Gödel's Second Incompleteness Theorem. |
| 18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
| Full Idea: We can conceive mathematics to be a stock of two kinds of formulas: first, those to which the meaningful communications of finitary statements correspond; and secondly, other formulas which signify nothing and which are ideal structures of our theory. | |
| From: David Hilbert (On the Infinite [1925], p.196), quoted by David Bostock - Philosophy of Mathematics 6.1 |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| Full Idea: The goal of my theory is to establish once and for all the certitude of mathematical methods. | |
| From: David Hilbert (On the Infinite [1925], p.184), quoted by James Robert Brown - Philosophy of Mathematics Ch.5 | |
| A reaction: This dream is famous for being shattered by Gödel's Incompleteness Theorem a mere six years later. Neverless there seem to be more limited certainties which are accepted in mathematics. The certainty of the whole of arithmetic is beyond us. |
| 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. |
| 17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
| Full Idea: By pushing ahead to ever deeper layers of axioms ...we also win ever-deeper insights into the essence of scientific thought itself, and become ever more conscious of the unity of our knowledge. | |
| From: David Hilbert (Axiomatic Thought [1918], [56]) | |
| A reaction: This is the less fashionable idea that scientific essentialism can also be applicable in the mathematic sciences, centring on the project of axiomatisation for logic, arithmetic, sets etc. |