44 ideas
| 10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
| Full Idea: We can define a set by 'enumeration' (by listing the items, within curly brackets), or by 'abstraction' (by specifying the elements as instances of a property), pretending that they form a determinate totality. The latter is written {x | x is P}. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.3) |
| 10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
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Full Idea:
The 'Cartesian Product' of two sets, written A x B, is the relation which pairs every element of A with every element of B. So A x B = { |
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| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.6) |
| 10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
| Full Idea: A binary relation in a set is a 'partial ordering' just in case it is reflexive, antisymmetric and transitive. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.6) |
| 10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
| Full Idea: Principle of Determinacy: For every object a and every set S, either a is an element of S or a is not an element of S. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.2) |
| 10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
| Full Idea: Principle of Specification: Whenever we can specify a determinate totality of objects, we shall say that there is a set whose elements are precisely the objects that we have specified. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §1.3) | |
| A reaction: Compare the Axiom of Specification. Zalabardo says we may wish to consider sets of which we cannot specify the members. |
| 10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
| Full Idea: A formula of a first-order language is a 'sentence' just in case it has no free variables. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.2) |
| 10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
| Full Idea: A propositional logic sentence is a 'logical consequence' of a set of sentences (written Γ |= φ) if for every admissible truth-assignment all the sentences in the set Γ are true, then φ is true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) | |
| A reaction: The definition is similar for predicate logic. |
| 10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
| Full Idea: A formula is the 'logical consequence' of a set of formulas (Γ |= φ) if for every structure in the language and every variable interpretation of the structure, if all the formulas within the set are true and the formula itself is true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5) |
| 10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
| Full Idea: In propositional logic, any set containing ¬ and at least one of ∧, ∨ and → is expressively complete. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.8) |
| 10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
| Full Idea: The semantic pattern of a first-order language is the ways in which truth values depend on which individuals instantiate the properties and relations which figure in them. ..So we pair a truth value with each combination of individuals, sets etc. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.3) | |
| A reaction: So truth reduces to a combination of 'instantiations', which is rather like 'satisfaction'. |
| 10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
| Full Idea: We can look at semantics from the point of view of how truth values are determined by instantiations of properties and relations, or by asking how we can build, using the resources of the language, a proposition corresponding to a given semantic pattern. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.6) | |
| A reaction: The second version of semantics is model theory. |
| 10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
| Full Idea: A truth assignment is a function from propositions to the set {T,F}. We will think of T and F as the truth values true and false, but for our purposes all we need to assume about the identity of these objects is that they are different from each other. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) | |
| A reaction: Note that T and F are 'objects'. This remark is important in understanding modern logical semantics. T and F can be equated to 1 and 0 in the language of a computer. They just mean as much as you want them to mean. |
| 10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
| Full Idea: A propositional logic sentence is 'logically true', written |= φ, if it is true for every admissible truth-assignment. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) |
| 10900 | Logically true sentences are true in all structures [Zalabardo] |
| Full Idea: In first-order languages, logically true sentences are true in all structures. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5) |
| 10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
| Full Idea: A propositional logic set of sentences Γ is 'satisfiable' if there is at least one admissible truth-assignment that makes all of its sentences true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.4) |
| 10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
| Full Idea: A set of formulas of a first-order language is 'satisfiable' if there is a structure and a variable interpretation in that structure such that all the formulas of the set are true. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.5) |
| 10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
| Full Idea: A structure is a model of a sentence if the sentence is true in the model; a structure is a model of a set of sentences if they are all true in the structure. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §3.6) |
| 10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
| Full Idea: Defining a set by induction enables us to use the method of proof by induction to establish that all the elements of the set have a certain property. | |
| From: José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.3) |
| 14080 | Are causal descriptions part of the causal theory of reference, or are they just metasemantic? [Kaplan, by Schaffer,J] |
| Full Idea: Kaplan notes that the causal theory of reference can be understood in two quite different ways, as part of the semantics (involving descriptions of causal processes), or as metasemantics, explaining why a term has the referent it does. | |
| From: report of David Kaplan (Dthat [1970]) by Jonathan Schaffer - Deflationary Metaontology of Thomasson 1 | |
| A reaction: [Kaplan 'Afterthought' 1989] The theory tends to be labelled as 'direct' rather than as 'causal' these days, but causal chains are still at the heart of the story (even if more diffused socially). Nice question. Kaplan takes the meta- version as orthodox. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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). |