60 ideas
10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
10900 | Logically true sentences are true in all structures [Zalabardo] |
10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
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] |
10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
19553 | Commitment to 'I have a hand' only makes sense in a context where it has been doubted [Hawthorne] |
23101 | Intuitions don't prove things; they just receptivity to interpretations [Kekes] |
19551 | How can we know the heavyweight implications of normal knowledge? Must we distort 'knowledge'? [Hawthorne] |
19552 | We wouldn't know the logical implications of our knowledge if small risks added up to big risks [Hawthorne] |
19554 | Denying closure is denying we know P when we know P and Q, which is absurd in simple cases [Hawthorne] |
23086 | Liberals say we are only responsible for fully autonomous actions [Kekes] |
23100 | Collective responsibility conflicts with responsibility's requirement of authonomy [Kekes] |
23087 | Much human evil is not autonomous, so moral responsibility need not be autonomous [Kekes] |
23089 | Evil people may not be autonomously aware, if they misjudge the situation [Kekes] |
23093 | Moral and causal responsibility are not clearly distinct [Kekes] |
23098 | Effects show the existence of moral responsibility, and mental states show the degree [Kekes] |
23094 | Ought implies can means moral responsibility needs autonomy [Kekes] |
23095 | Why should moral responsibility depend on autonomy, rather than social role or experience? [Kekes] |
23096 | Morality should aim to prevent all evil actions, not just autonomous ones [Kekes] |
23090 | Liberals assume people are naturally free, equal, rational, and morally good [Kekes] |
23117 | Love should be partial, and discriminate in favour of its object [Kekes] |
23119 | Sentimental love distorts its object [Kekes] |
23088 | Evil is not deviation from the good, any more than good is a deviation from evil [Kekes] |
23097 | What matters for morality is the effects of action, not the psychological causes [Kekes] |
23099 | It is said that if an agent is not autonomous then their evil actions don't reflect on their character [Kekes] |
23118 | Awareness of others' suffering doesn't create an obligation to help [Kekes] |
23109 | The veil of ignorance is only needed because people have bad motivations [Kekes] |
23114 | The chief function of the state is to arbitrate between contending visions of the good life [Kekes] |
23116 | Citizenship is easier than parenthood [Kekes] |
23103 | Power is meant to be confined to representatives, and subsequent delegation [Kekes] |
23107 | Prosperity is a higher social virtue than justice [Kekes] |
23081 | Liberal basics are pluralism, freedom, rights, equality, and distributive justice - for autonomy [Kekes] |
23085 | The key liberal values are explained by the one core value, which is autonomy [Kekes] |
23092 | Agents have little control over the capacities needed for liberal autonomy [Kekes] |
23102 | Liberals are egalitarians, but in varying degrees [Kekes] |
23084 | Are egalitarians too coercive, or not egalitarian enough, or lax over morality? [Kekes] |
23079 | Liberal justice ignores desert, which is the essence of justice [Kekes] |
23091 | Why do liberals not see a much wider range of values as basic? [Kekes] |
23112 | Liberals ignore contingency, and think people are good and equal, and institutions cause evil [Kekes] |
23082 | Liberal distribution cares more about recipients than donors [Kekes] |
23106 | To rectify the undeserved equality, we should give men longer and women shorter lives [Kekes] |
23121 | It is just a fact that some people are morally better than others [Kekes] |
23105 | It is not deplorable that billionaires have more than millionaires [Kekes] |
23120 | The problem is basic insufficiency of resources, not their inequality [Kekes] |
23108 | Justice combines consistency and desert; treat likes alike, judging likeness by desert [Kekes] |
23083 | Liberal welfare focuses on need rather than desert [Kekes] |
23113 | Sexual morality doesn't require monogamy, but it needs a group of sensible regulations [Kekes] |