58 ideas
| 17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
| 17765 | Propositional language can only relate statements as the same or as different [Walicki] |
| 17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
| 17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
| 17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
| 17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
| 17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
| 17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
| 17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
| 17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
| 17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
| 17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
| 17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
| 17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
| 17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
| 17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
| 17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
| 17754 | Inductive proof depends on the choice of the ordering [Walicki] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 23101 | Intuitions don't prove things; they just receptivity to interpretations [Kekes] |
| 23086 | Liberals say we are only responsible for fully autonomous actions [Kekes] |
| 23100 | Collective responsibility conflicts with responsibility's requirement of authonomy [Kekes] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| 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] |