30 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] |
| 17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
| 17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [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] |
| 17757 | Members of ordinals are ordinals, and also subsets of ordinals [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] |
| 7096 | We may still admire a person's character even if the traits are involuntary [Statman] |
| 7098 | There is a new sort of moral scepticism, about the possibility of moral theories [Statman] |
| 7099 | With a broad concept of flourishing, it might be possible without the virtues [Statman] |
| 7100 | Virtue theory isn't a genuine ethical theory, because it doesn't have universal application [Statman] |
| 7102 | Promises create moral duties that have nothing to do with character [Statman] |
| 7095 | Moral education is better by concrete example than abstract principle [Statman] |
| 7094 | Friends express friendship even when no utility is involved [Statman] |
| 7093 | Behaviour may be disgusting or inhumane, but violate no duty [Statman] |
| 7104 | The ancients recognised imperfect duties, but we have added perfect duties like justice [Statman] |
| 7103 | Abortion issues focus on the mother's right over her body, and the status of the foetus [Statman] |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |