31 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] |
| 7439 | The qualities involved in sensations are entirely intentional [Anscombe, by Armstrong] |
| 8353 | Freedom involves acting according to an idea [Anscombe] |
| 8352 | To believe in determinism, one must believe in a system which determines events [Anscombe] |
| 20041 | Intentional actions are those which are explained by giving the reason for so acting [Anscombe] |
| 8070 | It would be better to point to failings of character, than to moral wrongness of actions [Anscombe] |
| 8065 | 'Ought' and 'right' are survivals from earlier ethics, and should be jettisoned [Anscombe] |
| 8069 | Between Aristotle and us, a Judaeo-Christian legal conception of ethics was developed [Anscombe] |
| 8351 | With diseases we easily trace a cause from an effect, but we cannot predict effects [Anscombe] |
| 4777 | The word 'cause' is an abstraction from a group of causal terms in a language (scrape, push..) [Anscombe] |
| 10363 | Causation is relative to how we describe the primary relata [Anscombe, by Schaffer,J] |
| 8350 | Since Mill causation has usually been explained by necessary and sufficient conditions [Anscombe] |
| 1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |