28 ideas
| 6211 | Laughter is a sudden glory in realising the infirmity of others, or our own formerly [Hobbes] |
| 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] |
| 7771 | We need 'events' to explain adverbs, which are adjectival predicates of events [Davidson, by Lycan] |
| 8860 | Language-learning is not good enough evidence for the existence of events [Yablo on Davidson] |
| 15002 | If the best theory of adverbs refers to events, then our ontology should include events [Davidson, by Sider] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 6213 | A man cannot will to will, or will to will to will, so the idea of a voluntary will is absurd [Hobbes] |
| 6208 | Conceptions and apparitions are just motion in some internal substance of the head [Hobbes] |
| 6209 | There is no absolute good, for even the goodness of God is goodness to us [Hobbes] |
| 6210 | Life has no end (not even happiness), because we have desires, which presuppose a further end [Hobbes] |
| 6212 | Lust involves pleasure, and also the sense of power in pleasing others [Hobbes] |