29 ideas
16123 | Whenever you perceive a community of things, you should also hunt out differences in the group [Plato] |
16124 | No one wants to define 'weaving' just for the sake of weaving [Plato] |
16125 | To reveal a nature, divide down, and strip away what it has in common with other things [Plato] |
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] |
17757 | Members of ordinals are ordinals, and also subsets of ordinals [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] |
17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [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] |
5961 | The soul gets its goodness from god, and its evil from previous existence. [Plato] |
21650 | No language is semantically referential; it all occurs at the level of thought or utterance [Pietroski, by Hofweber] |
283 | The question of whether or not to persuade comes before the science of persuasion [Plato] |
282 | Non-physical beauty can only be shown clearly by speech [Plato] |
281 | The arts produce good and beautiful things by preserving the mean [Plato] |
22559 | Democracy is the worst of good constitutions, but the best of bad constitutions [Plato, by Aristotle] |
279 | Only divine things can always stay the same, and bodies are not like that [Plato] |