35 ideas
| 21793 | Genuine truth is the resolution of the highest contradiction [Hegel] |
| 21795 | What I hold true must also be part of my feelings and character [Hegel] |
| 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] |
| 16066 | Additional or removal of any part changes a thing, so people are never the same person [Epicharmus] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 436 | A dog seems handsome to another a dog, and even a pig to another pig [Epicharmus] |
| 18549 | Nineteenth century aesthetics focused on art rather than nature (thanks to Hegel) [Hegel, by Scruton] |
| 22043 | Hegel largely ignores aesthetic pleasure, taste and beauty, and focuses on the meaning of artworks [Hegel, by Pinkard] |
| 22042 | Natural beauty is unimportant, because it doesn't show human freedom [Hegel, by Pinkard] |
| 20413 | For Hegel the importance of art concerns the culture, not the individual [Hegel, by Eldridge] |
| 20394 | The purpose of art is to reveal to Spirit its own nature [Hegel, by Davies,S] |
| 21794 | The main purpose of art is to express the unity of human life [Hegel] |
| 20415 | Art forms a bridge between the sensuous world and the world of pure thought [Hegel] |
| 442 | Pleasures are like pirates - if you are caught they drown you in a sea of pleasures [Epicharmus] |
| 440 | Hands wash hands; give that you may get [Epicharmus] |
| 441 | Against a villain, villainy is not a useless weapon [Epicharmus] |
| 439 | God knows everything, and nothing is impossible for him [Epicharmus] |
| 443 | Human logos is an aspect of divine logos, and is sufficient for successful living [Epicharmus] |