33 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] |
14508 | A 'thisness' is a thing's property of being identical with itself (not the possession of self-identity) [Adams,RM] |
14511 | There are cases where mere qualities would not ensure an intrinsic identity [Adams,RM] |
16463 | Adams says actual things have haecceities, but not things that only might exist [Adams,RM, by Stalnaker] |
12031 | Essences are taken to be qualitative properties [Adams,RM] |
12034 | If the universe was cyclical, totally indiscernible events might occur from time to time [Adams,RM] |
14510 | Two events might be indiscernible yet distinct, if there was a universe cyclical in time [Adams,RM] |
16455 | Black's two globes might be one globe in highly curved space [Adams,RM] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
14507 | Are possible worlds just qualities, or do they include primitive identities as well? [Adams,RM] |
11964 | Possible worlds are world-stories, maximal descriptions of whole non-existent worlds [Adams,RM, by Molnar] |
16451 | Adams says anti-haecceitism reduces all thisness to suchness [Adams,RM, by Stalnaker] |
11901 | Haecceitism may or may not involve some logical connection to essence [Adams,RM, by Mackie,P] |
14512 | Moderate Haecceitism says transworld identities are primitive, but connected to qualities [Adams,RM] |
12032 | Direct reference is by proper names, or indexicals, or referential uses of descriptions [Adams,RM] |
6005 | Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley] |