26 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] |
8250 | So-called 'free logic' operates without existence assumptions [Meinong, by George/Van Evra] |
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] |
8719 | There can be impossible and contradictory objects, if they can have properties [Meinong, by Friend] |
8971 | There are objects of which it is true that there are no such objects [Meinong] |
8718 | Meinong says an object need not exist, but must only have properties [Meinong, by Friend] |
7756 | Meinong said all objects of thought (even self-contradictions) have some sort of being [Meinong, by Lycan] |
15781 | The objects of knowledge are far more numerous than objects which exist [Meinong] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |