28 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] |
18755 | Validity is explained as truth in all models, because that relies on the logical terms [McGee] |
18751 | Natural language includes connectives like 'because' which are not truth-functional [McGee] |
18761 | Second-order variables need to range over more than collections of first-order objects [McGee] |
18753 | An ontologically secure semantics for predicate calculus relies on sets [McGee] |
18754 | Logically valid sentences are analytic truths which are just true because of their logical words [McGee] |
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] |
18757 | Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee] |
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] |
18760 | The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee] |
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] |
18033 | The meaning of a representation is its role in thought, perception or decisions [Block] |
18762 | A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee] |