37 ideas
| 15063 | Some sentences depend for their truth on worldly circumstances, and others do not [Fine,K] |
| 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] |
| 15078 | There are levels of existence, as well as reality; objects exist at the lowest level in which they can function [Fine,K] |
| 15072 | Bottom level facts are subject to time and world, middle to world but not time, and top to neither [Fine,K] |
| 15071 | Tensed and tenseless sentences state two sorts of fact, which belong to two different 'realms' of reality [Fine,K] |
| 15075 | Modal features are not part of entities, because they are accounted for by the entity [Fine,K] |
| 15065 | What it is is fixed prior to existence or the object's worldly features [Fine,K] |
| 15076 | Essential features of an object have no relation to how things actually are [Fine,K] |
| 15073 | Self-identity should have two components, its existence, and its neutral identity with itself [Fine,K] |
| 15074 | We would understand identity between objects, even if their existence was impossible [Fine,K] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 15064 | Proper necessary truths hold whatever the circumstances; transcendent truths regardless of circumstances [Fine,K] |
| 15070 | It is the nature of Socrates to be a man, so necessarily he is a man [Fine,K] |
| 15069 | Possible worlds may be more limited, to how things might actually turn out [Fine,K] |
| 15068 | The actual world is a totality of facts, so we also think of possible worlds as totalities [Fine,K] |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| 15077 | It is said that in the A-theory, all existents and objects must be tensed, as well as the sentences [Fine,K] |
| 15067 | A-theorists tend to reject the tensed/tenseless distinction [Fine,K] |
| 15066 | B-theorists say tensed sentences have an unfilled argument-place for a time [Fine,K] |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |