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] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
20921 | How can we state relativism of sweet and sour, if they have no determinate nature? [Theophrastus] |
4761 | The 'error theory' of morals says there is no moral knowledge, because there are no moral facts [Mackie, by Engel] |
5990 | Theophrastus doubted whether nature could be explained teleologically [Theophrastus, by Gottschalk] |
8337 | Some says mental causation is distinct because we can recognise single occurrences [Mackie] |
8342 | Mackie tries to analyse singular causal statements, but his entities are too vague for events [Kim on Mackie] |
8343 | Necessity and sufficiency are best suited to properties and generic events, not individual events [Kim on Mackie] |
8385 | A cause is part of a wider set of conditions which suffices for its effect [Mackie, by Crane] |
8335 | Necessary conditions are like counterfactuals, and sufficient conditions are like factual conditionals [Mackie] |
8336 | The INUS account interprets single events, and sequences, causally, without laws being known [Mackie] |
8333 | A cause is an Insufficient but Necessary part of an Unnecessary but Sufficient condition [Mackie] |
8395 | Mackie has a nomological account of general causes, and a subjunctive conditional account of single ones [Mackie, by Tooley] |
8334 | The virus causes yellow fever, and is 'the' cause; sweets cause tooth decay, but they are not 'the' cause [Mackie] |
1472 | The propositions that God is good and omnipotent, and that evil exists, are logically contradictory [Mackie, by PG] |
1473 | Is evil an illusion, or a necessary contrast, or uncontrollable, or necessary for human free will? [Mackie, by PG] |