45 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] |
17377 | All descriptive language is classificatory [Dupré] |
17376 | We should aim for a classification which tells us as much as possible about the object [Dupré] |
17390 | Natural kinds don't need essentialism to be explanatory [Dupré] |
17389 | A species might have its essential genetic mechanism replaced by a new one [Dupré] |
17388 | It seems that species lack essential properties, so they can't be natural kinds [Dupré] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
17374 | The possibility of prediction rests on determinism [Dupré] |
17378 | Presumably molecular structure seems important because we never have the Twin Earth experience [Dupré] |
7404 | Nations are not obliged to help one-another, but are obliged not to harm one another [Grotius, by Tuck] |
7402 | Everyone has a right of self-preservation, and harming others is usually unjustifiable [Grotius, by Tuck] |
21938 | Democracy needs respect for individuality, but the 'community of friends' implies strict equality [Grotius] |
19845 | A person is free to renounce their state, as long as it is not a moment of crisis [Grotius, by Rousseau] |
22133 | Grotius and Pufendorf based natural law on real (rather than idealised) humanity [Grotius, by Ford,JD] |
7406 | A natural right of self-preservation is balanced by a natural law to avoid unnecessary harm [Grotius, by Tuck] |
7403 | Grotius ignored elaborate natural law theories, preferring a basic right of self-preservation [Grotius, by Tuck] |
23585 | It is permissible in a just cause to capture a place in neutral territory [Grotius] |
17381 | Phylogenetics involves history, and cladism rests species on splits in lineage [Dupré] |
17385 | Kinds don't do anything (including evolve) because they are abstract [Dupré] |
17375 | Natural kinds are decided entirely by the intentions of our classification [Dupré] |
17379 | Borders between species are much less clear in vegetables than among animals [Dupré] |
17384 | Even atoms of an element differ, in the energy levels of their electrons [Dupré] |
17387 | Ecologists favour classifying by niche, even though that can clash with genealogy [Dupré] |
17380 | Wales may count as fish [Dupré] |
17382 | Cooks, unlike scientists, distinguish garlic from onions [Dupré] |
17383 | Species are the lowest-level classification in biology [Dupré] |
17386 | The theory of evolution is mainly about species [Dupré] |
6892 | Moral principles have some validity without a God commanding obedience [Grotius, by Mautner] |