40 ideas
| 7823 | Lucretius was rediscovered in 1417 [Grayling] |
| 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] |
| 6408 | Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility [Grayling] |
| 12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 6414 | Two propositions might seem self-evident, but contradict one another [Grayling] |
| 7091 | The argument from analogy is not a strong inference, since the other being might be an actor or a robot [Grayling] |
| 7293 | It is legitimate to do harm if it is the unintended side-effect of an effort to achieve a good [Grayling] |
| 7809 | In an honour code shame is the supreme punishment, and revenge is a duty [Grayling] |
| 23262 | Experience, sympathy and history are sensible grounds for laying claim to rights [Grayling] |
| 23263 | Politics is driven by power cliques [Grayling] |
| 23255 | It is essential for democracy that voting is free and well informed [Grayling] |
| 23254 | Democracies should require a supermajority for major questions [Grayling] |
| 23260 | A cap on time of service would restrict party control and career ambitions [Grayling] |
| 23253 | Majority decisions are only acceptable if the minority interests are not vital [Grayling] |
| 23256 | Liberty and equality cannot be reconciled [Grayling] |
| 23258 | The very concept of democracy entails a need for justice [Grayling] |
| 23259 | There should be separate legislative, executive and judicial institutions [Grayling] |
| 7292 | War must also have a good chance of success, and be waged with moderation [Grayling] |
| 7824 | If suicide is lawful, but assisting suicide is unlawful, powerless people are denied their rights [Grayling] |
| 7819 | Religion gives answers, comforts, creates social order, and panders to superstition [Grayling] |
| 7817 | To make an afterlife appealing, this life has to be denigrated [Grayling] |
| 7818 | In Greek mythology only heroes can go to heaven [Grayling] |