48 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] |
| 17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
| 17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
| 17757 | Members of ordinals are ordinals, and also subsets of ordinals [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] |
| 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] |
| 14508 | A 'thisness' is a thing's property of being identical with itself (not the possession of self-identity) [Adams,RM] |
| 14511 | There are cases where mere qualities would not ensure an intrinsic identity [Adams,RM] |
| 12031 | Essences are taken to be qualitative properties [Adams,RM] |
| 12034 | If the universe was cyclical, totally indiscernible events might occur from time to time [Adams,RM] |
| 14510 | Two events might be indiscernible yet distinct, if there was a universe cyclical in time [Adams,RM] |
| 16455 | Black's two globes might be one globe in highly curved space [Adams,RM] |
| 17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
| 14507 | Are possible worlds just qualities, or do they include primitive identities as well? [Adams,RM] |
| 11964 | Possible worlds are world-stories, maximal descriptions of whole non-existent worlds [Adams,RM, by Molnar] |
| 16451 | Adams says anti-haecceitism reduces all thisness to suchness [Adams,RM, by Stalnaker] |
| 11901 | Haecceitism may or may not involve some logical connection to essence [Adams,RM, by Mackie,P] |
| 14512 | Moderate Haecceitism says transworld identities are primitive, but connected to qualities [Adams,RM] |
| 12032 | Direct reference is by proper names, or indexicals, or referential uses of descriptions [Adams,RM] |
| 3772 | The will, in the beginning, is entirely produced by desire [Mill] |
| 3769 | With early training, any absurdity or evil may be given the power of conscience [Mill] |
| 3767 | Motive shows the worth of the agent, but not of the action [Mill] |
| 3771 | Virtues only have value because they achieve some further end [Mill] |
| 3768 | Orthodox morality is the only one which feels obligatory [Mill] |
| 3764 | Actions are right if they promote pleasure, wrong if they promote pain [Mill] |
| 3776 | Utilitarianism only works if everybody has a totally equal right to happiness [Mill] |
| 7202 | The English believe in the task of annihilating evil for the victory of good [Nietzsche on Mill] |
| 5935 | Mill's qualities of pleasure is an admission that there are other good states of mind than pleasure [Ross on Mill] |
| 3766 | Better to be Socrates dissatisfied than a fool satisfied [Mill] |
| 3765 | Only pleasure and freedom from pain are desirable as ends [Mill] |
| 3763 | Ultimate goods such as pleasure can never be proved to be good [Mill] |
| 3770 | General happiness is only desirable because individuals desire their own happiness [Mill] |
| 6697 | Moral rules protecting human welfare are more vital than local maxims [Mill] |
| 3773 | No individual has the right to receive our benevolence [Mill] |
| 3774 | Rights are a matter of justice, not of benevolence [Mill] |
| 3775 | A right is a valid claim to society's protection [Mill] |