37 ideas
10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
10900 | Logically true sentences are true in all structures [Zalabardo] |
10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
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] |
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] |
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] |
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] |
3766 | Better to be Socrates dissatisfied than a fool satisfied [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] |
3774 | Rights are a matter of justice, not of benevolence [Mill] |
3773 | No individual has the right to receive our benevolence [Mill] |
3775 | A right is a valid claim to society's protection [Mill] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |