36 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] |
| 4020 | The modern self has disengaged reason, self-exploration, and personal commitment [Taylor,C] |
| 4002 | My aim is to map the connections between our sense of self and our moral understanding [Taylor,C] |
| 4006 | I can only be aware of myself as a person who changes by means of my personal history [Taylor,C] |
| 4003 | Selfhood and moral values are inextricably intertwined [Taylor,C] |
| 20239 | Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche] |
| 4021 | Willingness to risk life was the constitutive quality of the man of honour [Taylor,C] |
| 4005 | To have respect for people, you must feel their claims, or their injustices, or hold them in awe [Taylor,C] |
| 4004 | Consistency presupposes intrinsic description [Taylor,C] |
| 4010 | In later utilitarianism the modern stress on freedom leads to the rejection of paternalism [Taylor,C] |
| 22809 | The social contract sees society as constituted by and for individuals [Taylor,C] |
| 22811 | Assigning a right based on a human capacity implies that the capacity should be developed [Taylor,C] |
| 22815 | If freedom depends on society and culture, the greatest freedom is in shaping them [Taylor,C] |
| 22814 | Our reliance on other people close to us does not imply any political obligations [Taylor,C] |
| 22812 | For most people the primacy of rights mainly concerns freedom [Taylor,C] |
| 22810 | A right is not just a rule, but also asserts certain ideas of moral worth [Taylor,C] |
| 22813 | Property is not essential for life, but it may be essential for independence [Taylor,C] |
| 23417 | If the state is neutral, there won't be sufficient community to support a welfare state [Taylor,C, by Kymlicka] |
| 4009 | Nominalists defended the sovereignty of God against the idea of natural existing good and evil [Taylor,C] |