36 ideas
| 20455 | Philosophy really got started as the rival mode of discourse to tragedy [Critchley] |
| 20446 | Philosophy begins in disappointment, notably in religion and politics [Critchley] |
| 20449 | Science gives us an excessively theoretical view of life [Critchley] |
| 20448 | Phenomenology uncovers and redescribes the pre-theoretical layer of life [Critchley] |
| 10688 | 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall] |
| 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] |
| 10690 | Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall] |
| 10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
| 10691 | Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall] |
| 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] |
| 10695 | Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall] |
| 10689 | A step is a 'material consequence' if we need contents as well as form [Beall/Restall] |
| 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] |
| 10696 | A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall] |
| 10900 | Logically true sentences are true in all structures [Zalabardo] |
| 10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
| 10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
| 10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
| 10693 | Models are mathematical structures which interpret the non-logical primitives [Beall/Restall] |
| 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] |
| 10692 | Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall] |
| 10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
| 20454 | Wallace Stevens is the greatest philosophical poet of the twentieth century in English [Critchley] |
| 20456 | Interesting art is always organised around ethical demands [Critchley] |
| 20447 | The problems is not justifying ethics, but motivating it. Why should a self seek its good? [Critchley] |
| 20450 | The state, law, bureaucracy and capital are limitations on life, so I prefer federalist anarchism [Critchley] |
| 20452 | Anarchism used to be libertarian (especially for sexuality), but now concerns responsibility [Critchley] |
| 20451 | Belief that humans are wicked leads to authoritarian politics [Critchley] |