39 ideas
| 23064 | So-called wisdom is just pondering things instead of acting [Cioran] |
| 23072 | Systems are the worst despotism, in philosophy and in life [Cioran] |
| 23075 | A text explained ceases to be a text [Cioran] |
| 10528 | Definitions concern how we should speak, not how things are [Fine,K] |
| 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] |
| 23066 | Negation doesn't arise from reasoning, but from deep instincts [Cioran] |
| 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] |
| 10529 | If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K] |
| 10530 | Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K] |
| 23077 | The word 'being' is very tempting, but in fact means nothing at all [Cioran] |
| 23068 | People who really believe anti-realism don't bother to prove it [Cioran] |
| 23073 | Convictions are failures to study anything thoroughly [Cioran] |
| 23078 | Opinions are fine, but having convictions means something has gone wrong [Cioran] |
| 23076 | If people always acted without words we would take them for robots [Cioran] |
| 23065 | If only we could write like a reptile, of endless sensations and no concepts! [Cioran] |
| 10527 | An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K] |
| 23071 | We could only be responsible if we had consented before birth to who we are [Cioran] |
| 23070 | We morally dissolve if we spend time with excessive beauty [Cioran] |
| 23074 | In anxiety people cling to what reinforces it, because it is a deep need [Cioran] |
| 23069 | Fear cures boredom, because it is stronger [Cioran] |
| 23062 | It is better to watch the hours pass, than trying to fill them [Cioran] |
| 23067 | Suicide is pointless, because it always comes too late [Cioran] |
| 23063 | The first man obviously found paradise unendurable [Cioran] |