23 ideas
12104 | All ideas must be understood historically [Comte] |
12105 | Our knowledge starts in theology, passes through metaphysics, and ends in positivism [Comte] |
12112 | Metaphysics is just the oversubtle qualification of abstract names for phenomena [Comte] |
12106 | Positivism gives up absolute truth, and seeks phenomenal laws, by reason and observation [Comte] |
12111 | Positivism is the final state of human intelligence [Comte] |
12114 | Science can drown in detail, so we need broad scientists (to keep out the metaphysicians) [Comte] |
12116 | Only positivist philosophy can terminate modern social crises [Comte] |
13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
12108 | All real knowledge rests on observed facts [Comte] |
12109 | We must observe in order to form theories, but connected observations need prior theories [Comte] |
12107 | Positivism explains facts by connecting particular phenomena with general facts [Comte] |
12115 | Introspection is pure illusion; we can obviously observe everything except ourselves [Comte] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
12113 | The search for first or final causes is futile [Comte] |
12110 | We can never know origins, purposes or inner natures [Comte] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |