31 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] |
| 7491 | The phases of human thought are theological, then metaphysical, then positivist [Comte, by Watson] |
| 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] |
| 10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
| 10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
| 10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| 10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
| 10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
| 10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
| 10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
| 10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
| 10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
| 10763 | Completeness and compactness together give axiomatizability [Tharp] |
| 10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
| 10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
| 10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
| 10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
| 10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
| 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] |
| 20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
| 12115 | Introspection is pure illusion; we can obviously observe everything except ourselves [Comte] |
| 12113 | The search for first or final causes is futile [Comte] |
| 12110 | We can never know origins, purposes or inner natures [Comte] |