30 ideas
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] |
10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [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] |
22121 | The concept of being has only one meaning, whether talking of universals or of God [Duns Scotus, by Dumont] |
22122 | Being (not sensation or God) is the primary object of the intellect [Duns Scotus, by Dumont] |
22125 | Duns Scotus was a realist about universals [Duns Scotus, by Dumont] |
22127 | Scotus said a substantial principle of individuation [haecceitas] was needed for an essence [Duns Scotus, by Dumont] |
22126 | Avicenna and Duns Scotus say essences have independent and prior existence [Duns Scotus, by Dumont] |
22129 | Certainty comes from the self-evident, from induction, and from self-awareness [Duns Scotus, by Dumont] |
22130 | Scotus defended direct 'intuitive cognition', against the abstractive view [Duns Scotus, by Dumont] |
22128 | Augustine's 'illumination' theory of knowledge leads to nothing but scepticism [Duns Scotus, by Dumont] |
22131 | The will retains its power for opposites, even when it is acting [Duns Scotus, by Dumont] |
17371 | Some kinds are very explanatory, but others less so, and some not at all [Devitt] |
17373 | Species pluralism says there are several good accounts of what a species is [Devitt] |
17372 | The higher categories are not natural kinds, so the Linnaean hierarchy should be given up [Devitt] |
22123 | The concept of God is the unique first efficient cause, final cause, and most eminent being [Duns Scotus, by Dumont] |
22124 | We can't infer the infinity of God from creation ex nihilo [Duns Scotus, by Dumont] |