28 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] |
| 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] |
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| 22180 | Multiple realisability is said to make reduction impossible [Okasha] |
| 22172 | Not all sciences are experimental; astronomy relies on careful observation [Okasha] |
| 22177 | Randomised Control Trials have a treatment and a control group, chosen at random [Okasha] |
| 22174 | The discoverers of Neptune didn't change their theory because of an anomaly [Okasha] |
| 22175 | Science mostly aims at confirming theories, rather than falsifying them [Okasha] |
| 22182 | Theories with unobservables are underdetermined by the evidence [Okasha] |
| 22185 | Two things can't be incompatible if they are incommensurable [Okasha] |
| 22176 | Induction is inferences from examined to unexamined instances of a given kind [Okasha] |
| 22178 | If the rules only concern changes of belief, and not the starting point, absurd views can look ratiional [Okasha] |
| 22173 | Galileo refuted the Aristotelian theory that heavier objects fall faster [Okasha] |
| 17366 | Virtually all modern views of speciation rest on relational rather than intrinsic features [Okasha] |