36 ideas
| 16539 | A definition of a circle will show what it is, and show its generating principle [Lowe] |
| 16540 | Defining an ellipse by conic sections reveals necessities, but not the essence of an ellipse [Lowe] |
| 16548 | An essence is what an entity is, revealed by a real definition; this is not an entity in its own right [Lowe] |
| 16549 | Simple things like 'red' can be given real ostensive definitions [Lowe] |
| 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] |
| 16545 | The essence of lumps and statues shows that two objects coincide but are numerically distinct [Lowe] |
| 16546 | The essence of a bronze statue shows that it could be made of different bronze [Lowe] |
| 16551 | Grasping an essence is just grasping a real definition [Lowe] |
| 16542 | Explanation can't give an account of essence, because it is too multi-faceted [Lowe] |
| 16552 | If we must know some entity to know an essence, we lack a faculty to do that [Lowe] |
| 16533 | Logical necessities, based on laws of logic, are a proper sub-class of metaphysical necessities [Lowe] |
| 16531 | 'Metaphysical' necessity is absolute and objective - the strongest kind of necessity [Lowe] |
| 16532 | 'Epistemic' necessity is better called 'certainty' [Lowe] |
| 16543 | If an essence implies p, then p is an essential truth, and hence metaphysically necessary [Lowe] |
| 16544 | Metaphysical necessity is either an essential truth, or rests on essential truths [Lowe] |
| 16538 | We could give up possible worlds if we based necessity on essences [Lowe] |
| 16534 | 'Intuitions' are just unreliable 'hunches'; over centuries intuitions change enormously [Lowe] |
| 2975 | That honey is sweet I do not affirm, but I agree that it appears so [Timon] |
| 16535 | A concept is a way of thinking of things or kinds, whether or not they exist [Lowe] |
| 16550 | Direct reference doesn't seem to require that thinkers know what it is they are thinking about [Lowe] |
| 16547 | H2O isn't necessary, because different laws of nature might affect how O and H combine [Lowe] |