28 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] |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| 17462 | A single object must not be counted twice, which needs knowledge of distinctness (negative identity) [Rumfitt] |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| 17461 | Some 'how many?' answers are not predications of a concept, like 'how many gallons?' [Rumfitt] |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| 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] |
| 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] |