52 ideas
| 9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
| 9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
| 9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
| 9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
| 9617 | The 'iterative' view says sets start with the empty set and build up [Brown,JR] |
| 9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |
| 9605 | If a proposition is false, then its negation is true [Brown,JR] |
| 9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
| 9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
| 9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
| 9622 | 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR] |
| 9648 | π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR] |
| 9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
| 9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
| 9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
| 9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
| 9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
| 9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
| 9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
| 9606 | The irrationality of root-2 was achieved by intellect, not experience [Brown,JR] |
| 9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
| 9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
| 9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
| 9630 | The most brilliant formalist was Hilbert [Brown,JR] |
| 9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
| 9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
| 9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
| 9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
| 9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
| 17377 | All descriptive language is classificatory [Dupré] |
| 17376 | We should aim for a classification which tells us as much as possible about the object [Dupré] |
| 17390 | Natural kinds don't need essentialism to be explanatory [Dupré] |
| 17389 | A species might have its essential genetic mechanism replaced by a new one [Dupré] |
| 17388 | It seems that species lack essential properties, so they can't be natural kinds [Dupré] |
| 17374 | The possibility of prediction rests on determinism [Dupré] |
| 17378 | Presumably molecular structure seems important because we never have the Twin Earth experience [Dupré] |
| 9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
| 9609 | The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR] |
| 9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
| 20761 | If existence is absurd it can never have a meaning [Beauvoir] |
| 20746 | One is not born, but rather becomes a woman [Beauvoir] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
| 17381 | Phylogenetics involves history, and cladism rests species on splits in lineage [Dupré] |
| 17385 | Kinds don't do anything (including evolve) because they are abstract [Dupré] |
| 17375 | Natural kinds are decided entirely by the intentions of our classification [Dupré] |
| 17379 | Borders between species are much less clear in vegetables than among animals [Dupré] |
| 17384 | Even atoms of an element differ, in the energy levels of their electrons [Dupré] |
| 17387 | Ecologists favour classifying by niche, even though that can clash with genealogy [Dupré] |
| 17380 | Wales may count as fish [Dupré] |
| 17382 | Cooks, unlike scientists, distinguish garlic from onions [Dupré] |
| 17383 | Species are the lowest-level classification in biology [Dupré] |
| 17386 | The theory of evolution is mainly about species [Dupré] |