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] |
| 13479 | Given that thinking aims at truth, logic gives universal rules for how to do it [Burge] |
| 9605 | If a proposition is false, then its negation is true [Brown,JR] |
| 8132 | We now have a much more sophisticated understanding of logical form in language [Burge] |
| 17622 | We come to believe mathematical propositions via their grounding in the structure [Burge] |
| 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] |
| 16901 | The equivalent algebra model of geometry loses some essential spatial meaning [Burge] |
| 9159 | You can't simply convert geometry into algebra, as some spatial content is lost [Burge] |
| 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] |
| 16902 | Peano arithmetic requires grasping 0 as a primitive number [Burge] |
| 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] |
| 9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
| 9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
| 9630 | The most brilliant formalist was Hilbert [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] |
| 16892 | Is apriority predicated mainly of truths and proofs, or of human cognition? [Burge] |
| 9382 | Subjects may be unaware of their epistemic 'entitlements', unlike their 'justifications' [Burge] |
| 8126 | Anti-individualism says the environment is involved in the individuation of some mental states [Burge] |
| 8127 | Broad concepts suggest an extension of the mind into the environment (less computer-like) [Burge] |
| 8129 | Anti-individualism may be incompatible with some sorts of self-knowledge [Burge] |
| 8131 | Some qualities of experience, like blurred vision, have no function at all [Burge] |
| 3115 | Are meaning and expressed concept the same thing? [Burge, by Segal] |
| 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] |
| 7257 | All modern social systems seem to be conspiracies of the rich [More,T] |
| 7254 | If you try to get elected, you should be permanently barred from seeking office [More,T] |
| 7255 | Only Utopians fail to see glory in warfare [More,T] |
| 7253 | In Utopia, legal euthanasia is considered honourable [More,T] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
| 14349 | If there are no finks or antidotes at the fundamental level, the laws can't be ceteris paribus [Burge, by Corry] |
| 7256 | In Utopia, the Supreme Being is identical with Nature [More,T] |