46 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] |
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] |
14508 | A 'thisness' is a thing's property of being identical with itself (not the possession of self-identity) [Adams,RM] |
14511 | There are cases where mere qualities would not ensure an intrinsic identity [Adams,RM] |
12031 | Essences are taken to be qualitative properties [Adams,RM] |
12034 | If the universe was cyclical, totally indiscernible events might occur from time to time [Adams,RM] |
14510 | Two events might be indiscernible yet distinct, if there was a universe cyclical in time [Adams,RM] |
16455 | Black's two globes might be one globe in highly curved space [Adams,RM] |
14507 | Are possible worlds just qualities, or do they include primitive identities as well? [Adams,RM] |
11964 | Possible worlds are world-stories, maximal descriptions of whole non-existent worlds [Adams,RM, by Molnar] |
16451 | Adams says anti-haecceitism reduces all thisness to suchness [Adams,RM, by Stalnaker] |
11901 | Haecceitism may or may not involve some logical connection to essence [Adams,RM, by Mackie,P] |
14512 | Moderate Haecceitism says transworld identities are primitive, but connected to qualities [Adams,RM] |
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] |
12032 | Direct reference is by proper names, or indexicals, or referential uses of descriptions [Adams,RM] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |