27 ideas
10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
13044 | Infinity: There is at least one limit level [Potter] |
10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
17486 | Supervenience is simply modally robust property co-variance [Hendry] |
13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
10709 | Priority is a modality, arising from collections and members [Potter] |
3570 | Maybe knowledge is belief which 'tracks' the truth [Nozick, by Williams,M] |
2748 | A true belief isn't knowledge if it would be believed even if false. It should 'track the truth' [Nozick, by Dancy,J] |
17481 | Nuclear charge (plus laws) explains electron structure and spectrum, but not vice versa [Hendry] |
17478 | Maybe two kinds are the same if there is no change of entropy on isothermal mixing [Hendry] |
17484 | Maybe the nature of water is macroscopic, and not in the microstructure [Hendry] |
17479 | The nature of an element must survive chemical change, so it is the nucleus, not the electrons [Hendry] |
17485 | Maybe water is the smallest part of it that still counts as water (which is H2O molecules) [Hendry] |
17482 | Compounds can differ with the same collection of atoms, so structure matters too [Hendry] |
17483 | Water continuously changes, with new groupings of molecules [Hendry] |
17476 | Elements survive chemical change, and are tracked to explain direction and properties [Hendry] |
17477 | Defining elements by atomic number allowed atoms of an element to have different masses [Hendry] |
17480 | Generally it is nuclear charge (not nuclear mass) which determines behaviour [Hendry] |