22 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] |
13445 | Descartes showed a one-one order-preserving match between points on a line and the real numbers [Descartes, by Hart,WD] |
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] |
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] |
16774 | Descartes thinks distinguishing substances from aggregates is pointless [Descartes, by Pasnau] |
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] |
7400 | Descartes said images can refer to objects without resembling them (as words do) [Descartes, by Tuck] |
4310 | We have inner awareness of our freedom [Descartes] |
6553 | Descartes discussed the interaction problem, and compared it with gravity [Descartes, by Lycan] |
16764 | The soul conserves the body, as we see by its dissolution when the soul leaves [Toletus] |
19676 | Nature is devoid of thought [Descartes, by Meillassoux] |
6518 | Matter can't just be Descartes's geometry, because a filler of the spaces is needed [Robinson,H on Descartes] |