25 ideas
15957 | Essential definitions show the differences that discriminate things, and make them what they are [Boyle] |
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] |
13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
15965 | Boyle attacked a contemporary belief that powers were occult things [Boyle, by Alexander,P] |
16735 | In the 17th century, 'disposition' usually just means the spatial arrangement of parts [Boyle, by Pasnau] |
13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
16034 | Form is not a separate substance, but just the manner, modification or 'stamp' of matter [Boyle] |
15953 | To cite a substantial form tells us what produced the effect, but not how it did it [Boyle] |
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] |
15964 | Boyle's secondary qualities are not illusory, or 'in the mind' [Boyle, by Alexander,P] |
15962 | Boyle's term 'texture' is not something you feel, but is unobservable structures of particles [Boyle, by Alexander,P] |
1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
15960 | Explanation is deducing a phenomenon from some nature better known to us [Boyle] |
15952 | The corpuscles just have shape, size and motion, which explains things without 'sympathies' or 'forces' [Boyle, by Alexander,P] |
15972 | The corpuscular theory allows motion, but does not include forces between the particles [Boyle, by Alexander,P] |