26 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] |
13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
14329 | Some dispositional properties (such as mental ones) may have no categorical base [Price,HH] |
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] |
9032 | Before we can abstract from an instance of violet, we must first recognise it [Price,HH] |
9035 | If judgement of a characteristic is possible, that part of abstraction must be complete [Price,HH] |
9034 | There may be degrees of abstraction which allow recognition by signs, without full concepts [Price,HH] |
9036 | There is pre-verbal sign-based abstraction, as when ice actually looks cold [Price,HH] |
9037 | Intelligent behaviour, even in animals, has something abstract about it [Price,HH] |
9033 | Recognition must precede the acquisition of basic concepts, so it is the fundamental intellectual process [Price,HH] |
9030 | Abstractions can be interpreted dispositionally, as the ability to recognise or imagine an item [Price,HH] |
9029 | If ideas have to be images, then abstract ideas become a paradoxical problem [Price,HH] |
9031 | The basic concepts of conceptual cognition are acquired by direct abstraction from instances [Price,HH] |
16713 | Philosophers are the forefathers of heretics [Tertullian] |
6610 | I believe because it is absurd [Tertullian] |