21 ideas
17990 | Instances of minimal truth miss out propositions inexpressible in current English [Hofweber] |
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] |
17988 | Quantification can't all be substitutional; some reference is obviously to objects [Hofweber] |
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] |
17989 | Since properties have properties, there can be a typed or a type-free theory of them [Hofweber] |
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] |
9073 | Abstraction from an ambiguous concept like 'mole' will define them as the same [Barnes,J] |
9074 | Abstraction cannot produce the concept of a 'game', as there is no one common feature [Barnes,J] |
9072 | Defining concepts by abstractions will collect together far too many attributes from entities [Barnes,J] |
17991 | Holism says language can't be translated; the expressibility hypothesis says everything can [Hofweber] |