24 ideas
2510 | Traditionally philosophy is an a priori enquiry into general truths about reality [Katz] |
2516 | Most of philosophy begins where science leaves off [Katz] |
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] |
2521 | 'Real' maths objects have no causal role, no determinate reference, and no abstract/concrete distinction [Katz] |
13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
8511 | Stout first explicitly proposed that properties and relations are particulars [Stout,GF, by Campbell,K] |
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] |
2513 | We don't have a clear enough sense of meaning to pronounce some sentences meaningless or just analytic [Katz] |
2522 | Experience cannot teach us why maths and logic are necessary [Katz] |
2517 | Structuralists see meaning behaviouristically, and Chomsky says nothing about it [Katz] |
2519 | It is generally accepted that sense is defined as the determiner of reference [Katz] |
2520 | Sense determines meaning and synonymy, not referential properties like denotation and truth [Katz] |
2518 | Sentences are abstract types (like musical scores), not individual tokens [Katz] |