30 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] |
10653 | Maybe set theory need not be well-founded [Varzi] |
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] |
10648 | Mereology need not be nominalist, though it is often taken to be so [Varzi] |
10655 | Are there mereological atoms, and are all objects made of them? [Varzi] |
10659 | There is something of which everything is part, but no null-thing which is part of everything [Varzi] |
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] |
13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
10661 | 'Composition is identity' says multitudes are the reality, loosely composing single things [Varzi] |
10654 | The parthood relation will help to define at least seven basic predicates [Varzi] |
10651 | If 'part' is reflexive, then identity is a limit case of parthood [Varzi] |
10649 | 'Part' stands for a reflexive, antisymmetric and transitive relation [Varzi] |
10647 | Parts may or may not be attached, demarcated, arbitrary, material, extended, spatial or temporal [Varzi] |
13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
10658 | Sameness of parts won't guarantee identity if their arrangement matters [Varzi] |
10709 | Priority is a modality, arising from collections and members [Potter] |
10652 | Conceivability may indicate possibility, but literary fantasy does not [Varzi] |
21278 | All the signs of design found in a watch are also found in nature [Paley] |
21277 | Even an imperfect machine can exhibit obvious design [Paley] |
21275 | Unlike a stone, the parts of a watch are obviously assembled in order to show the time [Paley] |
21276 | From the obvious purpose and structure of a watch we must infer that it was designed [Paley] |
21357 | No organ shows purpose more obviously than the eyelid [Paley] |