27 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] |
7306 | If the only property of a name was its reference, we couldn't explain bearerless names [Miller,A] |
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] |
12270 | Being is one [Melissus, by Aristotle] |
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] |
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] |
7322 | Constitutive scepticism is about facts, and epistemological scepticism about our ability to know them [Miller,A] |
7325 | Dispositions say what we will do, not what we ought to do, so can't explain normativity [Miller,A] |
7324 | Explain meaning by propositional attitudes, or vice versa, or together? [Miller,A] |
7323 | If truth is deflationary, sentence truth-conditions just need good declarative syntax [Miller,A] |
7315 | 'Jones is a married bachelor' does not have the logical form of a contradiction [Miller,A] |
7328 | The principle of charity is holistic, saying we must hold most of someone's system of beliefs to be true [Miller,A] |
7329 | Maybe we should interpret speakers as intelligible, rather than speaking truth [Miller,A] |
7333 | The Frege-Geach problem is that I can discuss the wrongness of murder without disapproval [Miller,A] |
3059 | There is no real motion, only the appearance of it [Melissus, by Diog. Laertius] |
5100 | The void is not required for change, because a plenum can alter in quality [Aristotle on Melissus] |
456 | Nothing could come out of nothing [Melissus] |