21 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] |
18812 | Split out the logical vocabulary, make an assignment to the rest. It's logical if premises and conclusion match [Tarski, by Rumfitt] |
13344 | X follows from sentences K iff every model of K also models X [Tarski] |
10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
13343 | A 'model' is a sequence of objects which satisfies a complete set of sentential functions [Tarski] |
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] |
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] |
13345 | Sentences are 'analytical' if every sequence of objects models them [Tarski] |
4055 | It isn't obviously wicked to destroy a potential human being (e.g. an ununited egg and sperm) [Lockwood] |
4056 | If the soul is held to leave the body at brain-death, it should arrive at the time of brain-creation [Lockwood] |
4054 | I may exist before I become a person, just as I exist before I become an adult [Lockwood] |