20 ideas
15390 | Metaphysics attempts to give an account of everything, in terms of categories and principles [Simons] |
9967 | 'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien] |
9968 | A model is 'fundamental' if it contains only concrete entities [Jubien] |
17453 | The meaning of a number isn't just the numerals leading up to it [Heck] |
9965 | There couldn't just be one number, such as 17 [Jubien] |
17457 | A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck] |
17448 | In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck] |
17455 | Is counting basically mindless, and independent of the cardinality involved? [Heck] |
17456 | Counting is the assignment of successively larger cardinal numbers to collections [Heck] |
17450 | Understanding 'just as many' needn't involve grasping one-one correspondence [Heck] |
17451 | We can know 'just as many' without the concepts of equinumerosity or numbers [Heck] |
17459 | Frege's Theorem explains why the numbers satisfy the Peano axioms [Heck] |
9966 | The subject-matter of (pure) mathematics is abstract structure [Jubien] |
9963 | If we all intuited mathematical objects, platonism would be agreed [Jubien] |
9962 | How can pure abstract entities give models to serve as interpretations? [Jubien] |
9964 | Since mathematical objects are essentially relational, they can't be picked out on their own [Jubien] |
17454 | Children can use numbers, without a concept of them as countable objects [Heck] |
17458 | Equinumerosity is not the same concept as one-one correspondence [Heck] |
17449 | We can understand cardinality without the idea of one-one correspondence [Heck] |
9969 | The empty set is the purest abstract object [Jubien] |