13 ideas
18261 | A simplification which is complete constitutes a definition [Kant] |
9616 | A set is a collection into a whole of distinct objects of our intuition or thought [Cantor] |
23623 | Predicativism says only predicated sets exist [Hossack] |
23624 | The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack] |
23625 | Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack] |
22275 | Logic gives us the necessary rules which show us how we ought to think [Kant] |
23628 | The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack] |
23627 | 'Before' and 'after' are not two relations, but one relation with two orders [Hossack] |
15896 | Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine] |
23626 | Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack] |
23621 | Numbers are properties, not sets (because numbers are magnitudes) [Hossack] |
23622 | We can only mentally construct potential infinities, but maths needs actual infinities [Hossack] |
18260 | If we knew what we know, we would be astonished [Kant] |