13 ideas
10882 | Predicative definitions only refer to entities outside the defined collection [Horsten] |
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] |
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] |
10884 | A theory is 'categorical' if it has just one model up to isomorphism [Horsten] |
23626 | Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack] |
10885 | Computer proofs don't provide explanations [Horsten] |
10881 | The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten] |
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] |
16689 | The schools said spirits lack extension, and wonder how many could dance on a needle's point [More,H] |