17 ideas
9967 | 'Impure' sets have a concrete member, while 'pure' (abstract) sets do not [Jubien] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
9968 | A model is 'fundamental' if it contains only concrete entities [Jubien] |
17813 | Löwenheim-Skolem says any theory with a true interpretation has a model in the natural numbers [White,NP] |
17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
9965 | There couldn't just be one number, such as 17 [Jubien] |
17812 | Finite cardinalities don't need numbers as objects; numerical quantifiers will do [White,NP] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
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] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
9969 | The empty set is the purest abstract object [Jubien] |