13 ideas
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] |
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] |
17435 | Objects do not naturally form countable units [Koslicki] |
17433 | We can still count squares, even if they overlap [Koslicki] |
17439 | There is no deep reason why we count carrots but not asparagus [Koslicki] |
17434 | We struggle to count branches and waves because our concepts lack clear boundaries [Koslicki] |
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] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
17436 | We talk of snow as what stays the same, when it is a heap or drift or expanse [Koslicki] |
1460 | Religious experience deserves the same respect as our other key experiences, and is best called 'holy' [Taylor,AE, by PG] |