14 ideas
14779 | I reason in order to avoid disappointment and surprise [Peirce] |
14777 | That a judgement is true and that we judge it true are quite different things [Peirce] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
10304 | Very few things in set theory remain valid in intuitionist mathematics [Bernays] |
14780 | Only study logic if you think your own reasoning is deficient [Peirce] |
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] |
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] |
10303 | Restricted Platonism is just an ideal projection of a domain of thought [Bernays] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
10306 | Mathematical abstraction just goes in a different direction from logic [Bernays] |
14778 | Facts are hard unmoved things, unaffected by what people may think of them [Peirce] |