16 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] |
14775 | Numbers are just names devised for counting [Peirce] |
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] |
14776 | That two two-eyed people must have four eyes is a statement about numbers, not a fact [Peirce] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
14770 | Reasoning is based on statistical induction, so it can't achieve certainty or precision [Peirce] |
14774 | Innate truths are very uncertain and full of error, so they certainly have exceptions [Peirce] |
14773 | A truth is hard for us to understand if it rests on nothing but inspiration [Peirce] |
14772 | If we decide an idea is inspired, we still can't be sure we have got the idea right [Peirce] |
14771 | Only reason can establish whether some deliverance of revelation really is inspired [Peirce] |
14769 | Only imagination can connect phenomena together in a rational way [Peirce] |
22688 | The Aristotelian idea that choices can be perceived needs literary texts to expound it [Nussbaum] |