12 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] |
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] |
5040 | Necessary truths can be analysed into original truths; contingent truths are infinitely analysable [Leibniz] |
13159 | Only God sees contingent truths a priori [Leibniz] |
5039 | If non-existents are possible, their existence would replace what now exists, which cannot therefore be necessary [Leibniz] |
1655 | If goodness needs true opinion but not knowledge, you can skip the 'examined life' [Vlastos on Plato] |
5041 | God does everything in a perfect way, and never acts contrary to reason [Leibniz] |