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] |
17818 | How many? must first partition an aggregate into sets, and then logic fixes its number [Yourgrau] |
17822 | Nothing is 'intrinsically' numbered [Yourgrau] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
17817 | Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
17815 | We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau] |
17821 | You can ask all sorts of numerical questions about any one given set [Yourgrau] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
20239 | Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche] |