22 ideas
8207 | The quest for simplicity drove scientists to posit new entities, such as molecules in gases [Quine] |
8208 | In arithmetic, ratios, negatives, irrationals and imaginaries were created in order to generalise [Quine] |
10807 | Mathematics reduces to set theory, which reduces, with some mereology, to the singleton function [Lewis] |
10809 | We can accept the null set, but not a null class, a class lacking members [Lewis] |
10811 | The null set plays the role of last resort, for class abstracts and for existence [Lewis] |
10812 | The null set is not a little speck of sheer nothingness, a black hole in Reality [Lewis] |
10813 | What on earth is the relationship between a singleton and an element? [Lewis] |
10814 | Are all singletons exact intrinsic duplicates? [Lewis] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
10806 | Megethology is the result of adding plural quantification to mereology [Lewis] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
10816 | We can use mereology to simulate quantification over relations [Lewis] |
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] |
10808 | Mathematics is generalisations about singleton functions [Lewis] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
10815 | We don't need 'abstract structures' to have structural truths about successor functions [Lewis] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
8205 | Explaining events just by bodies can't explain two events identical in space-time [Quine] |
10810 | I say that absolutely any things can have a mereological fusion [Lewis] |
8206 | Necessity could be just generalisation over classes, or (maybe) quantifying over possibilia [Quine] |