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] |
9935 | Mathematical truth is always compromising between ordinary language and sensible epistemology [Benacerraf] |
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] |
17927 | Realists have semantics without epistemology, anti-realists epistemology but bad semantics [Benacerraf, by Colyvan] |
9936 | The platonist view of mathematics doesn't fit our epistemology very well [Benacerraf] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
16083 | Aristotelian matter seriously threatens the intrinsic unity and substantiality of its object [Gill,ML] |
17006 | Prime matter has no place in Aristotle's theories, and passages claiming it are misread [Gill,ML] |
16093 | Prime matter is actually nothing and potentially everything (or potentially an element) [Gill,ML] |