16 ideas
13430 | Infinity: there is an infinity of distinguishable individuals [Ramsey] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
13428 | Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
13427 | Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey] |
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] |
13334 | Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey] |
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] |
13426 | Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey] |
13425 | Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey] |
22328 | I just confront the evidence, and let it act on me [Ramsey] |
22325 | A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey] |
1556 | By nature people are close to one another, but culture drives them apart [Hippias] |