18 ideas
291 | Don't assume that wisdom is the automatic consequence of old age [Plato] |
10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
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] |
10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
293 | Being unafraid (perhaps through ignorance) and being brave are two different things [Plato] |