22 ideas
23269 | Philosophy must start from clearly observed facts [Galen] |
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] |
10631 | If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
10624 | The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
10629 | If structures are relative, this undermines truth-value and objectivity [Hale/Wright] |
10628 | The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
10622 | The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright] |
10626 | Objects just are what singular terms refer to [Hale/Wright] |
23266 | The spirit in the soul wants freedom, power and honour [Galen] |
23219 | Stopping the heart doesn't terminate activity; pressing the brain does that [Galen, by Cobb] |
23264 | Philosophers think faculties are in substances, and invent a faculty for every activity [Galen] |
23220 | The brain contains memory and reason, and is the source of sensation and decision [Galen] |
23265 | The rational part of the soul is the desire for truth, understanding and recollection [Galen] |
10630 | Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright] |
10627 | Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright] |
23268 | We execute irredeemable people, to protect ourselves, as a deterrent, and ending a bad life [Galen] |