26 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] |
| 14212 | A consistent theory just needs one model; isomorphic versions will do too, and large domains provide those [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] |
| 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] |
| 14213 | Anti-realists see the world as imaginary, or lacking joints, or beyond reference, or beyond truth [Lewis] |
| 14210 | A gerrymandered mereological sum can be a mess, but still have natural joints [Lewis] |
| 14215 | Causal theories of reference make errors in reference easy [Lewis] |
| 14209 | Descriptive theories remain part of the theory of reference (with seven mild modifications) [Lewis] |
| 6248 | Reason is too slow and doubtful to guide all actions, which need external and moral senses [Hutcheson] |
| 6238 | We approve of actions by a superior moral sense [Hutcheson] |
| 6239 | We dislike a traitor, even if they give us great benefit [Hutcheson] |
| 6240 | The moral sense is not an innate idea, but an ability to approve or disapprove in a disinterested way [Hutcheson] |
| 6242 | We cannot choose our moral feelings, otherwise bribery could affect them [Hutcheson] |
| 6247 | Everyone feels uneasy when seeing others in pain, unless the others are evil [Hutcheson] |
| 6244 | Human nature seems incapable of universal malice, except what results from self-love [Hutcheson] |
| 6243 | As death approaches, why do we still care about family, friends or country? [Hutcheson] |
| 6246 | My action is not made good by a good effect, if I did not foresee and intend it [Hutcheson] |
| 6241 | Contempt of danger is just madness if it is not in some worthy cause [Hutcheson] |
| 6245 | That action is best, which procures the greatest happiness for the greatest number [Hutcheson] |
| 6251 | The loss of perfect rights causes misery, but the loss of imperfect rights reduces social good [Hutcheson] |
| 6250 | We say God is good if we think everything he does aims at the happiness of his creatures [Hutcheson] |
| 6249 | If goodness is constituted by God's will, it is a tautology to say God's will is good [Hutcheson] |