15 ideas
| 8207 | The quest for simplicity drove scientists to posit new entities, such as molecules in gases [Quine] |
| 8208 | In arithmetic, ratios, negatives, irrationals and imaginaries were created in order to generalise [Quine] |
| 13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
| 13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
| 13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
| 13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
| 13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
| 13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
| 13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
| 13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
| 8205 | Explaining events just by bodies can't explain two events identical in space-time [Quine] |
| 8206 | Necessity could be just generalisation over classes, or (maybe) quantifying over possibilia [Quine] |
| 21991 | The middle class gain freedom through property, but workers can only free all of humanity [Marx, by Singer] |
| 21990 | Theory is as much a part of a revolution as material force is [Marx] |
| 7128 | Religion is the opium of the people, and real happiness requires its abolition [Marx] |