31 ideas
| 10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
| 21495 | Theoretical and practical politics are both concerned with the best lives for individuals [Russell] |
| 10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
| 10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
| 10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
| 10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
| 10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
| 10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
| 10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
| 10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
| 10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
| 10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
| 10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
| 16078 | Clay is intrinsically and atomically the same as statue (and that lacks 'modal properties') [Rudder Baker] |
| 16077 | The clay is not a statue - it borrows that property from the statue it constitutes [Rudder Baker] |
| 16080 | Is it possible for two things that are identical to become two separate things? [Rudder Baker] |
| 16076 | Constitution is not identity, as consideration of essential predicates shows [Rudder Baker] |
| 16081 | The constitution view gives a unified account of the relation of persons/bodies, statues/bronze etc [Rudder Baker] |
| 16082 | Statues essentially have relational properties lacked by lumps [Rudder Baker] |
| 21517 | Individuals need creativity, reverence for others, and self-respect [Russell] |
| 21523 | We would not want UK affairs to be settled by a world parliament [Russell] |
| 21522 | Democracy is inadequate without a great deal of devolution [Russell] |
| 21521 | Anarchy does not maximise liberty [Russell] |
| 21528 | Groups should be autonomous, with a neutral authority as arbitrator [Russell] |
| 21527 | On every new question the majority is always wrong at first [Russell] |
| 21526 | Unfortunately ordinary voters can't detect insincerity [Russell] |
| 21525 | When the state is the only employer, there is no refuge from the prejudices of other people [Russell] |
| 21518 | Men unite in pursuit of material things, and idealise greed as part of group loyalty [Russell] |
| 21519 | We need security and liberty, and then encouragement of creativity [Russell] |
| 21524 | The right to own land gives a legal right to a permanent income [Russell] |
| 21520 | That our heaven is a dull place reflects the misery of excessive work in life [Russell] |