21 ideas
291 | Don't assume that wisdom is the automatic consequence of old age [Plato] |
10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
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] |
3654 | The pineal gland links soul to body, and unites the two symmetrical sides of the body [Descartes, by PG] |
4015 | For Descartes passions are God-given preservers of the mind-body union [Descartes, by Taylor,C] |
4313 | Are there a few primary passions (say, joy, sadness and desire)? [Descartes, by Cottingham] |
23989 | There are six primitive passions: wonder, love, hatred, desire, joy and sadness [Descartes, by Goldie] |
20037 | Merely willing to walk leads to our walking [Descartes] |
16763 | We don't die because the soul departs; the soul departs because the organs cease functioning [Descartes] |
4016 | Descartes makes strength of will the central virtue [Descartes, by Taylor,C] |
293 | Being unafraid (perhaps through ignorance) and being brave are two different things [Plato] |