29 ideas
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] |
10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [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] |
1350 | Continuity is needed for existence, otherwise we would say a thing existed after it ceased to exist [Reid] |
21322 | We treat slowly changing things as identical for the sake of economy in language [Reid] |
21320 | Identity is familiar to common sense, but very hard to define [Reid] |
1367 | Identity can only be affirmed of things which have a continued existence [Reid] |
23644 | Without memory we could have no concept of duration [Reid] |
23643 | We all trust our distinct memories (but not our distinct imaginings) [Reid] |
1356 | A person is a unity, and doesn't come in degrees [Reid] |
1359 | Personal identity is the basis of all rights, obligations and responsibility [Reid] |
21319 | I can hardly care about rational consequence if it wasn't me conceiving the antecedent [Reid] |
21323 | The identity of a thief is only known by similarity, but memory gives certainty in our own case [Reid] |
21321 | Memory reveals my past identity - but so does testimony of other witnesses [Reid] |
21324 | If consciousness is transferable 20 persons can be 1; forgetting implies 1 can be 20 [Reid] |
21325 | Boy same as young man, young man same as old man, old man not boy, if forgotten! [Reid] |
21327 | If a stolen horse is identified by similitude, its identity is not therefore merely similitude [Reid] |
1366 | If consciousness is personal identity, it is continually changing [Reid] |
1352 | Thoughts change continually, but the self doesn't [Reid] |
5996 | Critolaus redefined Aristotle's moral aim as fulfilment instead of happiness [Critolaus, by White,SA] |