18 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] |
10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [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] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
16730 | If matter is entirely atoms, anything else we notice in it can only be modes [Gassendi] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
16619 | We observe qualities, and use 'induction' to refer to the substances lying under them [Gassendi] |
1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
16593 | Atoms are not points, but hard indivisible things, which no force in nature can divide [Gassendi] |
16729 | How do mere atoms produce qualities like colour, flavour and odour? [Gassendi] |
5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |