17 ideas
21959 | Metaphysics is the most general attempt to make sense of things [Moore,AW] |
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] |
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] |
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] |
18528 | The single imagined 'interval' between things only exists in the intellect [Auriol] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
21958 | Appearances are nothing beyond representations, which is transcendental ideality [Moore,AW] |
16589 | Prime matter lacks essence, but is only potentially and indeterminately a physical thing [Auriol] |
16651 | God can do anything non-contradictory, as making straightness with no line, or lightness with no parts [Auriol] |