19 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] |
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] |
6375 | The taste of chocolate is a 'finer-grained' sensation than the taste of sweetness [Polger] |
1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
6381 | The mind and the self are one, and the mind-self is a biological phenomenon [Polger] |
6378 | Teleological functions explain why a trait exists; causal-role functions say what it does [Polger] |
6380 | Identity theory says consciousness is an abstraction: a state, event, process or property [Polger] |
6379 | A mummified heart has the teleological function of circulating blood [Polger] |
6377 | Teleological notions of function say what a thing is supposed to do [Polger] |