21 ideas
5300 | Philosophers have interpreted the world, but the point is to change it [Marx] |
5297 | Whether human thinking can be 'true' must be decided in practice, not theory [Marx] |
10528 | Definitions concern how we should speak, not how things are [Fine,K] |
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] |
10529 | If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K] |
10530 | Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
22598 | The authentic self exists at the level of class, rather than the individual [Marx, by Dunt] |
10527 | An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K] |
5298 | The human essence is not found in individuals but in social relations [Marx] |
5299 | Religious feeling is social in origin [Marx] |