27 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] |
2705 | How can intuitionists distinguish universal convictions from local cultural ones? [Hare] |
2712 | You can't use intuitions to decide which intuitions you should cultivate [Hare] |
2706 | Emotivists mistakenly think all disagreements are about facts, and so there are no moral reasons [Hare] |
2709 | Prescriptivism sees 'ought' statements as imperatives which are universalisable [Hare] |
2704 | If morality is just a natural or intuitive description, that leads to relativism [Hare] |
2703 | Descriptivism say ethical meaning is just truth-conditions; prescriptivism adds an evaluation [Hare] |
2707 | If there can be contradictory prescriptions, then reasoning must be involved [Hare] |
2708 | An 'ought' statement implies universal application [Hare] |
2711 | Prescriptivism implies a commitment, but descriptivism doesn't [Hare] |
22262 | Kant's moral law has no foundation - because that would undermine its priority [Sandel] |
2710 | Moral judgements must invoke some sort of principle [Hare] |
22264 | Modern liberal rights in democracies protect individuals against the majority [Sandel] |
22261 | Liberals say rights always come first, and justice is neutral on social values [Sandel] |
22263 | Liberal justice means the withdrawal of the self, as transcendental or as unencumbered [Sandel] |
22805 | Liberalism concerns rights, and communitarianism concerns the common good [Sandel, by Avineri/De-Shalit] |