27 ideas
21406 | Because there is only one human reason, there can only be one true philosophy from principles [Kant] |
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] |
21081 | We are equipped with the a priori intuitions needed for the concept of right [Kant] |
21082 | A power-based state of nature may not be unjust, but there is no justice without competent judges [Kant] |
21089 | Monarchs have the highest power; autocrats have complete power [Kant] |
21086 | Hereditary nobility has not been earned, and probably won't be earned [Kant] |
21080 | Actions are right if the maxim respects universal mutual freedoms [Kant] |
21083 | Women have no role in politics [Kant] |
21407 | Equality is not being bound in ways you cannot bind others [Kant] |
21084 | In the contract people lose their rights, but immediately regain them, in the new commonwealth [Kant] |
21090 | If someone has largely made something, then they own it [Kant] |
21087 | Human life is pointless without justice [Kant] |
21088 | Justice asserts the death penalty for murder, from a priori laws [Kant] |
21085 | The church has a political role, by offering a supreme power over people [Kant] |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |