38 ideas
| 10147 | The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman] |
| 10148 | Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman] |
| 10149 | Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman] |
| 10150 | The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman] |
| 10146 | Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman] |
| 10158 | A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman] |
| 10162 | Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman] |
| 10160 | Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman] |
| 10159 | Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman] |
| 10161 | If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman] |
| 10156 | 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman] |
| 10155 | Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman] |
| 7222 | It is a crime for someone with a violent disposition to get drunk [Mill] |
| 7214 | Ethics rests on utility, which is the permanent progressive interests of people [Mill] |
| 7212 | Individuals have sovereignty over their own bodies and minds [Mill] |
| 7210 | The will of the people is that of the largest or most active part of the people [Mill] |
| 7227 | It is evil to give a government any more power than is necessary [Mill] |
| 7228 | Individuals often do things better than governments [Mill] |
| 7230 | Aim for the maximum dissemination of power consistent with efficiency [Mill] |
| 20515 | Maximise happiness by an area of strict privacy, and an area of utilitarian interventions [Mill, by Wolff,J] |
| 7229 | People who transact their own business will also have the initiative to control their government [Mill] |
| 7211 | Prevention of harm to others is the only justification for exercising power over people [Mill] |
| 7231 | The worth of a State, in the long run, is the worth of the individuals composing it [Mill] |
| 7217 | The main argument for freedom is that interference with it is usually misguided [Mill] |
| 7213 | Liberty arises at the point where people can freely and equally discuss things [Mill] |
| 20517 | Utilitarianism values liberty, but guides us on which ones we should have or not have [Mill, by Wolff,J] |
| 20516 | Mill defends freedom as increasing happiness, but maybe it is an intrinsic good [Wolff,J on Mill] |
| 7215 | True freedom is pursuing our own good, while not impeding others [Mill] |
| 7218 | Individuals are not accountable for actions which only concern themselves [Mill] |
| 7221 | Blocking entry to an unsafe bridge does not infringe liberty, since no one wants unsafe bridges [Mill] |
| 7223 | Pimping and running a gambling-house are on the border between toleration and restraint [Mill] |
| 7220 | Restraint for its own sake is an evil [Mill] |
| 7219 | Society can punish actions which it believes to be prejudicial to others [Mill] |
| 7226 | Benefits performed by individuals, not by government, help also to educate them [Mill] |
| 7224 | We need individual opinions and conduct, and State education is a means to prevent that [Mill] |
| 7225 | It is a crime to create a being who lacks the ordinary chances of a desirable existence [Mill] |
| 7216 | The ethics of the Gospel has been supplemented by barbarous Old Testament values [Mill] |
| 7607 | Nagarjuna and others pronounced the world of experience to be an illusion [Nagarjuna, by Armstrong,K] |