36 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] |
23616 | Legal excuses are duress, ignorance, and diminished responsibility [McMahan] |
23606 | Liberty Rights are permissions, and Claim Rights are freedom from intervention [McMahan] |
23595 | The worst unjustified wars have no aim at all [McMahan] |
23619 | A defensive war is unjust, if it is responding to a just war [McMahan] |
23620 | A person or state may be attacked if they are responsible for an unjustified threat [McMahan] |
23598 | You (e.g. a police officer) are not liable to attack just because you pose a threat [McMahan] |
23594 | Wars can be unjust, despite a just cause, if they are unnecessary or excessive or of mixed cause [McMahan] |
23597 | Just war theory says all and only persons posing a threat are liable to attack [McMahan] |
23600 | Proportionality in fighting can't be judged independently of the justice of each side [McMahan] |
23603 | Can an army start an unjust war, and then fight justly to defend their own civilians? [McMahan] |
23611 | Soldiers cannot freely fight in unjust wars, just because they behave well when fighting [McMahan] |
23612 | The law of war differs from criminal law; attacking just combatants is immoral, but legal [McMahan] |
23617 | If the unjust combatants are morally excused they are innocent, so how can they be killed? [McMahan] |
23599 | You don't become a legitimate target, just because you violently resist an unjust attack [McMahan] |
23596 | If all combatants are seen as morally equal, that facilitates starting unjust wars [McMahan] |
23604 | Volunteer soldiers accept the risk of attack, but they don't agree to it, or to their deaths [McMahan] |
23608 | If being part of a big collective relieves soldiers of moral responsibility, why not the leaders too? [McMahan] |
23610 | If soldiers can't refuse to fight in unjust wars, can they choose to fight in just wars? [McMahan] |
23613 | Equality is both sides have permission, or both sides are justified, or one justified the other permitted [McMahan] |
23615 | Fighting unjustly under duress does not justify it, or permit it, but it may excuse it [McMahan] |
23605 | Soldiers cannot know enough facts to evaluate the justice of their war [McMahan] |
23602 | Innocence implies not being morally responsible, rather than merely being guiltless [McMahan] |
23618 | Unconditional surrender can't be demanded, since evil losers still have legitimate conditions [McMahan] |
19399 | Prime matter is nothing when it is at rest [Leibniz] |