66 ideas
| 10987 | Three traditional names of rules are 'Simplification', 'Addition' and 'Disjunctive Syllogism' [Read] |
| 11004 | Necessity is provability in S4, and true in all worlds in S5 [Read] |
| 11018 | There are fuzzy predicates (and sets), and fuzzy quantifiers and modifiers [Read] |
| 11011 | Same say there are positive, negative and neuter free logics [Read] |
| 11020 | Realisms like the full Comprehension Principle, that all good concepts determine sets [Read] |
| 10986 | Not all validity is captured in first-order logic [Read] |
| 10972 | The non-emptiness of the domain is characteristic of classical logic [Read] |
| 11024 | Semantics must precede proof in higher-order logics, since they are incomplete [Read] |
| 10985 | We should exclude second-order logic, precisely because it captures arithmetic [Read] |
| 10970 | A theory of logical consequence is a conceptual analysis, and a set of validity techniques [Read] |
| 10984 | Logical consequence isn't just a matter of form; it depends on connections like round-square [Read] |
| 10973 | A theory is logically closed, which means infinite premisses [Read] |
| 11007 | Quantifiers are second-order predicates [Read] |
| 10978 | In second-order logic the higher-order variables range over all the properties of the objects [Read] |
| 10971 | A logical truth is the conclusion of a valid inference with no premisses [Read] |
| 10988 | Any first-order theory of sets is inadequate [Read] |
| 10974 | Compactness is when any consequence of infinite propositions is the consequence of a finite subset [Read] |
| 10975 | Compactness does not deny that an inference can have infinitely many premisses [Read] |
| 10977 | Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) [Read] |
| 10976 | Compactness makes consequence manageable, but restricts expressive power [Read] |
| 11014 | Self-reference paradoxes seem to arise only when falsity is involved [Read] |
| 11025 | Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read] |
| 10979 | Although second-order arithmetic is incomplete, it can fully model normal arithmetic [Read] |
| 10980 | Second-order arithmetic covers all properties, ensuring categoricity [Read] |
| 10997 | Von Neumann numbers are helpful, but don't correctly describe numbers [Read] |
| 11016 | Would a language without vagueness be usable at all? [Read] |
| 11019 | Supervaluations say there is a cut-off somewhere, but at no particular place [Read] |
| 11012 | A 'supervaluation' gives a proposition consistent truth-value for classical assignments [Read] |
| 11013 | Identities and the Indiscernibility of Identicals don't work with supervaluations [Read] |
| 10995 | A haecceity is a set of individual properties, essential to each thing [Read] |
| 11001 | Equating necessity with truth in every possible world is the S5 conception of necessity [Read] |
| 3016 | Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius] |
| 10992 | The point of conditionals is to show that one will accept modus ponens [Read] |
| 10989 | The standard view of conditionals is that they are truth-functional [Read] |
| 11017 | Some people even claim that conditionals do not express propositions [Read] |
| 10983 | Knowledge of possible worlds is not causal, but is an ontology entailed by semantics [Read] |
| 10982 | How can modal Platonists know the truth of a modal proposition? [Read] |
| 10996 | Actualism is reductionist (to parts of actuality), or moderate realist (accepting real abstractions) [Read] |
| 10981 | A possible world is a determination of the truth-values of all propositions of a domain [Read] |
| 11000 | If worlds are concrete, objects can't be present in more than one, and can only have counterparts [Read] |
| 10998 | The mind abstracts ways things might be, which are nonetheless real [Read] |
| 11005 | Negative existentials with compositionality make the whole sentence meaningless [Read] |
| 10966 | A proposition objectifies what a sentence says, as indicative, with secure references [Read] |
| 23616 | Legal excuses are duress, ignorance, and diminished responsibility [McMahan] |
| 23606 | Liberty Rights are permissions, and Claim Rights are freedom from intervention [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] |
| 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] |
| 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] |