20 ideas
8758 | We could talk of open sentences, instead of sets [Chihara, by Shapiro] |
14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
10833 | Many concepts can only be expressed by second-order logic [Boolos] |
10265 | Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro] |
8759 | We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro] |
10264 | Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro] |
7404 | Nations are not obliged to help one-another, but are obliged not to harm one another [Grotius, by Tuck] |
7402 | Everyone has a right of self-preservation, and harming others is usually unjustifiable [Grotius, by Tuck] |
21938 | Democracy needs respect for individuality, but the 'community of friends' implies strict equality [Grotius] |
19845 | A person is free to renounce their state, as long as it is not a moment of crisis [Grotius, by Rousseau] |
22133 | Grotius and Pufendorf based natural law on real (rather than idealised) humanity [Grotius, by Ford,JD] |
7406 | A natural right of self-preservation is balanced by a natural law to avoid unnecessary harm [Grotius, by Tuck] |
7403 | Grotius ignored elaborate natural law theories, preferring a basic right of self-preservation [Grotius, by Tuck] |
23585 | It is permissible in a just cause to capture a place in neutral territory [Grotius] |
6892 | Moral principles have some validity without a God commanding obedience [Grotius, by Mautner] |