14 ideas
| 8758 | We could talk of open sentences, instead of sets [Chihara, by Shapiro] |
| Full Idea: Chihara's programme is to replace talk of sets with talk of open sentences. Instead of speaking of the set of all cats, we talk about the open sentence 'x is a cat'. | |
| From: report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Thinking About Mathematics 9.2 | |
| A reaction: As Shapiro points out, this is following up Russell's view that sets should be replaced with talk of properties. Chihara is expressing it more linguistically. I'm in favour of any attempt to get rid of sets. |
| 18091 | Infinitesimals are ghosts of departed quantities [Berkeley] |
| Full Idea: The infinitesimals are the ghosts of departed quantities. | |
| From: George Berkeley (The Analyst [1734]), quoted by David Bostock - Philosophy of Mathematics 4.3 | |
| A reaction: [A famous phrase, but as yet no context for it] |
| 10265 | Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro] |
| Full Idea: Chihara's system is a version of type theory. Translate thus: replace variables of sets of type n with level n variables over open sentences, replace membership/predication with satisfaction, and high quantifiers with constructability quantifiers. | |
| From: report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Philosophy of Mathematics 7.4 |
| 8759 | We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro] |
| Full Idea: Chihara's system is similar to simple type theory; he replaces each type with variables over open sentences, replaces membership (or predication) with satisfaction, and replaces quantifiers over level 1+ variables with constructability quantifiers. | |
| From: report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Thinking About Mathematics 9.2 | |
| A reaction: This is interesting for showing that type theory may not be dead. The revival of supposedly dead theories is the bread-and-butter of modern philosophy. |
| 10264 | Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro] |
| Full Idea: Chihara has proposal a modal primitive, a 'constructability quantifier'. Syntactically it behaves like an ordinary quantifier: Φ is a formula, and x a variable. Then (Cx)Φ is a formula, read as 'it is possible to construct an x such that Φ'. | |
| From: report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Philosophy of Mathematics 7.4 | |
| A reaction: We only think natural numbers are infinite because we see no barrier to continuing to count, i.e. to construct new numbers. We accept reals when we know how to construct them. Etc. Sounds promising to me (though not to Shapiro). |
| 7404 | Nations are not obliged to help one-another, but are obliged not to harm one another [Grotius, by Tuck] |
| Full Idea: Grotius explored the implications of the idea that nation-states were under no obligation to help one another, but they were obliged not to harm each other. | |
| From: report of Hugo Grotius (On the Law of War and Peace [1625]) by Richard Tuck - Hobbes Ch.1 | |
| A reaction: This is quite a striking disanalogy between accepted personal morality and political morality. There are signs in recent years of some recognition that other nations should not just sit and watch suffering. |
| 7402 | Everyone has a right of self-preservation, and harming others is usually unjustifiable [Grotius, by Tuck] |
| Full Idea: Grotius said that all men would agree that everyone has a fundamental right to preserve themselves, and that wanton or unnecessary injury to another person is unjustifiable. | |
| From: report of Hugo Grotius (On the Law of War and Peace [1625]) by Richard Tuck - Hobbes Ch.1 | |
| A reaction: Who cares if it is 'justifiable'? Do I have to 'justify' killing a mosquito if it lands on my arm? Grotius is taking a step beyond saying that people should defend themselves, to say that they have a 'right' to - the only truly basic right. |
| 21938 | Democracy needs respect for individuality, but the 'community of friends' implies strict equality [Grotius] |
| Full Idea: There is no democracy without respect for irreducible singularity, but there is no democracy with the 'community of friends' without the calculation of majorities, without identifiable representable subjects, all equal. | |
| From: Hugo Grotius (On the Law of War and Peace [1625]), quoted by Simon Glendinning - Derrida: A Very Short Introduction 7 | |
| A reaction: [source not given] Derrida calls this conflict 'tragic'. The obvious reply is that equality is not an absolute. We can be equal in voting rights while being unequal in height or musical talent. |
| 19845 | A person is free to renounce their state, as long as it is not a moment of crisis [Grotius, by Rousseau] |
| Full Idea: Grotius thinks that each person can renounce his state and leave the country. (n15: provided it is not to evade one's duty the moment the homeland needs us; this would be criminal and punishable; it would not be withdrawal, but desertion) | |
| From: report of Hugo Grotius (On the Law of War and Peace [1625]) by Jean-Jacques Rousseau - The Social Contract (tr Cress) III.18 | |
| A reaction: The obvious example is Britons going to America in 1939, or (more controversially) conscripts going to Canada to avoid fighting in Vietnam. I'm unclear whether the idea in the note is that of Grotius or of Rousseau). Is tax exile OK, then? |
| 22133 | Grotius and Pufendorf based natural law on real (rather than idealised) humanity [Grotius, by Ford,JD] |
| Full Idea: Grotius and Pufendorf transformed the natural law tradition by starting from identifiable traits of human nature rather than ideas about what human beings ought to be. | |
| From: report of Hugo Grotius (On the Law of War and Peace [1625]) by J.D. Ford - Pufendorf, Samuel p.863 |
| 7406 | A natural right of self-preservation is balanced by a natural law to avoid unnecessary harm [Grotius, by Tuck] |
| Full Idea: For Grotius, there was a fundamental 'natural right' of self-preservation upon which all known moralities and codes of social behaviour must have been constructed, but it is balanced by a fundament duty or 'natural law' to abstain from harming others. | |
| From: report of Hugo Grotius (On the Law of War and Peace [1625]) by Richard Tuck - Hobbes Ch.2 | |
| A reaction: This theory has the virtue of economy, but I don't see how you can clearly justify those particular natural rights and laws, without allowing others to creep in, such as a right to a decent share of food, or a law requiring some fairness. |
| 7403 | Grotius ignored elaborate natural law theories, preferring a basic right of self-preservation [Grotius, by Tuck] |
| Full Idea: Grotius said there was a minimum core of morality (based on self-preservation), and disregarded the elaborate accounts of principles of natural law which Aristotelians had always sought to develop. | |
| From: report of Hugo Grotius (On the Law of War and Peace [1625]) by Richard Tuck - Hobbes Ch.1 | |
| A reaction: Aquinas would be the key Aristotelian here. I tend towards the Aristotelian view. If you go for the minimal view, it is not clear why there is a 'right' to self-preservation, rather than a mere desire for it. |
| 23585 | It is permissible in a just cause to capture a place in neutral territory [Grotius] |
| Full Idea: It is permissible for one who is waging a just war to take possession of a place situated in a country free from hostilities. | |
| From: Hugo Grotius (On the Law of War and Peace [1625], II.ii.x), quoted by Michael Walzer - Just and Unjust Wars 15 n | |
| A reaction: This rejects Combatant Equality, allowing the just to do what is morally forbidden to the unjust. |
| 6892 | Moral principles have some validity without a God commanding obedience [Grotius, by Mautner] |
| Full Idea: In the Prolegomena to his work there is a famous statement that moral principles laid down in the work would have some degree of validity even if there was no God commanding obedience. | |
| From: report of Hugo Grotius (On the Law of War and Peace [1625]) by Thomas Mautner - Penguin Dictionary of Philosophy p.229 | |
| A reaction: I am not clear why Grotius felt obliged to qualify his claim with the phrase 'some degree'. I don't see how God's command can affect the 'validity' of morality, or how there can be a middle ground between dependence on and independence of God. |