21 ideas
| 8013 | In the Reformation, morality became unconditional but irrational, individually autonomous, and secular [MacIntyre] |
| Full Idea: Three concepts about morality emerge from the Reformation period: that moral rules are unconditional demands that lack rational justification; that moral agents are sovereign in choices; and that secular powers have their own norms and justifications. | |
| From: Alasdair MacIntyre (A Short History of Ethics [1967], Ch.10) | |
| A reaction: I get the impression that a rather frank admission of the role of self-interest emerged at that time as well. It is only in the late seventeenth century that the possibility of a secular altruism begins to be investigated. But there's Shakespeare... |
| 8021 | The Levellers and the Diggers mark a turning point in the history of morality [MacIntyre] |
| Full Idea: The Levellers and the Diggers mark a turning point in the history of morality. | |
| From: Alasdair MacIntyre (A Short History of Ethics [1967], Ch.11) | |
| A reaction: John Lilburne, the Leveller, 'Free-Born John', was the most important of them. They mainly fought for rights of religious conscience, but it quickly escalated into a demand for economic and social rights. It spread to France and the United States. |
| 10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
| Full Idea: Impredicative Definitions are definitions of an object by reference to the totality to which the object itself (and perhaps also things definable only in terms of that object) belong. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], n 13) |
| 21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
| Full Idea: In the superior realist and simple theory of types, the place of the axiom of reducibility is not taken by the axiom of classes, Zermelo's Aussonderungsaxiom. | |
| From: report of Kurt Gödel (Russell's Mathematical Logic [1944], p.140-1) by Bernard Linsky - Russell's Metaphysical Logic 6.1 n3 | |
| A reaction: This is Zermelo's Axiom of Separation, but that too is not an axiom of standard ZFC. |
| 10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
| Full Idea: 'Mathematical Logic' is a precise and complete formulation of formal logic, and is both a section of mathematics covering classes, relations, symbols etc, and also a science prior to all others, with ideas and principles underlying all sciences. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.447) | |
| A reaction: He cites Leibniz as the ancestor. In this database it is referred to as 'theory of logic', as 'mathematical' seems to be simply misleading. The principles of the subject are standardly applied to mathematical themes. |
| 10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
| Full Idea: One may, on good grounds, deny that reference to a totality necessarily implies reference to all single elements of it or, in other words, that 'all' means the same as an infinite logical conjunction. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.455) |
| 10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
| Full Idea: In order to be sure that new expression can be translated into expressions not containing them, it is necessary to have a survey of all possible expressions, and this can be furnished only by syntactical considerations. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.448) | |
| A reaction: [compressed] |
| 10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
| Full Idea: The generalized Continuum Hypothesis says that there exists no cardinal number between the power of any arbitrary set and the power of the set of its subsets. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.464) |
| 10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
| Full Idea: It has turned out that the solution of certain arithmetical problems requires the use of assumptions essentially transcending arithmetic. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.449) | |
| A reaction: A nice statement of the famous result, from the great man himself, in the plainest possible English. |
| 10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
| Full Idea: Classes and concepts may be conceived of as real objects, ..and are as necessary to obtain a satisfactory system of mathematics as physical bodies are necessary for a satisfactory theory of our sense perceptions, with neither case being about 'data'. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.456) | |
| A reaction: Note that while he thinks real objects are essential for mathematics, be may not be claiming the same thing for our knowledge of logic. If logic contains no objects, then how could mathematics be reduced to it, as in logicism? |
| 10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
| Full Idea: Impredicative definitions are admitted into ordinary mathematics. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.464) | |
| A reaction: The issue is at what point in building an account of the foundations of mathematics (if there be such, see Putnam) these impure definitions should be ruled out. |
| 8006 | When Aristotle speaks of soul he means something like personality [MacIntyre] |
| Full Idea: When Aristotle speaks of the soul we could very often retain his meaning by speaking of personality. | |
| From: Alasdair MacIntyre (A Short History of Ethics [1967], Ch. 7) | |
| A reaction: MacIntyre contrasts this strongly with Plato's dualist view. Famously Aristotle thinks the soul is the 'form' of the body, but this implies that he also includes the higher-level functions of the body. Soul is character? |
| 8002 | Sophists don't distinguish a person outside one social order from someone outside all order [MacIntyre] |
| Full Idea: The sophist tradition failed to distinguish the difference between the concept of a man who stands outside and is able to question the conventions of some one given social order, and the concept of a man who stands outside social life as such. | |
| From: Alasdair MacIntyre (A Short History of Ethics [1967], Ch. 3) | |
| A reaction: A very nice distinction. Compare foreigners in Athens with Diogenes of Sinope, who renounced all cities. This is the germ of MacIntyre's view that morality is essentially dependent on some sort of social order. He is a reviver of virtue theory. |
| 8012 | The value/fact logical gulf is misleading, because social facts involve values [MacIntyre] |
| Full Idea: One reason why it is highly misleading to talk of a logical gulf between value and fact....is that we cannot characterize the social life of a tribe in their factual terms and escape their evaluations. | |
| From: Alasdair MacIntyre (A Short History of Ethics [1967], Ch.10) | |
| A reaction: Personally I like the objection that facts about functions cannot avoid the value of good functions, but this is very good. It is much better than simply trying to find a specific counterexample, such as facts about promises. Values just are facts. |
| 8005 | 'Happiness' is a bad translation of 'eudaimonia', which includes both behaving and faring well [MacIntyre] |
| Full Idea: The name 'eudaimonia' is badly but inevitably translated by 'happiness', badly because it includes both the notion of behaving well and the notion of faring well. | |
| From: Alasdair MacIntyre (A Short History of Ethics [1967], Ch. 7) | |
| A reaction: This seems to imply that it does not include the notion of feeling good. Aristotle, however, concludes that pleasure is part of eudaimonia. I take our 'happiness' to be an internal notion, while the Greek word is an external notion. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 8001 | 'Dikaiosune' is justice, but also fairness and personal integrity [MacIntyre] |
| Full Idea: The Greek 'dikaiosune' is inadequately translated as 'justice', but also as any other word; it combines the notion of fairness in externals with that of personal integrity in a way that no English word does. | |
| From: Alasdair MacIntyre (A Short History of Ethics [1967], Ch. 1) | |
| A reaction: 'Dikaiosune' is said to be the main topic of Plato's 'Republic'. Plato seems to have meant it to cover whatever makes a good character. Justice in behaviour presumably flows from internal justice of character (which is, roughly, inner harmony). |
| 8023 | My duties depend on my identity, which depends on my social relations [MacIntyre] |
| Full Idea: I cannot answer the question 'What ought I to do?' until I have answered the question 'Who am I?', and any answer to this question will specify my place in a nexus of social relationships. | |
| From: Alasdair MacIntyre (A Short History of Ethics [1967], Ch.13) | |
| A reaction: This is the beginning of the modern critique of deontological ethics coming from revived virtue theory. As it stands, MacIntyre's idea sounds contractual, but I think he intends it in a more organic way. I am a fan. |
| 8022 | I am naturally free if I am not tied to anyone by a contract [MacIntyre] |
| Full Idea: The essence of the claim to natural rights is that no one has a right against me unless he can cite some contract, my consent to it, and his performance of his obligations under it. | |
| From: Alasdair MacIntyre (A Short History of Ethics [1967], Ch.11) | |
| A reaction: This has become the foundation of western democracy, and the rebellious teenager's charter. Children have not consented to a contract with their parents. Close and loving relationships cease to be contractual. |
| 8031 | Fans of natural rights or laws can't agree on what the actual rights or laws are [MacIntyre] |
| Full Idea: It is notorious that adherents of theories about natural rights or natural laws offer lists of rights or laws which differ in substance from each other. | |
| From: Alasdair MacIntyre (A Short History of Ethics [1967], Ch.17) | |
| A reaction: There seems to have been a consensus early on that self-defence was a natural right, but divergence presumably occurs when you get bolder and more complex. There is a lot of divergence over which is Shakespeare's best play. |
| 8008 | The Bible is a story about God in which humans are incidental characters [MacIntyre] |
| Full Idea: The Bible is a story about God in which human beings appear as incidental characters. | |
| From: Alasdair MacIntyre (A Short History of Ethics [1967], Ch. 9) | |
| A reaction: Very illuminating. He creates man, is betrayed by man, drowns him and starts again, sends a redeemer who gets murdered, and finally enlightens a small band who continue the uphill struggle to promote God's way. What next? |