13 ideas
| 17879 | Axiomatising set theory makes it all relative [Skolem] |
| Full Idea: Axiomatising set theory leads to a relativity of set-theoretic notions, and this relativity is inseparably bound up with every thoroughgoing axiomatisation. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.296) |
| 17878 | If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem] |
| Full Idea: Löwenheim's theorem reads as follows: If a first-order proposition is satisfied in any domain at all, it is already satisfied in a denumerably infinite domain. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.293) |
| 17880 | Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem] |
| Full Idea: The initial foundations should be immediately clear, natural and not open to question. This is satisfied by the notion of integer and by inductive inference, by it is not satisfied by the axioms of Zermelo, or anything else of that kind. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.299) | |
| A reaction: This is a plea (endorsed by Almog) that the integers themselves should be taken as primitive and foundational. I would say that the idea of successor is more primitive than the integers. |
| 17881 | Mathematician want performable operations, not propositions about objects [Skolem] |
| Full Idea: Most mathematicians want mathematics to deal, ultimately, with performable computing operations, and not to consist of formal propositions about objects called this or that. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.300) |
| 3546 | 'Phronesis' should translate as 'practical intelligence', not as prudence [Annas] |
| Full Idea: The best translation of 'phronesis' is probably not 'prudence' (which implies a non-moral motive), or 'practical wisdom' (which makes it sound contemplative), but 'practical intelligence', or just 'intelligence'. | |
| From: Julia Annas (The Morality of Happiness [1993], 2.3) |
| 3547 | Epicureans achieve pleasure through character development [Annas] |
| Full Idea: Since having a virtue does not reduce to performing certain kinds of acts, the Epicurean will achieve pleasure only by aiming at being a certain kind of person. | |
| From: Julia Annas (The Morality of Happiness [1993], 2.4) | |
| A reaction: No Epicurean would want to merely possess virtues, without enacting them. I assume that virtues are sought as guides to finding the finest pleasures (such as friendship). |
| 3543 | Cyrenaics pursue pleasure, but don't equate it with happiness [Annas] |
| Full Idea: Cyrenaics claimed our final good was pleasure, best achieved by seeking maximum intensity of pleasurable experiences, but they explicitly admitted that this was not happiness. | |
| From: Julia Annas (The Morality of Happiness [1993], 1) |
| 3541 | Ancient ethics uses attractive notions, not imperatives [Annas] |
| Full Idea: Instead of modern 'imperative' notions of ethics (involving obligation, duty and rule-following), ancient ethics uses 'attractive' notions like those of goodness and worth | |
| From: Julia Annas (The Morality of Happiness [1993], Intro) |
| 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'). |
| 3550 | Principles cover life as a whole, where rules just cover actions [Annas] |
| Full Idea: Principles concern not just types of actions, but one's life as a whole, grasping truths about the nature of justice, and the like; they explain rules, giving the 'why' and not just the 'what'. | |
| From: Julia Annas (The Morality of Happiness [1993], 2.4) |
| 3551 | Virtue theory tries to explain our duties in terms of our character [Annas] |
| Full Idea: An ethics of virtue moves from an initial interest in what we ought to do to an interest in the kinds of people we are and hope to be, because the latter is taken to be the best way of understanding the former. | |
| From: Julia Annas (The Morality of Happiness [1993], 2.5) |
| 3552 | If excessively good actions are admirable but not required, then duty isn't basic [Annas] |
| Full Idea: Supererogatory actions are admirable and valuable, and we praise people for doing them, but they do not generate obligations to perform them, which casts doubt on obligation as the basic notion in ethics. | |
| From: Julia Annas (The Morality of Happiness [1993], 2.6) |
| 3542 | We should do good when necessary, not maximise it [Annas] |
| Full Idea: Why should I want to maximise my acting courageously? I act courageously when it is required. | |
| From: Julia Annas (The Morality of Happiness [1993], 1) |