9 ideas
| 10882 | Predicative definitions only refer to entities outside the defined collection [Horsten] |
| Full Idea: Definitions are called 'predicative', and are considered sound, if they only refer to entities which exist independently from the defined collection. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §2.4) |
| 10884 | A theory is 'categorical' if it has just one model up to isomorphism [Horsten] |
| Full Idea: If a theory has, up to isomorphism, exactly one model, then it is said to be 'categorical'. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §5.2) |
| 10885 | Computer proofs don't provide explanations [Horsten] |
| Full Idea: Mathematicians are uncomfortable with computerised proofs because a 'good' proof should do more than convince us that a certain statement is true. It should also explain why the statement in question holds. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §5.3) |
| 10881 | The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten] |
| Full Idea: The notion of an ordinal number is a set-theoretic, and hence non-arithmetical, concept. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §2.3) |
| 22692 | A work can be morally and artistically excellent, despite rejecting moral truth [John,E] |
| Full Idea: A work that rejects moral truth can be artistically excellent, in part because of its moral content. | |
| From: Eileen John (Artistic Value and Opportunistic Moralism [2006], Intr) | |
| A reaction: She cites the film 'Trainspotting', about desperate drug addicts, because it gives an amoral insight into their world. |
| 22693 | The works we value most are in sympathy with our own moral views [John,E] |
| Full Idea: The works we tend to value most highly are ones that are in sympathy with the moral views we actually accept. | |
| From: Eileen John (Artistic Value and Opportunistic Moralism [2006], Intro) | |
| A reaction: I would have to endorse this. She admits that we may rate other works very highly, but they won't appear on our list of favourites. This fact may well distort philosophical discussions of morality and art. |
| 22694 | We should understand what is morally important in a story, without having to endorse it [John,E] |
| Full Idea: Our responses to literature should show that we grasp whatever counts as morally important within the narrative, but not necessarily that we judge and feel in the way deemed appropriate by the work. | |
| From: Eileen John (Artistic Value and Opportunistic Moralism [2006], 'Accommodating') | |
| A reaction: She gives as an example a story by Hemingway which places a high value on the courageous hunting of big game. A second example is the total amorality of a Highsmith novel. This idea seems exactly right to me. |
| 22695 | We value morality in art because that is what we care about - but it is a contingent fact [John,E] |
| Full Idea: Moral value is valuable in art because people care about moral value. This runs deep, but it is a contingent matter, and the value of morality in art hinges on art's need to provide something precious to us. | |
| From: Eileen John (Artistic Value and Opportunistic Moralism [2006], 'Contingency') | |
| A reaction: I think this is exactly right. Thrillers are written with very little moral concern, for a readership which cares about brave and exciting deeds. Even there, violence has its ethics. |
| 5467 | Euler said nature is instrinsically passive, and minds cause change [Euler, by Ellis] |
| Full Idea: Euler thought the powers necessary for the maintenance of the changing universe would turn out to be just the passive ones of inertia and impenetrability. There are no active powers, he urged, other than those of God and living beings. | |
| From: report of Leonhard Euler (Letters to a German Princess [1765]) by Brian Ellis - The Philosophy of Nature: new essentialism Ch.4 | |
| A reaction: Very significant, I think, for revealing the religious framework behind early theories of natural laws. If there is nothing external to impose powers and movements on nature, the source must be sought within - hence essentialism. |