display all the ideas for this combination of texts
3 ideas
| 7038 | A theory with few fundamental principles might still posit a lot of entities [Heil] |
| Full Idea: It could well turn out that a simpler theory - a theory with fewer fundamental principles - posits more entities than a more complex competitor. | |
| From: John Heil (From an Ontological Point of View [2003], 13.6) | |
| A reaction: See also Idea 4036. The point here is that you can't simply translate Ockham as 'keep it simple', as there are different types of simplicity. The best theory will negotiate a balance between entities and principles. |
| 7037 | Parsimony does not imply the world is simple, but that our theories should try to be [Heil] |
| Full Idea: A commitment to parsimony is not a commitment to a conception of the world as simple. The idea, rather, is that we should not complicate our theories about the world unnecessarily. | |
| From: John Heil (From an Ontological Point of View [2003], 13.6) | |
| A reaction: In other words, Ockham's Razor is about us, not about the world. It would be absurd to make the a priori assumption that the world has to be simple. Are we, though, creating bad theories by insisting that they should be simple? |
| 10476 | The idea that groups of concepts could be 'implicitly defined' was abandoned [Hodges,W] |
| Full Idea: Late nineteenth century mathematicians said that, although plus, minus and 0 could not be precisely defined, they could be partially 'implicitly defined' as a group. This nonsense was rejected by Frege and others, as expressed in Russell 1903. | |
| From: Wilfrid Hodges (Model Theory [2005], 2) | |
| A reaction: [compressed] This is helpful in understanding what is going on in Frege's 'Grundlagen'. I won't challenge Hodges's claim that such definitions are nonsense, but there is a case for understanding groups of concepts together. |