display all the ideas for this combination of philosophers
2 ideas
| 9919 | The old debate classified representations as abstract, not entities [Burgess/Rosen] |
| Full Idea: The original debate was over abstract ideas; thus it was mental (or linguistic) representations that were classified as abstract or otherwise, and not the entities represented. | |
| From: JP Burgess / G Rosen (A Subject with No Object [1997], I.A.1.b) | |
| A reaction: This seems to beg the question of whether there are any such entities. It is equally plausible to talk of the entities that are 'constructed', rather than 'represented'. |
| 9141 | Abstraction theories build mathematics out of second-order equivalence principles [Cook/Ebert] |
| Full Idea: A theory of abstraction is any account that reconstructs mathematical theories using second-order abstraction principles of the form: §xFx = §xGx iff E(F,G). We ignore first-order abstraction principles such as Frege's direction abstraction. | |
| From: R Cook / P Ebert (Notice of Fine's 'Limits of Abstraction' [2004], 1) | |
| A reaction: Presumably part of the neo-logicist programme, which also uses such principles. The function § (extension operator) 'provides objects corresponding to the argument concepts'. The aim is to build mathematics, rather than the concept of a 'rabbit'. |