display all the ideas for this combination of philosophers
2 ideas
| 17312 | It is more explanatory if you show how a number is constructed from basic entities and relations [Koslicki] |
| Full Idea: Being the successor of the successor of 0 is more explanatory than being predecessor of 3 of the nature of 2, since it mirrors more closely the method by which 2 is constructed from a basic entity, 0, and a relation (successor) taken as primitive. | |
| From: Kathrin Koslicki (Varieties of Ontological Dependence [2012], 7.4) | |
| A reaction: This assumes numbers are 'constructed', which they are in the axiomatised system of Peano Arithmetic, but presumably the numbers were given in ordinary experience before 'construction' occurred to anyone. Nevertheless, I really like this. |
| 14505 | Some questions concern mathematical entities, rather than whole structures [Koslicki] |
| Full Idea: Those who hold that not all mathematical questions can be concerned with structural matters can point to 'why are π or e transcendental?' or 'how are the prime numbers distributed?' as questions about particular features in the domain. | |
| From: Kathrin Koslicki (The Structure of Objects [2008], 9.3.1 n6) | |
| A reaction: [She cites Mac Lane on this] The reply would have to be that we only have those particular notions because we have abstracted them from structures, as in deriving π for circles. |