5 ideas
| 8921 | Structuralism is now common, studying relations, with no regard for what the objects might be [Hellman] |
| Full Idea: With developments in modern mathematics, structuralist ideas have become commonplace. We study 'abstract structures', having relations without regard to the objects. As Hilbert famously said, items of furniture would do. | |
| From: Geoffrey Hellman (Structuralism [2007], §1) | |
| A reaction: Hilbert is known as a Formalist, which suggests that modern Structuralism is a refined and more naturalist version of the rather austere formalist view. Presumably the sofa can't stand for six, so a structural definition of numbers is needed. |
| 8922 | Maybe mathematical objects only have structural roles, and no intrinsic nature [Hellman] |
| Full Idea: There is the tantalizing possibility that perhaps mathematical objects 'have no nature' at all, beyond their 'structural role'. | |
| From: Geoffrey Hellman (Structuralism [2007], §1) | |
| A reaction: This would fit with a number being a function rather than an object. We are interested in what cars do, not the bolts that hold them together? But the ontology of mathematics is quite separate from how you do mathematics. |
| 17093 | Causation produces productive mechanisms; to understand the world, understand these mechanisms [Salmon] |
| Full Idea: Causal processes, causal interactions, and causal laws provide the mechanisms by which the world works; to understand why certain things happen, we need to see how they are produced by these mechanisms. | |
| From: Wesley Salmon (Scientific Explanation and the Causal Structure of the World [1984]), quoted by David-Hillel Ruben - Explaining Explanation Ch 7 | |
| A reaction: I don't think I've ever found a better quotation on explanation. That strikes me as correct, and (basically) there is nothing more to be said. I'm not sure about the 'laws'. This is later Wesley Salmon. |
| 17492 | Salmon's interaction mechanisms needn't be regular, or involving any systems [Glennan on Salmon] |
| Full Idea: While Salmon's mechanisms are processes involving interactions, the interactions are not necessarily regular, and they do not involve the operation of systems. | |
| From: comment on Wesley Salmon (Scientific Explanation and the Causal Structure of the World [1984]) by Stuart Glennan - Mechanisms 'hierarchical' | |
| A reaction: This is why modern mechanistic philosophy only began in 2000, despite Wesley Salmon's championing of the roughly mechanistic approach. |
| 8409 | Probabilistic causal concepts are widely used in everyday life and in science [Salmon] |
| Full Idea: Probabilistic causal concepts are used in innumerable contexts of everyday life and science. ...In causes of cancer, road accidents, or food poisoning, for example. | |
| From: Wesley Salmon (Probabilistic Causality [1980], p.137) | |
| A reaction: [Second half compresses his examples] This strikes me as rather a weak point. No one ever thought that a particular road accident was actually caused by the high probability of it at a particular location. Causes are in the mechanisms. |