6 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. |
| 3912 | I must exist in order to be mistaken, so that even if I am mistaken, I can't be wrong about my own existence [Augustine] |
| Full Idea: Since therefore I must exist in order to be mistaken, then even if I am mistaken, there can be no doubt that I am not mistaken in my knowledge that I exist…. I know that I exist, and I also know that I know. | |
| From: Augustine (City of God [c.427], Ch.XI.26) | |
| A reaction: Fine, but the main problem is his over-confidence about a stable personal identity that does the thinking. |
| 6683 | The contact of spirit and body is utterly amazing, and incomprehensible [Augustine] |
| Full Idea: The manner of contact of spirit with body, which produces a living being, is utterly amazing and beyond our powers of comprehension | |
| From: Augustine (City of God [c.427], XXI.10) | |
| A reaction: This leads to a rather clear objection against a theory which needs a miracle to explain a common natural phenomenon. At least Augustine was beginning to recognise that interaction is a bit of a problem. |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| Full Idea: Philosophers are the forefathers of heretics. | |
| From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2 |
| 6610 | I believe because it is absurd [Tertullian] |
| Full Idea: I believe because it is absurd ('Credo quia absurdum est'). | |
| From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2 | |
| A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though. |