3 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. |
| 16391 | Indexical thoughts are about themselves, and ascribe properties to themselves [Perry, by Recanati] |
| Full Idea: Perry's newer token-reflexive framework says indexical thoughts have token-reflexive content, that is, thoughts that are about themselves and ascribe properties to themselves. …They relate not to the subject, but to the occurrence of a thought. | |
| From: report of John Perry (Reference and Reflexivity [2001]) by François Recanati - Mental Files 18.1 | |
| A reaction: [There seem to be four indexical theories: this one, Recanati's, the earlier Kaplan-Perry one, and Lewis's] Is Perry thinking of second-level thoughts? 'I'm bored' has the content 'boredom' plus 'felt in here'? How does 'I'm bored' refer to 'I'm bored'? |