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. |
| 16980 | We need a logical use of 'object' as predicate-worthy, and an 'ontological' use [Strawson,P] |
| Full Idea: There is a good case for a conservative reform of the word 'object'. Objects in the 'logical' sense would be all predicate-worthy identifiabilia whatever. Objects in the 'ontological' sense would form one ontological category among many others. | |
| From: Peter F. Strawson (Entity and Identity [1978], I n4) | |
| A reaction: This ambiguity has caused me no end of confusion (and irritation!). I wish philosophers wouldn't hijack perfectly good English words and give them weird meanings. Nice to have a distinguished fellow like Strawson make this suggestion. |
| 16979 | It makes no sense to ask of some individual thing what it is that makes it that individual [Strawson,P] |
| Full Idea: For no object is there a unique character or relation by which it must be identified if it is to be identified at all. This is why it makes no sense to ask, impersonally and in general, of some individual object what makes it the individual object it is. | |
| From: Peter F. Strawson (Entity and Identity [1978], I) | |
| A reaction: He links this remark with the claim that there is no individual essence, but he seems to view an individual essence as indispensable to recognition or individuation of the object, which I don't see. Recognise it first, work out its essence later. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |