|
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.
|
|
14629
|
If we are told the source of necessity, this seems to be a regress if the source is not already necessary [Blackburn]
|
|
Full Idea:
If we ask why A must be the case, and A is then proved from B, that explains it if B must be so. If the eventual source cites some truth F, then if F just is so, there is strong pressure to feel that the original necessity has not been explained.
|
|
From:
Simon Blackburn (Morals and Modals [1987], 1)
|
|
A reaction:
[compressed] Ross Cameron wrote a reply to this which I like. I'm fishing for the idea that essence is the source of necessity (as Kit Fine says), but that essence itself is not necessary (as only I say, apparently!).
|
|
14529
|
If something underlies a necessity, is that underlying thing necessary or contingent? [Blackburn, by Hale/Hoffmann,A]
|
|
Full Idea:
Blackburn asks of what theorists propose as underlying the necessity of a proposition, the question whether they themselves are conceived as obtaining of necessity or merely contingently.
|
|
From:
report of Simon Blackburn (Morals and Modals [1987], p.120-1) by Bob Hale/ Aviv Hoffmann - Introduction to 'Modality' 1
|
|
A reaction:
I've seen a reply to this somewhere: I think the thought was that a necessity wouldn't be any less necessary if it had a contingent source, any more than the father of a world champion boxer has to be a world champion boxer.
|