15896
|
Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine]
|
|
Full Idea:
Cantor grafted the Power Set axiom onto his theory when he needed it to incorporate the real numbers, ...but his theory was supposed to be theory of collections that can be counted, but he didn't know how to count the new collections.
|
|
From:
report of George Cantor (The Theory of Transfinite Numbers [1897]) by Shaughan Lavine - Understanding the Infinite I
|
|
A reaction:
I take this to refer to the countability of the sets, rather than the members of the sets. Lavine notes that counting was Cantor's key principle, but he now had to abandon it. Zermelo came to the rescue.
|
15877
|
The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré]
|
|
Full Idea:
In Poincaré's view, we try to construct a language within which the brute facts of experience are expressed as comprehensively and as elegantly as possible. The job of science is the forging of a language precisely suited to that purpose.
|
|
From:
report of Henri Poincaré (The Value of Science [1906], Pt III) by Rom Harré - Laws of Nature 2
|
|
A reaction:
I'm often struck by how obscure and difficult our accounts of self-evident facts can be. Chairs are easy, and the metaphysics of chairs is hideous. Why is that? I'm a robust realist, but I like Poincaré's idea. He permits facts.
|