3 ideas
| 9141 | Abstraction theories build mathematics out of second-order equivalence principles [Cook/Ebert] |
| Full Idea: A theory of abstraction is any account that reconstructs mathematical theories using second-order abstraction principles of the form: §xFx = §xGx iff E(F,G). We ignore first-order abstraction principles such as Frege's direction abstraction. | |
| From: R Cook / P Ebert (Notice of Fine's 'Limits of Abstraction' [2004], 1) | |
| A reaction: Presumably part of the neo-logicist programme, which also uses such principles. The function § (extension operator) 'provides objects corresponding to the argument concepts'. The aim is to build mathematics, rather than the concept of a 'rabbit'. |
| 20486 | Only liberty, equality and sympathy can stand up to anti-social people [Kropotkin] |
| Full Idea: Liberty, equality and practical human sympathy are the only effective barriers we can oppose to the anti-social instincts of certain among us. | |
| From: Peter (Pyotr) Kropotkin (Law and Authority [1886], 1 'Anarchism'), quoted by Jonathan Wolff - An Introduction to Political Philosophy (Rev) | |
| A reaction: One might state it more succinctly as 'only the social can oppose the anti-social'. The dominance in society of essentially anti-social people seems to have become a major political fact in 2017, in the UK and the USA. |
| 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. |