5 ideas
18086 | Weierstrass eliminated talk of infinitesimals [Weierstrass, by Kitcher] |
Full Idea: Weierstrass effectively eliminated the infinitesimalist language of his predecessors. | |
From: report of Karl Weierstrass (works [1855]) by Philip Kitcher - The Nature of Mathematical Knowledge 10.6 |
18092 | Weierstrass made limits central, but the existence of limits still needed to be proved [Weierstrass, by Bostock] |
Full Idea: After Weierstrass had stressed the importance of limits, one now needed to be able to prove the existence of such limits. | |
From: report of Karl Weierstrass (works [1855]) by David Bostock - Philosophy of Mathematics 4.4 | |
A reaction: The solution to this is found in work on series (going back to Cauchy), and on Dedekind's cuts. |
7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
22817 | Citizenship involves a group of mutually supporting rights, which create community and equality [Miller,D] |
Full Idea: The idea of citizenship is that rights support each other. Protective and welfare rights provide a basis for a political role. This underpins a sense of membership, and an obligation to provide welfare. Rights confer equal status and self-respect. | |
From: David Miller (Community and Citizenship [1989], 3) | |
A reaction: A helpful eludation of what a richer concept of citizenship than mere membership might look like. Communitarians have a different concept of rights from that of liberals. |
22816 | Socialists reject nationality as a false source of identity [Miller,D] |
Full Idea: The socialist tradition has been overwhelmingly hostile to nationality as a source of identity, usually regarding it merely as an artificially created impediment to the brotherhood of man. | |
From: David Miller (Community and Citizenship [1989], 2) | |
A reaction: I have some sympathy with this, especially when nationalism is expressed in terms of enemies, but the question of what community a person can plausibly identify with is difficult. We start in hunter gather tribes of several hundred. |