3 ideas
| 18189 | ZFC could contain a contradiction, and it can never prove its own consistency [MacLane] |
| Full Idea: We have at hand no proof that the axioms of ZFC for set theory will never yield a contradiction, while Gödel's second theorem tells us that such a consistency proof cannot be conducted within ZFC. | |
| From: Saunders MacLane (Mathematics: Form and Function [1986], p.406), quoted by Penelope Maddy - Naturalism in Mathematics | |
| A reaction: Maddy quotes this, while defending set theory as the foundation of mathematics, but it clearly isn't the most secure foundation that could be devised. She says the benefits of set theory do not need guaranteed consistency (p.30). |
| 22457 | If the aim is good outcomes, why are killings worse than deaths? [Scheffler, by Foot] |
| Full Idea: It is not clear why, in the measurement of the goodness of states of affairs or total outcomes, killings for instance should count so much more heavily than deaths. | |
| From: report of Samuel Scheffler (The Rejection of Consequentialism [1982], pp.108-12) by Philippa Foot - Utilitarianism and the Virtues p.61 | |
| A reaction: Or drunken drivers worse than careless drivers. Or stolen bracelets than lost bracelets. The point is that morality is about the behaviour of people, and not about consequences. |
| 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. |