Combining Texts

All the ideas for 'Subjectivist's Guide to Objective Chance', 'Mathematics: Form and Function' and 'Moral Dilemmas Revisited'

unexpand these ideas     |    start again     |     specify just one area for these texts

---

4 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

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).

20. Action / C. Motives for Action / 5. Action Dilemmas / a. Dilemmas

22481	There is no restitution after a dilemma, if it only involved the agent, or just needed an explanation [Foot, by PG]
	Full Idea: The 'remainder' after a dilemma can't be a matter of apology and restitution, because the dilemma may only involve the agent's own life, and in the case of broken promises we only owe an explanation, if the breaking is justifiable.
	From: report of Philippa Foot (Moral Dilemmas Revisited [1995], p.183) by PG - Db (ideas)
	A reaction: But what if someone has been financially ruined by it? If the agent feels guilty about that, is getting over it the rational thing to do? (Foot says that is an new obligation, and not part of the original dilemma).

22482	I can't understand how someone can be necessarily wrong whatever he does [Foot]
	Full Idea: I do not see how …we can know how to interpret the idea of a situation in which someone will necessarily be wrong whatever he does.
	From: Philippa Foot (Moral Dilemmas Revisited [1995], p.188)
	A reaction: Seems right. If you think of hideous dilemmas (frequent in wartime), there must always be a right thing to do (or two equally right things to do), even if the outcome is fairly hideous. Just distinguish the right from the good.

26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory

9425	Lewis later proposed the axioms at the intersection of the best theories (which may be few) [Mumford on Lewis]
	Full Idea: Later Lewis said we must choose between the intersection of the axioms of the tied best systems. He chose for laws the axioms that are in all the tied systems (but then there may be few or no axioms in the intersection).
	From: comment on David Lewis (Subjectivist's Guide to Objective Chance [1980], p.124) by Stephen Mumford - Laws in Nature