Combining Texts

All the ideas for 'Ethical Studies', 'Mathematics: Form and Function' and 'Second Commentary on 'Isagoge''

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3 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).

8. Modes of Existence / D. Universals / 5. Universals as Concepts

15035	If universals are not separate, we can isolate them by abstraction [Boethius, by Panaccio]
	Full Idea: Boethius argued that universals can be successfully isolated by abstraction, even if they do not exist as separate entities in the world.
	From: report of Boethius (Second Commentary on 'Isagoge' [c.517]) by Claude Panaccio - Medieval Problem of Universals 'Sources'
	A reaction: Personally I rather like this unfashionable view. I can't think of any other plausible explanation, unless it is a less conscious psychological process of labelling. Boethius's idea led to medieval 'immanent realism'.

22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness

5655	Happiness is not satisfaction of desires, but fulfilment of values [Bradley, by Scruton]
	Full Idea: For Bradley, the happiness of the individual is not to be understood in terms of his desires and needs, but rather in terms of his values - which is to say, in terms of those of his desires which he incorporates into his self.
	From: report of F.H. Bradley (Ethical Studies [1876]) by Roger Scruton - Short History of Modern Philosophy Ch.16
	A reaction: Good. Bentham will reduce the values to a further set of desires, so that a value is a complex (second-level?) desire. I prefer to think of values as judgements, but I like Scruton's phrase of 'incorporating into his self'. Kant take note (Idea 1452).