Combining Texts

All the ideas for 'fragments/reports', 'Truth and Probability' and 'Mathematics: Form and Function'

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6 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
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).
10. Modality / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals
'If' is the same as 'given that', so the degrees of belief should conform to probability theory [Ramsey, by Ramsey]
     Full Idea: Ramsey suggested that 'if', 'given that' and 'on the supposition that' come to the same thing, and that the degrees of belief in the antecedent should then conform to probability theory.
     From: report of Frank P. Ramsey (Truth and Probability [1926]) by Frank P. Ramsey - Law and Causality B
     A reaction: [compressed]
14. Science / C. Induction / 6. Bayes's Theorem
Ramsey gave axioms for an uncertain agent to decide their preferences [Ramsey, by Davidson]
     Full Idea: Ramsey gave an axiomatic treatment of preference in the face of uncertainty, when applied to a particular agent.
     From: report of Frank P. Ramsey (Truth and Probability [1926]) by Donald Davidson - Truth and Predication 2
     A reaction: This is evidently the beginnings of Bayesian decision theory.
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / k. Ethics from nature
The goal is rationality in the selection of things according to nature [Diogenes of Babylon, by Blank]
     Full Idea: Diogenes of Babylon defined the goal to be rationality in the selection and rejection of the things according to nature.
     From: report of Diogenes (Bab) (fragments/reports [c.180 BCE]) by D.L. Blank - Diogenes of Babylon
     A reaction: This captures the central Stoic idea quite nicely. 'Live according to nature', but this always meant 'live according to reason', because that is (as Aristotle had taught) the essence of our nature. This only makes sense if reason and nature coincide.
22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good
The good is what is perfect by nature [Diogenes of Babylon, by Blank]
     Full Idea: Diogenes of Babylon defined the good as what is perfect by nature.
     From: report of Diogenes (Bab) (fragments/reports [c.180 BCE]) by D.L. Blank - Diogenes of Babylon
     A reaction: This might come close to G.E. Moore's Ideal Utilitarianism, but its dependence on the rather uneasy of concept of 'perfection' makes it questionable. Personally I find it appealing. I wish we had Diogenes' explanation.
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
Justice is a disposition to distribute according to desert [Diogenes of Babylon, by Blank]
     Full Idea: Diogenes of Babylon defined justice as the disposition which distributes to everyone what he deserves.
     From: report of Diogenes (Bab) (fragments/reports [c.180 BCE]) by D.L. Blank - Diogenes of Babylon
     A reaction: The questions that arise would be 'what does a new-born baby deserve?', and 'what do animals deserve?', and 'does the lowest and worst of criminals deserve anything at all?'