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All the ideas for 'Philosophical Explanations', 'Prcis of 'Ruling Passions'' and 'works'

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7 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics
8717 Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend]
     Full Idea: Hilbert wanted to derive ideal mathematics from the secure, paradox-free, finite mathematics (known as 'Hilbert's Programme'). ...Note that for the realist consistency is not something we need to prove; it is a precondition of thought.
     From: report of David Hilbert (works [1900], 6.7) by Michčle Friend - Introducing the Philosophy of Mathematics
     A reaction: I am an intuitive realist, though I am not so sure about that on cautious reflection. Compare the claims that there are reasons or causes for everything. Reality cannot contain contradicitions (can it?). Contradictions would be our fault.
6. Mathematics / C. Sources of Mathematics / 7. Formalism
10113 The grounding of mathematics is 'in the beginning was the sign' [Hilbert]
     Full Idea: The solid philosophical attitude that I think is required for the grounding of pure mathematics is this: In the beginning was the sign.
     From: David Hilbert (works [1900]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6
     A reaction: Why did people invent those particular signs? Presumably they were meant to designate something, in the world or in our experience.
10115 Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman]
     Full Idea: Hilbert replaced a semantic construal of inconsistency (that the theory entails a statement that is necessarily false) by a syntactic one (that the theory formally derives the statement (0 =1 ∧ 0 not-= 1).
     From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6
     A reaction: Finding one particular clash will pinpoint the notion of inconsistency, but it doesn't seem to define what it means, since the concept has very wide application.
6. Mathematics / C. Sources of Mathematics / 8. Finitism
10116 Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman]
     Full Idea: Hilbert's project was to establish the consistency of classical mathematics using just finitary means, to convince all parties that no contradictions will follow from employing the infinitary notions and reasoning.
     From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6
     A reaction: This is the project which was badly torpedoed by Gödel's Second Incompleteness Theorem.
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
3570 Maybe knowledge is belief which 'tracks' the truth [Nozick, by Williams,M]
     Full Idea: Nozick suggests that knowledge is just belief which 'tracks the truth' (hence leaving out justification).
     From: report of Robert Nozick (Philosophical Explanations [1981]) by Michael Williams - Problems of Knowledge Ch. 2
13. Knowledge Criteria / C. External Justification / 4. Tracking the Facts
2748 A true belief isn't knowledge if it would be believed even if false. It should 'track the truth' [Nozick, by Dancy,J]
     Full Idea: Nozick says Gettier cases aren't knowledge because the proposition would be believed even if false. Proper justification must be more sensitive to the truth ("track the truth").
     From: report of Robert Nozick (Philosophical Explanations [1981], 3.1) by Jonathan Dancy - Intro to Contemporary Epistemology 3.1
     A reaction: This is a bad idea. I see a genuine tree in my garden and believe it is there, so I know it. That I might have believed it if I was in virtually reality, or observing a mirror, won't alter that.
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
11911 Some philosophers always want more from morality; for others, nature is enough [Blackburn]
     Full Idea: The history of moral theory is largely a history of battles between people who want more (truth, absolutes...) - Plato, Locke, Cudworth, Kant, Nagel - and people content with what we have (nature) - Aristotle, Epicurus, Hobbes, Hume, Stevenson.
     From: Simon Blackburn (Précis of 'Ruling Passions' [2002], p.133)
     A reaction: [Thanks to Neil Sinclair for this one] As a devotee of Aristotle, I like this. I'm always impressed, though, by people who go the extra mile in morality, because they are in the grips of purer and loftier ideals than I am. They also turn into monsters!