Combining Texts

All the ideas for 'works', 'The Methods of Ethics (7th edn)' and 'The Value of Knowledge and the Pursuit of Understanding'

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9 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 / 2. Understanding
19261 Understanding is seeing coherent relationships in the relevant information [Kvanvig]
     Full Idea: What is distinctive about understanding (after truth is satisfied) is the internal seeing or appreciating of explanatory and other coherence-inducing relationships in a body of information that is crucial for understanding.
     From: Jonathan Kvanvig (The Value of Knowledge and the Pursuit of Understanding [2003], 198), quoted by Anand Vaidya - Understanding and Essence 'Distinction'
     A reaction: For me this ticks exactly the right boxes. Coherent explanations are what we want. The hardest part is the ensure their truth. Kvanvig claims this is internal, so we can understand even if, Gettier-style, our external connections are lucky.
16. Persons / F. Free Will / 2. Sources of Free Will
23111 If we say that freedom depends on rationality, the irrational actions are not free [Sidgwick]
     Full Idea: If we say that a man is a free agent in proportion as he acts rationally, we cannot also say that it is by free choice that he acts irrationally.
     From: Henry Sidgwick (The Methods of Ethics (7th edn) [1874], p.511), quoted by John Kekes - Against Liberalism 7.4
     A reaction: A very nice riposte. Clearly people can rationally choose to act irrationally, e.g. at a wild party.
23. Ethics / A. Egoism / 1. Ethical Egoism
23059 Self-interest is not rational, if the self is just a succession of memories and behaviour [Sidgwick, by Gray]
     Full Idea: Sidgwick said self-interest is not self-evidently rational. Unless we invoke a religious idea of the soul, human personality is no more than a succession of continuities in memory and behaviour. In that case, why should anyone favour their future self?
     From: report of Henry Sidgwick (The Methods of Ethics (7th edn) [1874]) by John Gray - Seven Types of Atheism 2
     A reaction: This sounds like Locke's account of the self, as psychological continuity. We can say that our continuous self is a fiction, the hero of our own narrative. Personally I think of the self as a sustained set of brains structures which change very little.
23. Ethics / E. Utilitarianism / 1. Utilitarianism
4129 It is self-evident (from the point of view of the Universe) that no individual has more importance than another [Sidgwick]
     Full Idea: It is a self-evident principle that the good of one individual is of no more importance, from the point of view of the Universe, than the good of any other, ..and as a rational being I am bound to aim at good generally, not merely at a particular part.
     From: Henry Sidgwick (The Methods of Ethics (7th edn) [1874], III.XIII.3)
     A reaction: Showing that even a very empirical theory like utilitarianism has an a priori basis. Of course, the principle is false. What about animals, the senile, criminals, androids? What bestows 'importance'?
24. Political Theory / D. Ideologies / 4. Social Utilitarianism
20588 Sidwick argues for utilitarian institutions, rather than actions [Sidgwick, by Tuckness/Wolf]
     Full Idea: Sidgwick's complex version of utilitarianism urges that institutions should be set in place to maximise utility, but that individual actions people undertake might not appear to be justifiable on utilitarian terms.
     From: report of Henry Sidgwick (The Methods of Ethics (7th edn) [1874]) by Tuckness,A/Wolf,C - This is Political Philosophy 1 Refs
     A reaction: This seems to be a specifically political version of utilitarianism, but isn't cited much by political philosophers who discuss utilitarianism.