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18244
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I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind]
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Full Idea:
Of my theory of irrationals you say that the irrational number is nothing else than the cut itself, whereas I prefer to create something new (different from the cut), which corresponds to the cut. We have the right to claim such a creative power.
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From:
Richard Dedekind (Letter to Weber [1888], 1888 Jan), quoted by Stewart Shapiro - Philosophy of Mathematics 5.4
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A reaction:
Clearly a cut will not locate a unique irrational number, so something more needs to be done. Shapiro remarks here that for Dedekind numbers are objects.
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24008
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Reference to a person's emotions is often essential to understanding their actions [Williams,B]
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Full Idea:
The reference to a man's emotions has a significance for our understanding of his moral sincerity, not as a substitute for or addition to how he acts, but as, on occasion, underlying our understanding of how he acts.
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From:
Bernard Williams (Morality and the emotions [1965], p.223)
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A reaction:
Williams aims to rescue emotion from the emotivists, and replace it at the centre of traditional modes of moral judgement. I suppose we could assess one rogue robot as behaving 'badly' in a community of robots.
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24009
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Moral education must involve learning about various types of feeling towards things [Williams,B]
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Full Idea:
If moral education does not revolve around what to fear, to be angry about, to despise, and where to draw the line between kindness and a stupid sentimentality - I do not know what it is. (Though there are principles, of truth-telling and justice).
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From:
Bernard Williams (Morality and the emotions [1965], p.225)
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A reaction:
He cites Aristotle as the obvious source of this correct idea. The examples of principle both require us to place a high value on truth and justice, and not just follow rules in the style of arithmetic.
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24012
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Kant's love of consistency is too rigid, and it even overrides normal fairness [Williams,B]
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Full Idea:
There is a certain moral woodenness or even insolence in Kant's blank regard for consistency. It smacks of Keynes's Principle of Unfairness - that if you can't do a good turn to everybody, you shouldn't do it to anybody.
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From:
Bernard Williams (Morality and the emotions [1965], p.226)
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A reaction:
He says it also turns each of us into a Supreme Legislator, which deifies man. It is clearly not the case that morality consists entirely of rules and principles, but Williams recognises their role, in truth-telling for example.
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