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13412
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Obtaining numbers by abstraction is impossible - there are too many; only a rule could give them, in order [Benacerraf]
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Full Idea:
Not all numbers could possibly have been learned à la Frege-Russell, because we could not have performed that many distinct acts of abstraction. Somewhere along the line a rule had to come in to enable us to obtain more numbers, in the natural order.
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From:
Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.165)
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A reaction:
Follows on from Idea 13411. I'm not sure how Russell would deal with this, though I am sure his account cannot be swept aside this easily. Nevertheless this seems powerful and convincing, approaching the problem through the epistemology.
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13413
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We must explain how we know so many numbers, and recognise ones we haven't met before [Benacerraf]
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Full Idea:
Both ordinalists and cardinalists, to account for our number words, have to account for the fact that we know so many of them, and that we can 'recognize' numbers which we've neither seen nor heard.
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From:
Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.166)
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A reaction:
This seems an important contraint on any attempt to explain numbers. Benacerraf is an incipient structuralist, and here presses the importance of rules in our grasp of number. Faced with 42,578,645, we perform an act of deconstruction to grasp it.
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13411
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If numbers are basically the cardinals (Frege-Russell view) you could know some numbers in isolation [Benacerraf]
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Full Idea:
If we accept the Frege-Russell analysis of number (the natural numbers are the cardinals) as basic and correct, one thing which seems to follow is that one could know, say, three, seventeen, and eight, but no other numbers.
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From:
Paul Benacerraf (Logicism, Some Considerations (PhD) [1960], p.164)
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A reaction:
It seems possible that someone might only know those numbers, as the patterns of members of three neighbouring families (the only place where they apply number). That said, this is good support for the priority of ordinals. See Idea 13412.
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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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