13190
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I don't admit infinite numbers, and consider infinitesimals to be useful fictions [Leibniz]
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Full Idea:
Notwithstanding my infinitesimal calculus, I do not admit any real infinite numbers, even though I confess that the multitude of things surpasses any finite number, or rather any number. ..I consider infinitesimal quantities to be useful fictions.
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From:
Gottfried Leibniz (Letters to Samuel Masson [1716], 1716)
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A reaction:
With the phrase 'useful fictions' we seem to have jumped straight into Harty Field. I'm with Leibniz on this one. The history of mathematics is a series of ingenious inventions, whenever they seem to make further exciting proofs possible.
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22454
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We tolerate inconsistency in ethics but not in other beliefs (which reflect an independent order) [Williams,B, by Foot]
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Full Idea:
Williams argued that we can tolerate inconsistency in moral principles though not in assertions, and that this is explained by the fact that it is the concern of the latter but not of the former to reflect an 'independent order of things'.
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From:
report of Bernard Williams (Consistency and realism (with 1972 note) [1966]) by Philippa Foot - Moral Realism and Moral Dilemma p.37
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A reaction:
Put like this, Williams seems to beg the question, which is whether there is an independent moral order to things. There seems to be an easy answer, which is that we are only intolerant of inconsistency when we are confident about it.
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