18084
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When successive variable values approach a fixed value, that is its 'limit' [Cauchy]
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Full Idea:
When the values successively attributed to the same variable approach indefinitely a fixed value, eventually differing from it by as little as one could wish, that fixed value is called the 'limit' of all the others.
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From:
Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4
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A reaction:
This seems to be a highly significan proposal, because you can now treat that limit as a number, and adds things to it. It opens the door to Cantor's infinities. Is the 'limit' just a fiction?
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14381
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A statue is essentially the statue, but its lump is not essentially a statue, so statue isn't lump [Yablo, by Rocca]
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Full Idea:
Yablo proposes the argument that Statue A is essentially a statue, and Lump 1 is not essentially a statue, so Statue A is not identical with Lump 1.
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From:
report of Stephen Yablo (Identity, Essence and Indiscernibility [1987]) by Michael della Rocca - Essentialists and Essentialism I
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A reaction:
Della Rocca and Yablo unashamedly elide necessary properties with essential properties, so this argument doesn't bother me too much. It concerns the statue and the clay having different modal properties.
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