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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5492
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How can essences generate the right powers to vary with distance between objects? [Armstrong]
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Full Idea:
In Newtonian physics the distance between two objects determines the attractive forces between them, but then the objects will have to be sensitive to the distance, in order to 'know' what forces to generate; but distance isn't a causal power.
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From:
David M. Armstrong (Two Problems for Essentialism [2001], p.170)
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A reaction:
Ellis replies that he is not troubled, because he believes in essential properties which are separate from their causal roles. Indeed, how else could you explain their causal roles? Still, distance must be mentioned when explaining gravity.
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