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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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5963
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Some say emotion is a sort of reason, and others say virtue concerns emotion [Plutarch]
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Full Idea:
Some philosophers make the emotions varieties of reason, on the ground that all desire and grief and anger are judgments, while others declare that the virtues have to do with emotions, as when fear is the province of courage.
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From:
Plutarch (68: Generation of the soul in 'Timaeus' [c.85], 1025d)
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A reaction:
The second idea comes from Aristotle, but the second is interesting, and corresponds to the views coming from modern neuroscience, where even the most basic thought seems to involve emotion. What could be the motivation for 'pure' reason?
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7903
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The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
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Full Idea:
The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
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From:
Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
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A reaction:
What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').
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