13231
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Explanatory proofs rest on 'characterizing properties' of entities or structure [Steiner,M]
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Full Idea:
My proposal is that an explanatory proof makes reference to the 'characterizing property' of an entity or structure mentioned in the theorem, where the proof depends on the property. If we substitute a different object, the theory collapses.
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From:
Mark Steiner (Mathematical Explanation [1978], p.34)
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A reaction:
He prefers 'characterizing property' to 'essence', because he is not talking about necessary properties, since all properties are necessary in mathematics. He is, in fact, reverting to the older notion of an essence, as the core power of the thing.
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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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19376
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A machine is best defined by its final cause, which explains the roles of the parts [Leibniz]
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Full Idea:
Any machine ...is best defined in terms of its final cause, so that in the description of the parts it is therefore apparent in what way each of them is coordinated with the others for the intended us.
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From:
Gottfried Leibniz (The Human Body is a sort of Machine [1683], p.290), quoted by Richard T.W. Arthur - Leibniz 3 'Machines'
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A reaction:
We would use the 'function', an inherently teleological concept, and a concept which is almost indispensable for giving an illuminating description of the world. If nature is dispositional, it points towards things. Leibniz views persons as machines.
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