10180
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Mathematicians do not study objects, but relations between objects [Poincaré]
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Full Idea:
Mathematicians do not study objects, but relations between objects; it is a matter of indifference if the objects are replaced by others, provided the relations do not change. They are interested in form alone, not matter.
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From:
Henri Poincaré (Science and Hypothesis [1902], p.20), quoted by E Reck / M Price - Structures and Structuralism in Phil of Maths §6
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A reaction:
This connects modern structuralism with Aritotle's interest in the 'form' of things. Contrary to the views of the likes of Frege, it is hard to see that the number '7' has any properties at all, apart from its relations. A daffodil would do just as well.
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15643
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Nominal essence mistakenly gives equal weight to all underlying properties that produce appearances [Eagle]
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Full Idea:
Nominal essence does not allow for gradations in significance for the underlying properties. Those are all essential for the object behaving as it observably does, and they must all be given equal weight when deciding what the object does.
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From:
Antony Eagle (Locke on Essences and Kinds [2005], IV)
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A reaction:
This is where 'scientific' essentialism comes in. If we take one object, or one kind of object, in isolation, Eagle is right. When we start to compare, and to set up controlled conditions tests, we can dig into the 'gradations' he cares about.
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5880
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Xenocrates held that the soul had no form or substance, but was number [Xenocrates, by Cicero]
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Full Idea:
Xenocrates denied that the soul had form or any substance, but said that it was number, and the power of number, as had been held by Pythagoras long before, was the highest in nature.
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From:
report of Xenocrates (fragments/reports [c.327 BCE]) by M. Tullius Cicero - Tusculan Disputations I.x.20
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A reaction:
This shows how strong the Pythagorean influence was in the Academy. This is not totally stupid. Dawkins holds that the essence of DNA is information, which can be expressed mathematically. Xenocrates was a functionalist.
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