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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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2171
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The 'will' doesn't exist; there is just conclusion, then action [Homer, by Williams,B]
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Full Idea:
Homer left out another mental action lying between coming to a conclusion and acting on it; and he did well, since there is no such action, and the idea is the invention of bad philosophy.
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From:
report of Homer (The Iliad [c.850 BCE]) by Bernard Williams - Shame and Necessity II - p.37
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A reaction:
This is a characteristically empiricist view, which is found in Hobbes. The 'will' seems to have a useful role in folk psychology. We can at least say that coming to a conclusion that I should act, and then actually acting, are not the same thing.
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21819
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Plato says the Good produces the Intellectual-Principle, which in turn produces the Soul [Homer, by Plotinus]
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Full Idea:
In Plato the order of generation is from the Good, the Intellectual-Principle; from the Intellectual-Principle, the Soul.
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From:
report of Homer (The Iliad [c.850 BCE], 509b) by Plotinus - The Enneads 5.1.08
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A reaction:
The doctrine of Plotinus merely echoes Plato, in that case, except that the One replaces the Form of the Good. Does this mean that what is first in Plotinus is less morally significant, and more concerned with reason and being?
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