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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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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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