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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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3425
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Reduction has been defined as deriving one theory from another by logic and maths [Nagel,E, by Kim]
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Full Idea:
Ernest Nagel defines reduction as the possibility of deriving all laws of one theory by logic and mathematics to another theory, with appropriate 'bridging principles' (either definitions, or empirical laws) connecting the expressions of the two theories.
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From:
report of Ernest Nagel (The Structure of Science [1961]) by Jaegwon Kim - Philosophy of Mind p.213
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A reaction:
This has been labelled as 'weak' reduction, where 'strong' reduction would be identity, as when lightning is reduced to electrical discharge. You reduce x by showing that it is y in disguise.
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8326
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Science has shown that causal relations are just transfers of energy or momentum [Fair, by Sosa/Tooley]
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Full Idea:
Basic causal relations can, as a consequence of our scientific knowledge, be identified with certain physicalistic [sic] relations between objects that can be characterized in terms of transference of either energy or momentum between objects.
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From:
report of David Fair (Causation and the Flow of Energy [1979]) by E Sosa / M Tooley - Introduction to 'Causation' §1
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A reaction:
Presumably a transfer of momentum is a transfer of energy. If only anyone had the foggiest idea what energy actually is, we'd be doing well. What is energy made of? 'No identity without substance', I say. I like Fair's idea.
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10379
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Fair shifted his view to talk of counterfactuals about energy flow [Fair, by Schaffer,J]
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Full Idea:
Fair, who originated the energy flow view of causation, moved to a view that understands connection in terms of counterfactuals about energy flow.
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From:
report of David Fair (Causation and the Flow of Energy [1979]) by Jonathan Schaffer - The Metaphysics of Causation 2.1.2
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A reaction:
David Fair was a pupil of David Lewis, the king of the counterfactual view. To me that sounds like a disappointing move, but it is hard to think that a mere flow of energy through space would amount to causation. Cause must work back from an effect.
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15877
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The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré]
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Full Idea:
In Poincaré's view, we try to construct a language within which the brute facts of experience are expressed as comprehensively and as elegantly as possible. The job of science is the forging of a language precisely suited to that purpose.
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From:
report of Henri Poincaré (The Value of Science [1906], Pt III) by Rom Harré - Laws of Nature 2
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A reaction:
I'm often struck by how obscure and difficult our accounts of self-evident facts can be. Chairs are easy, and the metaphysics of chairs is hideous. Why is that? I'm a robust realist, but I like Poincaré's idea. He permits facts.
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