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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12741
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If experience is just a dream, it is still real enough if critical reason is never deceived [Leibniz]
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Full Idea:
Even if this whole life were said to be only a dream, and the visible world only a phantasm, I should call this dream or phantasm real enough if we were never deceived by it when we make good use of reason.
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From:
Gottfried Leibniz (De modo distinguendi phaenomena [1685], A6.4.1502), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 7
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A reaction:
I find this response more satisfactory than his response in Idea 12740. As a supporter of the coherence account of justification, I take the closest we get to knowledge to be when our full critical faculties and experience are brought to bear, and shared.
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12740
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The strongest criterion that phenomena show reality is success in prediction [Leibniz]
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Full Idea:
The most powerful criterion of the reality of phenomena, sufficient even by itself, is success in predicting future phenomena from past and present ones.
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From:
Gottfried Leibniz (De modo distinguendi phaenomena [1685], A6.4.1502), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 7
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A reaction:
I would say that this is clutching at straws, as there is no reason at all to deny that dreams could be thoroughly coherent and predictable in their events. We must just live with these doubts, not try to defeat them.
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12721
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Light, heat and colour are apparent qualities, and so are motion, figure and extension [Leibniz]
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Full Idea:
Concerning bodies I can demonstrate that not merely light, heat, color, and similar qualities are apparent but also motion, figure, and extension.
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From:
Gottfried Leibniz (De modo distinguendi phaenomena [1685], A6.4.1504), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 4
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A reaction:
Leibniz is not consistent on this. Here he is flirting with idealism, but he often backs away from that. In Discourse §12 he makes secondary qualities certainly subjective, and primary qualities possibly so. He admits the primaries contain eternal truths.
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