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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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2748
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A true belief isn't knowledge if it would be believed even if false. It should 'track the truth' [Nozick, by Dancy,J]
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Full Idea:
Nozick says Gettier cases aren't knowledge because the proposition would be believed even if false. Proper justification must be more sensitive to the truth ("track the truth").
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From:
report of Robert Nozick (Philosophical Explanations [1981], 3.1) by Jonathan Dancy - Intro to Contemporary Epistemology 3.1
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A reaction:
This is a bad idea. I see a genuine tree in my garden and believe it is there, so I know it. That I might have believed it if I was in virtually reality, or observing a mirror, won't alter that.
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3028
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The chief good is unity, sometimes seen as prudence, or God, or intellect [Eucleides]
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Full Idea:
The chief good is unity, which is known by several names, for at one time people call it prudence, at another time God, at another intellect, and so on.
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From:
Eucleides (fragments/reports [c.410 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 02.9.2
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A reaction:
So the chief good is what unites and focuses our moral actions. Kant calls that 'the will'.
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