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10585
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Symmetrical and transitive relations are formally like equality
[Russell]
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Full Idea:
Relations which are both symmetrical and transitive are formally of the nature of equality.
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From:
Bertrand Russell (The Principles of Mathematics [1903], §209)
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A reaction:
This is the key to the whole equivalence approach to abstraction and Frege's definition of numbers. Establish equality conditions is the nearest you can get to saying what such things are. Personally I think we can say more, by revisiting older views.
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