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Ideas for 'fragments/reports', 'Against Structural Universals' and 'The Principles of Science'

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18. Thought / E. Abstraction / 7. Abstracta by Equivalence
Mathematicians abstract by equivalence classes, but that doesn't turn a many into one [Lewis]
     Full Idea: When mathematicians abstract one thing from others, they take an equivalence class. ....But it is only superficially a one; underneath, a class are still many.
     From: David Lewis (Against Structural Universals [1986], 'The pictorial')
     A reaction: This is Frege's approach to abstraction, and it is helpful to have it spelled out that this is a mathematical technique, even when applied by Frege to obtaining 'direction' from classes of parallels. Too much philosophy borrows inappropriate techniques.