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Single Idea 10585

[from 'The Principles of Mathematics' by Bertrand Russell, in 8. Modes of Existence / A. Relations / 4. Formal Relations / b. Equivalence relation ]

Full Idea

Relations which are both symmetrical and transitive are formally of the nature of equality.

Gist of Idea

Symmetrical and transitive relations are formally like equality

Source

Bertrand Russell (The Principles of Mathematics [1903], §209)

Book Reference

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.219


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.