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Full Idea
Frege decided that all logical objects, or at least all those needed for mathematics, could be defined by logical abstraction, except the classes needed for such definitions. ..This definition by equivalence classes has been adopted as a standard device.
Gist of Idea
Frege introduced the standard device, of defining logical objects with equivalence classes
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §64-68) by Michael Dummett - Frege philosophy of mathematics
Book Ref
Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.233
A Reaction
This means if we are to understand modern abstraction (instead of the psychological method of ignoring selected properties of objects), we must understand the presuppositions needed for a definition by equivalence.
9854 | We can introduce new objects, as equivalence classes of objects already known [Frege, by Dummett] |
9883 | Frege introduced the standard device, of defining logical objects with equivalence classes [Frege, by Dummett] |
9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
8920 | Equivalence relations are reflexive, symmetric and transitive, and classify similar objects [Lipschutz] |
10104 | 'Equivalence' is a reflexive, symmetric and transitive relation; 'same first letter' partitions English words [George/Velleman] |
10103 | Grouping by property is common in mathematics, usually using equivalence [George/Velleman] |