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Single Idea 10584

[filed under theme 18. Thought / E. Abstraction / 7. Abstracta by Equivalence ]

Full Idea

The possession of a common property of a certain type always leads to a symmetrical transitive relation. The principle of Abstraction asserts the converse, that such relations only spring from common properties of the above type.

Gist of Idea

A certain type of property occurs if and only if there is an equivalence relation

Source

Bertrand Russell (The Principles of Mathematics [1903], §157)

Book Ref

Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.167


A Reaction

The type of property is where only one term is applicable to it, such as the magnitude of a quantity, or the time of an event. So symmetrical and transitive relations occur if and only if there is a property of that type.