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 Reference
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.