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2 ideas
14430 | If a relation is symmetrical and transitive, it has to be reflexive [Russell] |
Full Idea: It is obvious that a relation which is symmetrical and transitive must be reflexive throughout its domain. | |
From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], II) | |
A reaction: Compare Idea 13543! The relation will return to its originator via its neighbours, rather than being directly reflexive? |
14432 | 'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a [Russell] |
Full Idea: The relation of 'asymmetry' is incompatible with the converse. …The relation 'husband' is asymmetrical, so that if a is the husband of b, b cannot be the husband of a. | |
From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], V) | |
A reaction: This is to be contrasted with 'non-symmetrical', where there just happens to be no symmetry. |