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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.
Gist of Idea
'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a
Source
Bertrand Russell (Introduction to Mathematical Philosophy [1919], V)
Book Ref
Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.42
A Reaction
This is to be contrasted with 'non-symmetrical', where there just happens to be no symmetry.
| 14430 | If a relation is symmetrical and transitive, it has to be reflexive [Russell] |
| 14432 | 'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a [Russell] |
| 10586 | 'Reflexiveness' holds between a term and itself, and cannot be inferred from symmetry and transitiveness [Russell] |
| 17691 | Nothing is genuinely related to itself [Armstrong] |
| 14974 | A relation is 'Euclidean' if aRb and aRc imply bRc [Cresswell] |
| 13543 | A relation is not reflexive, just because it is transitive and symmetrical [Bostock] |
| 13802 | Relations can be one-many (at most one on the left) or many-one (at most one on the right) [Bostock] |
| 11927 | Reflexive relations are syntactically polyadic but ontologically monadic [Molnar] |
| 18361 | A reflexive relation entails that the relation can't be asymmetric [David] |
| 21352 | 'Multigrade' relations are those lacking a fixed number of relata [MacBride] |
| 13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
| 7967 | Being taller is an external relation, but properties and substances have internal relations [Macdonald,C] |