more from this thinker | more from this text
Full Idea
It is obvious that a relation which is symmetrical and transitive must be reflexive throughout its domain.
Gist of Idea
If a relation is symmetrical and transitive, it has to be reflexive
Source
Bertrand Russell (Introduction to Mathematical Philosophy [1919], II)
Book Ref
Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.16
A Reaction
Compare Idea 13543! The relation will return to its originator via its neighbours, rather than being directly reflexive?
Related Idea
Idea 13543 A relation is not reflexive, just because it is transitive and symmetrical [Bostock]
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] |