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Full Idea
It is easy to fall into the error of supposing that a relation which is both transitive and symmetrical must also be reflexive.
Gist of Idea
A relation is not reflexive, just because it is transitive and symmetrical
Source
David Bostock (Intermediate Logic [1997], 4.7)
Book Ref
Bostock,David: 'Intermediate Logic' [OUP 1997], p.176
A Reaction
Compare Idea 14430! Transivity will take you there, and symmetricality will get you back, but that doesn't entitle you to take the shortcut?
Related Idea
Idea 14430 If a relation is symmetrical and transitive, it has to be reflexive [Russell]
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] |