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Full Idea
The property of a relation which insures that it holds between a term and itself is called by Peano 'reflexiveness', and he has shown, contrary to what was previously believed, that this property cannot be inferred from symmetry and transitiveness.
Gist of Idea
'Reflexiveness' holds between a term and itself, and cannot be inferred from symmetry and transitiveness
Source
Bertrand Russell (The Principles of Mathematics [1903], §209)
Book Ref
Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.219
A Reaction
So we might say 'this is a sentence' has a reflexive relation, and 'this is a wasp' does not. While there are plenty of examples of mental properties with this property, I'm not sure that it makes much sense of a physical object. Indexicality...
| 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] |