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8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation

[ways relations can be categorised and formalised]

12 ideas
If a relation is symmetrical and transitive, it has to be reflexive [Russell]
'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a [Russell]
'Reflexiveness' holds between a term and itself, and cannot be inferred from symmetry and transitiveness [Russell]
Nothing is genuinely related to itself [Armstrong]
A relation is 'Euclidean' if aRb and aRc imply bRc [Cresswell]
A relation is not reflexive, just because it is transitive and symmetrical [Bostock]
Relations can be one-many (at most one on the left) or many-one (at most one on the right) [Bostock]
Reflexive relations are syntactically polyadic but ontologically monadic [Molnar]
A reflexive relation entails that the relation can't be asymmetric [David]
'Multigrade' relations are those lacking a fixed number of relata [MacBride]
A relation is a set consisting entirely of ordered pairs [Potter]
Being taller is an external relation, but properties and substances have internal relations [Macdonald,C]