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Single Idea 13802
[filed under theme 8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
]
Full Idea
A relation is 'one-many' if for anything on the right there is at most one on the left (∀xyz(Rxz∧Ryz→x=y), and is 'many-one' if for anything on the left there is at most one on the right (∀xyz(Rzx∧Rzy→x=y).
Gist of Idea
Relations can be one-many (at most one on the left) or many-one (at most one on the right)
Source
David Bostock (Intermediate Logic [1997], 8.1)
Book Ref
Bostock,David: 'Intermediate Logic' [OUP 1997], p.328
The
12 ideas
with the same theme
[ways relations can be categorised and formalised]:
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14430
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If a relation is symmetrical and transitive, it has to be reflexive
[Russell]
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14432
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'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a
[Russell]
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10586
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'Reflexiveness' holds between a term and itself, and cannot be inferred from symmetry and transitiveness
[Russell]
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17691
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Nothing is genuinely related to itself
[Armstrong]
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14974
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A relation is 'Euclidean' if aRb and aRc imply bRc
[Cresswell]
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13543
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A relation is not reflexive, just because it is transitive and symmetrical
[Bostock]
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13802
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Relations can be one-many (at most one on the left) or many-one (at most one on the right)
[Bostock]
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11927
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Reflexive relations are syntactically polyadic but ontologically monadic
[Molnar]
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18361
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A reflexive relation entails that the relation can't be asymmetric
[David]
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21352
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'Multigrade' relations are those lacking a fixed number of relata
[MacBride]
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13043
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A relation is a set consisting entirely of ordered pairs
[Potter]
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7967
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Being taller is an external relation, but properties and substances have internal relations
[Macdonald,C]
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