| if A precedes B, and B precedes C, necessarily A precedes C. This would be true whatever the nature of A, B, and C,although the ideas can be made more precise by thinkingof A, B, and C as events occurring at specific times.
|if A precedes B, and B precedes C, necessarily A precedes C. This would be true whatever the nature of A, B, and C,although the ideas can be made more precise by thinkingof A, B, and C as events occurring at specific times.
|-
|-
| includes
|includes
| if A includes B, and B includes C, necessarily A includes
|if A includes B, and B includes C, necessarily A includes
|-
|-
| included in
|included in
|
|
|-
|-
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|-
|-
|supports
|supports
|
|-
|-
|implies
|implies
|
|-
|-
|causes
|causes
|
|-
|-
|}
|}
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The generic phrase ''''is subordinate to'''' can be used to represent any of the above relations.
The generic phrase ''''is subordinate to'''' can be used to represent any of the above relations.
Without it, the development
Transitive relations are quite common. However, one shoud be careful not to grant transitivity when it is not present.
of knowledge would have been considerably more
difficult. On the other band, its prevalence may induce a
For ecxample, the contextual relation "is preferred to" is not transitive.
tendency to take it for granted when it is not present. The
contextual relation "is preferred to" is a good case in point.
Preference is subjective, and subjective relations may or
may not be transitive. Thus if a person says "blue is
preferred to red" and "red is preferred to yellow," it still
may be that the person will say "yellow is preferred to
blue," hence, transitivity is violated. For this particular
contextual relation, one can speak of"transitive preference"
and "intransitive preference."
This mathematical definition of transitivity can be
If a person says "blue is preferred to red" and "red is preferred to yellow," it still may be that the person will say "yellow is preferred to blue," hence, transitivity is violated.
readily interpreted for many contextual relations.
Such contextual relations can be referred to as "transitive preference" and "intransitive preference."
Revision as of 08:15, 9 January 2022
Mathematical Definition
A binary relation R defined on a set S is said to be transitive if, for any elements A, B, and C in the set S, given that A R B and B R C, it necessarily follows that A R C.
Examples of Transitive Relations
R
Explanation
precedes
if A precedes B, and B precedes C, necessarily A precedes C. This would be true whatever the nature of A, B, and C,although the ideas can be made more precise by thinkingof A, B, and C as events occurring at specific times.
includes
if A includes B, and B includes C, necessarily A includes
included in
is less than
is greater than
supports
implies
causes
The generic phrase 'is subordinate to' can be used to represent any of the above relations.
Transitive relations are quite common. However, one shoud be careful not to grant transitivity when it is not present.
For ecxample, the contextual relation "is preferred to" is not transitive.
If a person says "blue is preferred to red" and "red is preferred to yellow," it still may be that the person will say "yellow is preferred to blue," hence, transitivity is violated.
Such contextual relations can be referred to as "transitive preference" and "intransitive preference."