TRANSITIVITY
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(2) |
| ID | ◀ 3629 ▶ |
| Object type | Methodology or model |
- “Relation of two parts through a middle part” (after J. FEIBLEMAN & J. FRIEND, 1969, p.32).
A typical transitive relation is: If A<B and B<C, then A<C. On the contrary, if AC, nothing precise can be said about the relation of A to C.
FEIBLEMAN and FRIEND give the following example: “… The parts of an apple are transitive, for if the skin …encloses the flesh, and the flesh encloses the seeds, then the skin encloses the seeds”. Conversely “An aggregation of three grains of sand is intransitive, since the extreme parts are not related to each other by a middle part” (Ibid).
It is possibly not that simple. In composite systems, we find a kind of global statistical transitivity. The set of the grains of sand, or the set of gregarious locusts has an influence on the individuals, whose behavior become oriented. And the set is obviously composed of these same individuals who acquired some collective properties, due to their aggregation.
This is one of these cases where an abstract definition of a concept must be carefully scrutinized, in order to avoid semantic pitfalls.