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Annex 1 of Representation,
Comprehension and Communication of Sets: the Role of Number), (1978)
Originally published in International Classification, 6, 1979, 2, pp. 92-103
Abstract | Part 1-3 | Notes | References | Annex 2 | Annex 3 | Annex 4
The definitions given below are those of J. G. Bennett ((45), vol. 3, pp. 10 11) and are given as a basis for his elaboration of a multi-term sequence in Annex 2. In the main part of this article "set" has been used to signify what Bennett defines as "system", although the two terms have been used interchangeably.
"1. A system is a set of independent but mutually relevant terms. The relevance of the terms requires them to be compatible. No one term of the system can be understood without reference to all the others.
2. The order of a system is given by the number of terms....
3. In systems, there are no fixed meanings attributable to the term, which depend upon the structure of the system as a whole, so the various connectivities are common to all systems of the same order.
4. Every system exemplifies modes of connectedness that are typical of the number of terms. Thus there are zero connectivities in a monad (one-term), one in a dyed (two-term) . . . If the connectivities are distinguished according to direction, the number is doubled. All the connectivities are significant and must be taken into account if the structure represented by the system is to be understood.
5. Each order of system is associated with a particular mode of experiencing the world, called the systemic attribute....
6. The mutual relevance of all the terms of a system requires that they should be of the same logical type and make contributions to the systemic attribute of one and the same kind. This we shall indicate by a common designation....
7. The independence of the terms of a system requires that each should have a distinctive character. An important part of the study of systems consists in identifying the term characters of systems of a given order ....
8. The mutual relevance of terms of a complex system can be found, to a first approximation, by taking all the terms in pairs. These are called the first-order Connectivities . . . Connectivities of a higher order can be studied as sub-systems from the tetrad (4-term) onwards . . ."
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