## Systems Of Interpretation • 5

Figure 2. An Elementary Sign Relation

An elementary sign relation is an ordered triple $(o, s, i).$  It is called elementary because it is one element of a sign relation $L \subseteq O \times S \times I,$ where $O$ is a set of objects, $S$ is a set of signs, and $I$ is a set of interpretant signs that are collectively called the domains of the relation.

But what is the significance of that ordering?

In any presentation of subject matter we have to distinguish the natural order of things from the order of consideration or presentation in which things are taken up on a given occasion.

The natural order of things comes to light through the discovery of invariants over a variety of presentations and representations.  That type of order tends to take a considerable effort to reveal.

The order of consideration or presentation is often more arbitrary, making some aspects of the subject matter more salient than others depending on the paradigm or perspective one has chosen.

In the case of sign relations, the order in which we take up the domains $O, S, I$ or the components of a triple $(o, s, i)$ is wholly arbitrary so long as we maintain the same order throughout the course of discussion.

### References

• Awbrey, J.L., and Awbrey, S.M. (Autumn 1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), pp. 40–52.  ArchiveJournalOnline.
• Awbrey, S.M., and Awbrey, J.L. (September 1999), “Organizations of Learning or Learning Organizations : The Challenge of Creating Integrative Universities for the Next Century”, Second International Conference of the Journal ‘Organization’, Re-Organizing Knowledge, Trans-Forming Institutions : Knowing, Knowledge, and the University in the 21st Century, University of Massachusetts, Amherst, MA.  Online.
• Awbrey, S.M., and Awbrey, J.L. (May 2001), “Conceptual Barriers to Creating Integrative Universities”, Organization : The Interdisciplinary Journal of Organization, Theory, and Society 8(2), Sage Publications, London, UK, pp. 269–284.  Abstract.

### 2 Responses to Systems Of Interpretation • 5

1. Mary Libertin says:

The first time I saw this figure I assumed the triangle was on the O-S plane. Now I see the triangle can be in neither but in a different dimension or in another plane. That plane would be made more visible if there were a frame around the figure that belonged as part of the figure. Any clarification?

• Jon Awbrey says:

That’s a hasty sketch, drawn up for a conference talk, probably at a time when I didn’t have my usual graphics utility, and maybe smushed up in transit between a Mac and a PC.  The published version is prettier.

But you are right to intuit that the central “spot”, as Peirce called it, is located on a different logical plane, since it is really a place-holder for the whole sign relation or possibly the individual triple.  Normally I would have labeled it with a letter to indicate the whole sign relation, say $L,$ or else the individual triple, say $\ell = (o, s, i).$

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