Re: Triadic Relations • (1) • (2) • (3)

Re: Conceptual Graphs • Edwina Taborsky

- ET:
- A few comments on your outline of the Sign. I think one has to be careful not to set up a Saussurian linguistic dyad. …

Dear Edwina,

I copied your comments to a draft page and will take them up in the fullness of time, but a few remarks by way of general orientation to relations, triadic relations, sign relations, and sign transformations, partly prompted by the earlier discussion of complex systems, may be useful at this point.

One does not come to terms with systems of any complexity — adaptive, anticipatory, intelligent systems, and those with a capacity to support scientific inquiry, whether as autonomous agents or assistive utilities — without the use of mathematical models to negotiate the gap between our naturally evolved linguistic capacities and the just barely scrutable realities manifesting in phenomena.

Peirce’s quest to understand how science works takes its first big steps with his lectures on the Logic of Science at Harvard and the Lowell Institute (1865–1866), where he traces the bearings of deduction, induction, and hypothesis on the conduct of scientific inquiry. There Peirce makes a good beginning by taking up Boole’s functional recasting of logic, a major advance over traditional logic rooted in the paradigms of historical grammars. But developing a minimal adequate mathematical basis for the logic of science will take drilling down to a deeper core.

The mathematics we need to build models of inquiry as a sign-relational process appears for the first time in history with Peirce’s early work, especially his 1870 Logic of Relatives. It has its sources in the mathematical realism of Leibniz and De Morgan, the functional logic of Boole, and the algebraic research of Peirce’s own father, Benjamin Peirce, whose *Linear Associative Algebra* Charles edited for publication in the *American Journal of Mathematics* (1881).

My own contributions to this pursuit I’ve collected over the years under the heading of Inquiry Driven Systems, portions of which I’ve shared here and there across the Web for lo! this whole millennium in progress. A few resources along those lines are listed below.

### References

- Awbrey, S.M., and Awbrey, J.L. (2001), “Conceptual Barriers to Creating Integrative Universities”,
*Organization : The Interdisciplinary Journal of Organization, Theory, and Society* 8(2), Sage Publications, London, UK, 269–284. Abstract. Online.
- Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action • The Risk of Inquiry”,
*Inquiry : Critical Thinking Across the Disciplines* 15(1), 40–52.

Archive. Journal. Online (doc) (pdf).
- Awbrey, S.M., and Awbrey, J.L. (1991), “An Architecture for Inquiry • Building Computer Platforms for Discovery”,
*Proceedings of the Eighth International Conference on Technology and Education*, Toronto, Canada, 874–875. Online.
- Awbrey, J.L., and Awbrey, S.M. (1990), “Exploring Research Data Interactively. Theme One : A Program of Inquiry”,
*Proceedings of the Sixth Annual Conference on Applications of Artificial Intelligence and CD-ROM in Education and Training*, Society for Applied Learning Technology, Washington, DC, 9–15. Online.

### Resources

cc: Category Theory • Conceptual Graphs • Cybernetics (1) (2) • Ontolog (1) (2)

cc: Peirce List (1) (2) • Structural Modeling (1) (2) • Systems Science (1) (2)

cc: FB | Relation Theory • Laws of Form