Figure 3. Aspects of a Sign Relation

Re: Peirce List • Kirsti Määttänen

One of the chief advantages of Peirce’s systems of logical graphs, entitative and existential, is the way they escape the bounds of 1-dimensional syntax and thus make it clear that many constraints of order imposed by the ordinary lines of linguistic text are not of the essence for logic but purely rhetorical accidents.  That does, of course, leave open the question of what constraints imposed by the 2-dimensional medium of Peirce’s logical graphs might also be inessential to logic.

As far as visualizations of sign relations go, without worrying about their use as a calculus, there is the above 3-dimensional example from a paper Susan Awbrey and I presented at conference in 1999 and revised for publication in 2001.

Resources

• Logical Graphs : Introduction
• Logical Graphs : Formal Development
• Logical Graphs : With Animated Proofs

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.  Archive.  Journal.  Online.
• 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.