Thanks for your comments. They prompt me to say a little more about the mathematical character of the sign relational models I’m using.
Peirce without mathematics is like science without mathematics. In every direction of research he pioneered or prospected, information, inquiry, logic, semiotics, we trace his advances only so far, barely scratch the surface before we need to bring in mathematical models adequate to the complexity of the phenomena under investigation.
In recent years there has been a tendency in certain quarters to ignore the mathematical substrate of Peirce’s pragmatic thought, even a refusal to use the mathematical tools he crafted to the task of sharpening our understanding. I do not recall that attitude being prevalent when I began my studies of Peirce’s work some fifty years ago. The issue in the “reception of Peirce” over most of that time has largely been the tendency of people imbued in the traditions of “analytic philosophy” to dismiss Peirce out of hand. But that school of thought had no problem with using mathematics, aside from the short-sighted attempts to reduce mathematics to logic and all relations to dyadic ones.
Maybe this late resistance to Peirce’s mathematical groundwork has come about through an overly selective viewing of his entire spectrum of work or maybe it’s just a matter of taste. Whatever the case, it’s critical for people who are looking for adequate models of the complex phenomena involved in belief systems, communication, intelligent systems, knowledge representation, scientific inquiry, and so on to recognize that all the resources we need for working with relations in general as sets of ordered tuples and sign relations in particular as sets of ordered triples are already available in Peirce’s technical works from 1870 on.
Okay, it looks like I’ve used up my morning again with more preliminary matters but it seemed important to clear up a few things about the overall mathematical approach.
- Peirce, C.S. (1902), “Parts of Carnegie Application” (L 75), in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 4, 13–73. Online.
- Awbrey, J.L., and Awbrey, S.M. (1995), “Interpretation as Action : The Risk of Inquiry”, Inquiry : Critical Thinking Across the Disciplines 15(1), pp. 40–52. Archive. Journal. Online.