Two different senses of completeness and incompleteness in regard to signs arose in discussion at this point, as illustrated by the following exchange:
- “Socrates” for Peirce would be an incomplete sign …. Signs (i.e. complete signs) for Peirce are propositions, not names (which are signs, but incomplete).
- The proper unit of analysis and classification is the whole sign relation where and are the object, sign, and interpretant sign domains, respectively. In that sense, one could say the individual sign is always incomplete until one specifies the sign relational setting in which it is conceived to have significance.
- Some signs are incomplete because although they must refer to object and interpretant, they do not do so explicitly. So a proposition is “complete” in regard to the object, but not in regard to the interpretant. An argument is complete in both respects, a term or rhema in neither.
One factor in the divergence appears to be a difference in the context of application, whether signs are regarded in the light of descriptive or normative semiotics. Another appears to be a difference in the level of analysis, whether the prospective completion of a sign is considered to be a sign relational triple or its degree of completeness evaluated in the context of a whole sign relation
I am using language that is common in the mathematical theory of relations, which itself got one of its biggest growth spurts from Peirce’s own logic of relative terms. The concepts of relational domains, elementary relations (ordered tuples), and components or correlates of ordered tuples are all straightforward translations of Peirce’s own concepts. And they do help very much, I would say they are of critical importance in applying the theory of triadic sign relations to practical settings in logic, mathematics, computing, and the sciences in general.
The basic ideas can be found in my notes on Peirce’s 1870 Logic of Relatives: