## Sign Relations • Comment 6

Re: Semiotic TriangleJAFBJAFB

Two different senses of completeness and incompleteness in regard to signs arose in discussion at this point, as illustrated by the following exchange:

FB:
“Socrates” for Peirce would be an incomplete sign ….  Signs (i.e. complete signs) for Peirce are propositions, not names (which are signs, but incomplete).
JA:
The proper unit of analysis and classification is the whole sign relation $L \subseteq O \times S \times I,$ where $O,$ $S,$ and $I$ 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.
FB:
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 $(o, s, i),$ or its degree of completeness evaluated in the context of a whole sign relation $L \subseteq O \times S \times I.$

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:

This entry was posted in C.S. Peirce, Inquiry, Logic of Relatives, Peirce, Relation Theory, Semiotics, Sign Relations and tagged , , , , , , . Bookmark the permalink.

### 10 Responses to Sign Relations • Comment 6

1. Francesco says:

I don’t see how the descriptive/normative semiotics can be of any relevance here, esp. since it is not a Peircean distinction.  For Peirce, logic is semiotics;  this at least should be uncontestable.  Now, what is logic?  It’s the study of arguments.  And one of the things that Peirce says most often is that in an argument the premise is a sign of the conclusion.  Thus whatever else it might mean, “sign” certainly means “proposition”, because in an argument a proposition (the premise) is a sign of another proposition (the conclusion).  From this it follows that if propositions are composed of signs, these signs of which propositions are composed are not complete but incomplete signs.  This is the sense of my comment above.

• Jon Awbrey says:

Francesco,

Thanks for the reply.  These are recurring issues.  I think I remarked on them somewhere else just recently, so let me go hunt up the relevant links and quotes and continue in another blog post where it will be easier to assemble the pieces.

Regards,
Jon

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