## Sign Relations • Discussion 7

Dear Alex,

Please forgive the long and winding dissertation.  I’ve been through many discussions of Peirce’s definition of “logic as formal semiotic” but I keep discovering new ways of reading what I once regarded as a straightforward proposition.  That’s all useful information but it makes me anxious to avoid any missteps of interpretation I might have made in the past.  At any rate, I think I’ve set enough background and context to begin addressing your comments now.

For ease of reference here is Peirce’s twofold definition again.

Logic will here be defined as formal semiotic.  A definition of a sign will be given which no more refers to human thought than does the definition of a line as the place which a particle occupies, part by part, during a lapse of time.  Namely, a sign is something, A, which brings something, B, its interpretant sign determined or created by it, into the same sort of correspondence with something, C, its object, as that in which itself stands to C.  It is from this definition, together with a definition of “formal”, that I deduce mathematically the principles of logic.  I also make a historical review of all the definitions and conceptions of logic, and show, not merely that my definition is no novelty, but that my non-psychological conception of logic has virtually been quite generally held, though not generally recognized.  (C.S. Peirce, NEM 4, 20–21).

A Sign is unusually active in Peirce’s definition:

A (a sign) brings B (interpretant sign) into correspondence with C (object of sign).

Moreover, A determines B or even creates B.

It would be nice to get an example of such an active sign, its interpretant sign, and an object.  My point is to make the Peirce definition as clear as to be formalized.

Several issues stand out.  There are questions about paraphrases, the active character of signs, and the nature of what is being defined.

• The problem of paraphrases arises at this point because it affects how literally we ought to take the words in a natural language proxy for a logical or mathematical formula.

For example, a conventional idiom in describing a mathematical function $f : X \to Y$ is to say $f$ “maps” or “sends” an element of $X$ to an element of $Y.$  A concrete verb may quicken the intuition but the downside is its power to evoke excess meanings beyond the abstract intention.  It is only as we become more familiar with the formal subject matter of sign relations that we can decide what kind of “bringing” and “creating” and “determining” is really going on in all that sign, object, interpretant relating, whether at the abstract level or in a given application.

• There is the question of a sign’s active character.  Where’s the dynamic function in all that static structure?  Klaus Krippendorff raised the same question in regard to the Parable of the Sunflower back at the beginning of this discussion.

[Peirce’s] triadic explanations do not cover the dynamics of the sunflower’s behavior.  It favors static descriptions which cybernetics is fundamentally opposed to, moreover including the cybernetician as enactor of his or her conceptual system.

I have not forgotten this question.  Indeed, it’s the question at the heart of my work on Inquiry Driven Systems, which led me back to grad school in Systems Engineering “to develop mutual applications of systems theory and artificial intelligence to each other”.

Anything approaching an adequate answer to that question is going to be one of those things requiring more background and context, all in good time, but there are a few hints we can take from Peirce’s text about the way forward.

A definition of a sign will be given which no more refers to human thought than does the definition of a line as the place which a particle occupies, part by part, during a lapse of time.

My reading of that tells me about a division of labor across three levels of abstraction.  There is a level of psychological experience and social activity, a level of dynamic process and temporal pattern, and a level of mathematical form.

To be continued …

### References

• 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.  ArchiveJournalOnline.

### Resources

cc: CyberneticsOntolog • Peirce List (1) (2)Structural ModelingSystems Science

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