## Sign Relations • Discussion 3

Re: Sign Relations • Definition
Re: Ontolog Forum • Alex Shkotin (1) (2)

Regarding Peirce’s definition of a sign linked above, Alex Shkotin writes:

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.

Dear Alex,

Thanks for your comment.  It points to a problem lurking in the wings through all these discussions, so let’s nudge it on stage and throw a better light on it.

I remember my first formal logic prof in college being rather adamant about the difference between a logical formula, which supposedly bore its “logical form” on its sleeve — I recall the very figure he used — and any of its diverse and sundry natural language paraphrases.  As time wore on I would reconfigure many of the lessons impressed on me in those days, but that one has stuck, I’m guessing because it goes without saying in mathematical and scientific practice.

This treble clef, to vary the figure — forms as objects, formulas as signs, and paraphrases as interpretant signs — is the key to a fundamental theme.

A very wide field of discussion opens up at this point.  To begin we have the logical jump from forms to formulas and the semiotic drift from formulas to paraphrases.  Further on we’ll encounter a range of tensions between formal and informal contexts of inquiry.

Susan Awbrey and I discussed a related set of issues in our “Conceptual Barriers” paper.  Here is how we set up our treatment of three problematics.

• Problematic 1 is the tension that arises along a dimension of increasing formalization in our mental models of the world, between what we may call the ‘informal context’ of real-world practice and the ‘formal context’ of specialized study.
• Problematic 2 is the difficulty in communication that is created by differing mental models of the world, in other words, by the tendency among groups of specialists to form internally coherent but externally disparate systems of mental images.
• Problematic 3 is a special type of communication difficulty that commonly arises between the ‘Two Cultures’ of the scientific and the humanistic disciplines.  A significant part of the problem derives from the differential emphasis that each group places on its use of symbolic and conceptual systems, limiting itself to either the denotative or the connotative planes of variation, but seldom integrating the two.

Please excuse the sweeping preamble.  It wasn’t meant to sweep your observations under the rug — it’s just so many discussions here and there on the web in recent days are reminding me of the larger designs beyond my more mundane focus on brass tacks matters.  I’ll bring this all back to bear on the everyday life of signs the next chance I get.

### References

• Awbrey, S.M., and Awbrey, J.L. (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.  AbstractOnline.
• 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.

### Resources

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

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