Inquiry Into Inquiry

Re: Semiotic Triangle • JC

Peirce being prickly as usual his distinctions all tend toward tri-stinctions and on this field he wields his trident:  Tone, Token, Type.

Here’s a link to a few pertinent passages:

• Tone, Token, Type

Re: Semiotic Triangle • Francesco Bellucci

I am still looking for a way to build a bridge between the different senses of complete and incomplete being used in this discussion but while that bridge is under construction it may help to say what I’m saying another way.

Signs do not do anything at all by themselves — except take up space in their media — they do not denote, or mean, or propose anything at all except insofar as they are interpreted to do so.

Of course we all speak of signs denoting this or connoting that, but that is just loose talk, elliptical or informal manners of speaking, which our practice and theory of semiotics has the task of rendering clear.

One way of carrying out the required formalization is to introduce explicit interpreters and to specify exactly what interpretant signs they relate to just what signs in reference to just what objects.

But once we’ve specified that much, it becomes clear we are simply specifying a particular sign relation for specified object, sign, and interpretant domains.  It can be a rhetorical convenience to keep the figure of the interpreter as a hypostatic abstraction or personification of the sign relation but all the information about the interpreter’s semiotic conduct is contained in the bare sign relation itself.

Re: Semiotic Triangle • JA • FB • JA • FB

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 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.

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 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:

• Peirce’s 1870 Logic Of Relatives

Note. The following links afford a review of the discussion up to this point.
Re: Semiotic Triangle • JC • JA • JA • JC • JA • JA • JC • JA • FB • JA • JA

Peirce gives his clearest and most complete definition of signs and sign relations in the context of defining logic.  Here’s a link to a couple of variants:

• C.S. Peirce • On the Definition of Logic

There is more discussion in the following article and section:

• Sign Relations • Definition

The proper unit of analysis is the whole sign relation where and are the object, sign, and interpretant sign domains, respectively.  In that sense, one could say that the individual sign is always incomplete until one specifies the sign relational setting in which it is conceived to have significance.

Re: John Corcoran • Semiotic Triangle • My Comment

The following passage is very instructive on several points, illuminating especially the relationship between interpreters (sign‑using agents) and interpretant signs.

My study of Peirce’s information formula, “Information = Comprehension × Extension”, provides a measure of context for the above passage.

• Information = Comprehension × Extension • Selection 18

There’s additional discussion in the following article and section.

• Inquiry Driven Systems • C’est Moi

Reference

• Peirce, C.S. (1866), “The Logic of Science, or, Induction and Hypothesis”, Lowell Lectures of 1866, pp. 357–504 in Writings of Charles S. Peirce : A Chronological Edition, Volume 1, 1857–1866, Peirce Edition Project, Indiana University Press, Bloomington, IN, 1982.

Resources

• C.S. Peirce • Upon Logical Comprehension and Extension
• My Notes • Information = Comprehension × Extension

Re: Semiotic Triangle • John Corcoran

A sign relation is a formal structure that satisfies a very general definition, on the same order of generality as a mathematical group or geometry.  So any consideration of what a particular sign relation contains will be very context-dependent.

We can study sign relations in the abstract or in connection with particular applications.  In applications, sign relations describe structures of interpretation, for example, the conduct of sign-using interpreters.  Applications divide broadly into descriptive and normative types.

Descriptively, we could be describing the interpretive conduct of someone named “Socrates” who happens to speak English and who uses the word “I” to denote himself.  In that case, we would probably want to include the signs “Socrates” and “I” in both the sign domain and the interpretant domain of the sign relation that we use to describe the usage of that agent.

Re: Semiotic Triangle • John Corcoran

In a typical sign relation where Socrates belongs to the object domain one sign in the sign domain could be the name “Socrates” and one interpretant in the interpretant domain could be the name “Socrates”.

Slightly more interesting examples are discussed in the following article and section.

• Sign Relations
• Examples of Sign Relations

Re: Semiotic Triangle • John Corcoran

Peirce’s triadic sign relations are sets of ordered triples having the form where is the object, is the sign, and is the interpretant sign (usually shortened to interpretant).  In other words, a specific sign relation is a subset of the cartesian product where is the object domain, is the sign domain, and is the interpretant domain.

There is more discussion in the following papers.

• Interpretation as Action • The Risk of Inquiry (doc) (pdf)
• Conceptual Barriers to Creating Integrative Universities