Sign relation

A sign relation is the basic construct in the theory of signs, also known as semeiotic or semiotics, as developed by Charles Sanders Peirce.

Anthesis

Thus, if a sunflower, in turning towards the sun, becomes by that very act fully capable, without further condition, of reproducing a sunflower which turns in precisely corresponding ways toward the sun, and of doing so with the same reproductive power, the sunflower would become a Representamen of the sun. (C.S. Peirce, "Syllabus" ("c". 1902), "Collected Papers", CP 2.274).

In his picturesque illustration of a sign relation, along with his tracing of a corresponding sign process, or "semiosis", Peirce uses the technical term "representamen" for his concept of a sign, but the shorter word is precise enough, so long as one recognizes that its meaning in a particular theory of signs is given by a specific definition of what it means to be a sign.

Definition

One of Peirce's clearest and most complete definitions of a sign is one that he gives, not incidentally, in the context of defining "logic", and so it is informative to view it in that setting.

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).

In the general discussion of diverse theories of signs, the question frequently arises whether signhood is an absolute, essential, indelible, or "ontological" property of a thing, or whether it is a relational, interpretive, and mutable role that a thing can be said to have only within a particular context of relationships.

Peirce's definition of a "sign" defines it in relation to its "object" and its "interpretant sign", and thus it defines signhood in "relative terms", by means of a predicate with three places. In this definition, signhood is a role in a triadic relation, a role that a thing bears or plays in a given context of relationships — it is not as an "absolute", "non-relative" property of a thing-in-itself, one that it possesses independently of all relationships to other things.

Some of the terms that Peirce uses in his definition of a sign may need to be elaborated for the contemporary reader.

* Correspondence. From the way that Peirce uses this term throughout his work, it is clear that he means what he elsewhere calls a "triple correspondence", and thus this is just another way of referring to the whole triadic sign relation itself. In particular, his use of this term should not be taken to imply a dyadic correspondence, like the kinds of "mirror image" correspondence between realities and representations that are bandied about in contemporary controversies about "correspondence theories of truth".

* Determination. Peirce's concept of determination is broader in several directions than the sense of the word that refers to strictly deterministic causal-temporal processes. First, and especially in this context, he is invoking a more general concept of determination, what is called a "formal" or "informational" determination, as in saying "two points determine a line", rather than the more special cases of causal and temporal determinisms. Second, he characteristically allows for what is called "determination in measure", that is, an order of determinism that admits a full spectrum of more and less determined relationships.

* Non-psychological. Peirce's "non-psychological conception of logic" must be distinguished from any variety of "anti-psychologism". He was quite interested in matters of psychology and had much of import to say about them. But logic and psychology operate on different planes of study even when they have occasion to view the same data, as logic is a "normative science" where psychology is a "descriptive science", and so they have very different aims, methods, and rationales.

igns and inquiry

There is a close relationship between the pragmatic theory of signs and the pragmatic theory of inquiry. In fact, the correspondence between the two studies exhibits so many congruences and parallels that it is often best to treat them as integral parts of one and the same subject. In a very real sense, inquiry is the process by which sign relations come to be established and continue to evolve. In other words, inquiry, "thinking" in its best sense, "is a term denoting the various ways in which things acquire significance" (John Dewey). Thus, there is an active and intricate form of cooperation that needs to be appreciated and maintained between these converging modes of investigation. Its proper character is best understood by realizing that the theory of inquiry is adapted to study the developmental aspects of sign relations, a subject which the theory of signs is specialized to treat from structural and comparative points of view.

Examples of sign relations

Because the examples to follow have been artificially constructed to be as simple as possible, their detailed elaboration can run the risk of trivializing the whole theory of sign relations. Despite their simplicity, however, these examples have subtleties of their own, and their careful treatment will serve to illustrate many important issues in the general theory of signs.

Imagine a discussion between two people, Ann and Bob, and attend only to that aspect of their interpretive practice that involves the use of the following nouns and pronouns: "Ann", "Bob", "I", "you".

The "object domain" of this discussion fragment is the set of two people {Ann, Bob}. The "syntactic domain" or the "sign system" that is involved in their discussion is limited to the "set" of four signs {"Ann", "Bob", "I", "You"}.

In their discussion, Ann and Bob are not only the passive objects of nominative and accusative references but also the active interpreters of the language that they use. The "system of interpretation" (SOI) associated with each language user can be represented in the form of an individual "three-place relation" called the "sign relation" of that interpreter.

Understood in terms of its "set-theoretic extension", a sign relation L is a "subset" of a "cartesian product" O × S × I. Here, O, S, I are three sets that are known as the "object domain", the "sign domain", and the "interpretant domain", respectively, of the sign relation L L for some "s" IPA|∈ S }.

As it happens, the sign relations L_A and L_B are fully symmetric with respect to exchanging signs and interpretants, so all of the data of "proj"_OSL_A is echoed unchanged in "proj"_OIL_Aand all of the data of "proj"_OSL_B is echoed unchanged in "proj"_OIL_B.

emiotic equivalence relations

ix ways of looking at a sign relation

In the context of 3-adic relations in general, Peirce provides the following illustration of the six "converses" of a 3-adic relation, that is, the six differently ordered ways of stating what is logically the same 3-adic relation:

: So in a triadic fact, say, the example : we make no distinction in the ordinary logic of relations between the "subject nominative", the "direct object", and the "indirect object". We say that the proposition has three "logical subjects". We regard it as a mere affair of English grammar that there are six ways of expressing this: : These six sentences express one and the same indivisible phenomenon. (C.S. Peirce, "The Categories Defended", MS 308 (1903), EP 2, 170-171).

IOS

ISO

OIS

Words spoken are symbols or signs (σύμβολα) of affections or impressions (παθήματα) of the soul (ψυχή); written words are the signs of words spoken. As writing, so also is speech not the same for all races of men. But the mental affections themselves, of which these words are primarily signs (polytonic|σημεῖα), are the same for the whole of mankind, as are also the objects (πράγματα) of which those affections are representations or likenesses, images, copies (polytonic|ὁμοιώματα). (Aristotle, "De Interpretatione", 1.16^a4).

OSI

IO

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, "Application to the Carnegie Institution", L75 (1902), NEM 4, 20-21).

OI

A "Sign" is anything which is related to a Second thing, its "Object", in respect to a Quality, in such a way as to bring a Third thing, its "Interpretant", into relation to the same Object, and that in such a way as to bring a Fourth into relation to that Object in the same form, "ad infinitum". (CP 2.92; quoted in Fisch 1986: 274)

References

Bibliography

Primary sources

* Charles Peirce (Bibliography)

econdary sources

* Deledalle, Gérard (2000), "C.S. Peirce's Philosophy of Signs", Indiana University Press.

* Eisele, Carolyn (1979), in "Studies in the Scientific and Mathematical Philosophy of C.S. Peirce", Richard Milton Martin (ed.), Mouton, The Hague.

* Esposito, Joseph (1980), "Evolutionary Metaphysics: The Development of Peirce's Theory of Categories", Ohio University Press (?).

* Fisch, Max (1986), "Peirce, Semeiotic, and Pragmatism", Indiana University Press.

* Houser, N., Roberts, D.D., and Van Evra, J. (eds.)(1997), "Studies in the Logic of C.S. Peirce", Indiana University Press.

* Liszka, J.J. (1996), "A General Introduction to the Semeiotic of C.S. Peirce", Indiana University Press.

* Misak, C. (ed.)(2004), "Cambridge Companion to C.S. Peirce", Cambridge University Press.

* Moore, E., and Robin, R. (1964), "Studies in the Philosophy of C.S. Peirce, Second Series", University of Massachusetts Press, Amherst, MA.

* Murphey, M. (1961), "The Development of Peirce's Thought". Reprinted, Hackett, Indianapolis, IN, 1993.

* Walker Percy (2000), pp. 271-291 in "Signposts in a Strange Land", P. Samway (ed.), Saint Martin's Press.

ee also

* Cartesian product
* Descriptive science
* Dyadic relation
* Formal grammar
* Formal language
* Inquiry
* Logic of information
* Logic of relatives
* Logical matrix
* Meaning
* Normative science
* Pragmatics
* Pragmatic information
* Projection
* Relation
* Semantics
* Semeiotic
* Semiosis
* Semiotics
* Semiotic information
* Set theory
* Sign
* Sign relational complex
* Theory of relations
* Triadic relation
* Types of relations

External links

* [http://www.helsinki.fi/science/commens/dictionary.html The Commens Dictionary of Peirce's Terms]
** [http://www.helsinki.fi/science/commens/terms/semeiotic.html Entry for "Semeiotic"]