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.
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 ⊆ O × S × I.
Broadly speaking, the three domains of a sign relation can be any sets whatsoever, but the kinds of sign relations that are typically contemplated in a computational setting are usually constrained to having I ⊆ S. In this case, interpretants are just a special variety of signs, and this makes it convenient to lump signs and interpretants together into a single class called the syntactic domain. In the forthcoming examples, S and I are identical as sets, so the same elements manifest themselves in two different roles of the sign relations in question. When it is necessary to refer to the whole set of objects and signs in the union of the domains O, S, I for a given sign relation L, one may refer to this set as the world of L and write W = WL = O∪S∪I.
To facilitate an interest in the abstract structures of sign relations, and to keep the notations as brief as possible as the examples become more complicated, it serves to introduce the following general notations:
| O | = | Object Domain |
| S | = | Sign Domain |
| I | = | Interpretant Domain |
Introducing a few abbreviations for use in considering the present Example, we have the following data:
| O | = | {Ann, Bob} | = | {A, B} |
| S | = | {"Ann", "Bob", "I", "You"} | = | {"A", "B", "i", "u"} |
| I | = | {"Ann", "Bob", "I", "You"} | = | {"A", "B", "i", "u"} |
In the present Example, S = I = Syntactic Domain.
The next two Tables give the sign relations associated with the interpreters A and B, respectively, putting them in the form of relational databases . Thus, the rows of each Table list the ordered triples of the form (o, s, i) that make up the corresponding sign relations, LA and LB ⊆ O × S × I. It is often tempting to use the same names for objects and for relations involving these objects, but it is best to avoid this in a first approach, taking up the issues that this practice raises after the less problematic features of these relations have been treated.
Sign Relation of Interpreter A| Object | Sign | Interpretant |
|---|
| A | "A" | "A" |
| A | "A" | "i" |
| A | "i" | "A" |
| A | "i" | "i" |
| B | "B" | "B" |
| B | "B" | "u" |
| B | "u" | "B" |
| B | "u" | "u" |
Sign Relation of Interpreter B| Object | Sign | Interpretant |
|---|
| A | "A" | "A" |
| A | "A" | "u" |
| A | "u" | "A" |
| A | "u" | "u" |
| B | "B" | "B" |
| B | "B" | "i" |
| B | "i" | "B" |
| B | "i" | "i" |
These Tables codify a rudimentary level of interpretive practice for the agents A and B, and provide a basis for formalizing the initial semantics that is appropriate to their common syntactic domain. Each row of a Table names an object and two co-referent signs, making up an ordered triple of the form (o, s, i) that is called an elementary relation, that is, one element of the relation's set-theoretic extension.
Already in this elementary context, there are several different meanings that might attach to the project of a formal semiotics, or a formal theory of meaning for signs. In the process of discussing these alternatives, it is useful to introduce a few terms that are occasionally used in the philosophy of language to point out the needed distinctions.
Dyadic aspects of sign relations
For an arbitrary triadic relation L ⊆ O × S × I, whether it is a sign relation or not, there are six dyadic relations that can be obtained by projecting L on one of the planes of the OSI-space O × S × I. The six dyadic projections of a triadic relation L are defined and notated as follows:
| LOS | = | projOS(L) | = | { (o, s) ∈ O × S : (o, s, i) ∈ L for some i ∈ I } |
| LSO | = | projSO(L) | = | { (s, o) ∈ S × O : (o, s, i) ∈ L for some i ∈ I } |
| LIS | = | projIS(L) | = | { (i, s) ∈ I × S : (o, s, i) ∈ L for some o ∈ O } |
| LSI | = | projSI(L) | = | { (s, i) ∈ S × I : (o, s, i) ∈ L for some o ∈ O } |
| LOI | = | projOI(L) | = | { (o, i) ∈ O × I : (o, s, i) ∈ L for some s ∈ S } |
| LIO | = | projIO(L) | = | { (i, o) ∈ I × O : (o, s, i) ∈ L for some s ∈ S } |
By way of unpacking the set-theoretic notation, here is what the first definition says in ordinary language. The dyadic relation that results from the projection of L on the OS-plane O × S is written briefly as LOS or written more fully as projOS(L), and it is defined as the set of all ordered pairs (o, s) in the cartesian product O × S for which there exists an ordered triple (o, s, i) in L for some interpretant i in the interpretant domain I.
In the case where L is a sign relation, which it becomes by satisfying one of the definitions of a sign relation, some of the dyadic aspects of L can be recognized as formalizing aspects of sign meaning that have received their share of attention from students of signs over the centuries, and thus they can be associated with traditional concepts and terminology. Of course, traditions may vary as to the precise formation and usage of such concepts and terms. Other aspects of meaning have not received their fair share of attention, and thus remain anonymous on the contemporary scene of sign studies.
Denotation
One aspect of a sign's complete meaning is concerned with the reference that a sign has to its objects, which objects are collectively known as the denotation of the sign. In the pragmatic theory of sign relations, denotative references fall within the projection of the sign relation on the plane that is spanned by its object domain and its sign domain.
The dyadic relation that makes up the denotative, referential, or semantic aspect or component of a sign relation L is notated as Den(L). Information about the denotative aspect of meaning is obtained from L by taking its projection on the object-sign plane, in other words, on the 2-dimensional space that is generated by the object domain O and the sign domain S. This semantic component of a sign relation L is written in any one of the forms, LOS, projOSL, L12, proj12L, and it is defined as follows:
- Den(L) = projOSL = { (o, s) ∈ O × S : (o, s, i) ∈ L for some i ∈ I }.
Looking to the denotative aspects of LA and LB, various rows of the Tables specify, for example, that A uses "i" to denote A and "u" to denote B, whereas B uses "i" to denote B and "u" to denote A. All of these denotative references are summed up in the projections on the OS-plane, as shown in the following Tables:
projOS(LA)| Object | Sign |
|---|
| A | "A" | | A | "i" | | B | "B" | | B | "u" | | projOS(LB)| Object | Sign |
|---|
| A | "A" | | A | "u" | | B | "B" | | B | "i" | |
Connotation
Another aspect of meaning concerns the connection that a sign has to its interpretants within a given sign relation. As before, this type of connection can be vacuous, singular, or plural in its collection of terminal points, and it can be formalized as the dyadic relation that is obtained as a planar projection of the triadic sign relation in question.
The connection that a sign makes to an interpretant is here referred to as its connotation. In the full theory of sign relations, this aspect of meaning includes the links that a sign has to affects, concepts, ideas, impressions, intentions, and the whole realm of an agent's mental states and allied activities, broadly encompassing intellectual associations, emotional impressions, motivational impulses, and real conduct. Taken at the full, in the natural setting of semiotic phenomena, this complex system of references is unlikely ever to find itself mapped in much detail, much less completely formalized, but the tangible warp of its accumulated mass is commonly alluded to as the connotative import of language.
Formally speaking, however, the connotative aspect of meaning presents no additional difficulty. For a given sign relation L, the dyadic relation that constitutes the connotative aspect or connotative component of L is notated as Con(L).
The connotative aspect of a sign relation L is given by its projection on the plane of signs and interpretants, and is thus defined as follows:
- Con(L) = projSIL = { (s, i) ∈ S × I : (o, s, i) ∈ L for some o ∈ O }.
All of these connotative references are summed up in the projections on the SI-plane, as shown in the following Tables:
projSI(LA)| Sign | Interpretant |
|---|
| "A" | "A" | | "A" | "i" | | "i" | "A" | | "i" | "i" | | "B" | "B" | | "B" | "u" | | "u" | "B" | | "u" | "u" | | projSI(LB)| Sign | Interpretant |
|---|
| "A" | "A" | | "A" | "u" | | "u" | "A" | | "u" | "u" | | "B" | "B" | | "B" | "i" | | "i" | "B" | | "i" | "i" | |
Ennotation
The aspect of a sign's meaning that arises from the dyadic relation of its objects to its interpretants has no standard name. If an interpretant is considered to be a sign in its own right, then its independent reference to an object can be taken as belonging to another moment of denotation, but this neglects the mediational character of the whole transaction in which this occurs. Denotation and connotation have to do with dyadic relations in which the sign plays an active role, but here we have to consider a dyadic relation between objects and interpretants that is mediated by the sign from an off-stage position, as it were. As a relation between objects and interpretants that is mediated by a sign, this aspect of meaning may be referred to as the ennotation of a sign, and the dyadic relation that constitutes the ennotative aspect of a sign relation L may be notated as Enn(L).
The ennotational component of meaning for a sign relation L is captured by its projection on the plane of the object and interpretant domains, and it is thus defined as follows:
- Enn(L) = projOIL = { (o, i) ∈ O × I : (o, s, i) ∈ L for some s ∈ S }.
As it happens, the sign relations LA and LB are fully symmetric with respect to exchanging signs and interpretants, so all of the data of projOSLA is echoed unchanged in projOILA and all of the data of projOSLB is echoed unchanged in projOILB.
projOI(LA)| Object | Interpretant |
|---|
| A | "A" | | A | "i" | | B | "B" | | B | "u" | | projOI(LB)| Object | Interpretant |
|---|
| A | "A" | | A | "u" | | B | "B" | | B | "i" | |
Charles Sanders Peirce was an American scientist, mathematician, logician, and philosopher who is sometimes known as "the father of pragmatism". According to philosopher Paul Weiss, Peirce was "the most original and versatile of America's philosophers and America's greatest logician". Bertrand Russell wrote "he was one of the most original minds of the later nineteenth century and certainly the greatest American thinker ever".
In mathematics, a finitary relation over sets X1, ..., Xn is a subset of the Cartesian product X1 × ⋯ × Xn; that is, it is a set of n-tuples (x1, ..., xn) consisting of elements xi in Xi. Typically, the relation describes a possible connection between the elements of an n-tuple. For example, the relation "x is divisible by y and z" consists of the set of 3-tuples such that when substituted to x, y and z, respectively, make the sentence true.
In the philosophy of language, a proper name – examples include a name of a specific person or place – is a name which ordinarily is taken to uniquely identify its referent in the world. As such it presents particular challenges for theories of meaning, and it has become a central problem in analytic philosophy. The common-sense view was originally formulated by John Stuart Mill in A System of Logic (1843), where he defines it as "a word that answers the purpose of showing what thing it is that we are talking about but not of telling anything about it". This view was criticized when philosophers applied principles of formal logic to linguistic propositions. Gottlob Frege pointed out that proper names may apply to imaginary and nonexistent entities, without becoming meaningless, and he showed that sometimes more than one proper name may identify the same entity without having the same sense, so that the phrase "Homer believed the morning star was the evening star" could be meaningful and not tautological in spite of the fact that the morning star and the evening star identifies the same referent. This example became known as Frege's puzzle and is a central issue in the theory of proper names.
Semiotics is the systematic study of sign processes (semiosis) and meaning-making. Semiosis is any activity, conduct, or process that involves signs, where a sign is defined as anything that communicates something, usually called a meaning, to the sign's interpreter. The meaning can be intentional, such as a word uttered with a specific meaning; or unintentional, such as a symptom being a sign of a particular medical condition. Signs can also communicate feelings and may communicate internally or through any of the senses: visual, auditory, tactile, olfactory, or gustatory (taste). Contemporary semiotics is a branch of science that studies meaning-making and various types of knowledge.
"Pragmaticism" is a term used by Charles Sanders Peirce for his pragmatic philosophy starting in 1905, in order to distance himself and it from pragmatism, the original name, which had been used in a manner he did not approve of in the "literary journals". Peirce in 1905 announced his coinage "pragmaticism", saying that it was "ugly enough to be safe from kidnappers". Today, outside of philosophy, "pragmatism" is often taken to refer to a compromise of aims or principles, even a ruthless search for mercenary advantage. Peirce gave other or more specific reasons for the distinction in a surviving draft letter that year and in later writings. Peirce's pragmatism, that is, pragmaticism, differed in Peirce's view from other pragmatisms by its commitments to the spirit of strict logic, the immutability of truth, the reality of infinity, and the difference between (1) actively willing to control thought, to doubt, to weigh reasons, and (2) willing not to exert the will, willing to believe. In his view his pragmatism is, strictly speaking, not itself a whole philosophy, but instead a general method for the clarification of ideas. He first publicly formulated his pragmatism as an aspect of scientific logic along with principles of statistics and modes of inference in his "Illustrations of the Logic of Science" series of articles in 1877-8.
Semiosis, or sign process, is any form of activity, conduct, or process that involves signs, including the production of meaning. A sign is anything that communicates a meaning, that is not the sign itself, to the interpreter of the sign. The meaning can be intentional such as a word uttered with a specific meaning, or unintentional, such as a symptom being a sign of a particular medical condition. Signs can communicate through any of the senses, visual, auditory, tactile, olfactory, or taste.
In semiotics, a sign is anything that communicates a meaning that is not the sign itself to the interpreter of the sign. The meaning can be intentional, as when a word is uttered with a specific meaning, or unintentional, as when a symptom is taken as a sign of a particular medical condition. Signs can communicate through any of the senses, visual, auditory, tactile, olfactory, or taste.
A pragmatic theory of truth is a theory of truth within the philosophies of pragmatism and pragmaticism. Pragmatic theories of truth were first posited by Charles Sanders Peirce, William James, and John Dewey. The common features of these theories are a reliance on the pragmatic maxim as a means of clarifying the meanings of difficult concepts such as truth; and an emphasis on the fact that belief, certainty, knowledge, or truth is the result of an inquiry.
In semiotics, linguistics, anthropology, and philosophy of language, indexicality is the phenomenon of a sign pointing to some element in the context in which it occurs. A sign that signifies indexically is called an index or, in philosophy, an indexical.
Interpretant is a subject / sign that refers to the same object as another sign, transitively.
In semiotics, a modality is a particular way in which information is to be encoded for presentation to humans, i.e. to the type of sign and to the status of reality ascribed to or claimed by a sign, text, or genre. It is more closely associated with the semiotics of Charles Peirce (1839–1914) than Ferdinand de Saussure (1857–1913) because meaning is conceived as an effect of a set of signs. In the Peircean model, a reference is made to an object when the sign is interpreted recursively by another sign, a conception of meaning that does in fact imply a classification of sign types.
An existential graph is a type of diagrammatic or visual notation for logical expressions, proposed by Charles Sanders Peirce, who wrote on graphical logic as early as 1882, and continued to develop the method until his death in 1914.
Representation is the use of signs that stand in for and take the place of something else. It is through representation that people organize the world and reality through the act of naming its elements. Signs are arranged in order to form semantic constructions and express relations.
The logic of information, or the logical theory of information, considers the information content of logical signs and expressions along the lines initially developed by Charles Sanders Peirce. In this line of work, the concept of information serves to integrate the aspects of signs and expressions that are separately covered, on the one hand, by the concepts of denotation and extension, and on the other hand, by the concepts of connotation and comprehension.
In philosophy—more specifically, in its sub-fields semantics, semiotics, philosophy of language, metaphysics, and metasemantics—meaning "is a relationship between two sorts of things: signs and the kinds of things they intend, express, or signify".
In semiotics, the study of sign processes (semiosis), the meaning of a sign is its place in a sign relation, in other words, the set of roles that the sign occupies within a given sign relation.
John Deely was an American philosopher and semiotician. He was a professor of philosophy at Saint Vincent College and Seminary in Latrobe, Pennsylvania. Prior to this, he held the Rudman Chair of Graduate Philosophy at the Center for Thomistic Studies, located at the University of St. Thomas (Houston).
Charles Sanders Peirce began writing on semiotics, which he also called semeiotics, meaning the philosophical study of signs, in the 1860s, around the time that he devised his system of three categories. During the 20th century, the term "semiotics" was adopted to cover all tendencies of sign researches, including Ferdinand de Saussure's semiology, which began in linguistics as a completely separate tradition.
On May 14, 1867, the 27–year-old Charles Sanders Peirce, who eventually founded pragmatism, presented a paper entitled "On a New List of Categories" to the American Academy of Arts and Sciences. Among other things, this paper outlined a theory of predication involving three universal categories that Peirce continued to apply in philosophy and elsewhere for the rest of his life. The categories demonstrate and concentrate the pattern seen in "How to Make Our Ideas Clear", and other three-way distinctions in Peirce's work.
The following outline is provided as an overview of and topical guide to semiotics: