Sign relation
Encyclopedia
A sign relation is the basic construct in the theory of signs, also known as semeiotic
or semiotics
, as developed by Charles Sanders Peirce.
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.
", and so it is informative to view it in that setting.
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.
. 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.
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:
Introducing a few abbreviations for use in considering the present Example, we have the following data:
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 database
s. 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.
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.
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:
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.
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:
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:
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:
All of these connotative references are summed up in the projections on the SI-plane, as shown in the following Tables:
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:
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.
Semeiotic
Semeiotic is a spelling variant of a word used by Charles Sanders Peirce, likewise as "Semiotic," "Semiotics", and "Semeotic", to refer to his philosophical logic, which he cast as the study of signs, or semiotic. Some, not all, Peircean scholars have used "semeiotic" to refer to distinctly...
or semiotics
Semiotics
Semiotics, also called semiotic studies or semiology, is the study of signs and sign processes , indication, designation, likeness, analogy, metaphor, symbolism, signification, and communication...
, 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
Semiosis
Semiosis is any form of activity, conduct, or process that involves signs, including the production of meaning. Briefly – semiosis is sign process...
, 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 "logicLogic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
", 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
Ontology
Ontology is the philosophical study of the nature of being, existence or reality as such, as well as the basic categories of being and their relations...
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
Triadic relation
In mathematics, a ternary relation or triadic relation is a finitary relation in which the number of places in the relation is three. Ternary relations may also be referred to as 3-adic, 3-ary, 3-dimensional, or 3-place....
, 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 scienceNormative scienceA normative science is a form of inquiry, typically involving a community of inquiry and its accumulated body of provisional knowledge, that seeks to discover good ways of achieving recognized aims, ends, goals, objectives, or purposes....
where psychology is a descriptive scienceDescriptive scienceThe term descriptive science is used to identify a category of science and distinguish it from other categories of science. The exact demarcation line can vary a bit depending on the purpose of making the distinction, but essentially it refers to those parts of science whose emphasis lies in...
, and so they have very different aims, methods, and rationales.
Signs and inquiry
There is a close relationship between the pragmatic theory of signs and the pragmatic theory of inquiryInquiry
An inquiry is any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem. A theory of inquiry is an account of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim.-Deduction:...
. 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
John Dewey
John Dewey was an American philosopher, psychologist and educational reformer whose ideas have been influential in education and social reform. Dewey was an important early developer of the philosophy of pragmatism and one of the founders of functional psychology...
). 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
Triadic relation
In mathematics, a ternary relation or triadic relation is a finitary relation in which the number of places in the relation is three. Ternary relations may also be referred to as 3-adic, 3-ary, 3-dimensional, or 3-place....
called the sign relation of that interpreter.
Understood in terms of its set-theoretic
Set theory
Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
extension
Extension (semantics)
In any of several studies that treat the use of signs - for example, in linguistics, logic, mathematics, semantics, and semiotics - the extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension or intension, which consists very roughly of...
, a sign relation L is a subset
Subset
In mathematics, especially in set theory, a set A is a subset of a set B if A is "contained" inside B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment...
of a cartesian product
Cartesian product
In mathematics, a Cartesian product is a construction to build a new set out of a number of given sets. Each member of the Cartesian product corresponds to the selection of one element each in every one of those sets...
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 database
Relational database
A relational database is a database that conforms to relational model theory. The software used in a relational database is called a relational database management system . Colloquial use of the term "relational database" may refer to the RDBMS software, or the relational database itself...
s. 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.
| 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" |
| 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 relationsBinary relation
In mathematics, a binary relation on a set A is a collection of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2 = . More generally, a binary relation between two sets A and B is a subset of...
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:
EWLINE
|
EWLINE
|
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:
EWLINE
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EWLINE
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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.
EWLINE
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Six 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
A gives B to C - we make no distinction in the ordinary logic of relations between the subjectSubject (grammar)The subject is one of the two main constituents of a clause, according to a tradition that can be tracked back to Aristotle and that is associated with phrase structure grammars; the other constituent is the predicate. According to another tradition, i.e...
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:A gives B to C A benefits C with B B enriches C at expense of A C receives B from A C thanks A for B B leaves A for C - These six sentences express one and the same indivisible phenomenon. (C.S. Peirce, "The Categories Defended", MS 308 (1903), EP 2, 170-171).
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 , are the same for the whole of mankind, as are also the objects (πράγματα) of which those affections are representations or likenesses, images, copies . (AristotleAristotleAristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
, De Interpretatione, 1.16a4).
SIO
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).
SOI
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)
See also
- Cartesian productCartesian productIn mathematics, a Cartesian product is a construction to build a new set out of a number of given sets. Each member of the Cartesian product corresponds to the selection of one element each in every one of those sets...
- Descriptive scienceDescriptive scienceThe term descriptive science is used to identify a category of science and distinguish it from other categories of science. The exact demarcation line can vary a bit depending on the purpose of making the distinction, but essentially it refers to those parts of science whose emphasis lies in...
- Dyadic relationBinary relationIn mathematics, a binary relation on a set A is a collection of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2 = . More generally, a binary relation between two sets A and B is a subset of...
- Formal grammarFormal grammarA formal grammar is a set of formation rules for strings in a formal language. The rules describe how to form strings from the language's alphabet that are valid according to the language's syntax...
- Formal languageFormal languageA formal language is a set of words—that is, finite strings of letters, symbols, or tokens that are defined in the language. The set from which these letters are taken is the alphabet over which the language is defined. A formal language is often defined by means of a formal grammar...
- InquiryInquiryAn inquiry is any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem. A theory of inquiry is an account of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim.-Deduction:...
- Logic of informationLogic of informationThe 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...
- Logic of relatives
- Logical matrix
- MeaningMeaning (semiotics)In semiotics, the meaning of a sign is its place in a sign relation, in other words, the set of roles that it occupies within a given sign relation. This statement holds whether sign is taken to mean a sign type or a sign token...
- Normative scienceNormative scienceA normative science is a form of inquiry, typically involving a community of inquiry and its accumulated body of provisional knowledge, that seeks to discover good ways of achieving recognized aims, ends, goals, objectives, or purposes....
- PragmaticsPragmaticsPragmatics is a subfield of linguistics which studies the ways in which context contributes to meaning. Pragmatics encompasses speech act theory, conversational implicature, talk in interaction and other approaches to language behavior in philosophy, sociology, and linguistics. It studies how the...
- Pragmatic information
- Projection
- RelationRelation (mathematics)In set theory and logic, a relation is a property that assigns truth values to k-tuples of individuals. Typically, the property describes a possible connection between the components of a k-tuple...
- SemanticsSemanticsSemantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....
- SemeioticSemeioticSemeiotic is a spelling variant of a word used by Charles Sanders Peirce, likewise as "Semiotic," "Semiotics", and "Semeotic", to refer to his philosophical logic, which he cast as the study of signs, or semiotic. Some, not all, Peircean scholars have used "semeiotic" to refer to distinctly...
- SemiosisSemiosisSemiosis is any form of activity, conduct, or process that involves signs, including the production of meaning. Briefly – semiosis is sign process...
- SemioticsSemioticsSemiotics, also called semiotic studies or semiology, is the study of signs and sign processes , indication, designation, likeness, analogy, metaphor, symbolism, signification, and communication...
- Semiotic information
- Set theorySet theorySet theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics...
- SignSign (semiotics)A sign is understood as a discrete unit of meaning in semiotics. It is defined as "something that stands for something, to someone in some capacity" It includes words, images, gestures, scents, tastes, textures, sounds – essentially all of the ways in which information can be...
- Sign relational complexSign relational complexIn semiotics, a sign relational complex is a generalization of a sign relation that allows for empty components in the elementary sign relations, or sign relational triples of the form ....
- Theory of relationsTheory of relationsThe theory of relations treats the subject matter of relations in its combinatorial aspect, as distinguished from, though related to, its more properly logical study on one side and its more generally mathematical study on another....
- Triadic relationTriadic relationIn mathematics, a ternary relation or triadic relation is a finitary relation in which the number of places in the relation is three. Ternary relations may also be referred to as 3-adic, 3-ary, 3-dimensional, or 3-place....
- Types of relations
Secondary 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 MartinRichard Milton MartinRichard Milton Martin was an American logician and analytic philosopher. In his Ph.D. thesis written under Frederic Fitch, Martin discovered virtual sets a bit before Quine, and was possibly the first non-Pole other than Joseph Henry Woodger to employ a mereological system...
(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 PercyWalker PercyWalker Percy was an American Southern author whose interests included philosophy and semiotics. Percy is best known for his philosophical novels set in and around New Orleans, Louisiana, the first of which, The Moviegoer, won the National Book Award for Fiction in 1962...
(2000), pp. 271–291 in Signposts in a Strange Land, P. Samway (ed.), Saint Martin's Press.