Peirce's Semiotic

His indexical and meta-indexical theory of the proposition does not create the split between logic and indexicality that plagues Frege's account or the langue-parole dichotomy that troubles Saussure. Predicates describe qualities or states of affairs, while indices point to objects, external reality, or aspects of their context of use. Propositions are meta-indexical in that they represent the predicates as holding true of the objects picked out by indices. The barrier between indexicality and logical form does not exist for Peirce; a theory of speech acts inspired by Peirce would not need the distinction between locution and illocution that Austin presupposed.

The indexical aspect built into all referring terms renders hypotheses about them testable by inquiry; scientific inquiry is a public, self-correcting process, and reality is that which the community of inquirers would ultimately agree upon as true. Peirce's accounts of the roles of abduction, induction, and deduction in a social process of scientific inquiry foreshadow Putnam's discussion of the linguistic division of labor; his analysis of logical and final interpretants as hypotheses about the imagined indexical effects of certain terms also foreshadows Kripke's and Putnam's discussions of necessary truths that are a posteriori; in Peirce's vocabulary, these are abductions or explanatory hypotheses about indexical connections that will be discovered to be true at the end of the ideal process of scientific inquiry.

Peirce's account also complements Saussure's in its insistence that a sign consists of a signifier possessing certain qualities that allow it to be a sign, an object, and an interpretant. Peirce thus adds the signifier dimension missing from Frege's account, while at the same time creating a semiotics that will accommodate propositions that are missing from Saussure's analysis. He does not subscribe to Saussure's idea of grammatical categories as the product of systematic correlations of differences in sound with differences in meaning, but he is able to situate linguistic signs within a larger sign theory without reducing them to other types of signs.

Finally, Peirce's general sign theory contains within it this author's idea of a potentially infinite process of semiosis; it provides a semiotic account of the Derridean notion of iterability. According to Peirce, a sign is irreducibly triadic, and contains within it the ability to produce another sign both similar to and different from it. There is no direct sign-object relation in Peirce's account; rather, a sign mediates the relation between itself and an object in such a way as to cause another sign to relate to it in the same way it relates to the object and so on. De Man used Peirce's account to show that grammar and rhetoric were in a constantly productive and infinitely iterable relation to one another. Derrida points out that Peirce "seems to have been more attentive than Saussure to the irreducibility of this becoming-unmotivated" (Derrida 1976, 48) in the semiotic process and then proceeds to characterize Peirce's breakthrough:

Peirce goes very far in the direction that I have called the de-construction of the transcendental signified, which, at one time or another, would place a reassuring end to the reference from sign to sign. I have identified logocentrism and the metaphysics of presence as the exigent, powerful, systematic and irrepressible desire for such a signified. Now Peirce considers the indefiniteness of reference as the criterion that allows us to recognize that we are indeed dealing with a system of signs. What broaches the movement of signification is what makes its interruption impossible. The thing itself is a sign. (Derrida 1976, 49)

Interest in Charles Sanders Peirce enjoys periodic revivals, which sweep across several disciplines at once without any of them being aware of what the others are doing with his work. He first came to prominence as one of the founders of American pragmatism, a field in which his work was popularized by William James and others. In succeeding generations, he became the intellectual father figure of Jakobson's post-Praguean semiotics, as well as pragmatism's voice in the verificationist debates of postwar analytic philosophy. With the "linguistic turn" of the sixties, Peirce's scientific constructivist view of reality influenced figures as intellectually diverse as Quine, Rorty, and Habermas, while poststructuralists such as De Man and Deleuze have used his semiotics to develop rhetorical analyses of texts and films. Perhaps because of the breadth of his work in mathematics, logic, the philosophy of science, metaphysics, and semiotics, there has been little attempt to understand how the various parts of his work go together, and he is often invoked piecemeal to back up already established positions. Indeed, when he was alive, Peirce had already complained that James and others had appropriated his definition of pragmatism for their own purposes, even going so far as "to express some meaning that it was designed to exclude" (1961, 5:414, 276).[1] He felt compelled to invent a new term, "pragmaticism," which was "ugly enough to be safe from kidnappers" (ibid.).

Peirce's disagreements with James's interpretations of pragmatism lay in part with his objections to the latter's nominalism and psychologism. James, like most of pragmatism's early acolytes, lacked the logical and scientific training that Peirce had. Therefore, when James, George Herbert Mead, Charles Morris, and others developed pragmatism, they tended to move toward a behaviorist psychology in which the overall framework that combined logic, semiotics, and inference was lost.

The original philosophical impetus for Peirce's work was Kant. From his teenage days under the constant tutelage of his father, one of the leading mathematicians of his day, Peirce studied Kant's philosophy. Although he would eventually abandon Kant's schemas, he admired the "architectonic" structure of Kant's thought. Kant had relied on his generation's understanding of syllogistic logic to develop a classification of the fundamental types of judgments, and from these he derived twelve basic categories. Peirce agreed that a system of basic categories should be based on logic, but he felt that Kant's "most astounding ignorance of traditional logic" (1961, 1:560), not to speak of the discoveries of Boole and DeMorgan, meant that the whole enterprise needed an updating and fundamental revision. His own logical and mathematical discoveries would lead him to develop a set of fundamental categories that would start from an analysis of the internal structure of propositions and their relations to different types of inference; these discoveries are also at the heart of his semiotics, which replaced the Kantian subject-object dichotomy with a triadic conception of semiosis.

In his work after 1870, Peirce jettisons the Kantian framework in favor of an approach that more closely links his semiotics and logic to issues surrounding scientific methodology and even eventually evolutionary theory. The reasons for these shifts lie in his understanding of DeMorgan's logic of relatives, which he saw as making problematic Kant's analytic -synthetic distinction, and his experience as a practicing scientist (Peirce had a degree in chemistry, worked part-time for the Harvard Observatory, and would later direct some classic research in photometry). He proposes three forms of argument -deduction, abduction or hypothesis, and induction - which he sees as the fundamental logical components of scientific inquiry; Peirce defines reality as that which an ideal scientific community would come to agree upon as true, at least in part because of his belief that the self-correcting nature of scientific inquiry would weed out competing theories and eventually hit upon what reality was.

A key component in Peirce's "architectonic" is his theory of propositional form, which reaches its mature development only after the thinker's codiscovery, with his student Thomas Mitchell, of quantification theory in the 1880s. Subject terms and proper names function as what Peirce calls "indices"; they denote single individuals, and the logical quantifiers 'all' and 'some' are indeterminate indices that define ways of picking out individuals in a manner similar to present-day game-theoretic interpretations of quantification. The linkage of quantifiers and indices is crucial to Peirce's theory of reality and inference because indices are signs that draw attention to objects and events; they are the semiotic pathways to what exists, and reality consists of true explanatory theories about the real, to be discovered through abduction, induction, and deduction. His indexical interpretation of propositions supplies the realist component of his anti-Cartesian epistemology and contrasts sharply with that of the other discoverer of quantification theory, Gottlob Frege. For Frege, working out of a different logical tradition, indexicality is a residual problem in Frege's theory of propositional form, and Frege's epistemology takes a distinctly Platonic and idealist turn.

Interwoven with Peirce's semiotic and logical theories is a theory of meaning, belief, and habit. It is usually this dimension of Peirce's thought that is picked up in past and current versions of pragmatism. The ultimate meaning of a concept is how it would influence our habits of action. Habits are themselves patterns of behavior whose general nature is created by the sign processes that mediate them, and beliefs are general dispositions to behave in certain ways. given our desires and the contexts we find ourselves in.

By the end of his career, Peirce had moved from his earlier Kantian presuppositions to a full-fledged evolutionary theory of both reality and love, and to a community-based constructivist epistemology and theology. He replaced Kant's categories with a classification of sign types internally structured by his metaphysical categories of "firstness," "secondness," and "thirdness," which in turn will ground Peirce's later and more speculative work on evolutionary cosmology, the ultimate good of the "unlimited community," and "evolutionary love." Although there has been a tendency to dismiss this later work as wild speculation brought about by his reduced living conditions (Peirce was dismissed from his only teaching post at Johns Hopkins in 1884 and died broke in 1914), many of its themes can be found in his earlier work. Peirce's early metaphysics is a tripartite Kantian system of categories that are clearly related to his beliefs about the Trinity. Versions of these categories remain throughout his work, and in his later life Peirce explicitly uses them to reexamine some of the cosmological and religious themes that were part of the background of his earliest ideas. Whatever the merit of his cosmological and theological schemes, Peirce's present-day influence lies in his cofounding of pragmatism and his theory of signs. With the general decline of interest in metaphysics in analytic philosophy, Peirce's categories of firstness, secondness, and thirdness have received little attention; even his work in logic has been overshadowed by that of the Frege-Russell tradition. Despite his Platonic theory of thoughts and idealist metaphysics, Frege has had a much greater influence on the development of the philosophy of language and poststructural linguistics than Peirce. This is particularly unfortunate in that Peirce's sign theory explicitly links logic, inference, metaphysics, and epistemology in ways that open up these fields of inquiry to problems of the social constitution of reality and the public nature of all sign processes.

In 1866 Peirce began publishing a series of articles that were intended as part of a larger essay entitled "Search for a Method." Although heavily influenced by Kant's ideas, they already show the start of Peirce's divergences from Kant; the break with Kant would not become final until after 1870 with his article "The Logic of Relatives," but these earlier articles already show how Peirce's sign theory and his classification of forms of logical argument were intimately connected. In 1898, he would look back on his earlier work and write:

In the early sixties I was a passionate devotee of Kant, at least as regarded the Transcendental Analytic in the Critic of the Pure Reason. I believed more implicitly in the two tables of the Functions of Judgment and the Categories than if they had been brought down from Sinai. Hegel, so far as I knew him through a book by Vera repelled me. Now Kant points out certain relations between the categories. I detected others; but these others, if they had any orderly relation to a system of conceptions, at all, belonged to a larger system than that of Kant's list. Here there was a problem to which I devoted three hours a day for two years, rising from it, at length, with the demonstrative certitude that there was something wrong about Kant's formal logic. (Peirce 1961, 4:2)

The fundamental problem is that Kant thought that all syllogisms could be reduced to a mode of deduction known as Barbara. Peirce felt that this reduction itself involved additional logical principles not derivable from Barbara. These considerations would lead Peirce to rework the notion of logical argument to include induction and hypothesis (abduction).

One of the papers alluded to by Peirce in his 1898 statement was "On the Natural Classification of Arguments," in which he lays out the essential parts of an argument. These include a set of propositions that constitute the premises of the argument; the judgment that if these premised propositions are true, then some other proposition, the conclusion, must be, or is likely to be, true; and a "leading principle" of the argument, which is the principle implied in this judgment. A valid argument is one whose leading principle is true, and both the premises and leading principle must be true if an argument should determine the necessary or probable truth of the conclusion. The first form of argument that Peirce treats is that of deduction, which includes the syllogistic forms used by Kant. Peirce then introduces two other forms of argument, induction and hypothesis, which are not parts of the Kantian schema. Induction is a form of statistical generalization that Peirce defines as an "argument which assumes that a whole collection, from which a number of instances have been taken at random, has all the common characters of those instances" (1961, 2:511). The form that induction might take for a set of propositions might be:

S, S', S" are taken at random as M's,

Hypothesis, which Peirce would later identify as abduction, is a form of argument in which there is an analogical relation between premises and conclusion. It takes the following form:

Any M is, for instance, P, P', P", & etc.,

In his later work, Peirce will make argue that hypothesis or abduction is reasoning to the best explanation; given certain premises (for example, some observed phenomena), the conclusion is the best explanation for the occurrence of the phenomena; abduction is a way of generating new hypotheses and will work with deduction and induction as part of the self-correcting method of scientific inquiry.

In a subsequent article, "On a New List of Categories," Peirce builds on his analysis of the forms of argument to create a general sign theory. This article, although written in a heavily Kantian manner, already diverges from Kant in at least two important ways. First is Peirce's use of forms of argument as the basis for his classification of categories; second is his replacement of Kant's subject/object epistemology with a theory of semiosis in which representation (Peirce's term is "interpretant") is seen as playing a mediating role within a sign and between signs.

Peirce felt that his theory of categories established

that the function of conceptions is to reduce the manifold of sensuous impressions to unity and that the validity of a conception consists in the impossibility of reducing the content of consciousness without the introduction of it. (1961, 1:545)

The unity to which understanding reduces these impressions is that of a proposition that consists of a subject term to express the substance referred to and a predicate term to express some quality of that substance. The copulative force of predication, expressed in the "is" of predication, is a conception of being that unites the quality expressed by the predicate to the substance expressed by the subject term. This linkage of substance and being is the source of human cognition. The universal conception nearest to sense, a conception expressed in our notion of substance, is that of the present, in general. This conception, expressed by the subject position of a proposition, indicates what is present to the mind before any act of discrimination or comparison has been made. In itself, such a conception has "no proper unity" and is merely a representation of what is contained in attention itself before anything has been predicated of it. In its unanalyzed but general form as the "stuff of attention," this "it" attended to by the mind is identical with the conception of substance.

This conception of substance is, however, completely indeterminate and has no proper unity. The unity of conception expressed by propositional form consists in the connection of the predicate to the subject. The predicate expresses some quality, and the copula indicates a determination of the subject, that it "actually is" or "would be" expressing that quality. Substance and being are "the beginning and end of all conception" and represent the maximal opposition through which cognition works.

The conception of being unites the quality expressed by the predicate to the substance expressed by the subject. There are three conceptions of being in the movement from predication to substance. The first conception is that of the quality indicated by the predicate. Since a proposition asserts that the quality named by the predicate applies to the subject, this presupposes that the quality is abstractable from the substance, and then is considered as independent of that to which it applies. Its applicability to the subject is purely hypothetical. In the proposition 'This stove is black', 'blackness', in order to be predicated of 'this stove', must be discriminated from the stove and considered in itself. This pure abstraction is the first conception of being and Peirce calls it the "ground."

The second conception of being is that of relation or reference to a correlate. A quality can be known only through its contrast or similarity to some other, which Peirce terms a "correlate." In the case of 'This stove is black', blackness is discriminated and contrasted to the "manifold" of sensory impressions from which it is abstracted. At the same time, the copulative nature of the "is" of predication indicates that this reference to a correlate involves a comparison, which introduces the third conception of being, that of an interpretant. According to Peirce, every act of comparison requires besides the related thing (or "relate"), the ground, and the correlate, also

a mediating representation which represents the relate to be a representation of the same correlate which this mediating representation itself represents. (1961, 1:554)

The mediating representation Peirce calls an "interpretant." His example is that of a dictionary in which the French word 'homme' is translated by the English word 'man'. The French word is a thing (the relate) that refers to a ground or quality that is abstracted from the relate and then compared and applied to its correlate (two-legged creatures). The interpretant word 'man' represents the word 'homme' as standing for its correlate in the same way that ,man' does. The interpretant is the last conception in passing from being to substance. Peirce then concludes that he has analyzed the nature of five fundamental categories - the two overarching categories of being and substance and the three conceptions of being - quality (reference to a ground), relation (reference to a correlate), and representation (reference to an interpretant). The categories of being are the foundation for his future ontology of firstness, secondness, and thirdness.

This passage from the many to the one is numerical. The conception of third is that of an object which is so related to two others, that one of these must be related to the other in the same way in which the third is related to the other. Now this coincides with the conception of an interpretant. An other is plainly equivalent to a correlate. The conception of second differs from that of other, in implying the possibility of a third. In the same way, the conception of self implies the possibility of an other. The ground is the self abstracted from the concreteness which implies the possibility of another. (1961, 1:556)

From these categories he derives three types of representations – likenesses (later called "icons"), indices, and symbols. Icons are representations whose relation to their objects is merely that of sharing some common quality; indices relate to their objects via a connection in fact; and symbols have their ground by imputing some character as existing between the representation and its object.

Peirce then analyzes how his three categories of being are essential to logic. For him, logic deals with second intentions, which are the objects of understanding considered as representations. First intentions are the objects of those representations. The objects of understanding considered as representations are signs that are potentially general. Logic applies to symbols, not to icons and indices, because these cannot in themselves be used to construct arguments. Logic is the science that investigates the general relation of symbols to their objects, and becomes one of a trivium of sciences. These sciences correspond to each of Peirce's three ontological categories.

The first would treat of the formal conditions of symbols having meaning, that is of the reference of symbols in general to their grounds or implied characters, and this might be called formal grammar; the second, logic, would treat of formal conditions of the truth of symbols; and the third would treat of the force of symbols, or their power of appealing to a mind, that is, of their reference in general to interpretants, and this might be called formal rhetoric. (1961, 1:559)

A corresponding trichotomy would exist among types of symbols.

(1)   Symbols which directly determine only their grounds or imputed qualities, and are thus but sums of marks or terms.

(2)   Symbols which also independently determine their objects by means of other term or terms, and thus, expressing their own objective validity, become capable of truth or falsehood, that is, are propositions; and

(3)   Symbols which also independently deter-mine their interpretant, and thus minds to which they appeal, by premising a proposition or propositions which such a mind is to admit. These are arguments. (1961, 1:559)

A term such as a proper name or common noun is a symbol that evokes the idea of its referent but in itself is neither true nor false. A proposition is constructed out of symbols and can be asserted; its subject-predicate structure is such that the subject term refers to an object or objects that the predicate represents in some manner, thereby making the whole propositional sign either true or false. An argument consists of a set of propositions (the premises) that determine a representation (its conclusion) that represents the argument as representing its object. An argument represents its conclusion as true by virtue of the truth of its premises and the validity of its leading principle. The description that Peirce then gives of the types of arguments - deduction, induction, and abduction -harks back to "On the Natural Classification of Arguments."

In 1868 Peirce wrote a series of articles ("Questions Concerning Certain Faculties Claimed for Man," "Some Consequences of Four Incapacities," and "Grounds of Validity for the Laws Of Logic") for the Journal of Speculative Philosophy in which he stated several themes that would remain as he developed his versions of pragmatism and pragmaticism and his theory of signs. In these articles, Peirce argues that every thought is a sign and thinking is a sign process; there are no cognitions that are not products of inferences, and even knowledge of the internal world is derived from "hypothetical reasoning from our knowledge of external facts" (1961, 5:265).

Inductions and hypotheses produce thoughts that can be either true or false, depending on whether what is thought about is real or unreal. Our conception of what is real depends on our ability to correct ourselves, to discover what is unreal or an illusion. What is unreal is idiosyncratic, and subject to the whims of individual thoughts, whereas the real is that which would stand in the long run. The real is "that which, sooner or later, information and reasoning would finally result in, and which is therefore independent of the vagaries of me and you" (1961, 5:311). What the ideal community of inquirers would always continue to reaffirm as true is reality, while the unreal is that which it would always deny.

Finally, as what anything really is, is what it may finally come to be known to be in the ideal state of complete information, so that reality depends on the ultimate decision of the community; so thought is what it is, only by virtue of its addressing a future thought which is in its value as though identical with it, though more developed. In this way, the existence of thought now depends on what is to be hereafter; so that it has only a potential existence, dependent on the future thought of the community. (1961, 5:316)

With the development of his semiotic theory, Peirce began to combine different interests of his into an integrated outlook on how inference, logic, scientific inquiry, reality, and meaning might work together that would lay the foundation for his versions of pragmatism and pragmaticism. In 1877 and 1878 he published two articles, "The Fixation of Belief" and "How to Make Our Ideas Clear," for Popular Science Monthly that he viewed as continuing the arguments of the Journal of Speculative Philosophy pieces.

In "The Fixation of Belief," Peirce integrates his ideas about sign processes and the social constitution of reality into a theory of mind and inquiry in which surprise, doubt, belief, and inference were functionally intertwined. The ultimate meaning of a concept is how it would influence our habits of action if, given our other beliefs and desires, we accepted it as true, that is, if we believed it. Meaning is related to inquiry because the aim of inquiry is to arrive at permanently settled-on beliefs by overcoming doubt. Belief leads to fixed habits of action, whereas doubt leaves one uncertain about how to act. Inference is the way we change our beliefs in light of our experience in the world. Unexpected experiences surprise us, leading us to the disturbing state of doubting our beliefs. In order to reduce this feeling, we form hypotheses about what has happened, thereby changing our expectations about what will occur; if these are confirmed, we move back to a state of belief, with the cycle then ready to repeat itself.

Reality is that which exists independently of anyone's beliefs. Unlike other ways of fixing belief, such as those of authority, tenacity, or a priori reasoning, the scientific mode of fixing belief is ultimately self-correcting, and is the only one that, if systematically applied, will lead different inquirers to the same results. In "How to Make Our Ideas Clear," Peirce describes the scientist's faith in the process of inquiry.

This great hope is embodied in the conception of truth and reality. The opinion which is fated to be ultimately agreed to by all who investigate, is what we mean by the truth, and the object represented in this opinion is the real. That is the way I would explain reality. (196 1, 5:407)

Consider what the effects, that might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these effects is the whole of our conception of the object. (1961, 5:402)

The pragmatic maxim also links meaning to inquiry. The pragmatic analysis of the meaning of a sign shows what the implications are of hypotheses containing that sign; unlike definitions, which work only between words, pragmatic analysis ties meaning to reality. Since "the essence of belief is the establishment of habit" (1961, 5:398), and since different beliefs are "distinguished by the different modes of action to which they give rise" (ibid.), clarifying our beliefs involves applying the pragmatic maxim to them, that is, seeing what practical consequences follow from holding a given belief. Doubt is the spur to inquiry; when doubt ceases, there is no reason to inquire further, and belief is fixed. When we act on our beliefs and encounter unexpected results, the doubt that arises is also a "new starting-place for thought" (1961, 5:397). If finding out what is true is the aim of inquiry, then it will be tied to belief and doubt; a true hypothesis would be that which cannot be doubted and would be believed at the end of inquiry. Pragmatism makes explicit what is already present in Peirce's semiotic theory of inquiry.

In his later work Peirce would continue his Kantian search for a set of fundamental categories that would unify his discoveries in logic and mathematics. In these early articles, he has already abandoned the strict syllogistic reasoning that Kant employed, adding hypothesis and induction. The introduction of a mediating representation, or interpretant, also signaled at least two departures from Kant. First, the concept of an interpretant is crucial for Peirce's sign theory. Not only is it one of the three parts of every sign, but it indicates the power of signs to be signs of each other, as part of a potentially infinite process of semiosis. Subject-object epistemologies posit the basic problem to be the relation between minds or quasi-minds and external objects. In Kant's theory, the basic categories emerge from the logical structure of judgments. For Peirce, it was more important to understand how signs could generate other signs, and that potential had to be built into the structure of signs.

Peirce's second departure from Kant would be to rework his metaphysical categories in light of his work on the logic of relations. The Kant-inspired categories of being and substance would be dropped. Instead, Peirce believed he could show that triadic relations could not be reduced to dyadic or monadic relations and that all higher-order relations could be reduced to some combination of the three types. If signs are irreducibly triadic, then dyadic, subject object models of knowledge would be inadequate for a triadic sign process. The logic of relations provided Peirce with a formally justified alternative to Kant's theory of judgment, and provided a mathematical backing for his categories of firstness, secondness, and thirdness. In addition, Peirce's metaphysical category of thirdness could not be derived from either firstness or secondness, and a whole set of categories, such as interpretants, habits, laws, and signs, would have a reality of their own. In 1905 Peirce wrote an addendum to "On a New List of Categories" that registers these changes and foreshadows some of the later use he will make of his own metaphysical categories for his speculations about evolutionary cosmology and other topics.

After a series of inquiries, I came to see that Kant ought not to have confined himself to divisions of propositions, or "judgments," as the Germans confuse the subject by calling them, but ought to have taken account of all elementary and significant differences of form among signs of all sorts, and that, above all, he ought not to have left out of account fundamental forms of reasoning. At last, after the hardest two years' mental work that I have ever done in my life, I found myself with but a single assured result of any positive importance. This was that there are but three elementary forms of predication or signification, which as I originally named them ... were qualities (of feeling), (dyadic) relations, and (predications of) representations. (1961, 1:561)

Although the origins of Peirce's future work in semiotics can be found in his 1867-68 articles, the full integration of his semiotics and logic does not appear until after his discovery of quantification theory in the early 1880s. Peirce's approach to quantification incorporates and extends his semiotic analysis of the proposition. In 1885 Peirce published a paper, "On the Algebra of Logic," in which he laid out the rules for modern quantification theory. These include the expansion of Boolean algebras to a logic of relations allowing multiplace predicates, quantification rules, scope distinctions for quantifiers, and a treatment of identity. In this and other works, Peirce treats the quantifiers as special types of indices.

This treatment of quantifiers as indices (compared, for example, with Frege's treatment of them as second-order predicates) arises from Peirce's theory of relations.

If from any proposition having more than one subject (used to include "objects") we strike out the indices of the subjects, as in "_______praises______to_____," "____dat in matrimonium_______," what remains and requires at least two insertions of subject nouns to make a proposition is a "relative term," or "relative rhema," called briefly a "relative." (1961, 3:636)

The blanks in a relation are to be filled in by indices that designate the object characterized by the relation. The quantifiers indicate "indexical directions of what to do to find the object meant" because "they inform the hearer how he is to pick out one of the objects intended" (1961, 2.289). For example, the "universal selectives" such as 'any', 'every', and 'all' "mean that the hearer is at liberty to select any instance he likes within limits expressed or understood, and the assertion is intended to apply to that one" (1961, 2:289).

Peirce also treats identity in terms of indices. In developing his notation, he defines identity as a relation between two indices:

Our notation, so far as we have developed it, does not show us even how to express that two indices, i and j, denote one and the same thing.... But this relation of identity has peculiar properties. The first is that if i and j are identical, whatever is true of i is true of j.... The other property is that if everything which is true of i is true of j, then i and j are identical. (1961, 3:399)

This implies that codenoting terms are intersubstitutable without changing the truth values of propositions of which they are parts.

The ontological implications of Peirce's semiotic arise from his treatment of singular terms, identity, and quantifiers. Reference presupposes the uniqueness and specificity of the object(s) to which a term refers. For Peirce, the only truly referring items are indices, and all the terms that can be inserted in the blank spaces of relational expressions are either indices or representations of indices. Even proper names have an indexical component.

A proper name, when one meets with it for the first time, is existentially connected with some percept or other equivalent individual knowledge of the individual it names. It is then, and then only, a genuine Index. The next time one meets with it, one regards it as an Icon of that Index. The habitual acquaintance with it having been acquired, it becomes a Symbol whose Interpretant represents it as an Icon of an Index of the Individual named. (1961, 2:329)

Peirce interprets the logical quantifiers 'some' and 'all' (which he calls "selectives") as a special type of index. If a term does not pick out a definite singular object, it is "indeterminate." There are two types of indeterminacy, indefiniteness (signaled by the quantifier 'some') and generality (signaled by 'any'). Peirce treats quantification as part of a contested dialogue between an utterer and an interpreter. The utterer asserts a proposition and tries to defend it against the attacks of his interpreter.

The utterer is essentially a defender of his own proposition, and wishes to interpret it so that it will be defensible. The interpreter, not being so interested, and being unable to interpret it fully without considering to what extreme it may reach, is relatively in a hostile attitude, and looks for the interpretation least defensible. (MS 9, 3-4)[2]

Peirce describes the use of the quantifier 'some' as one in which the utterer is free to pick out the object designated by the quantified subject term ('there is some object such that . . .'). In order for the proposition to be true, the utterer needs to pick out some object for which the predicate is true. In the case of a general selective or universal quantifier, the choice is left to the interpreter. For example, if the utterer asserts the proposition 'all men are mortal,' then the interpreter/opponent is given the opportunity to pick out some object that contradicts the proposition. Complex quantified propositions involving several selectives have a similar structure, with each existential quantifier indicating an mutterer's choice and each universal quantifier the interpreter's. The choices are made sequentially, and with each speaker knowing what the other has done.

whichever of the two makes his choice of the object he is to choose, after the other has made his choice, is supposed to know what that choice was. This is an advantage to the defense or attack, as the case may be. (MS 9, 3)

Peirce's understanding of the logic of relatives and his development of quantification theory allow him to use his metaphysical categories to analyze the internal structures of propositions and their relationship to both external reality and processes of inference. A proposition is built from different levels of generality, as signaled by the differences between indexical subject terms and iconic predicates. The selectives 'some' and 'all' allow us to move from singular reference to the intermediate forms of generality essential for mathematical reasoning. Peirce's mature sign theory combines these logical discoveries with his metaphysical speculations, allowing us to see how propositions and arguments are constructed of elements with different semiotic properties.

Peirce's formal semiotic is derived from his theory of the proposition, logical relations, and the metaphysical categories of "firstness," "secondness," and "thirdness." According to Peirce, all logical relations are either monadic, dyadic, or triadic. More complicated relations can be shown to be combinations of triads that in rum are irreducible to dyadic or monadic relations (1961, 1:363). Since this typology applies to all possible relations, it should be applicable to all the fundamental categories of thought and nature.

But there is one triad in particular which throws a strong light on the nature of all the others. Namely, we find it necessary to recognize in logic three kinds of characters, three kinds of facts. First there are singular characters which are predicable of single objects, as when we say that anything is white, large, etc. Secondly, there are dual characters which appertain to pairs of objects; these are implied by all relative terms as "lover," .,similar," "other," etc. Thirdly, there are plural characters, which can all be reduced to triple characters but not to dual characters. Thus, we cannot express the fact that A is a benefactor of B by any descriptions of A and B separately; we must introduce a relative term. This is requisite, not merely in English, but in every language which might be invented. (1961, 1:370)

monadic relatives include ordinary nonrelative predicates. dyadic relations can be either genuine or degenerate. A genuine dyadic relation (also called a "real" relation) "subsists in virtue of a fact which would be totally impossible were either of the related objects destroyed" (1961, 1:365). For example, the relation "sister of " contains a relative property that neither term of the relation could possess if the other term were destroyed. A degenerate dyadic relation "subsists in virtue of two facts, one only of which would disappear in the annihilation of either of the relates" (ibid.). For example, a dyadic relation of similarity such as 'as blue as' yields a relative property (in this case, 'blue') which either term of the relation could possess independently of the existence of the other. Triadic relations may be doubly or singly degenerate. If the terms in the relation retain their relative properties independently of one another, the triadic relation is doubly degenerate. A singly degenerate relation occurs when the dyadic members of the relation retain their relative properties independently of the third.

From this typology of relations, it is possible to derive both Peirce's metaphysical categories and his sign theory. His metaphysical categories of firstness, secondness, and thirdness result from applying this typology to the categories of thought and nature.

The first [category] is that whose being is simply in itself, not referring to anything nor lying behind anything. The second is that which is what it is by force of something to which it is second. The third is that which is what it is owing to things between which it mediates and which it brings into relation to each other. (1961, 1:356).

Pure firstness is exemplified by qualities of feeling that exist as mere possibilities "entirely separated from all conception or reference to anything else" (1961, 1:356). Firsts are simple, unanalyzable, independent qualities of feeling that are analytically separable from the actual experiencing of these qualities.

The typical ideas of firstness are qualities of feeling, or mere appearances. The scarlet of your royal liveries, the quality itself, independently of its being perceived or remembered, is an example, by which I do not mean that you are to imagine that you do not perceive or remember it, but that you are to drop out of account that which may be attached to it in perceiving or in remembering, but which does not belong to the quality. For example, when you remember it, your idea is said to be dim and when it is before your eyes, it is vivid. But dimness or vividness do not belong to your idea of the quality. They might no doubt, if considered simply as a feeling; but when you think of vividness you do not consider it from that point of view. You think of it as a degree of disturbance of your consciousness. The quality of red is not thought of as belonging to you, or as attached to liveries. It is simply a peculiar positive possibility regardless of anything else. If you ask a mineralogist what hardness is, he will say that it is what one predicates of a body that one cannot scratch with a knife. But a simple person will think of hardness as a simple positive possibility the realization of which causes a body to be like a flint. That idea of hardness is an idea of firstness. The unanalyzed total impression made by any manifold not thought of as actual fact, but simply as a quality, as simple positive possibility of appearance, is an idea of firstness. (1961, 8:329)

Unlike secondness and thirdness, which are orders of complexity, firstness has no structure

The idea of the absolutely first must be entirely separated from all conception of or reference to anything else; for what involves a second is it~ self a second to that second. The first must therefore be present and immediate, so as not to be second to a representation. It must be fresh and new, for if old it is second to its former state. It must be initiative, original, spontaneous, and free; otherwise it is second to a determining cause. It is also something vivid and conscious; so only it avoids being the object of some sensation. It precedes all synthesis and all differentiation; it has no unity and no parts. (1961, 1:357)

A firstness is exemplified in every quality of a total feeling. It is perfectly simple and without parts; and everything has its quality. Thus the tragedy of King Lear has its firstness, its flavor sui generis. That wherein all such qualities agree is universal firstness, the very being of firstness. The word possibility fits it, except that possibility implies a relation to what exists, while universal firstness is the mode of being of itself. That is why a new word was required for it. Otherwise, "possibility" would have answered the purpose. (1961, 1:53 1)

Like all dyadic relations, secondness involves othemess. An object cannot be a second of itself but rather has some element of its being that necessarily involves another.

Secondness is that mode of being of that which is such as it is, with respect to a second but regardless of any third. (1961, 8:328)

An example of an idea of secondness is the experience of effort.... no third element enters. (196 1, 8:330)

Peirce associates secondness with existence and actuality.

We may say with some approach to accuracy that the general firstness of all true Secondness is existence, though this term more particularly applies to Secondness in so far as it is an element of the reacting first and second. If we mean Secondness as it is an element of the occurrence, the firstness of it is actuality. But actuality and existence are words expressing the same idea in different applications. Secondness, strictly speaking, is just when and where it takes place, and has no other being; and therefore different Secondnesses, strictly speaking, have in themselves no quality in common. (1961, 1:532)

Thirdness is the domain of triadic relations, and its basic property is that of mediation and combination. "Now the word 'means' is almost an exact synonym to the word third" (1961, 1:532). The most basic triadic relation is that possessed by a representamen, of which signs are a subclass. A representamen is anything that is capable of establishing ("mediating") a triadic relation between itself, an object, and an interpretant. A sign is a representamen with a mental interpretant.

A representamen is a subject of a triadic relation To a second, called its OBJECT, FOR a third, called its interpretant, this triadic relation being such that the representamen determines its interpretant to stand in the same triadic relation to the same object for some interpretant. (196 1,541)

The following definition makes a reference to cognition.

A representamen is the First Correlate of a triadic relation, the Second Correlate being termed its Object, and the possible Third Correlate being termed its interpretant, by which triadic relation the possible interpretant is determined to be the First Correlate of the same triadic relation to the same Object, and for some possible interpretant. A Sign is a representamen of which some interpretant is a cognition of a mind. Signs are the only representamens that have been much studied. (1961, 2:242)

In a draft of a letter to his patron, Lady Welby, Peirce writes

A "sign" is anything, A, which

1) in addition to other characters of its own,

2) stands in a dyadic relation r, to a purely active correlate, B,

3) and is also in a triadic relation to B for a purely passive correlate C, this triadic relation being such as to determine C to be a dyadic relation, S, to B, the relation S corresponding in a recognized way to the relation r. (1977, 192)

Peirce offers the following description of a representamen that is not a sign (because it does not have a mental interpretant): "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" (1961, 1:274). Using the letters given in Peirce's letter to Lady Welby, we can create the diagram in

figure 4. 1.

Sunflower A is a representamen of the sun if and only if it is the first correlate of a triadic relation whose second correlate, B, is the sun and whose third correlate (the interpretant) is sunflower C. Sunflower A causes sunflower C to stand in a dyadic relation, S, to B in some way that corresponds to the way, r, in which it itself stands in relation to the sun. Furthermore, sunflower A not only causes C to assume this triadic relation but also gives C the reproductive power to produce another sunflower that would stand in some way, say, t, with respect to the sun as r does to s and so on ad infinitum. Although this example may seem a little fantastic, there is a similarity between thirdness and genetic reproduction. Peirce has two ways of elaborating his sign theory. The first is to appeal to language and conversation as a metaphor for what goes on in thinking generally (1977, 80-81). The second is to present his sign theory within the context of a theory of relations and metaphysics in which the dialogic metaphors of utterer and interpreter are dropped in favor of a more rigorous treatment of the different types of sign relations (see the discussion of this issue in Singer 1984, 66-69, 93-94).

In the dialogic model, a sign would seem to be embedded in a matrix of utterer-sign-object-interpretant-interpreter, where the interpretant is a cognition or representation (created by inference) in the mind of the interpreter. For example, a sentence is a sign made up of other signs, namely words, and, when uttered, the sentence stands for something (its "object," in the broadest sense of the term). In a successful communication, the utterance of the sign produces in the interpreter a representation that is at least partially equivalent to that of the utterer. Since the interpretant itself is a sign, it must be capable of determining an interpretant of its own, and so on ad infinitum. Peirce uses the metaphor of conversation to describe thinking as a kind of internal dialogue.

A thought is a special variety of sign. All thinking is necessarily a sort of dialogue, an appeal from the momentary self to the better considered self of the immediate and of the general future. (1977, 195)

If thinking is an inner dialogue between present and future selves, then each instance of this dialogue involves the creation of an equivalent or more developed sign, that is, a shared sign or "corninterpretant" between these selves. Again, a linguistic analogy makes clearer what Peirce had in mind. The speaker utters signs standing for some "object," thereby producing signs (the "interpretants") in the listener that also stand for that object in some way that corresponds to the speaker's signs. Furthermore, insofar as each instance of discourse maintains some continuity with what was talked about earlier (usually through such textual devices as anaphora or cataphora), each successive use of signs in the discourse creates in the listener an interpretant evincing a signobject relation similar to that of the original sign. Although the actual chain of sign-object-interpretants ends with the end of discourse (for example, if the participants change topics), the signs introduced still possess the capability of producing other possible dialogues, of being further developed, even if the signs' original user or anyone else never actually uses or develops them.

A few clarifying points about Peirce's use of the word "sign." First, a sign is anything that could determine the triadic relation between itself, an object, and an interpretant. A sign can possess this capability regardless of whether or not it actually brings about such a triadic relation. As Peirce puts it, the representamen relation "must therefore consist in a power of the representamen to determine some interpretant to being a representamen of the same object" (1961, 1:542, Peirce's emphasis).

Second, Peirce restricts signs to representamens with mental interpretants, created by creatures who are capable of learning. This means that a sign must be something that has the potential to determine an interpretant that is created by inference. In the sunflower example, the interpretant is brought about by some biological process and presumably not by an inference. Anything that could not determine such inferences would not be a sign.

Third, Peirce's notion of an object is extremely broad.

The Objects - for a Sign may have any number of them - may each be a singly known existing thing or thing believed formerly to have existed or expected to exist, or a collection of such things, or a known quality or relation or fact, which single Object may be a collection or whole of parts, or it may have some other mode of being, such as some act permitted whose being does not prevent its negation from being equally permitted, or something of a general nature desired, required, or invariably found under certain general circumstances. (1961, 2:232)

Peirce's definition of a sign also commits him to an intensionalist theory of semiosis. This intensionalism rests upon his notion of sign and interpretant, which is quite different from Morris's extensionalist and behavioristic interpretations. Morris's definition of the semantic aspect of semiosis is purely extensional - a sign is defined by the class of objects it denotes. Morris defines Peirce's interpretant as the behavioral consequences of the sign, a "habit of the organism to respond [to the sign]" (1938, 109). Peirce subscribes to neither analysis; he insists, as Frege did in another, but related, context, that there are different modes of presentation linking sign and object and that a sign is something that is capable of causing something else, its interpretant, to stand in the same relation to the sign's object as the sign does. The sign must be able to determine an interpretant to represent the sign itself, and its mode of presentation, to its object. The isomorphism "of modes of presentation" is thus real, not degenerate, and part of the definition of a sign entails its possessing a real intensional quality - there must be some quality of the sign and its relation to its object that the sign represents and then uses to determine the interpretant of the sign.

Finally, Peirce directly links thirdness to the generality of desire (1961, 1: 341) and the notion of purpose:

[the] idea of purpose makes the act appear as a means to an end. Now the word means is almost an exact synonym to the word third. It certainly involves Thirdness. (1961, 1:532)

Peirce also says that the representamen relation "must therefore consist in a power of the representamen to determine some interpretant to being a representamen of the same object" (1961, 1:542). Extending these statements to the case in which the interpretant is a sign created by an inference in an organism capable of learning (a "scientific intelligence" with mental interpretants), a sign is something that is capable of bringing about in its interpreter another sign ("the interpretant") to assume the same relation to the object through the creation of an intensional isomorphism between sign-object and interpretant object relations. A sign acts like a goal-directed system with the potential for infinite reproducibility. A sign serves as an "effector" in that it is capable of determining an interpretant. It also acts as a "sensor," because there must be some reproductive capability that determines that the relation between interpretant and object is similar to that of sign and object, with the original signobject relation as the "goal setting" that must get reproduced. Peirce's theory of signs thus has a self-correcting capability built into it. Since all thought is in signs, then all thought is self-correcting, and the bases of inference lie in this self-correcting aspect of all semiosis. Although the sunflower example also involves self-cortection, Peirce does not consider it an instance of sign processes, because it does not involve a mental interpretant determined by inference. Sunflowers do not learn -they cannot modify their internal representations through interactions with the environment. There is no self-correcting relationship between the organism's "goal settings" and its interactions with the world.

Peirce applies his metaphysical categories to each of the three correlates of the sign relation, thus obtaining three trichotomies of signs. The first trichotomy is the sign in itself as a firstness, or mere quality (" quali sign"); as a secondness, or actual existent ("sinsign"); and as a thirdness, or law ("legisign"). The second trichotomy concerns the nature of the relation between the sign and its object as a firstness ("icon"), secondness ("index"), or thirdness ("symbol"). The last trichotomy pertains to the relation between sign and interpretant. If the interpretant represents the sign as a sign of possibility, the sign is a "rheme"; as a sign of existence, a "dicisign"; and as a sign of law, an "argument."

In the first trichotomy, the sign is considered simply in itself, without reference to the other correlates. The sign can be either a quality (qualisign), an actual existent thing or event (a sinsign), or a law (legisign). A qualisign cannot act semiotically unless it is embodied in some sinsign, but this embodiment has nothing to do with its quality as a sign. A sinsign is an existent that functions as a sign. Since all existents have some qualities, sinsigns presuppose qualisigns.

A legisign is a general type that signifies through instances, or replicas (also called "tokens"). An example of a legisign is a word. For example, there are several tokens, or instances, of the word 'the' in this paragraph. Each instance is an instantiation of a type that "itself has no existence although it has a real being, consisting in the fact that existents will conform to it" (1961, 2:292), the existents being the individual tokens, or replicas. A legisign is a law that determines the production of sinsigns each of which conforms to the abstract type Thus legisigns presuppose sinsigns and, in turn, also qualisigns.

Peirce felt that his second trichotomy of icon-index-symbol was of special importance. This trichotomy divided signs according to the relation of a sign to its object. If a sign can refer to its object "merely by virtue of characters of its own, and which it possesses, just the same, whether any such Object actually exists or not" (1961, 2:247), it is an icon. An icon refers to its object because it possesses some properties that also happen to be shared by or similar to those of its object. Since it possesses these qualities whether or not its object actually exists, an icon is a doubly degenerate sign.

Peirce divides icons into images, diagrams, and metaphors.

An icon whose representative quality is a simple quality, such as a color, that could represent another object of similar color, is an image. Icons that represent the relations of parts of their objects through analogous relations in their own parts are diagrams. Finally, metaphors are those icons "which represent the representative character of a representamen by representing a parallelism in something else" (1961, 2:277).

An index is a sign "which refers to the Object that it denotes by virtue of being really affected by that Object" (1961, 2:247). An index is a singly degenerate sign, since the dyadic members of the relation can exist and retain their relational property independently of being represented by the third correlate, the interpretant. According to Peirce, since an index is in a "dynamical" relation to its object, it necessarily has some property in common with its object, and it is through this property (minimally spatiotemporal contiguity) that it refers to its object. This property is an icon, so all indexes involve icons. However, although the index does contain such an icon as a necessary component, the icon is not sufficient to make the sign an index. The additional element is the condition that the sign be actually modified by the object, and it is this actual modification that makes the sign a true secondness. Examples of indices are a bullet hole as an index of the passage of a bullet, a weather vane as an index of the wind direction, and, in a "mediated" or "degenerate" sense, demonstratives such as 'this' or 'that.' If an index creates an interpretant sign in some interpreter so that the interpretant stands in the same existential and dynamical relation to the object as the index, then an index has the effect of drawing the attention of the interpreter to its object. An index "fixes" what is represented but has no descriptive role (Goudge 1969, 53).

A symbol is a sign "which refers to the Object that it denotes by virtue of a law, usually an association of general ideas, which operates to cause the symbol to be interpreted as referring to that Object" (Peirce 196 1, 2:249). A symbol is a general type, or legisign, that acts through tokens, or replicas, so as to be interpreted as standing in a genuine triadic relation to its object.

A symbol is a sign which would lose the character which renders it a sign if there were no interpretant. Such is any utterance of speech which signifies what it does only by virtue of its being understood to have that signification. (Peirce 1961, 2:304)

In the third trichotomy, a rheme is a sign that, "for its interpretant, is a sign of qualitative possibility, that is, is understood as representing such a kind of possible object" (Peirce 1961, 2:250). Any rheme may be capable of giving information, but its interpretant does not represent the rheme as doing so but instead interprets the rheme as a sign of essence.

A dicisign is a sign that for its interpretant is a sign of actual existence. Such a sign represents its object with respect to actual existence and is capable of being either true or false. A dicisign conveys information as distinguished from an icon from which information may be derived (Peirce 1961, 2:309). Its paradigmatic form is a proposition. A proposition consists of a subject that is an index of a second existing independently of its being represented and a predicate that is an icon of a firstness, or quality. In a proposition, these two components are represented as connected in such a way that if the dicisign has any object, the dicisign must be an index of a secondness subsisting between the object and the quality (Peirce 1961, 2:312). For example, the form ' is an author' is a rheme indicating some qualitative possibility, which when combined with some index (such as a proper name), yields a proposition (dicisign) that is either true or false.

Finally, an argument is a sign that is represented by its interpretant as a sign of law. An argument is a sign "which is understood to represent its Object in its character as Sign" (Peirce 1961, 2:252); it thus represents its object in a full triadic relation, that is, as a law. Its paradigm is the syllogism.

The Interpretant of the Argument represents it as an instance of a general class of Arguments, which class on the whole will always tend to the truth. It is this law, in some shape, which the argument urges; and this ,,urging" is the mode of representation proper to Arguments. (1961, 2:253)

Since every sign includes all three correlates, any particular sign can be characterized by the nature of its correlates as described in the three trichotomies of signs. Of the twenty-seven possible classes of signs, only ten actually occur. This is because of Peirce's principle that a first, or possibility, can determine only a first; a second, or existent, can determine either another second or, degenerately, a first; and finally a third, or law, determines a third or, degenerately, a second (one degree of degeneracy) or a first (two degrees of degeneracy). Put another way, Peirce's principle states that a possibility can determine only a possibility and that laws are determined only by laws.

Applying this principle to the sign trichotomies yields ten classes of signs rather than twenty-seven (table 4. 1). The principle is applied in sequence to the correlates, because each of the later correlates presupposes the previous ones. There can be no sign-object relation without the sign itself, and there can be no Interpretant to represent that relation without the relation. A qualisign-icon-rheme, or qualisign, is a sign whose first correlate is a quality. Since a quality is whatever it is merely in its own characters, it can relate to its second correlate only through properties it possesses in and of itself. A qualisign must possess some property that is similar to the properties contained by its object, and it possesses this property independently of whether its object exists or not. Since a quality is a mere logical possibility, such a sign must also be a rheme - that is, a sign understood as representing such and such a kind of possible object, a sign that represents its object merely through the sign's own qualities. Peirce's example is a feeling of red.

A sinsign-icon-rheme, or iconic sinsign, is "any object of experience in so far as some quality of it makes it determine the idea of an object" (Peirce 1961, 2:55). As a sinsign, it will embody certain qualisigns. As an icon, it will refer to its object merely through properties of its own that happen to be similar to those of its object. Since the second correlate is a firstness, and thus can determine only a firstness, its Interpretant must be a rheme. Peirce's example is an individual diagram that is an existent that can refer to an object because of some properties (the "diagram") the sign has that are similar to those of its object.

Table 4.1 Peirce s Classification of Signs

A sinsign-index-rheme, or rhematic indexical sinsign, is "any object of experience so far as it directs attention to an Object by which its presence is caused" (Peirce 1961, 2:256). As a sinsign, it must be an existent of some kind. As an index, it must be an existent in some sort of "dynamical" connection with its object, a relation of mutual existence and entailment. As a rheme, the interpretant of such a sign represents it as representing its object as if it were merely a "mark" or "character." The rhematic indexical sinsign involves an iconic sinsign of a peculiar sort. The iconic sinsign involved is the property that the sign and its object share in common because they are causally related. The minimal property would be the sign's spatial and temporal location, which it could possess independently of its object (thus making it iconic, a quality the sign possesses in and of itself), but which it shares with its object. Since its object also possesses this property, the sign can function so as to represent the object. The rhematic indexical sinsign thus involves an iconic sinsign as a necessary component. It differs from an iconic sinsign such as an individual diagram in being in a dynamic relation with its object. In the case of the iconic sinsign, the sign possesses its quality independent of its object. In the case of the rhematic indexical sinsign, the sign's very existence entails that of its object. Peirce's example is a spontaneous cry. The spontaneity of the cry makes it a sinsign that is not a token of some legisign. The cry is caused or brought about by its object, its utterer, and thus is capable of drawing attention to him.

A sinsign-index-dicent, or dicent sinsign, is "any object of direct experience, in so far as it is a sign, and, as such, affords information concerning its Object" ( Peirce 196 1, 2:255). It involves a rhematic iconic sinsign to embody the information, that is, a sign that represents its object through its own characters, and a rhematic indexical sinsign that draws attention to the object characterized by the iconic sinsign. A dicent sinsign thus brings together both these signs. Peirce's example is a weathercock that indicates the direction of the wind. The weathercock has an iconic element because its position is similar to the direction in which the wind blows. It contains a rhematic indexical sinsign because it draws attention to the object (the wind) by which its position is determined.

A legisign-icon-rheme, or iconic legisign, "is any general law or type, in so far as it requires each instance of it to embody a definite quality which renders it fit to call up in the mind the idea of a like object" (Peirce 1961, 2:258). Since it is an icon, its interpretant can only represent the sign in its characters or simply as such and such a possibility. Since it is a legisign, its mode of being will be to govern the production of single tokens, each of which will be an iconic sinsign that possesses some quality that makes it a token of the type. Peirce offers the example of a diagram, apart from its factual individuality (which would make it an iconic sinsign).

A legisign-index-rheme, or rhematic indexical legisign, is "any general type or law, however established, which requires each instance of it to be affected by its Object in such a manner as merely to draw attention to that Object" (Peirce 1961, 2:259). Since it is a legisign, it operates through tokens, each of which is a rhematic indexical sinsign, that is, an individual existent that draws attention to its object, with which it co-occurs.

Since all rhematic indexical sinsigns involve iconic sinsigns, each token of a rhematic indexical legisign will involve iconic sinsigns. The particular iconic sinsign involved requires that the sign occupy (minimally) a spatiotemporal position similar to that of its object and that it is through this property that the sign can indicate its object. In addition to this iconic property, each token will function as an index by causing the interpretant to assume a similar relation to the object. Each token must therefore possess spatial-temporal co-occurrence with its object (the iconic aspect) and be able to draw attention to that object.

The rhematic indexical legisign is a law governing rhematic indexical sinsigns. Since the latter embody iconic sinsigns, the rhematic indexical legisign must also involve an iconic legisign that governs the production of the iconic sinsigns embodied in every token (each a rhematic indexical sinsign) of the rhematic indexical legisign. The interpretant of this type of legisign must represent it as an iconic legisign -that is, each token must possess spatiotemporal contiguity with its object. A description of such an iconic legisign would be a rule of use of the sign. For example, the legisign '1' specifies that every use of this sign refers to the speaker who utters the token. Since the interpretant represents the rhematic indexical legisign as an iconic sinsign, and since each sign determines its interpretant to stand in the same relation to the object as it does, this has the effect of determining the interpretant to stand in an indexical relation to the object through the mediation of a rule of use. Peirce's example of a rhematic indexical legisign is a demonstrative pronoun such as 'this' or' that'. Such a sign is a type each token of which indicates some relation of copresence between the sign, its utterer, and some referred to entity to which the sign directs attention.

A dicent indexical legisign "is any general type or law, however established, which requires each instance of it to be really affected by its object in such a manner as to furnish definite information concerning that Object" (Peirce 196 1, 2:2 6o). It will involve an iconic legisign to signify the information and a rhematic indexical legisign to draw attention to the subject of that information. Each token of a dicent indexical legisign is a dicent sinsign that consists of an iconic sinsign and a rhematic indexical sinsign.

Peirce's example is a street cry that identifies its utterer through its "tone and theme." Each token of a street cry functions as a genuine index of its utterer, since it is produced by him, and also as an icon by providing information regarding the utterer - who the utterer is. A description of an instance of such a sign might be "through his tone and voice, that is Mr. So and So," with "that" representing the indexical portion and "is Mr. So and So" the information.

A legisign-symbol~rheme, or symbolic rheme, "is a sign connected with its Object by an association of general ideas in such a way that its Replica calls up an image in the mind which image, owing to certain habits or dispositions of that mind, tends to produce a general concept, and the Replica is interpreted as a sign of an Object that is an instance of that concept" (Peirce 1961, 2:26 1). As a legisign, it functions through tokens. As a symbol, it represents its object through neither an iconic nor an indexical relationship to its object but rather through its relation to its interpretant. It is a rheme, or a sign that its interpretant represents as characterizing its object merely through properties of its own. Its interpretant thus represents the sign as either a rhematic indexical legisign or an iconic legisign, or both. If it represents it as a rhematic indexical legisign, it represents the sign as a law that requires each token to be really affected by its object so as to draw attention to the object. Peirce supplies as an example the noun "camel." Peirce's illustration of a rhematic symbol whose interpretant represents it as an iconic legisign is "phoenix."

A rhematic symbol is a law that represents its objects through tokens that do not bear an iconic or indexical relation to their objects. That is, the sign has no property in common with its object nor any existential relation with it. Instead, each token stands for its object by virtue of a law that causes the symbol to be interpreted as referring to that object.

A legisign-symbol-dicent, or dicent symbol, is "a sign connected with its object by an association of general ideas, and acting like a rhematic Symbol, except that its intended interpretant represents the dicent Symbol, in respect to what it signifies, as really affected by its Object, so that the existence or law which it calls to mind must be actually connected with the indicated Object" (Peirce 1961, 2:262). The sign represents itself as a genuine index of some object independent of the sign. It contains a subject, which is or represents an index of a second existing independently of its being represented, and a predicate that represents an icon of a firstness (a quality or essence). The two parts of the dicent symbol are represented as connected such that if the sign has any object, that object has the qualities or properties indicated in the predicate. Peirce's example is an ordinary proposition such as 'Women are wise,' which indicates that the objects of the sign 'women' are wise. Such a sign may be true or false but in itself provides no grounds for its truth or falsity.

A legisign-symbol-argument is "a sign whose interpretant represents its object as being an ulterior sign through a law, namely, the law that the passage from all such premises to such conclusions tends to the truth" (Peirce 1961, 2:262). Since its object is general, such a sign must be a symbol, and as a symbol it must be a legisign. Peirce offers the example of the traditional syllogism, which not only consists of dicent symbols (propositions) that in themselves may be true or false but then represents itself as a sign that is governed by the general laws of inference. There are three kinds of arguments - deductions, inductions, and abductions. Every argument consists of a set of propositions that are the premises, a proposition that is the conclusion, and a leading principle. The leading principle represents the way in which the conclusion is connected to the premises or may be said to follow from the premises. Although each type of argument has a different leading principle, they all state that if the premises of the argument are true, then the conclusion is, or is likely to be, true. In a deductive argument, the connection is through laws of syllogistic reasoning and logical quantification, as exemplified by "All men are mortal. Socrates is a man. Therefore Socrates is mortal." An inductive argument is one whose leading principle is one of statistical inference. For example, from the fact that a number of cases have a similar property, we can infer that that property would hold true of the whole class if our sampling procedures have been fair. An abduction is a hypothesis whose leading principle is its being the best explanation of a given set of circumstances. Peirce provides the following example to distinguish induction and abduction.

A certain anonymous writing is upon a tom piece of paper. It is suspected that the author is a certain person. His desk, to which only he has had access, is searched, and in it is found a piece of paper, the torn edge of which exactly fits, in all its irregularities, that of the paper in question. It is a fair hypothetical inference that the suspected man was actually the author. (1961, 2:632)

Peirce argues that if the conclusion were based only on induction, all one would be justified in concluding was that the two pieces of paper whose irregularities matched would be found to match in other characteristics. The inference from the shape of the paper to its ownership is "precisely what distinguishes hypothesis from induction" (1961,2:632).

In his later work, Peirce incorporates his pragmatic approach to meaning into his theory of signs. In an unpublished manuscript, he wrote that in his earlier article "How to Make Our Ideas Clear," he "did not there show how I had myself derived the [pragmatic maxim] from a logical and non-psychological study of the essential nature of signs" (MS 137, quoted in Misak 1991, 16). The key to this transformation is Peirce's theory of objects and their relations to reality and semiosis, and his theory of interpretants and their relations to inquiry. Although the pragmatic maxim "is intended to furnish a method for the analysis of concepts," it also "involves a whole system of philosophy" (1961, 8:191). The first step is to recognize that "the problem of what the 'meaning' of an intellectual concept is can only be solved by the study of the interpretants or proper significate effects of signs" (1961, 5:475), which led Peirce to clarify his theory of objects and interpretants.

Peirce distinguishes two types of objects according to the degree to which they are represented by signs:

We must distinguish between the Immediate Object, - i.e., the Object as represented in the sign, - and the Real (no, because perhaps the Object is altogether fictive, I must choose a different term, therefore), say rather the Dynamical Object, which from the nature of things, the Sign cannot express, which it can only indicate and leave the interpreter to find out by collateral experience. (1961, 8:314)[3]

Peirce's example is the sign 'It is a stormy day', spoken by Peirce to his wife. The immediate object is "the notion of the present weather so far as this is common to her mind and mine -not the character of it but the identity of it" (1961, 8:314). The "dynamical object" would be the actual weather conditions at the moment. The dynamic object lies outside the sign process itself, and can be known only by collateral observation or acquaintance. It is the "object as it is regardless of any particular aspect of it, the Object in such relations as unlimited and final study would show it to be" (1961, 8: 183). Another example Peirce gives of the distinction is the object of the sign 'blue'. Its immediate object would be the perceptual sensations associated with the color; the dynamic object would be the real existential condition that produces those perceptions and that "causes the emitted light to have short mean wave-length" (1961, 8: 183). Presumably in this case, it would mean specifying certain causal conditions ultimately discoverable by scientific inquiry. Peirce also points out that "the Object of a Sign may be something to be created by the sign" (1961, 8:178); his examples are fictional characters such as Hamlet and the state of affairs to be brought about by a command.

In addition to these two types of objects, there are at least three classes of interpretants that correspond to Peirce's categories of firstness, secondness, and thirdness. In an unpublished paper entitled "A Survey of Pragmaticism," Peirce introduces these as the emotional, immediate, and logical interpretants. An interpretant as a pure firstness is what Peirce calls the "emotional interpretant"; it is the feeling produced by a sign in the "quasi-mind" that interprets it. An interpretant considered as a secondness is the "energetic" interpretant; it is the particular reaction the sign produces - for example, a soldier's immediate response to an officer's command. A sign produces another sign, its logical interpretant, which, as a sign, is a "general," or thirdness; it is the general aspect of the meaning of a sign that processes of inference can develop or unfold over the potentially infinite process of semiosis. Peirce argues that the ultimate logical interpretant cannot be a concept but instead consists of the dispositions to action produced by the sign, the regular ways in which the sign mediates behavior.

In advance of ascertaining the nature of this effect, it will be convenient to adopt a designation for it, and I will call it the logical interpretant, without as yet determining whether this term shall extend to anything besides the meaning of a general concept, though certainly closely related to that, or not. Shall we say that this effect may be a thought, that is to say, a mental sign? No doubt, it may be so; only, if this sign be of an intellectual kind - as it would have to be - it must itself have a logical interpretant; so that it cannot be the ultimate logical interpretant of the concept. It can be proved that the only mental effect that can be so produced and that is not a sign but is of a general application is a habit change; meaning by habit change a modification of a person's tendencies toward action, resulting from previous experience or from previous exertions of his will or acts, or from a complexus of both kinds of cause. (1961, 5:476)

Peirce offers the example of someone attempting to solve a "map-coloring" problem. The subject will run through his mind various hypotheses, test out their consequences, and change his ideas about what to do next. According to Peirce, this process is the refinement of mental habits through inference, "experimentation in the inner world" (196 1, 5:491). Peirce's conclusion is that under given conditions, the interpreter will have formed the habit of acting in a given way whenever he may desire a given kind of result. The real and living conclusion is that habit; the verbal formulation merely expresses it.... The deliberately formed, self-analyzing habit - self analyzing because formed by the aid of analysis of the exercises that nourished it - is the living definition, the veritable and final logical interpretant. Consequently, the most perfect account of a concept that words can convey will consist in a description of the habit which that concept is calculated to produce. (Ibid.)

In articles probably written after "A Survey of Pragmaticism" (some of the manuscripts are undated), Peirce introduces a slightly different trichotomy of interpretant, which he also links to firstness, secondness, and thirdness.

As to the interpretant, i.e., the "signification," or "interpretation" rather, of a sign, we must distinguish an Immediate and a Dynamical, as we must the Immediate and Dynamical Objects. But we must also note that there is certainly a third kind of interpretant, which I call the Final interpretant, because it is that which would finally be decided to be the true interpretation if consideration of the matter were carried so far that an ultimate opinion were reached. (1961, 8: 184)

The immediate interpretant is an abstraction, a firstness, or possibility. It consists of the sign's capacity for being interpreted, what makes it recognizable as a sign of something. The dynamic interpretant is a secondness, a single event; it consists of what is experienced in a given act of interpretation (some form of effort) that distinguishes it from any other act of interpretation. The final interpretant is linked to Peirce's notion of inquiry. It is the fixed belief that inquiry would ultimately discover to be true. The difference between the dynamic and final interpretants, between situation-specific meaning and timeless meaning fixed by inquiry, echoes the gap between the fallibility of individual belief and that of the ideal community of inquirers.

Peirce also makes more explicit the relations between abduction, interpretants, and pragmatism. Abduction is the only mode of inference (sign formation) that introduces a new idea. Deduction reveals the logical implications of hypotheses arrived at by abduction, and induction is used to confirm their truth or falsity.

Deduction proves that something must be; Induction shows that something is actually operative; Abduction merely suggests that something may be. Its only justification is that from its suggestion deduction can draw a prediction which can be tested by induction, and that, if we are ever to learn anything or to understand phenomena at all, it must he by abduction that this is to be brought about. (1961, 5:171)

The essence of pragmatic analysis is to unfold the logic of abduction. Peirce uses his symbiotically grounded theory of abduction to link perception to his view of reality. They are part of a unified semiotic process, and constitute the key to his semiotic realism:

abductive inference shades into perceptual judgment without any sharp line of demarcation between them; or, in other words, our first premises, the perceptual judgments, are to be regarded as an extreme case of abductive inferences, from which they differ in being absolutely beyond criticism. (1961, 5:181)

The only difference between perceptual and abductive judgments is that we cannot imagine denying a perceptual judgment as it presents itself to us at a given moment, even though later it may prove to be an illusion. Since we can question the truth of an abductive judgment, Peirce argues that only the "test of inconceivability" distinguishes the two types of judgments.

I not only opine, however, that every general element of every hypothesis, however wild or sophisticated it may be, [is] given somewhere in perception, but I will venture so far as to assert that every general form of putting concepts together is, in its elements, given in perception.... The only symptom by which the two can be distinguished is that we cannot form the least conception of what it would be to deny the perceptual judgment. (1961, 5:186)

If we take a dicent proposition as an example, the indexical components of the expression ultimately refer to perceptions (immediate objects) that point to some external reality (dynamic objects), while its iconic aspects characterize that reality in some way. The final or ultimate logical interpretant of the dicent proposition would be that set of general meanings the scientific community would agree upon in its ideal process of scientific inquiry. Since such a sign represents some relation between a predicate and its indexical subject as holding to be true (it is an assertion), the scientific community can test these propositions, thereby determining more and more information about the objects referred to by the signs. The final interpretants of these signs are those general meanings discoverable by the scientific process, and they would be the accurate descriptions of all the conceivable effects of affirming or denying a given concept. The general meaning of a proposition is "applicable to every situation and to every purpose upon which the proposition has any bearing," and it is "simply the general description of all the experimental phenomena which the assertion of the proposition virtually predicts" (1961, 5:427). For example, if we took the statement 'this glass in front of us is filled with water', testing whether or not the liquid in the glass was water rather than some other liquid would involve determining its chemical structure. For Peirce, the truth of that statement would depend on what the process of scientific inquiry would discover in the long run about what the term 'water' refers to. Now if our present-day scientific hypotheses about water are true and water is indeed H2O, and if the liquid in the glass has that chemical composition, then the proposition is true.

The final interpretant is that which everyone would agree upon if inquiry reaches its ideal conclusion. It transcends the situation- specific nature of the dynamic interpretant. In the case of the dynamic objects of signs, it would be those hypotheses about the nature of those objects which science eventually proved to be true. The self-correcting nature of inference is thus built into the sign process itself, and is part of the pragmatic meaning of any concept. The pragmatic method allows inquirers to unfold the meaning of signs by seeing what consequences flow from adopting hypotheses of which they are a part These hypotheses are in the form of propositions generated by abduction; the scientific, experimentalist way of thinking is now internal to the sign theory itself. In his 1905 article "What Pragmatism Is," Peirce uses these ideas about inquiry, habit change, and meaning to update his pragmatic maxim:

if one can define accurately all the conceivable experimental phenomena which the affirmation or denial of a concept could imply, one will have therein a complete definition of the concept, and there is absolutely nothing more in it. (1961, 5:412)

Peirce's theory of inference and his semiotic analysis of the proposition work together to create his theory of reality. His analysis of the proposition involves a coordination between meta-indexical and indexical moments. A proposition is a sign that represents itself as an index by representing an indexical connection as existing between the subject and the predicate. Since the subject term is also an index, a proposition contains two indexical moments, or, more precisely, one moment indicated by the subject term, and another, meta-indexical moment that must represent the former indexical relation and its predicative counterpart as indexically linked. Moving from object to sign to interpretant in a dicent symbol, there is an "upshifting" from indexicality (the subject term to metaindexicality (the copulative core of the predication) to a symbolic rhematic level (the predicate term). From the movement of interpretant to sign to object, there is a corresponding "downshifting." This semiotic downshifting would imply that cognitions whose form is propositional involve a semiotic process in which the meta-indexical properties of linguistic signs can be read "down" toward, or projected onto, their "referents," which are indexical signs standing in some existensial relation to their objects. Since quantifiers are indexical specifications of how to pick out objects, one can discover the ontological implications of a theory by looking at the quantificational structure of its propositions. For example, the quantified proposition 'x(Fx)' is true if and only if one can pick out some object designated by an index, say, 'a', that "falls under" 'Fx'. Since the formula 'x(Fx)' abstracts away from any particular way of picking out the object, then if 'F(a)' is true and 'a' is the index substituted for lx', then the object designated by 'a' also satisfies 'Fx', and 'x(Fx)' is true. The key to "what there is" lies in the systematic investigation of the quantificational structure of a theory because these expressions are inherently indexical or meta-indexical (they refer to indices).

Looking over the evolution of Peirce's thought, we can extract several themes that are relevant to contemporary discussions about knowledge, meaning, and inference. First, Peirce combines both functionalist and dispositionalist approaches in his account of mental processes. Second, he links these processes to a semiotic epistemology that distinguishes between different levels of abstraction and different kinds of mediation. Third, because Peirce's semiotic theory of propositional structure is so closely tied to his epistemology, his approach differs from those which start with logical form and then ask how it gets instantiated by language or mental processes. Fourth, his emphasis on abduction, or reasoning to the best explanatory hypothesis, is an alternative to viewing knowledge either as justified true belief or causally produced. Finally, Peirce's arguments that truth and reality depend on the social construction of inquiry foreshadow some of the present debates over the role of a "division of linguistic labor" in the constitution of meaning, denotation, and extension.

Peirce's functionalism is different from contemporary approaches to language that derive from Turing machine analogies or computer models. Instead, it lies in the interfunctional relations he sees between belief, doubt, desire, and inquiry and the self-correcting nature of semiosis. Beliefs are certain behavioral dispositions that manifest themselves in a given context only given certain desires, but they may be changed through processes of inference that change our representations of the world. semiosis is self-correcting in its reproduction of thirdness; every sign causes another sign to stand in the same relation to its object as it does. Semiosis holds together the different parts of Peirce's theory of inference and inquiry. His semiotic theory places linguistic signs in a larger theory of sign processes in general and distinguishes between the different kinds of generality and multifunctionality that signs consist of. Sign processes are constitutive of mental processes; meaning does not exist as something external to the interpreter that must be grasped but is part of the process by which signs generate one another.

Peirce's semiotics sees logic and propositionality as internal to the sign process itself. His theory of logical form links logic to epistemology through his insistence on the indexical and meta-indexical analysis of propositions, which links signs both to external reality and to processes of inquiry and inference. His account of quantification is quite different from that of Frege and other logicians, who tend to see indexicality as a residual category to be eliminated by way of translation or interpretation.

Peirce's theory of abduction allows him to see perceptual and theoretical knowledge as all relying on some form of reasoning to the best explanation. Perceptual knowledge is based on inferences that take our sensory stimulations as data; it consists of hypotheses based on the "immediate objects" of sign processes. The hypothesis that there is a blue object in front of me is the best explanation of my sensory stimulations, just as the hypothesis that water is H20 is the best explanation of that substance's properties.

Modem analytic philosophy has used a logical tradition deriving from Frege's account of quantification theory for much of its present work on language, meaning, and epistemology. Austin's theory of speech acts includes a "locutionary act" that preserves "normal sense and reference," while semantic approaches have generally used some variant of Frege's quantification theory to analyze the logical structure of sentences and epistemic and modal contexts. Frege's logical work was not directed at developing a theory of knowledge or inquiry, however, but rather at securing a logical basis for mathematics. Peirce's theory, by contrast, while perhaps not as mathematically sophisticated as Frege's (though containing an alternative account of quantification), provides a systematic alternative for understanding how language, inquiry, meaning, and knowledge work.

A Peircean approach might lead to a radical revision of Austin's speech act philosophy. The key change would be in the nature of the locutionary act, which preserves Frege's sense and reference distinction.