Valencies of Predicates. Thought of the Day 125.0

Naturalizing semiotics - The triadic sign of Charles Sanders Pei

Since icons are the means of representing qualities, they generally constitute the predicative side of more complicated signs:

The only way of directly communicating an idea is by means of an icon; and every indirect method of communicating an idea must depend for its establishment upon the use of an icon. Hence, every assertion must contain an icon or set of icons, or else must contain signs whose meaning is only explicable by icons. The idea which the set of icons (or the equivalent of a set of icons) contained in an assertion signifies may be termed the predicate of the assertion. (Collected Papers of Charles Sanders Peirce)

Thus, the predicate in logic as well as ordinary language is essentially iconic. It is important to remember here Peirce’s generalization of the predicate from the traditional subject-copula-predicate structure. Predicates exist with more than one subject slot; this is the basis for Peirce’s logic of relatives and permits at the same time enlarging the scope of logic considerably and approaching it to ordinary language where several-slot-predicates prevail, for instance in all verbs with a valency larger than one. In his definition of these predicates by means of valency, that is, number of empty slots in which subjects or more generally indices may be inserted, Peirce is actually the founder of valency grammar in the tradition of Tesnière. So, for instance, the structure ‘_ gives _ to _’ where the underlinings refer to slots, is a trivalent predicate. Thus, the word classes associated with predicates are not only adjectives, but verbs and common nouns; in short all descriptive features in language are predicative.

This entails the fact that the similarity charted in icons covers more complicated cases than does the ordinary use of the word. Thus,

where ordinary logic considers only a single, special kind of relation, that of similarity, – a relation, too, of a particularly featureless and insignificant kind, the logic of relatives imagines a relation in general to be placed. Consequently, in place of the class, which is composed of a number of individual objects or facts brought together by means of their relation of similarity, the logic of relatives considers the system, which is composed of objects brought together by any kind of relations whatsoever. (The New Elements of Mathematics)

This allows for abstract similarity because one phenomenon may be similar to another in so far as both of them partake in the same relation, or more generally, in the same system – relations and systems being complicated predicates.

But not only more abstract features may thus act as the qualities invoked in an icon; these qualities may be of widely varying generality:

But instead of a single icon, or sign by resemblance of a familiar image or ‘dream’, evocable at will, there may be a complexus of such icons, forming a composite image of which the whole is not familiar. But though the whole is not familiar, yet not only are the parts familiar images, but there will also be a familiar image in its mode of composition. ( ) The sort of idea which an icon embodies, if it be such that it can convey any positive information, being applicable to some things but not to others, is called a first intention. The idea embodied by an icon, which cannot of itself convey any information, being applicable to everything or nothing, but which may, nevertheless, be useful in modifying other icons, is called a second intention. 

What Peirce distinguishes in these scholastic standard notions borrowed from Aquinas via Scotus, is, in fact, the difference between Husserlian formal and material ontology. Formal qualities like genus, species, dependencies, quantities, spatial and temporal extension, and so on are of course attributable to any phenomenon and do not as such, in themselves, convey any information in so far as they are always instantiated in and thus, like other Second Intentions, in the Husserlian manner dependent upon First Intentions, but they are nevertheless indispensable in the composition of first intentional descriptions. The fact that a certain phenomenon is composed of parts, has a form, belongs to a species, has an extension, has been mentioned in a sentence etc. does not convey the slightest information of it until it by means of first intentional icons is specified which parts in which composition, which species, which form, etc. Thus, here Peirce makes a hierarchy of icons which we could call material and formal, respectively, in which the latter are dependent on the former. One may note in passing that the distinctions in Peirce’s semiotics are themselves built upon such Second Intentions; thus it is no wonder that every sign must possess some Iconic element. Furthermore, the very anatomy of the proposition becomes just like in Husserlian rational grammar a question of formal, synthetic a priori regularities.

Among Peirce’s forms of inference, similarity plays a certain role within abduction, his notion for a ‘qualified guess’ in which a particular fact gives rise to the formation of a hypothesis which would have the fact in question as a consequence. Many such different hypotheses are of course possible for a given fact, and this inference is not necessary, but merely possible, suggestive. Precisely for this reason, similarity plays a seminal role here: an

originary Argument, or Abduction, is an argument which presents facts in its Premiss which presents a similarity to the fact stated in the conclusion but which could perfectly be true without the latter being so.

The hypothesis proposed is abducted by some sort of iconic relation to the fact to be explained. Thus, similarity is the very source of new ideas – which must subsequently be controlled deductively and inductively, to be sure. But iconicity does not only play this role in the contents of abductive inference, it plays an even more important role in the very form of logical inference in general:

Given a conventional or other general sign of an object, to deduce any other truth than that which it explicitly signifies, it is necessary, in all cases, to replace that sign by an icon. This capacity of revealing unexpected truth is precisely that wherein the utility of algebraic formulae consists, so that the iconic character is the prevailing one.

The very form of inferences depends on it being an icon; thus for Peirce the syllogistic schema inherent in reasoning has an iconic character:

‘Whenever one thing suggests another, both are together in the mind for an instant. [ ] every proposition like the premiss, that is having an icon like it, would involve [ ] a proposition related to it as the conclusion [ ]’. Thus, first and foremost deduction is an icon: ‘I suppose it would be the general opinion of logicians, as it certainly was long mine, that the Syllogism is a Symbol, because of its Generality.’ …. The truth, however, appears to be that all deductive reasoning, even simple syllogism, involves an element of observation; namely deduction consists in constructing an icon or diagram the relation of whose parts shall present a complete analogy with those of the parts of the objects of reasoning, of experimenting upon this image in the imagination, and of observing the result so as to discover unnoticed and hidden relations among the parts. 

It then is no wonder that synthetic a priori truths exist – even if Peirce prefers notions like ‘observable, universal truths’ – the result of a deduction may contain more than what is immediately present in the premises, due to the iconic quality of the inference.

Intuition

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During his attempt to axiomatize the category of all categories, Lawvere says

Our intuition tells us that whenever two categories exist in our world, then so does the corresponding category of all natural transformations between the functors from the first category to the second (The Category of Categories as a Foundation).

However, if one tries to reduce categorial constructions to set theory, one faces some serious problems in the case of a category of functors. Lawvere (who, according to his aim of axiomatization, is not concerned by such a reduction) relies here on “intuition” to stress that those working with categorial concepts despite these problems have the feeling that the envisaged construction is clear, meaningful and legitimate. Not the reducibility to set theory, but an “intuition” to be specified answers for clarity, meaningfulness and legitimacy of a construction emerging in a mathematical working situation. In particular, Lawvere relies on a collective intuition, a common sense – for he explicitly says “our intuition”. Further, one obviously has to deal here with common sense on a technical level, for the “we” can only extend to a community used to the work with the concepts concerned.

In the tradition of philosophy, “intuition” means immediate, i.e., not conceptually mediated cognition. The use of the term in the context of validity (immediate insight in the truth of a proposition) is to be thoroughly distinguished from its use in the sensual context (the German Anschauung). Now, language is a manner of representation, too, but contrary to language, in the context of images the concept of validity is meaningless.

Obviously, the aspect of cognition guiding is touched on here. Especially the sensual intuition can take the guiding (or heuristic) function. There have been many working situations in history of mathematics in which making the objects of investigation accessible to a sensual intuition (by providing a Veranschaulichung) yielded considerable progress in the development of the knowledge concerning these objects. As an example, take the following account by Emil Artin of Emmy Noether’s contribution to the theory of algebras:

Emmy Noether introduced the concept of representation space – a vector space upon which the elements of the algebra operate as linear transformations, the composition of the linear transformation reflecting the multiplication in the algebra. By doing so she enables us to use our geometric intuition.

Similarly, Fréchet thinks to have really “powered” research in the theory of functions and functionals by the introduction of a “geometrical” terminology:

One can [ …] consider the numbers of the sequence [of coefficients of a Taylor series] as coordinates of a point in a space [ …] of infinitely many dimensions. There are several advantages to proceeding thus, for instance the advantage which is always present when geometrical language is employed, since this language is so appropriate to intuition due to the analogies it gives birth to.

Mathematical terminology often stems from a current language usage whose (intuitive, sensual) connotation is welcomed and serves to give the user an “intuition” of what is intended. While Category Theory is often classified as a highly abstract matter quite remote from intuition, in reality it yields, together with its applications, a multitude of examples for the role of current language in mathematical conceptualization.

This notwithstanding, there is naturally also a tendency in contemporary mathematics to eliminate as much as possible commitments to (sensual) intuition in the erection of a theory. It seems that algebraic geometry fulfills only in the language of schemes that essential requirement of all contemporary mathematics: to state its definitions and theorems in their natural abstract and formal setting in which they can be considered independent of geometric intuition (Mumford D., Fogarty J. Geometric Invariant Theory).

In the pragmatist approach, intuition is seen as a relation. This means: one uses a piece of language in an intuitive manner (or not); intuitive use depends on the situation of utterance, and it can be learned and transformed. The reason for this relational point of view, consists in the pragmatist conviction that each cognition of an object depends on the means of cognition employed – this means that for pragmatism there is no intuitive (in the sense of “immediate”) cognition; the term “intuitive” has to be given a new meaning.

What does it mean to use something intuitively? Heinzmann makes the following proposal: one uses language intuitively if one does not even have the idea to question validity. Hence, the term intuition in the Heinzmannian reading of pragmatism takes a different meaning, no longer signifies an immediate grasp. However, it is yet to be explained what it means for objects in general (and not only for propositions) to “question the validity of a use”. One uses an object intuitively, if one is not concerned with how the rules of constitution of the object have been arrived at, if one does not focus the materialization of these rules but only the benefits of an application of the object in the present context. “In principle”, the cognition of an object is determined by another cognition, and this determination finds its expression in the “rules of constitution”; one uses it intuitively (one does not bother about the being determined of its cognition), if one does not question the rules of constitution (does not focus the cognition which determines it). This is precisely what one does when using an object as a tool – because in doing so, one does not (yet) ask which cognition determines the object. When something is used as a tool, this constitutes an intuitive use, whereas the use of something as an object does not (this defines tool and object). Here, each concept in principle can play both roles; among two concepts, one may happen to be used intuitively before and the other after the progress of insight. Note that with respect to a given cognition, Peirce when saying “the cognition which determines it” always thinks of a previous cognition because he thinks of a determination of a cognition in our thought by previous thoughts. In conceptual history of mathematics, however, one most often introduced an object first as a tool and only after having done so did it come to one’s mind to ask for “the cognition which determines the cognition of this object” (that means, to ask how the use of this object can be legitimized).

The idea that it could depend on the situation whether validity is questioned or not has formerly been overlooked, perhaps because one always looked for a reductionist epistemology where the capacity called intuition is used exclusively at the last level of regression; in a pragmatist epistemology, to the contrary, intuition is used at every level in form of the not thematized tools. In classical systems, intuition was not simply conceived as a capacity; it was actually conceived as a capacity common to all human beings. “But the power of intuitively distinguishing intuitions from other cognitions has not prevented men from disputing very warmly as to which cognitions are intuitive”. Moreover, Peirce criticises strongly cartesian individualism (which has it that the individual has the capacity to find the truth). We could sum up this philosophy thus: we cannot reach definite truth, only provisional; significant progress is not made individually but only collectively; one cannot pretend that the history of thought did not take place and start from scratch, but every cognition is determined by a previous cognition (maybe by other individuals); one cannot uncover the ultimate foundation of our cognitions; rather, the fact that we sometimes reach a new level of insight, “deeper” than those thought of as fundamental before, merely indicates that there is no “deepest” level. The feeling that something is “intuitive” indicates a prejudice which can be philosophically criticised (even if this does not occur to us at the beginning).

In our approach, intuitive use is collectively determined: it depends on the particular usage of the community of users whether validity criteria are or are not questioned in a given situation of language use. However, it is acknowledged that for example scientific communities develop usages making them communities of language users on their own. Hence, situations of language use are not only partitioned into those where it comes to the users’ mind to question validity criteria and those where it does not, but moreover this partition is specific to a particular community (actually, the community of language users is established partly through a peculiar partition; this is a definition of the term “community of language users”). The existence of different communities with different common senses can lead to the following situation: something is used intuitively by one group, not intuitively by another. In this case, discussions inside the discipline occur; one has to cope with competing common senses (which are therefore not really “common”). This constitutes a task for the historian.

Catharsis

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One of the ways in which Freud was able to reveal repressed unconscious representations in discourse was through a technique popularly known as “the talking cure”. Coined by “Anna O” – a patient of Josef Breuer, Freud’s family doctor – the talking cure was considered by Freud to be effective in the treatment of hysteria. The technique, not unlike the notion of “free association”, requires the patient to say out loud whatever comes to her/his mind no matter how insignificant or superficial it may seem. By encouraging the patient to concentrate on putting neurotic or psychotic experiences into words, the uninterrupted narrative flow allows the psychoanalyst to reconstruct the patient’s unconscious mind. Focusing on unconscious representations revealed during discourse, the psychoanalyst is able to perceive lapsus or other manifestations of the unconscious which may escape the patient’s field of perception. At the discretion of the psychoanalyst, these unconscious representations are in turn brought to the patient’s attention who will ideally be able to understand the root of an undesired behavior. According to Freud, becoming familiar with the exact nature of these neurotic and psychotic behaviors makes it possible for the patient to suppress them.

The success of the talking cure, also known as the cathartic method, depends on the patient’s ability to put thoughts into words through the free assembly of signifiers. Through extensive research on the connection between the spoken word and the idea it represented, Freud argued that the organization of words, as well as their subsequent verbalization, have a direct link not only with cognition, but also with kinesthetics. In their analysis of the case of “Anna O.” – a patient of Breuer suffering from acute hysteria – both Freud and Breuer recognized the therapeutic benefits of the cathartic method. During the course of her hysteria, the patient essentially repressed the anguish of her father’s death into the unconscious mind, the cathexis of which resurfaced as a series of somatic manifestations. The patient’s symptoms, ranging from partial paralysis to severe coughing, completely disappeared toward the final phases of her treatment, much to the surprise of Freud and Breuer. They later attributed the patient’s cure to her verbalized reenactment of emotionally charged scenes associated with her father’s death, in the same manner as Aristotle remarked on the soothing effects of catharsis.

Further elaborating on Freud’s relationship between thoughts and words, Lacan perceived the unconscious mind. as being comprised of individual signifiers. Combining Saussurian linguistics and Freudian psychoanalysis, Lacan’s perception of the unconscious mind expounded on the ‘word-presentations’ mentioned by Freud in The Ego and the Id. Whereas Freud conceived the unconscious mind as containing “thing-presentations” that could be verbalized in the conscious mind, only by their subsequent passage through the pre-conscious, Lacan demonstrated that these “thing-presentations” already behave like signifiers without first having to filter through the pre-conscious. Lacan points out that the unconscious is manifested not only in speech through unconscious lapsus, but also in dreams, qualified by Freud as “the via regia to the unconscious”.

Because dreams both contain verbal cues and take on characteristics of linguistic tropes such as metaphor and metonymy, Lacan reasons that the unconscious must be structured like a language. To support this theory, he likens metaphor and metonymy to two functions of Freud’s dream-work: condensation and displacement, respectively. According to Lacan, metaphor behaves like condensation in that a signifier belonging to a particular signifying chain can be substituted with a new signifier from a different signifying chain in order to be reassigned a new meaning. Thus, metaphor appears both in narration and in dreams when a signifier-word is attributed a meaning other than that which is normally associated with it. In this way, condensation acts as a censoring agent to protect the ego from images, drives or impulses that it has repressed. Closely related to metonymy, dreams can also be censored through displacement. Instead of compressing images, drives or impulses into a metaphor as is the case with condensation, displacement disguises unconscious representations by replacing a repressed signifier in a signifying chain with another signifier from the same chain. This implies that the signifier that has been replaced in the signifying chain is related to the new signifier, as is the case of metonymy which uses only one part of a thing to describe the whole thing.

It would appear that, like language, the unconscious is governed by the relationship between individual units, in much the same way that words are governed by the rules of grammar and tropes to create meaning. In this respect, not only are unconscious and conscious signifiers similar to one another, but Freud’s cathartic method further corroborates their equivalence. With the assistance of a psychoanalyst, the “talking cure” brings unconscious drives, impulses and the images they create to the conscious realm through psychic discharge, which in the context of psychoanalysis, takes on the form of verbalized discourse. Instead of remaining confined to the unconscious and surfacing in unexpected or undesired ways through psychotic or neurotic behaviors, unconscious cathexes are channeled into language which, as Freud pointed out in “Words and Things”, is closely related to somatic activity. If unconscious cathexes can be converted into speech instead of into debilitating behaviors, then the connection between elements of the unconscious and those of the conscious can be clearly established.

But, for Freud, art is (as is love) an attenuated and inhibited form of sexuality that has a “mildly intoxicating quality of feeling.” The full power of human affects is exhausted and satisfied only in sexuality, “the prototype of all happiness.” For Lacan, the deepest passions are not localized or limited to genital sexuality, but engage the entire corporeal being in many, unpredictable forms of jouissance. Art is a way into jouissance. By doing violence to its own structural and meaning-making properties, art bewilders, perplexes, shocks, or enraptures, causing a “resonating of the body” that the speaking being (‘parlêtre’) wants and enjoys, even at the price of pain or anxiety. It has techniques and ways of making interventions that psychoanalysis can perhaps adapt for producing an encounter in the analysand with his or her own wordless real. By contrast, though Freud praised art for preceding psychoanalysis in understanding our psychic constitution, he did not see it as having any kind of direct application or usefulness for analytic practice. For the late Lacan, psychoanalysis is no longer the Freudian “talking cure” but a search for new paths to accomplish a kind of tuning of the jouissance that underlies all thought and discourse.

¿..Structuralism..?

This is a puerile dig from the archives. Just wanted to park it here to rest and rust and then probably forgotten, until a new post on structuralism as a philosophy of mathematics comes up, which, it shall soon. In the meanwhile, this could largely be skipped.

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Structuralism is an umbrella term involving a wide range of disciplines that came to fruition with the work of Swiss linguist Ferdinand de Saussure. The basic idea revolves round the study of underlying structures of significations that are meaningfully derived from ‘texts’. A ‘text’ is anything that owes its existence to a document or anything that has the potential of getting documented. The analyses for the discovery of structures underlying all these significations and texts and the conditions of possibilities for the existence of these significations and texts is what structuralism purportedly does. Saussure’s ‘Course in General Linguistics’, published posthumously, and seeing the light of the day because of his students’ note taking influenced ‘Structural Linguistics’, thereby explaining the adequacy of language for describing things concrete and abstract and in the process expanding the applicability of what language could do.

The starting point of Saussure’s analysis is Semiology, a science that undertakes the study of signs in society. These signs that express ideas build up the system of language for him. Signs are comprised of langue (language) and parole (speech). Langue is an abstract homogeneous system of language that is internalized by a given speech community, whereas parole is a concrete heterogeneous act of putting language into practice. In Saussurian jargon, Langue describes the social, impersonal phenomenon of language as a system of signs, while parole describes the individual, personal phenomenon of language as a series of speech acts made by a linguist subject. Signs attain their iconic status for Saussure due to meaning production when they enter into relationships with their referents.(1) Every sign is composed of a pair, a couple viz, signifier and signified, where signifier is a sound image (psychologically considered rather than materially), and signified is a concept. Signifier is the sensible part of the sign. A signified on the other hand is a connotation, an attachment that the signifier carries, a meaning, or a mental image of an entity that somehow misses out manifesting in the proximity. In other words, the signified of a signifier is not itself a sensible part of the sign. Signifier without the signified and vice versa strips a sign of its essence and therefore any meaning whatsoever (metaphysics ruled out for the moment!), and meaningfulness of signs in any discourse is derived from internal systemic relations of difference. This is precisely what is meant when Saussure says that language is a system of differences without positive terms (for the record: this is accepted even in Derrida’s post-structuralist critique of Saussure). The positivity of terms needs deliberation here. We recognize language, or more generally the marks inhabiting the language by virtue of how each and every mark is distinct/difference from each and every other mark inhabiting the same language. This distinction or difference is neither a resident with the sensible part of the sign, or signifier, nor with the mental/insensible part of the sign, or signified. Now, if the signifier and the signified are separated somehow, then language as guided by differences connoting negativity is legitimate. But, as has been mentioned; a sign is meaningful only when the signifier and the signified are coupled together, the meaning attaches itself a positive value. This only means that language is governed by differences. In the words of Saussure,

Whether we take signified or the signifier, language has neither ideas nor sounds that existed before the linguistic system, but only conceptual and phonic differences that have issued from the system. The idea or a phonic substance that a sign contains is of less importance than the other signs that surround it. Proof of this is that the value of a term may be modified without either its meaning or sound being affected, solely because a neighboring term has been modified.

Signs were value laden, for only then would linguistics become an actual science, and for this realization to manifest, signs in any language system were determined by other signs in the same language system that helped delimiting meaning and a possible bracketed range of usage rather than a confinement to internal sound-pattern and concept. A couple of ramifications follow for Saussure from here on viz, signs cannot exist in isolation, but emanate from the system in which they are to be analyzed (this also means that the system cannot be built upon isolated signs), and grammatical facts are consolidated by taking recourse to syntagmatic and paradigmatic analyses. The former is based on the syntactic or surface structure in semiotics, whereas the latter is operative on the syntagms by means of identifying its paradigms. The syntagmatic and paradigmatic analyses were what made Saussure assert the primacy of relations of difference that made any language operate. Syntagms particularly belong to speech, and thereby direct the linguist in identifying the frequency of its usage before being incorporated into language, whereas, paradigms relationalize associatively thus building up clusters of signs in the mind before finally imposing themselves on syntagms for the efficient functionality of the language.

So, fundamentally structuralism is concerned with signifiers and relations between signifiers, and requires a diligent effort to make visible what is imperceptible and at the same time responsible for the whole phenomenon to exist, and that being the absent signified. The specialty of absent signified is to carry out the efficacy of structuralism as a phenomenon, without itself sliding into just another singifier, and this is where Derrida with his critique of structuralism comes in, in what is known as post-structuralism. But, before heading into the said territory, what is required is an attempt to polish structuralism by viewing it under some lenses, albeit very briefly.

Structural anthropology as devised by Claude Lévi-Strauss in his Structural Anthropology (1 and 2) studied certain unobservable social structures that nonetheless generated observable social phenomenon. Lévi-Strauss imported most of his ideas from the structuralist school of Saussure, and paralleled Saussure’s view on the unknow-ability of grammar usage while conversing, with the unknow-ability of the workings of the social structures in day-to-day life. Thought as such is motivated by various patterns and structures that show proclivities towards redundancy in these very various situations. This means that the meaning or the signified is derived from a decision that somehow happens to have taken place in the past, and hence already decided. And the very construction of thoughts, experience is what structural anthropology purports to do, but with beginnings that were oblivious to social/cultural systems and wedded to objectivity of scientific perspective. Although criticized for the lack of foundations of a complete scientific account and ignorant towards an integration of cultural anthropology and neuroscience, the structural anthropology remains embraced amongst anthropologists.

Other important political variant of structuralism is attributed to Louis Althusser, who coined the idea of structural Marxism as against humanistic Marxism by emphasizing on Marxism as a science that has ‘studying’ objective structures as its goal, as against the prison house of pre-scientific humanistic ideology embraced by humanistic Marxism. The major tenet of this school of Marxism lay in its scathing critique of the instrumentalist version that argued for the institutions of the state as directly under the control of those capitalist powers, and instead sought out to clarify the functionality of these institutions in order to reproduce the capitalist society as a whole.

After these brief remarks on structural anthropology and structural Marxism, it is time for a turn to examine the critiques of structuralism in order to pave a smooth slide into post-structuralism. The important reaction against structuralism is its apparent reductionist tendency, wherein deterministic structural forces are pitted over the capacities of people to act, thus anthropologically weakening. Within the anthropological camp itself, Kuper had this to say,

Structuralism came to have something of the momentum of the millennial movement and some of its adherents thought that they formed a secret society of a seeing in a world of the blind. Conversion was not just a matter of accepting a new paradigm. It was, almost, a question of salvation.

Another closely allied criticism is confining to biological explanations for cultural constructions, and therefore ignoring the social constructions in the process. This critique is also attached with the Saussurian version, for it was considered as too closed off to social change. This critique could not have been ameliorated for the presence of Voloshinov, who thematized dialectical struggles within words to argue for the language to happen primarily through a ‘clash of social forces’ between people who use words, and thereby concluding that to study changes in signs and to chart those changes mandates the study of class struggles within society.

(1) Back in the 19th Century an important figure for semiotics, the pragmatic philosopher Charles Sanders Peirce, isolated three different types of sign: The symbolic sign is like a word in so far as it refers by symbolising its referent. It neither has to look like it nor have any natural relation to it at all. Thus the word cat has no relation to that ginger monster that wails all night outside my apartment. But its owner knows what I’m talking about when I say “your cat kept me awake all night.” A poetic symbol like the sun (which may stand for enlightenment and truth) has an obviously symbolic relation to what it means. But how do such relationships come about? Saussure has an explanation. The indexical sign is like a signpost or a finger pointing in a certain direction. An arrow may accompany the signpost to San Francisco or to “Departures.” The index of a book will have a list of alphabetically ordered words with page numbers after each of them. These signs play an indexical function (in this instance, as soon as you’ve looked one up you’ll be back in the symbolic again). The iconic sign refers to its object by actually resembling it and is thus more likely to be like a picture (as with a road sign like that one with the courteous workman apologising for the disruption).