Valencies of Predicates. Thought of the Day 125.0

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.

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Complete Manifolds’ Pure Logical Necessity as the Totality of Possible Formations. Thought of the Day 124.0

In Logical Investigations, Husserl called his theory of complete manifolds the key to the only possible solution to how in the realm of numbers impossible, non-existent, meaningless concepts might be dealt with as real ones. In Ideas, he wrote that his chief purpose in developing his theory of manifolds had been to find a theoretical solution to the problem of imaginary quantities (Ideas Pertaining to a Pure Phenomenology and to a Phenomenological Philosophy).

Husserl saw how questions regarding imaginary numbers come up in mathematical contexts in which formalization yields constructions which arithmetically speaking are nonsense, but can be used in calculations. When formal reasoning is carried out mechanically as if these symbols have meaning, if the ordinary rules are observed, and the results do not contain any imaginary components, these symbols might be legitimately used. And this could be empirically verified (Philosophy of Arithmetic_ Psychological and Logical Investigations with Supplementary Texts).

In a letter to Carl Stumpf in the early 1890s, Husserl explained how, in trying to understand how operating with contradictory concepts could lead to correct theorems, he had found that for imaginary numbers like √2 and √-1, it was not a matter of the possibility or impossibility of concepts. Through the calculation itself and its rules, as defined for those fictive numbers, the impossible fell away, and a genuine equation remained. One could calculate again with the same signs, but referring to valid concepts, and the result was again correct. Even if one mistakenly imagined that what was contradictory existed, or held the most absurd theories about the content of the corresponding concepts of number, the calculation remained correct if it followed the rules. He concluded that this must be a result of the signs and their rules (Early Writings in the Philosophy of Logic and Mathematics). The fact that one can generalize, produce variations of formal arithmetic that lead outside the quantitative domain without essentially altering formal arithmetic’s theoretical nature and calculational methods brought Husserl to realize that there was more to the mathematical or formal sciences, or the mathematical method of calculation than could be captured in purely quantitative analyses.

Understanding the nature of theory forms, shows how reference to impossible objects can be justified. According to his theory of manifolds, one could operate freely within a manifold with imaginary concepts and be sure that what one deduced was correct when the axiomatic system completely and unequivocally determined the body of all the configurations possible in a domain by a purely analytical procedure. It was the completeness of the axiomatic system that gave one the right to operate in that free way. A domain was complete when each grammatically constructed proposition exclusively using the language of the domain was determined from the outset to be true or false in virtue of the axioms, i.e., necessarily followed from the axioms or did not. In that case, calculating with expressions without reference could never lead to contradictions. Complete manifolds have the

distinctive feature that a finite number of concepts and propositions – to be drawn as occasion requires from the essential nature of the domain under consideration –  determines completely and unambiguously on the lines of pure logical necessity the totality of all possible formations in the domain, so that in principle, therefore, nothing further remains open within it.

In such complete manifolds, he stressed, “the concepts true and formal implication of the axioms are equivalent (Ideas).

Husserl pointed out that there may be two valid discipline forms that stand in relation to one another in such a way that the axiom system of one may be a formal limitation of that of the other. It is then clear that everything deducible in the narrower axiom system is included in what is deducible in the expanded system, he explained. In the arithmetic of cardinal numbers, Husserl explained, there are no negative numbers, for the meaning of the axioms is so restrictive as to make subtracting 4 from 3 nonsense. Fractions are meaningless there. So are irrational numbers, √–1, and so on. Yet in practice, all the calculations of the arithmetic of cardinal numbers can be carried out as if the rules governing the operations are unrestrictedly valid and meaningful. One can disregard the limitations imposed in a narrower domain of deduction and act as if the axiom system were a more extended one. We cannot arbitrarily expand the concept of cardinal number, Husserl reasoned. But we can abandon it and define a new, pure formal concept of positive whole number with the formal system of definitions and operations valid for cardinal numbers. And, as set out in our definition, this formal concept of positive numbers can be expanded by new definitions while remaining free of contradiction. Fractions do not acquire any genuine meaning through our holding onto the concept of cardinal number and assuming that units are divisible, he theorized, but rather through our abandonment of the concept of cardinal number and our reliance on a new concept, that of divisible quantities. That leads to a system that partially coincides with that of cardinal numbers, but part of which is larger, meaning that it includes additional basic elements and axioms. And so in this way, with each new quantity, one also changes arithmetics. The different arithmetics do not have parts in common. They have totally different domains, but an analogous structure. They have forms of operation that are in part alike, but different concepts of operation.

For Husserl, formal constraints banning meaningless expressions, meaningless imaginary concepts, reference to non-existent and impossible objects restrict us in our theoretical, deductive work, but that resorting to the infinity of pure forms and transformations of forms frees us from such conditions and explains why having used imaginaries, what is meaningless, must lead, not to meaningless, but to true results.

Metaphysical Continuity in Peirce. Thought of the Day 122.0

Continuity has wide implications in the different parts of Peirce’s architectonics of theories. Time and time again, Peirce refers to his ‘principle of continuity’ which has not immediately anything to do with Poncelet’s famous such principle in geometry, but, is rather, a metaphysical implication taken to follow from fallibilism: if all more or less distinct phenomena swim in a vague sea of continuity then it is no wonder that fallibilism must be accepted. And if the world is basically continuous, we should not expect conceptual borders to be definitive but rather conceive of terminological distinctions as relative to an underlying, monist continuity. In this system, mathematics is first science. Thereafter follows philosophy which is distinguished form purely hypothetical mathematics by having an empirical basis. Philosophy, in turn, has three parts, phenomenology, the normative sciences, and metaphysics. The first investigates solely ‘the Phaneron’ which is all what could be imagined to appear as an object for experience: ‘ by the word phaneron I mean the collective total of all that is in any way or in any sense present to the mind, quite regardless whether it corresponds to any real thing or not.’ (Charles Sanders Peirce – Collected Papers of Charles Sanders Peirce) As is evident, this definition of Peirce’s ‘phenomenology’ is parallel to Husserl’s phenomenological reduction in bracketing the issue of the existence of the phenomenon in question. Even if it thus is built on introspection and general experience, it is – analogous to Husserl and other Brentano disciples at the same time – conceived in a completely antipsychological manner: ‘It religiously abstains from all speculation as to any relations between its categories and physiological facts, cerebral or other.’ and ‘ I abstain from psychology which has nothing to do with ideoscopy.’ (Letter to Lady Welby). The normative sciences fall in three: aesthetics, ethics, logic, in that order (and hence decreasing generality), among which Peirce does not spend very much time on the former two. Aesthetics is the investigation of which possible goals it is possible to aim at (Good, Truth, Beauty, etc.), and ethics how they may be reached. Logic is concerned with the grasping and conservation of Truth and takes up the larger part of Peirce’s interest among the normative sciences. As it deals with how truth can be obtained by means of signs, it is also called semiotics (‘logic is formal semiotics’) which is thus coextensive with theory of science – logic in this broad sense contains all parts of philosophy of science, including contexts of discovery as well as contexts of justification. Semiotics has, in turn, three branches: grammatica speculativa (or stekheiotics), critical logic, and methodeutic (inspired by mediaeval trivium: grammar, logic, and rhetoric). The middle one of these three lies closest to our days’ conception of logic; it is concerned with the formal conditions for truth in symbols – that is, propositions, arguments, their validity and how to calculate them, including Peirce’s many developments of the logic of his time: quantifiers, logic of relations, ab-, de-, and induction, logic notation systems, etc. All of these, however, presuppose the existence of simple signs which are investigated by what is often seen as semiotics proper, the grammatica speculativa; it may also be called formal grammar. It investigates the formal condition for symbols having meaning, and it is here we find Peirce’s definition of signs and his trichotomies of different types of sign aspects. Methodeutic or formal rhetorics, on the other hand, concerns the pragmatical use of the former two branches, that is, the study of how to use logic in a fertile way in research, the formal conditions for the ‘power’ of symbols, that is, their reference to their interpretants; here can be found, e.g., Peirce’s famous definitions of pragmati(ci)sm and his directions for scientific investigation. To phenomenology – again in analogy to Husserl – logic adds the interest in signs and their truth. After logic, metaphysics follows in Peirce’s system, concerning the inventarium of existing objects, conceived in general – and strongly influenced by logic in the Kantian tradition for seeing metaphysics mirroring logic. Also here, Peirce has several proposals for subtypologies, even if none of them seem stable, and under this headline classical metaphysical issues mix freely with generalizations of scientific results and cosmological speculations.

Peirce himself saw this classification in an almost sociological manner, so that the criteria of distinction do not stem directly from the implied objects’ natural kinds, but after which groups of persons study which objects: ‘the only natural lines of demarcation between nearly related sciences are the divisions between the social groups of devotees of those sciences’. Science collects scientists into bundles, because they are defined by their causa finalis, a teleologial intention demanding of them to solve a central problem.

Measured on this definition, one has to say that Peirce himself was not modest, not only does he continuously transgress such boundaries in his production, he frequently does so even within the scope of single papers. There is always, in his writings, a brief distance only from mathematics to metaphysics – or between any other two issues in mathematics and philosophy, and this implies, first, that the investigation of continuity and generality in Peirce’s system is more systematic than any actually existing exposition of these issues in Peirce’s texts, second, that the discussion must constantly rely on cross-references. This has the structural motivation that as soon as you are below the level of mathematics in Peirce’s system, inspired by the Comtean system, the single science receives determinations from three different directions, each science consisting of material and formal aspects alike. First, it receives formal directives ‘from above’, from those more general sciences which stand above it, providing the general frameworks in which it must unfold. Second, it receives material determinations from its own object, requiring it to make certain choices in its use of formal insights from the higher sciences. The cosmological issue of the character of empirical space, for instance, can take from mathematics the different (non-)Euclidean geometries and investigate which of these are fit to describe spatial aspects of our universe, but it does not, in itself, provide the formal tools. Finally, the single sciences receive in practice determinations ‘from below’, from more specific sciences, when their results by means of abstraction, prescission, induction, and other procedures provide insights on its more general, material level. Even if cosmology is, for instance, part of metaphysics, it receives influences from the empirical results of physics (or biology, from where Peirce takes the generalized principle of evolution). The distinction between formal and material is thus level specific: what is material on one level is a formal bundle of possibilities for the level below; what is formal on one level is material on the level above.

For these reasons, the single step on the ladder of sciences is only partially independent in Peirce, hence also the tendency of his own investigations to zigzag between the levels. His architecture of theories thus forms a sort of phenomenological theory of aspects: the hierarchy of sciences is an architecture of more and less general aspects of the phenomena, not completely independent domains. Finally, Peirce’s realism has as a result a somewhat disturbing style of thinking: many of his central concepts receive many, often highly different determinations which has often led interpreters to assume inconsistencies or theoretical developments in Peirce where none necessarily exist. When Peirce, for instance, determines the icon as the sign possessing a similarity to its object, and elsewhere determines it as the sign by the contemplation of which it is possible to learn more about its object, then they are not conflicting definitions. Peirce’s determinations of concepts are rarely definitions at all in the sense that they provide necessary and sufficient conditions exhausting the phenomenon in question. His determinations should rather be seen as descriptions from different perspectives of a real (and maybe ideal) object – without these descriptions necessarily conflicting. This style of thinking can, however, be seen as motivated by metaphysical continuity. When continuous grading between concepts is the rule, definitions in terms of necessary and sufficient conditions should not be expected to be exhaustive.

Initial Writing Systems. Thought of the Day 84.0

The discovery of the Sumerian civilization marks the culmination of the systematical exploration of the subsoil in the Near East, which got started in the late nineteenth-century. In the middle of that century, it was possible to spell and read the documents made with clay and covered with strange cuneiform or wedge-shaped signs, which had been found in the territory of Iraq a long time ago. This fact brought about the proliferation of excavations in the ancient Mesopotamia, just as it occurred in the Valley of Kings when the hieroglyphics were deciphered. Since these excavations were made in depth, they caused the vestiges or traces arranged in parallel layers to outcrop.

After having gone through layers with Arabian, Greek and Persian traces, the excavations got to testimonies dating from the middle of the first millennium B.C. The exploration thus reached the layer that stored the vast majority of the cuneiform documents. Consequently, were discovered the palaces, statues, treasures and weapons of the great Assyrian kings, who are mentioned in the Old Testament due to their conquests. In this way, the Assyriology was born as a scientific discipline from the cuneiform texts and the archeology of Mesopotamia.

Under that layer, other layers were discovered, which led to conclude that the apogee of the bellicose Assyrians proceeding from the north had been preceded in about one millennium by a people possessing a higher culture. These people originating from southern Mesopotamia were based on the Babylonians, whose code of laws (Hammurabi) symbolized their great cultural development and political equilibrium.

It was found out that the aforesaid code along with documents of that time were identical with the Assyrian annals and tablets, but with differences which determined that the Assyrian and Babylonian dialects came from an only language known as Akkadian. The Akkadian language is related to the Arabian, Aramean and Hebrew languages, and it is classified as a Semitic one. Then, the conclusion was that the empires of Babylon (in the early second millennium B.C.) and Nineveh (in the early first millennium B.C.) were of Semitic origin.

At the time that those archeological excavations were made, the cuneiform writing represented an enigma. This writing is composed of a large quantity of signs or characters (300 at its height), consisting of wedge-like strokes engraved on raw clay.

Initially, these linear drawings stood for concrete specific objects. In a second stage, each of the signs of this writing can be read in a text in two different ways:

1. As the name of the object which originally was represented by that character.
2. As the mark of a sound (syllable), but never an elemental irreducible sound like, for instance, those of the Latin alphabet.

Therefore, the cuneiform writing is ambivalent (both ideographic and phonetic). Thus, the drawing of a spike (e.g. a spike of wheat) within a cuneiform text can be read, according to the context, as the names of “grains” or the syllable “she”. In the same way, the engraving of a bird was ideographically interpreted as “volatile”, o else phonetically as the syllable “hu”.

The cuneiform signs were initially just a reproduction of objetcs. With time, they noticed that by means of such a rudimentary procedure as this, just a limited quantity of all that is possible to express in articulate language could be expressed. Only concrete typical objects could be depicted, but not actions or abstractions. For that reason, the solution was to disassociate in the character its reference to the object which reproduced, on one hand, and its pronunciation (phonetic value), on the other hand. So, the creators of this writing could write all that the spoken language expressed.

For example, the abstract word “vision” in Akkadian language is “shehu”, which could be represented by the drawing of a spike (i.e. a spike of a grain) followed by that of a bird (she + hu), but neither characters is related to a grain or something volatile in this case. Notwithstanding, in a different part of the text, those two characters might be directly translated as cereal and bird. This fact causes the decipherment of the cuneiform signs to be greatly difficult.

Because the Akkadian and Semitic name of the objects indicated by the cuneiform signs never corresponded to the phonetic value of those characters, it was inferred that the people who invented the cuneiform writing could not be Semites. The existence of another different and more ancient civilization prior to the Semitic Akkadians was then presumed.

The archeological excavations offered new cuneiform inscriptions, which, unlike the Babylonian and Assyrian texts, were written with ideograms only used due to their objective value, without any possibility of representing direct phonetic reading in either Akkadian or Semitic languages. Finally, the people who lived in southern Mesopotamia, whose monuments and cities underlying the Babylonian traces (2000 B.C.), were identified with the people who invented the cuneiform script.

As the ancient texts designated that zone of Mesopotamia adjacent to the Persian Gulf by the name of “Country of Sumer” (from the Akkadian term “shumerum”), it was agreed to call the predecessors of the Semitic Babylonians “Sumerians”. In the course of time, the investigations advanced until it was possible to reconstruct the Sumerian language, which had been lost for thousands years. Besides, this language had never could be classified within the well-known linguistic families.

The Sumerian language is really strange as far as its vocabulary (mostly monosyllabic) and even more its grammar (reconstructed in the most part) are concerned. In it, a big portion of the linguistic categories, which are indispensable according to our own way of viewing and expressing the things, is absent. As it was above mentioned, the Sumerian world is a finding of the nineteenth-century. It is the first civilization of the world, with the complexities this fact implies, namely: social and political organization, foundation of cities and states, creation of institutions, laws, organized production of assets, regulation of commerce, monumental artistic manifestations, and the invention of a writing system that would let knowledge be fixed and propagated. The appearance of this civilization dates from the fourth millennium B.C., in low Mesopotamia, between the rivers Tigris and Euphrates, to the south of Baghdad.

Two very ancient civilizations such as the Egyptian one and the Protoindian civilization of the Indus valley, are several centuries later than that of Sumer. Unlike Egypt and its pyramids, which reminds us of the glories of that civilization, or Israel and Greece, which built monuments that reminds us of their golden ages, in Sumer no testimonies of its past splendor were left. All that we know about Sumer at present, comes from the archeological excavations. All knowledge about this civilization has been extracted from clay tablets containing plenty of tiny cuneiform characters. These texts that are so difficult of being deciphered and understood, have been extracted by the hundreds of thousands, and they cover all aspects related to the writers’ lives: government, justice administration, economy, everyday life, science, history, literature and religion.

¿..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.

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).