Finite semiotics: cognitive sets, semiotic vectors, and

semiosic oscillation

Abstract: The grounding of semiotics in the finiteness of cognition is extended into

constructs and methods for analysis by incorporating the assumption that cognition can be

similar within and between agents. After examining and formalising cognitive similarity as

an ontological commitment, the recurrence of cognitive states is examined in terms of a

“cognitive set”. In the individual, the cognitive set is seen as evolving under the bidirectional,

cyclical determination of thought by the historical environment. At the population level, the

distributed “global” cognitive set is argued to be constrained to a manifold in which the

cognition of individuals is determined only when their cognitive sets meet certain conditions

in the world: a result seen as consistent with Lotman’s semiosphere.

With these foundations in place, dimensional modelling of the semiosic field is inaugurated.

Firstly, measures of cognitive similarity are formalised as cognitive “distance” and on this

basis the concept of a semiotic vector is defined. Secondly, semiotic vectors are seen to shape

a general pattern of oscillation in semiosis, and thus to imply zero points in semiosic

potential. Thirdly, semiosic oscillation in individual agents is shown to be consistent with a

novel diachronic or longitudinal interpretation of Greimas' semiotic square expanded into a

“semiotic pipe” in which cognition traverses an n-dimensional space structured by axes of

oscillation. Finally, the expanded theory of finite semiotics is advanced as a useful basis for

two new complementary disciplines: (1) a computational, mathematical science of “natural

semiotic processing” (NSP) to trace and model semiotic vectors and oscillation; and (2) a

prescriptive, rhetorical art of “technological influencing” (TI) to guide its inputs and

applications.

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Keywords: finite semiotics, cognitive set, semiotic vector, semiosic oscillation, natural

semiotic processing, technological influencing

Introduction

While it explored some combinatorial possibilities for sememes, the theory of semiotics

based on the finiteness of cognition advanced in Shackell (In press-a, In press-b) remained

agnostic about the most obvious assumption made in any discourse by any interlocutor: that

cognition in agents can be similar. While seemingly beyond critique, this performatively

consistent notion merits careful ontological treatment. Such care is not new: it was the

assumption of cognitive synonymy that Quine (1951) dissected in his famous critique of

analyticity. Now, in the information age, it is especially important to beware of the concept if

only because it is so blithely assumed in the metaphors of information itself (its

“reproduction”, “transference”, “possession”, for example). In fact, many sound-seeming

analyses in all fields (semiotics not excluded) rely on relatively bold assumptions about the

homogeneity of cognition. The progress of simulated and virtual environments – and in the

broader sense Baudrillard’s ([1981]1994) hyperreality – make the need for careful

circumspection about cognitive similarity even more pressing.

After providing some brief background to finite semiotics, this article examines the ontology

of cognitive similarity and integrates an explicit formulation into finite semiotics. The

motivation is to derive new robust constructs that will prove useful in expanding and

“ruggedizing” semiotic analysis in the face of technology – not least by providing new

models and procedures amenable to computational treatment.

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Background

The formal foundations for the theory of finite semiotics outlined in Shackell (In press-a, In

press-b) can be précised as:

1. Cognition being finite, each agent (human being) is or is not having what seems to

them a particular thought at any moment.

2. As cognition is finite there is a sequence to cognition.

3. The sequence of cognition bears a relation to the world. For example, hot weather

often precedes thoughts of drinking water. Similarly, hearing the words “Look out!”

can cause an agent to suddenly change its thinking, as can consumption of alcohol, or

the positioning of text in front of the eyes. This progressive development of habits of

semiosis by an agent progressing through a world containing the externalities of the

cognition of other agents can be called semioformation.

4. The movement from one cognitive state to another we can label semiosis. The study

of how this movement occurs we can label semiotics.

5. The effect of semiosis in an agent on the semiosis of other agents (through action of

the body as part of the world, for example) can be called its valency.

6. The observation that much semiosis has a zero valency (i.e. no effect on the cognition

of others) is important to the structure and stability of cognition.

The semiosic field

The above propositions, applied at the population level, lead to the construct of the semiosic

field which is simply a formal model of global cognition highlighting the limits and relativity

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of the cognition of any one agent. A basic representation adapted from Shackell (In press-a)

is offered in Figure 1.

Figure 1. The semiosic field of all agents

Equivalence of the semiosic and epistemological fields

An important corollary of finite semiotics is that due to the dependence of knowledge on

thought (for what is never thought cannot be knowledge), the semiosic field is coextensive

with epistemological space. This is seen as a source of relativistic effects in examination of

the field by any single agent.

Cognitive similarity

The obviousness of cognitive similarity

Shackell (In press-a) presented some combinatorial possibilities for the semiosic field if

cognitive states are grouped into sememes (which can be regarded as simply larger units of

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equivalence than individual thoughts). The a priori case for the existence of such patterns

was made in terms of intuitions from daily life: if an agent’s thoughts are always novel how

are agents able to do similar things at different times? For example, how can two people

recite from memory the same speech from Hamlet? Or assemble the same piece of IKEA

furniture? At the broadest level, if the thoughts of individuals were somehow always unique,

how would communication and knowledge transfer ever be possible?

Entropy and cognitive similarity

While self-evident, these arguments nonetheless face an equally obvious and compelling

refutation: thought always arises from new initial conditions in a changing world. Each

thought arises from different inputs into different bodies with differently developing and

degrading sensory apparatus. Moreover, despite the fact that we often attribute our thoughts

and capabilities to memory or learning (that we may have read Hamlet several times or

learned to use an Allen key from a YouTube video), what we think is always due in some

part to unnoticed factors: what we ate or drank and hour ago, and whether we are currently

washing dishes or admiring the Grand Canyon. Given our divergent and idiosyncratic

pathways through life, it is difficult to countenance the idea that each thought in an individual

is not, at least in some detail, unique. Our notion of identity, for example, relies upon it.

The objection can be stated in general physical terms: how can thought within and between

individuals be similar given the context of the progression of the universal state to entropy?

One possible response is that isolated systems, by the input of energy, can nonetheless

become and remain ordered. Agents could be argued to be such systems with their neurology

maintained in synchronised patterns by the action of the environment. However, current

materialist explanations of cognitive similarity involving neurology rapidly become

inadequate when attempts are made to compare specific thoughts or cognitive processes (e.g.

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Uttal, 2013) rather than to make broad purposive generalisations (such as inform thought

activation technology, or create treatments for Alzheimer’s disease). Even if we allow that

neurology could arrive at a complete description in which thoughts across individuals could

be correlated at a material level, the approach only multiplies in complexity because the

thinking that must traverse that result would itself have to be categorizable and subject to the

laws of finite semiosis and trans-metacognition. Moreover, the discreteness, countability and

combinatorics of thoughts in a completely described individual raise impossible questions of

identicality and mereology.

The intractability of this paradox – of the obviousness yet impossibility of cognitive

similarity – is such that it is rarely made explicit, even though it would seem incumbent upon

any method or theory that assumes cognitive similarity to have the onus of proof. Even, for

example, in the reasoning of someone as meticulous and aware of the incremental creation of

reality as Piaget there is no question that a child passing the concrete operational phase is

acquiring some universal set of thoughts that can be compared and normalised across all

children (Cf. Piaget, 2013 [1954]).

It not only behoves semiotics to be more circumspect in this area – cognitive similarity is an

issue of universal relevance in which semiotics should be a touchstone for other disciplines.

Cognitive similarity by finite semiotic principles

A resolution to the paradox of the obviousness yet impossibility of cognitive similarity can be

derived by reasserting the germinal idea that cognition is finite. By this principle, a thought

that cognition is similar is ipso facto finite thought itself occurring in some agent at some

time parallel to thought in other agents. Such thoughts, therefore, are part of (and moreover

cannot stand apart from in any objective space outside cognition) the greater path-dependent

trajectory of the semiosic field via which thoughts are sustained, disseminated and find their

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conditions of possibility. Thoughts of cognitive similarity are by the fact of their

communicability involved in what Foucault called “discursive formations” (Foucault,

[1969]2002, Part II, Ch. 2) rather than any objective reality, which by the equivalence of the

semiotic and the epistemological fields must be limited to what is thought. Hence the

experiential, performative obviousness of cognitive similarity – what might be called its

“psychological reality” – is not at odds with the entropic, idiosyncratic movement of the

world from which it arises, for in no sense is cognitive similarity a consistent, immutable

object. Rather it is an object arising as part of the evolution of discursive formations in the

“crease” where the semiotic and epistemological, in the creation of the objective, are

systematically confused as distinct. Cognitive similarity, in other words, is most

fundamentally viewed as simply some set of changing ideas that has valency from time to

time as part of the progress of the universal state regardless of what it supposedly represents

in that universal state. This idea was explored in Shackell (In press-b) in terms of structural

elements of the semiosic field dubbed “recovery functions”.

The structural mechanism of the universal state that promotes cognitive similarity as self-

evident is not far to find. The world in all its guises, as McLuhan ([1964]1994) argued, is the

medium upon which we must put any message. Only certain messages will bind with any

particular historically constituted medium and have any valency (that is, have any impact on

the cognition of others). Messages inconsistent with cognitive similarity cannot be bound,

and so cognitive similarity is experienced as obvious in every reception. Consider in this

regard, what a performative contradiction it is to attempt to convince someone that they can

never have any thoughts exactly like your own.

Another way to express this position is that there is no consistently identifiable, objective

cognitive similarity, but there are nonetheless recurrent instances of its identification. These

identifications have their own reticulating valency due to the allocations of finite cognition

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they occupy. As our cognition is lead along the paths of these valencies, the immediacy of

this allocation leads us to feel an objective truth (i.e. a “meaning”) about the notion that our

thoughts are similar. To say or think otherwise, while possible, is to be never heard and to

render alien or idiosyncratic one’s own reality. Consider those scenes in the absurdist plays of

Ionesco (for instance, La Leçon (Ionesco, 2010 [1951])) in which characters speak without

effect except to themselves: this is the flavour of any challenge to cognitive similarity.

From another perspective, the preceding arguments simply expose the idea of cognitive

similarity as one of Wittgenstein’s language games (Wittgenstein, 1953). What is in fact

fundamental to assume, is not similarity but the structural limitation of valency to states

consistent with similarity, which are the only messages, as has been suggested, that can be

bound to any medium within an episteme.

Cognitive economy or catallaxy?

In light of the above discussion, and to avoid ontological over-commitment, we should not

think of the semiosic field as an economy of thought in which identical agents merely respond

asymmetrically in response to differential placement. Instead we should borrow some

vocabulary from Hayek (1978 [1976], pp. 108-109) and conceive the semiosic field as a

catallaxy in which homogeneity (the underpinning notion of cognitive similarity, for

example) is an emergent property of heterogeneity. By this revision, the articulable object

“thought” is realised uniquely in each agent but is recognisable and has its effect only by a

systemic valency or pragmatics of use. To illustrate, consider that a person who wishes to

communicate a notion of “thought” must project into the minds of all others some existing

notion of “thought” in order to enlist it in discourse. Unavoidably, in so acting they contribute

and reticulate a larger but diffuse mythology of thought which no one individual embodies

but which nonetheless shapes the conditions of possibility for each individual’s conception.

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The individual enunciates thought as a concept; but the concept is already inscribed a world

allowing its enunciation. Assuming a catallaxy rather than an economy of thought enriches

our effort to divine the placement of agents and avoid the pitfalls of an unnecessary,

normative assumption that all agents are identical.

Cognitive similarity, valency and relatedness

It does not seem difficult to accept that two people performing what appears to us an identical

activity (driving a car, for example) might have cognition that is similar at least in in some

partial sense. To extend the car driving example, it would seem unlikely that the system of

roads and vehicles would continue to operate if the cognition of all drivers did not bear some

similarity. The contrary, anti-hermeneutic view would seem to challenge to an absurd extent

what Eco defended as the limits of interpretation (Eco, 1992).

But consider a driver who never thinks of driving in the fast lane, or even a driver who never

makes a left turn: these drivers can coexist within the system of roads with others who do

have thoughts leading to such actions. Can cognition that is absent be said to be similar to

anything? Prima facie, it appears not, but if we remember that thought only ever comes into

existence by its valency, we must notice that absent thought always has a zero valency. By

zero valency, therefore, any thought may be similar in terms of valency, especially where it

reinforces or serves a discipline of the body such as enforced by driving. Thinking of horse

races, Uluru or the price of gold makes no difference when we are driving: the car is still

moving, being seen by other drivers, and any relevant system of traffic and roads is

patronised and promoted. The concept of cognitive similarity, therefore, must be permitted to

include cognitive relatedness as it functions within systems.

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For clarity of presentation, for the remainder of this article I will continue to use the term

cognitive similarity but contend that by introducing additional complexity it could be

substituted mutatis mutandis for cognitive relatedness when needed.

Cognitive similarity constituted for finite semiotics

The above discussion notwithstanding, it is obvious that in any analysis of thought or

cognition, cognitive similarity must be assumed as a practical matter. Most simply because

communication as culturally normalised cannot proceed without it. Finite semiotics is no

exception. However, by recognising that doing so is a prescriptive rather than descriptive

assumption, a unique semiotic perspective can be leveraged that is unavailable to other

disciplines, for these begin their investigations beyond any such ontological scrutiny.

Therefore, if finite semiotics is to incorporate cognitive similarity as a means of creating

constructs for analysis, it does so in careful recognition that:

1. Cognitive similarity exists only by a stream of not necessarily identical identifications

of similarity.

2. Similar thought is indistinguishable from and entangled with similar valency of

thought.

3. Cognitive similarity is not an ontologically rigorous assertion and is more of the

nature of a stable or stubborn element in the current semiosic field.

4. Cognitive similarity is best viewed as something useful for creating disciplinary,

determinative technologies of cognition.

A formalisation of cognitive similarity on this basis is offered in Definition 1.

Definition 1: Cognitive similarity

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Cognitive similar is a structural element of the current semiosic field that may be

asserted in modelling the field for the creation of new techniques and technologies to

determine some future aspects of it.

The cognitive set

To extend the analysis of the semiosic field with a stipulation that it features cognitive

similarity as we have defined it, let us first treat the idea of recurrent semiosis in a single

agent. By asserting some threshold for similarity beyond which cognitive states may be

treated as identical, we can reduce the number of unique states in semiosis and formalise the

“cognitive set”, being simply the set of unique cognitive states for an agent subject to that

threshold.

In the manner of Saussure (1959 [1916]), this set can be treated diachronically and

synchronically.

The diachronic cognitive set

Taken together over some period an individual agent’s cognitive states comprise their

diachronic “cognitive set” for that period. Where some states recur, one can say that the set is

reduced. This is illustrated in Figure 2 and formalised in Definition 2.

Figure 2. Semiosis implying a diachronic cognitive set reducible to {A, B, C}

Definition 2: Diachronic cognitive set

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The diachronic cognitive set for an agent is the ordered set of cognitive states over

some defined interval (potentially an entire lifetime), having dimensions of time and

state differentiation.

The synchronic cognitive set

For any agent with cognitive states that may be equivalent there will be a first and a last

occurrence of any particular cognitive state. On first occurrence, it enters the possibilities for

cognition. On last occurrence, it exits those possibilities. At a particular time, therefore, only

a subset of the diachronic cognitive set may be in play for an agent and so the agent’s

synchronic cognitive set contains those possible cognitive moves (that is, semiosic

possibilities) for an agent. This is illustrated in Figure 3 and formalised in Definition 3.

Figure 3. Semiosis showing the evolution of synchronic cognitive sets from {A, B, C} to {B,

C, D}

Definition 3: Synchronic cognitive set

The synchronic cognitive set for an agent is the set of cognitive states that will yet

recur.

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Our experience of cognitive sets

Cognitive sets are obviously responsive to context. Simple evidence of the progression of

cognitive sets is that people thought about different things in different historical periods. For

obvious reasons, in the 1980s people did not think about Facebook or Google. In the 1880s,

people thought more about horses than they did about automobiles. Today not many people

think about discovering new continents, but they did in the time of Columbus. New things

arise; new thoughts arise in the presence of those things; new things arise…and so on in a

cyclical fashion.

The progressive restriction and evolution of the cognitive set can be confirmed in several

other ways taking evidence from common experience. Firstly, we can assess our own

cognition and interrogate its finiteness with the question, “Did I think about X in the last time

period?” For example, did I think about Mount Everest in the last minute?” The answer will

likely be no. Similarly, one might ask, “Did I think about a platypus in the last week?” If one

has never heard of a platypus the answer must be no, but even if one has an advanced degree

in monotreme mammalogy one may also answer in the negative due to a recent preoccupation

with echidnas. What is evidenced is the existence and dynamism of our cognitive set.

From a second perspective, we might recognise that at least some portion of what we think

changes daily, weekly, monthly, yearly. Some days we think about tsunamis; some days we

think about football finals; some days we think about neither.

From a third point of view we can observe that our thoughts influence or determine the

cognitive sets of others. For example, when we inform our colleagues that it is raining, or ask

if they are going to the circus, we are relying upon our notion of their existing cognitive set to

allow us to determine its next states. In fact, there is some epidemiology of thought at play in

such transactions that involves cognitive sets. Moreover, this distributional mechanism

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involves the historical development of the cognitive set, for we would not mention the circus

to a colleague if we had never heard of one, or if the circus had never been invented.

On the basis of these common experiences, some formal possibilities for cognitive sets may

be identified:

1. Restricted time periods will contain only subsets of the full cognitive set (partiality)

2. States may not occur and recur with equal frequency (cardinality)

3. There may be constraints in the ordering of cognitive states (ordinality)

Of these, the factors occasioning ordinality in cognitive sets is of particular interest.

Ordinality of cognitive sets

It is intuitive that states in our cognitive sets are not equally affiliated or likely. This is borne

out by many daily experiences as well as by many well documented psychological effects and

biases (for example, priming effects (Meyer & Schvaneveldt, 1971); or prospect theory

(Kahneman & Tversky, 1979)). Although it is possible as an artistic or academic provocation,

one does not typically think of going out to pick purple lemons or going to watch the sun

change its direction and set in the east. On the other hand, one does more often think of

picking yellow lemons and going to the western side of a building to watch the sun set.

The world, or in our preferred term the universal state, imposes this ordinality on our

cognitive sets, and this influence is in turn coextensive with the historical effects of semiosis

in evolving language, creating buildings, transmitting iconography and so on.

Ordinality and semioformation

An explanation for the more frequent occurrence and co-occurrence of certain cognitive

states is provided by the finite semiotics concept of semioformation: the agent enters an

environment prepared for it by other agents (that is, containing their externalities) such that

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the cumulative effect of the environment is to progressively order cognitive states into an

interrogable, recoverable reality that is stabilised by each environmental transaction.

Cognitive sets are therefore consistent with an historically dynamic – but to the individual

seemingly stable – engendering of cognitive states. If the sun was once thought by some to

revolve around the earth, it was simply because such thoughts were part of that epoch’s

cognitive set and had valencies that sustained their inclusion. Moreover, that geocentric

cognitive set, now so ludicrous to us and serving as an exemplar of delusion, is nonetheless

validated by its being prologue to our present cognitive set.

This realisation allows us to restate the notion of cognitive similarity: cognitive similarity,

like the object “thought” upon which it relies, is not part of the universal state; it is part of the

larger cognitive set sustained in us through semioformation in common environments over

long, intergenerational periods of time. One might notice in this regard that if modern

philosophy began with the logic of Descartes’ cogito ergo sum, it also began with the

simultaneous elevation of the object “thought” into the discourse of modernity.

With the addition of cognitive sets to the tools of finite semiotics we can reformalise

semioformation as in Definition 4.

Definition 4: Semioformation in terms of cognitive sets

Semioformation is the evolution of synchronic cognitive sets under the progressive

influence of the universal state.

The cognitive set and the non-local common environment

In the examples above, the relation of the cognitive set to semioformation and hence the more

narrowly defined “perceived” environment is highlighted. If a rock falls nearby we think of

the rock, of danger, of the provenance of the rock, whether to run or not and so on. If we live

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where it snows we will have many thoughts of snow; if we live at the beach we will have

thoughts of sand and water. Besides these directly driven thoughts we may have others that

relate to some previous environment such as when we think about a character in a book we

read years ago, or for no apparent reason think that we need to eat at McDonalds. Our

thoughts, it seems, tend to modulate with the environment to keep us fed, hydrated, warm,

and entertained. In other words, the cognitive set is often homogenised to tendentious

valencies from the common environment. Thus, for example, a community living the in snow

enjoys a semioformation leading to communication about snow beneficial and promotional to

its members when they stay clear of an avalanche zone.

Today, however, our environment may contain common elements that are of remote origin

reproduced to appear local in many places. This is not new. For example, for centuries now

books printed in London have become local artefacts in many homes in New York and have

affected thought there. But this process of homogenised artefacts has, of course, become

endemic to our age. By telecommunication, any number of reproductions of remote artefacts

are now found in our local environments to the extent that we can travel to remote corners of

the world and be as understood when we ask, “Are you on Facebook?” as “Is that air you are

breathing?” These elements make up what we can might call the non-local common

environment (NLCE), and it is in communion with these artefacts that we increasingly spend

our time. The NLCE is the basis of the hyperreal, for it seduces thought into content and

patterns divorced from traditional valencies in which thought has reticular effects on itself

through the intermediation of unique local environments. Being shot in the local

environment, for example, will change your life; being shot in the non-local common

environment is just a way to kill time before dinner.

Definition 5: Non-local common environment

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The non-local common environment is the reproduced set of artefacts presented to our

senses from remote locations constituting a common environment that is not local.

These artefacts have cryptic, distorting, discontinuous or untraceable effects on the

local environment and its progressive determination of cognition. In other words, they

may promote the hyperreal.

Cognitive sets at the population level: the semiotic manifold

If we compare the cognitive sets of two agents with some adjacency (for example, in

conversation) we will likely be able to discern some co-occurrence patterns in which the

cognitive state of one affects the other. In a simple scenario, this may be considered thought

transference. Consider when Agent 1 tells Agent 2 some fact that is encoded by thoughts A B

C (for example, “Paris is in France”):

Agent 1 A B C D E F G H I J K

Agent 2 M N O A B C R Q S G

In this example the cognitive states A B C are being replicated in Agent 2; however, the

states R Q S (for example, “I already knew that!”), due to path dependence could also be said

to result via some complex function from A B C. Conversely, one should also remember that

A B C in Agent 1 have some path dependent origin of their own (not shown). There is,

therefore, a set of constraints on thought arising from semioformation that gives rise to path

dependence of thought that in turn increases cognitive similarity. More specifically, and

counterintuitively perhaps, one might say that language is a limiter and determiner of

cognition.

To formalise this in a mathematical way: if we assert that any cognitive state is definable by

some set of parameters in a high dimensional space, and that this space is constrained by

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ontological and environmental factors (including language artefacts), then thought (and hence

semiosis) in the semiosic field is limited to some manifold. This semiotic manifold arises by

the interplay of the valencies of individual agents.

The semiotic manifold and Lotman’s semiosphere

The idea of a semiotic manifold is consistent with Lotman’s notion of the semiosphere

(Lotman, 2001 [1990]). Via semioformation each agent develops a complex set of

potentialities which interface with the world, including other agents. Where these

potentialities interact, semiotic valency occurs. Over historical time periods these valencies

have evolved reticular patterning which promotes their cyclical recurrence. This recurrence

stabilises the semiotic manifold and promotes common, but geographical and culturally

nuanced, experiences of reality. This view of the mechanics of the semiosphere assuming

finite cognition is illustrated in Figure 4.

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Figure 4: Finite semiotic representation of valency occurring between two agents implying

Lotman’s semiosphere.

Semiotic vectors

In our abstract analysis of the cognitive set, we have presented semiosis as occurring between

cognitive states with the character of a movement between two discrete values (in our terms,

between two discretised states). By introducing a metaphor of space we can view this

movement between values as a vector motivated by a “semiotic force” thus far called

semioformation. The notion of a semiotic vector is a useful formality for analysis and to this

end a definition is offered below.

Definition 6: Semiotic vector

If at time t 1 an agent has cognition A, and at some later time t 2 has cognition B, then

some net cognitive movement or semiosis has occurred that we can call a semiotic

vector V A → B.

This definition compels us to formalise the relativity of any observation as a vector itself:

Corollary 1 to Definition 6: Vector identification implies and interrogating vector

By the principle of equivalence of the semiosic and epistemological fields, the

identification of cognitive states A and B in the definition above must also be part of

the semiosic field and the result also of a semiotic vector bearing some relation to

states A and B.

For semiotics, as for cognitive science and other psychological and social disciplines, it is

interesting to note that by this corollary, a “sign” is only created by the action of a vector of

sign recovery – a vector created and asserted purposively only by semiotics itself.

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Notation of semiotic vectors

A conceptual difficulty in semiotics is to separate the idea of words from thoughts, for as

Wittgenstein pointed out, to depart from words leaves little to be said (Wittgenstein, 1974

[1922], 7). As an attempt at clarity I will hereafter refer to cognitive states that demarcate

semiotic vectors not in quotation marks as in “baking a cake” but with double chevrons as in

>>baking a cake>> with the intention to refer not to the words but to the abstract directional

thought behind the description, which finite semiotics has been careful to preserve and

advance as a theoretical object.

Measurement and description of semiosis

As the identification of a semiotic vector must be via a vector itself, we cannot claim that any

vector can be objectively identified. This is, of course, a major impediment to quantitative

semiotic analysis and one that has prevented semiotics – some might say for the better –

enjoying a place among the disciplines favoured by the rise of computational technology. The

thrust of semiotics, contrary to this trend, has never been to know the detail of signs or

thoughts, but to recognise general patterns in their occurrence. The semiosic field expanded

into a spatial model offers, I believe, a new opportunity to formalise the constraints

engendering such general patterns and offer something unique to computational approaches.

This is explored below beginning with the notion of the absence of signs or zero semiosis.

Zero points of semiosis

From experience, we may notice that over time semiotic vectors frequently return semiosis to

some point of zero semiosis (for example, daydreaming, resting, sleeping, or, ultimately,

deceased) and are ultimately zero sum according to our spatial metaphor. For example, if

sleep is considered a period of zero semiosis, each period in between must be considered a

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displacement from this zero point. Moreover, in terms of personal experience regarding

particular habits of discretisation (that is, objects) we can associate points of zero semiosis

arbitrarily with frequent states. In terms of a hot day, for example, >>it is hot>> can become

a zero point. More broadly, consider how psychology interrogates our mood as a baseline

consisting of happy (“well-adjusted”) or unhappy (“depressed”) thoughts.

In general terms, when an individual is not thinking about an object, that individual can be

said to be at a point of zero semiosis regarding that object. If Figure 5 below, for example, A

could be arbitrarily considered a zero point relative to B, or vice versa.

The semiosic field in two and more dimensions

Having introduced in the semiotic vector a spatial metaphor to stand for the similarity or

dissimilarity of thought over time, the analytical possibilities multiply for our representation

of the semiosic field. If the previous model was one dimensional due to its agnosticism about

cognitive similarity we can now add subsequent dimensions to account for similarity. For

example, we can represent more and less similar cognition in an agent as displacement from

some arbitrary axis as in Figure 5.

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Figure 5. Similarity of cognitive states as displacement from an axis, also showing semiosis

returning to two synonymous states (A).

Axes of oscillation

What might a measure (albeit prescriptive) of thought differentiation look like? As

participants in the semiosic field, how can we begin to chart thought in it? A first step is to

assay some obvious pattern. One such pattern is the antonymic, a pattern with a history in

word association (e.g. Clark, 1970) and cognitive modelling (e.g. Rumelhart, 1978). If we

take the prevalence of vectors such as >>night>> versus >>day>>, >>rich>> versus

>>poor>>, >>good>> versus >>bad>> we get a sense that thought is patterned to some

extent as opposites. Moreover, we can map this pattern to semioformation as something

reflecting the continuity of the environment and thought: if see clearly and feel the sun on our

backs we have thoughts relating to day; if we begin to see less clearly and feel colder and

have thoughts more related to night. Hence, the antonymic facet of the earth’s rotation is

reflected in thought.

From this we can construct an antonymic axis against which to locate the progression of a

cognitive set as in Figure 6. In this case, it seems intuitive to locate the horizontal axis at the

midpoint between values.

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Figure 6. Dimensional modelling of antonymic cognitive states over time (intervening states

not shown)

In this analysis of antonymic states in semiosis, it is easy to see that some oscillation takes

place.

A general pattern in semiosis: oscillation

The analysis above allows us to conveniently define the zero axis and nominate it as the

“point of zero semiosis” in regard to two antonyms. More broadly, however, consider that the

notion of the antonymic can be replaced by any purposive axis of interrogation applied to

cognitive states over time. For any measure of thought differentiation that allows for

equivalence there will be a tendency for semiosis to attain a state, depart from it and return.

We could, for example, impose an axis of “purple-ness” on thought and observe that

cognition occasionally tends to purple states then departs only to return again under certain

conditions. All we are really noticing here is that similarity in cognition demands that, under

interrogation, the general pattern must be one of oscillation.

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If we wish to ground this point in experience we can observe again that there are “natural”

zero points in cognition around which it oscillates: when we are unconscious or asleep,

thinking of nothing, unaware of our thoughts et cetera. More generally, however, there are

implied zero points each time we depart from a cognitive state, and although this is not

“natural” in the same sense as sleep, we can see that it fulfils the same definition and

moreover can be analytically useful, for if we position zero semiosis in the middle of an n-

dimensional representation of semiosis, we can construct a general model of semiosic

oscillation. This modelling to oscillation affords us the opportunity to construct and apply

oscillation axes (which in Figure 6 was an antonymic measure). This is intuitively in accord

with our experience of semiosis: we do not feel that our cognition wanders too far from some

baseline or “normal” state except in response to some change in our environment. For

example, we may think of eating an orange when we see one but this does not normally

become a multi-day marathon of intense cognition about eating oranges leading to a gorging

death. Rather we think of the orange, eat the orange, forget the orange (that is, return to a

point of zero semiosis in regard to >>orange eating>>).

This idea is, of course, not new. The primacy of opposition in semiotics traces back to

Jakobson’s binarism, which he brought into focus towards the end of his career with the

comment that “every single constituent of a linguistic system is built on an opposition of two

logical contradictories” (Jakobson, 1972, p. 76). If such a statement is true of language, it

must be true of the thought that recognises, selects and assembles it. Moreover, we can invert

this statement to suggest that a perception of language as oppositional is in fact due to the

deeper, oscillatory constraints of cognitive sets.

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Semiotic oscillation as a reframing and extension of the semiotic

square

From the above discussion, the well-known construct of the semiotic square can be reframed

as an identification of several dominant oscillation axes. For reference, Figure 7 is the

seminal representation of the semiotic square by Greimas and Rastier (1968). Figure 8 is the

representation adapted by Chandler (2017) from Nöth (1990).

Figure 7. The semiotic square inaugurated by Greimas and Rastier (1968, pp. 88,90)

Figure 8. The semiotic square by Chandler (2017, p. 125)

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The axes of complementarity, contrariety and contradiction might be represented for finite

semiotic purposes as a three dimensional space based around a point of zero semiosis:

Figure 9. The semiotic square rearranged into a three dimensional space of oscillation axes

around a point of zero semiosis.

The selection of these dominant axes is closely aligned with an objectivist view of logic

dating back to Aristotle, and in fact have been said to derive from what has been called “The

Traditional Square of Opposition” (Parsons, 2017). The implication is that they encapsulate a

certain universal truth is made axiomatic historically by the amount of cognition devoted to

them. Although it might be argued that the semiotic square embodies the most dominant

semiotic relations of Western discourse, finite semiotics must remain open minded on this

point. Particularly where hyperreality impinges, it seems obvious that a vast number of

oscillation axes are in operation in an individual or culture at any point in time. These axes,

particularly in light of behavioural idiosyncrasy and cognitive biases, should not be restricted

to the coherent or consistent. In the entertainment media for example, a contemporary

celebrity like Jennifer Aniston may oscillate between pregnant and not pregnant, but also

between “popular” and “old”, while the long departed James Dean may still oscillate between

“popular” and “young”. Similarly, a natural feature such as Niagara falls oscillates in thought

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more often as American or Canadian rather than American or Mexican. In fast food

restaurants, Coke may oscillate with Pepsi, but also with 7-Up or water given the context.

And in Times Square a pedestrian may experience an oscillation between Coke and M&Ms

due to the path of their travel.

The commercial practice of semiotics makes great ad hoc use of axes of oscillation. For

example, to audit a product or brand, a marketer may use respondent studies to chart the

current semiosis about it. A bottled water, despite its neutrality-defining content, may be

plotted as “strong” or “artificial” or “expensive” or “smooth” or “reliable”. A wider study of

similar products may be performed to identify new oscillations to remould cognition about

the brand. These manoeuvres then expand over time as the semiotic space becomes more

saturated requiring more oscillation and so on. Consider, for example, the use of coloured or

textured plastic in bottled water to suggest coolness or expense, or the once seeming

irrelevance of a name such as “Fiji” in regard to marketing water (especially given that

outbreaks of cholera in that part of the world are not unknown). By endowing a brand with

markers across a number of axes, oscillations can be set up that bring it to mind in highly

relevant and restricted contexts.

Such analysis, of course, does not always yield results – expected or otherwise. This is

because the action of oscillation axes is not as synchronic as these analyses suggest. Their

operation is occurs over time in a variety of realisations that cannot be foreseen. The semiotic

square offers not a synchronic description of potential object positions in a stable system, but

a set of axes by which objects oscillate in a process of attracting attention and allocating finite

cognition. The closer the axes are to describing a closed semiotic subsystem, the more likely

they are to have determinative (hence, to the creator, predictive) power. In other words, the

semiotic square provides not a description of natural properties of some concept but a

proposal for a set of axes that will attract and consume cognition over time.

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The semiotic “pipe”

If we conceptualise axes of oscillation as constituting an n-dimensional space (that might be

drawn in two dimensions, for simplicity, as a “wheel”) and add the arrow of time (in effect,

simply another axis of oscillation) we can begin to conceptualise the motion of semiosis as a

wave moving along a pipe with the n-dimensions of the axes of oscillation at any point

forming a cross-section. This is illustrated in Figure 9. The continuous wave of semiosis can

be seen to be only partially discretised upon interrogation into “conscious” thoughts, while

the intermediating motion occurs around various unrecognised, dynamic, but influential axes

of oscillation.

Figure 10. Semiosis as movement along a “pipe” of oscillation axes. (Note: the circular pipe

and symmetrically distributed and proportioned axes of oscillation are a simplification for

initial theoretical illustration only. A pipe topology and axial dynamics of extreme

complexity are assumed.)

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The oscillatory experience of semiosis

To make clear the intention of the model presented so far, let us consider an agent’s

experience in the semiosic field. An agent comes into existence by having valency in the

semiosic field and beginning semioformation (typically known as “being born”). This

ongoing process sees the agent think in response to changes in the environment in accordance

with their evolving potentialities (in particular, in response to environmental changes

introduced by other agents such as speech, the built environment and so on). Simple

oscillations build into more complex oscillations as the cognitive set grows and evolves.

In a “natural” or “traditional” environment, oscillations are closely aligned to the common,

cenoscopic environment. A rainy day leads to thoughts of rain, thoughts of mud, thoughts of

shelter. In more evolved “symbolic” environments cognition is also regulated over very long

trajectories by axes from the NLCE: books, movies, television, video games, food packaging.

This environment operates by hyperreal oscillation in which the valency of thought is cryptic

to the agent. A movie in which it rains (regardless of whether it is actually raining outside)

triggers oscillations of hardship, or romance, or fecundity whose valency serves to promote

the medium of the movie via ticket sales, streaming services and so on.

Two new finite semiotic fields: Natural Semiotic Processing

and Technological Influencing

Natural semiotic processing (NSP)

The theoretical discussion above of semiosis under cognitive similarity implies that cognition

is comparable in high dimensional spaces. Modelling of these spaces – which I would argue

currently occurs more or less informally in areas such as design, marketing, journalism,

content programming, cultural analysis, and politics – would allow application of

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mathematical models involving vector spaces, directed graphs and sparse matrices such as

those currently employed in natural language processing and artificial intelligence. This could

create an assistive set of computational tools for semiotic analysis that could exploit the

current availability of data and formalise procedures and evaluation. The critical step in

beginning this effort and establishing a discipline of natural semiotic processing (NSP) is the

formal assignment of values to these dimensions – an endeavour that will demand new

sensitivity to the finiteness of cognition and the determinative mechanisms of technology.

Cognitive sets, the semiotic manifold, semiotic vectors, and semiotic oscillation provide a

conceptual toolset. To accompany them, lateral or triangulational means of differentiating

thought need to be developed and this must come from a more purposive modelling.

Technological influencing (TI)

If natural semiotic processing is destined to be the science of how, technological influencing

must be the art of why. The source material and useful outputs of a new discipline of natural

semiotic processing lie in the relation of opinion, behaviour, and belief to technological

exposure. Hence a governing discipline more grounded in the social sciences, equipped by

natural semiotic processing, is necessary. Moreover, only such a discipline can provide the

subjective direction and inputs for its companion. This discipline would better help us

understand advertising, marketing, branding, political discourse under the rise of technology,

and, most importantly, inform the evolution of an ethics of technological influencing which

seems currently in abeyance. Moreover, it can serve as a gateway into technology for the

ideas of semiotics.

Conclusion

This article explored the implications for finite semiotics that cognition within and between

individuals may be considered similar. To this end, a number of new theoretical terms were

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introduced including cognitive sets, semiotic vectors and semiotic oscillation. Two new

methodologies were also inaugurated on this basis: cognitive set analysis and semiosic

oscillation analysis.

The opportunity exists for these methodologies to inform new endeavours in two companion

areas dubbed natural semiotic processing (via their computational implementation) and

technological influencing (as driver, architect and conscience). It perhaps cannot be restated

often enough that the press of technological change and the hyperreal divorce of cognition

from its effects on itself make this area of prime academic, commercial and ethical

importance.

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