Both necessity and arbitrariness of the sign

Information

Vasil Penchev

• Bulgarian Academy of Sciences:Institute for the Study of Socities and knowledge:Department of Logical Systems and Modelsvasildinev@gmail.com

• « Le cours de linguistique générale 1916-2016 » « Arbtrariness of the sign »,

Suitzerland, Geneva, University of Geneva, 10-12 January 2017:

11 January, 14:40-15:10

Introduction

Suassure’s sign es a “Janus” with two faces:

• There exists a fundamental problem about the relation of information and the sign as it is defined in Saussure:

o Any sign is a unit, on the one hand• Any sign is an element from a system of designation, on the

other hando The sign is seen inside in the former case

• The sign is seen outside in the latter caseo Saussure’s concept of sign means both,

but they could not be equated to each other

The contradiction explicated:

• The creative contradiction to the sign penetrated his main work

o He used the term “sign” in different and practically disjunctive contexts referring correspondingly to a single sign

and to a certain system of signs, to which it belonged• Thus that implicite contradiction could be reconciled and

logically admissible remaining disjunctively divided between both kinds of contexts, which should not mixed

o The tension between them generated the plot and intrigue of his Course

Those two “faces” of his ‘sign’ unified as duality:

• Therefore, his concept generates in turn the duality of information in any signo Suasure did not use the concept of information or it under

other name, or analogical of it• However, the concept of information (by the way, utilized by

Peirce to unify both uses of ‘sign’) may be in turn defined of that quality or quantity meant in both kinds of uses of “sign”

o One may conclude that the entire unite of the Coursedefined right that unity of information as ‘sign”

• It is the hidden name of the “soul” of the Course

Sausure’s ‘sign’ inside• The sign meant internally or actually is both necessary and

isomorphic to a single bit of informationo Futhermore, its formal strcture coincides with

(and thus sign is isomorphic to) those of:• A bijective mapping (of an element of a set into an element of

another or the same set, particularly an identitet) o The disjunctive choice between two equiprobable alternatives

• Assigning ‘false” or ‘true’ to any statemento Frege’s “Bedeutung” of a statement

or a system of statements (text)

The sign inside as a bit of information:• Indeed, any sign is interpretable either as a signifier or the

signified just as in an empty cell of information can be recorded either “0” or “1”o An example of that interpretation: any calculation representable

by processing binary information by a Turing machine (embodied in any of our computers) can be interpreted as a process of

designation• That Turing macine’s ultimate result (if any) cam be then seen as

the sign of a certain thingo One can say that ‘calculation’ is processing signs “inside”

with the above sense linked to Saussure semiology

Further philosophical interpretations:• Seen in thus, i.e. inside, the sign is a totality, in which the link

between the signifier and signified is necessaryo The opposite statement is not less true or interesting:

• Any totality e.g the universe or the being in a philosophical sense can be interpreted as a single sign or bit informationo Than those signifier and significant of that sign or those disjunctive

alternatives of that bit of information mignt be thought as the transcendent thing by itself and its transcendental representation

for us or as ‘object’ and ‘subject’, ‘good’, and ‘evil’ accordingly, etc.• Even language as the universal system of signs might be seen as

Wittgenstein as generalized ‘Bedingungen der Möglichkeit’

On the contrary, the sign “outside”• On the contrary, the sign considered outside, is uncertainly arbitraryo That arbitrariness of sign is usually interpreted as its conventionality

in the sense that any given significant might be designated equivalently by arbitrary many different signifiers such as words in

different languages• However that kind of the formal representation of the arbitrariness

of ‘sign’ is not general enough though being intuitiveo The arbitrariness of sign in general should be understood as the

correspondence of many significants to many signifiers or as that of an arbitrary and uncertain system of significants to an arbitrary and

uncertain system of signifiers

The sign outside as the potential of signifying

• The sign “outside” is the potential for the sign meant actually only as some set of signified (things) to assign (a-sign) any signifiero Therefore, it is the process of competing the structure of the sign

as actual, seen “inside” according the term above• One may say that any signified can be designated by any signifier

or by any other signified meant as a signifiero If that potential process of possible signifying is represented

anyway somehow actually, it would address infinity• The so-called potential infinity turns out to be transformed into

actual infinity transferring from the externality to the internality of sign

The environment of sign

• Then the sign needs the non-sign outside of it, in which only it might find a corresponding signifier

o The sign includes its environment gradualy,signifier by signifier

• That process being able to complete only into actual infinity transforms the sign into a kind of totality and its environment into its internalityo Then the sign might be understood as a way of expessing

the externality of totality internaly right as the necessary signifier of it already seen ‘inside’

Back from philosophy to linguistics

• The choice of a signifier is often restricted to a finite set of elements such as an alphabet or a vocabularyo Anyway the finiteness of an alphabet seems to be different

form that of a vocabulary (or dictionary, or thesaurus are synonyms)

• Any alphabet is meant as finite in principle and furthermore, its symbols are thought as the digits in a numeric system (e.g. ten digits or 26 letters)o Thus ‘alphabet’ is rather a set of signifiers (letetrs) referring

to another system of signifiers (words) as signified

Vocabulary vs aplhabet• Vocabulary in comparison with alphabet might be defined as

a system of primary signifiers referring to signified immediatelyo Thus, the number of units in the vocabulary will increase

proportionally to the signified things• The number of units in an alphabet might be pactiacally

constant for the necessary number of “letters” would increase much slower, namely logarithmically o Thus. ‘vocabulary’ means an increasing finite number (of

“words”), and ‘alphabet’ a constant (and much smaller) finite number (of “letters”)

The quantity of informationof a vocabulary unit

• The quantity of information depends on the number of elements of that vocabulary being arbitrary and more than a bit in generalo It corresponds to the number of letters in a given alphabet,

necessary to designate unambiguously enough any unit in that vocabulary

• This implies that information in a single unit “outside” will depend on the number of vocabulary units increasing logarithmically

The contradiction explicated by the quantity of information

A sign “inside”

Signified Signifier

Sign

Information = constant = 1 bit

SignAn inceasing system

of signs

A sign “outside”

Information ⇒ logarithmically increasing ⇒ potentially

infinite

Information of any one and the same sign

The problem

The impossible equationfor the information of any one single sign

• Information in a sign is not unambiguous:o It turns out to be:

• Both constant and increasingo Both one bit and an arbitrary number of bits

converging to infinity • Neverthless those two should be able to be equated to each

other as far as:o The sign is one and the same, and

• It is the only carier of its information

The information of sign:a property or a relation

• Information is necessarily a single bit “inside”, but quite uncertain “outside” (depending on the utilized alphabet or vocabulary or even on all texts written by that alphabet or vocabulary)o It is both property and relation both “inside” and “outside”

• It reflects quantitatively the transformation of a property into a relation in both caseso However, the resulatative relation consists of two members

“inside” and of arbitrariliy many members “outside”

Saussure’s implicit creative intuition penetrating

his Course

The unity of ‘sign’

• The concept of sign needs and therefore generates a space between the necessity and unity of the sign and its arbitrariness and uncertainness among the elements of alphabet or vocabulary depending furthermore on all their uses (all words or texts recorded by means of them)o The entire Course can be consider as the craul of that space

of ‘sign’ designating it again and again “outside”• The tension of that contradiction generates its “plot”

o Nevrtheelss, the two contexts of uses of “sign” are always separated conserving its scientific consistency

The sign wandering in signifying

• The sign being always and moving in that space can be only partial, motivated by the unrealizable aspiration to complete ultimately the infinite process of signifying

• Saussure’s “sign” needed to explore the entire spase of his Course in order to be able to return at last back in itself, in its

simple essence of a single bit of information: the signified and signifier

• Its message can be seen as that hidden identity and suffering of the sign designating all …

Saussure’s ontology

• Even much more: Saussure’s semiology is an implicit ontology as the being of all is what appears in that infinite process of signifying

o The suffering to signify generates the world• Saussure’ sign creates the ontology of Course just as any real

language or the language at all creates the world as an ontology of signifying

o The hypothetic endpoint of that infinite process is justthe sign inside as a single and simple disjunctive opposition of

the “signified and signifier” just as in a bit of information: “subject and object”, “good and evil”, etc.

The resolving of the above problem in quantum mechanics and information in relation to semiology

What quantum mechanics means• Quantum mechanics had to resolve the problem of how to

describe uniformly both quantum leaps and smooth motion, namely by the Schrödinger equation

o The structure of its problem is isomorphic to the suffering of Saussure’s ontology to signify all by the single and universal

scheme of ‘sign’. Here is how:• The motion of quantum leap corresponds to the jump from the

signified to the signifier in any sign “inside”o The smooth motion of classical physics corresponds to a

trajectory of signifying from the same signified to the same signifier via all the rest

• And quantum mechanics claims to equate both by the Schrödinger equation. What implies is …

The new viewpoint of quantum information

• It was reformulated thoroughly in terms of quantum information in the end of the 20th century

o Its units are quantum bits just the units of classical information are the usual bits

• A quantum bit is defined as the normed superposition of two orthogonal subspaces of the separable complex Hilbert spaceo Then any wave function being an element of that space is

representable as a series of qubits for any two successive “axes” of it (einω, ei(n+1)ω) are those orthogonal spaces

Quantum information and infinity

• Though involved differently in quantum mechanics, quantum information can be equated unambiguously to the generalization of information to infinite sets and serieso Then a qubit can be interpreted as the generalization of the

choice between equally probable alternatives to an infinite set of alternatives

• The problem of both quantum mechanics and Saussure semiology seems after that as follows:o Under which conditions can a bit of information be equal to a

qubit of quantum information?• The answer of quantum mechanics is right the Schrödinger

equation

The Schrödinger equation

• The Schrödinger equation itself can be also exhaustedly interpreted in terms of quantum information

o The essense of that is:

𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶1 ⁄𝐶𝐶 𝑏𝑏𝑏𝑏𝐶𝐶 𝜕𝜕𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶2 ⁄𝐶𝐶 𝑞𝑞𝑞𝑞𝑏𝑏𝑏𝑏𝐶𝐶 𝜕𝜕𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑡𝑡2

o This in turn implies that there exist some:

𝐴𝐴 𝑏𝑏𝑏𝑏𝐶𝐶 = 𝑚𝑚𝐶𝐶𝑚𝑚𝑚𝑚𝑏𝑏𝐶𝐶𝑚𝑚 𝐶𝐶 𝑞𝑞𝑞𝑞𝑏𝑏𝑏𝑏𝐶𝐶

as well as its reverse mapping

The link between quantum mechanics and Saussure’s semiology

• That latter interpretation links it to Saussure’s tension of the sign generating an implicit ontology as semiologyo Indeed, the ontological problem of Sausure’s semiology was

how to express the sign “inside” (a bit of information) by the sign “outside” (a qubit of information)

• The Schrödinger equation represents the general condition, under which any possible solution exists and thus, that those solution existo Thus furthermore, the generating tension of Sausure’s Course

between the sign both “inside” and “outside” is implied to be also both consistent and solvable

The interpretation of the Schrödinger equation as the solving of Sausure’s implicite problem

• Then the Schrödinger equation can be seen as a solution of the problem above about the relation of information and Saussure’s sign:

o Both “arbitrary sign” outside and corresponding quantum information are equated to both “necessary sign” inside and

corresponding information• The unification of smooth and discrete motion in quantum

mechanics implies the unification of Saussure’s semiology and that physical theory of motion rather than only the unification of the sign both “inside” and “outside” in the former

Conclusions:• There is a fundamental contradiction or rather tension in Sausure’d

Course: between the necessity of the sign within itself and its arbitrariness within a system of signso That tension penetrates the entire Course and generates its “plot”

• It can be expressed by the quantity of information generalized to quantum information by quantum mechanics

o Then the problem is how a bit to be expressed by a qubit or vice versa

• The structure of the main problem of quantum mechanics is isomorphic

o Thus its solution, namely the set of solutions of the Schrödinger equation, implies the solution of the above contradictionor tesnion

Thank you for your kind attention!Je vous remercie de votre aimable attention!

Je vous remercie de votre aimable attention!Je vous remercie de votre aimable attention!

Je vous remercie de votre aimable attention! Je vous remercie de votre aimable attention!

Je vous remercie de votre aimable attention! Je vous remercie de votre aimable attention!

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