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 signs. 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. 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. Thus its solution, namely the set of solutions of the Schrödinger equation, implies the solution of the above contradictionor tension.

1. Both necessity and
arbitrariness of the sign
Information

2. Vasil Penchev
• Bulgarian Academy of Sciences:
Institute for the Study of Socities and knowledge:
Department of Logical Systems and Models
vasildinev@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

3. Introduction

4. 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 hand
o The sign is seen inside in the former case
• The sign is seen outside in the latter case
o Saussure’s concept of sign means both,
but they could not be equated to each other

5. 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

6. Those two “faces” of his ‘sign’
unified as duality:
• Therefore, his concept generates in turn the duality of
information in any sign
o 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 Course
defined right that unity of information as ‘sign”
• It is the hidden name of the “soul” of the Course

7. Sausure’s ‘sign’ inside
• The sign meant internally or actually is both necessary and
isomorphic to a single bit of information
o 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 statement
o Frege’s “Bedeutung” of a statement
or a system of statements (text)

8. 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 thing
o One can say that ‘calculation’ is processing signs “inside”
with the above sense linked to Saussure semiology

9. Further philosophical interpretations:
• Seen in thus, i.e. inside, the sign is a totality, in which the link
between the signifier and signified is necessary
o 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 information
o 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’

10. On the contrary, the sign “outside”
• On the contrary, the sign considered outside, is uncertainly arbitrary
o 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 intuitive
o 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

11. 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 signifier
o 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 signifier
o 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

12. 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 internality
o 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’

13. 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 vocabulary
o 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

14. Vocabulary vs aplhabet
• Vocabulary in comparison with alphabet might be defined as
a system of primary signifiers referring to signified
immediately
o 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”)

15. The quantity of information
of a vocabulary unit
• The quantity of information depends on the number of
elements of that vocabulary being arbitrary and more than
a bit in general
o 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

16. The contradiction explicated
by the quantity of information
A sign “inside”
Signified Signifier
Sign
Information = constant = 1 bit
Sign
An inceasing system
of signs
A sign “outside”
Information ⇒ logarithmically
increasing ⇒ potentially
infinite
Information of
any one and the same sign

17. The problem

18. The impossible equation
for the information of any one single sign
• Information in a sign is not unambiguous:
o It turns out to be:
• Both constant and increasing
o 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

19. 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 cases
o However, the resulatative relation consists of two members
“inside” and of arbitrariliy many members “outside”

20. Saussure’s implicit creative
intuition penetrating
his Course

21. 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

22. 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 …

23. 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 just
the 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.

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

25. 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 …

26. 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
space
o 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

27. 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 series
o 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

28. The Schrödinger equation
• The Schrödinger equation itself can be also exhaustedly
interpreted in terms of quantum information
o The essense of that is:
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶1 ⁄𝑎𝑎 𝑏𝑏𝑏𝑏𝑏𝑏 𝜕𝜕𝑡𝑡𝑡𝑡 𝑡𝑡𝑡𝑡 = 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶2 ⁄𝑎𝑎 𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞 𝜕𝜕𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
2
o This in turn implies that there exist some:
𝐴𝐴 𝑏𝑏𝑏𝑏𝑏𝑏 = 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑎𝑎 𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞𝑞
as well as its reverse mapping

29. 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 semiology
o 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 exist
o 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

30. 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

31. 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 signs
o 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

32. 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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