Granular semiotics can be obtained from the Saussure one considering both signifier and signified as complementary to each other and each of them equivalent to the sign as a whole as well • The indivisible unity of sign can be interpreted as the indivisible unity ontological quantum being both “word” and “thing” • A model in Hilbert space corresponding to that of quantum mechanics can be assigned to granular semiotics • Granular semiotic outlines much better a series of properties of real language: partial uncertainty, addressing the consensus and communication of people, granularity of meaning, and a series of others

1. Semiotics of ontological
quanta
Highlights

2. Vasil Penchev
• Bulgarian Academy of Sciences: Institute for the Study of Societies and
Knowledge
• vasildinev@gmail.com
13:30-14:00, May 16, 2015
Venues: University Conference Center (Kopcińskiego 16/18) and Faculty of
Philology (Pomorska 171/173)
In: PhiLang 2015 – Fourth International Conference on Philosophy of
Language and Linguistics
University of Łódź, Łódź, 14-16 May 2015

3. Key words:
• Zadeh
• Rieger
• granular semiotics
• ontological quanta
• quantum semiotics

4. Granular semiotics:
• A granular semiotics originating from L. Zadeh and B. Rieger is
interpreted in terms of quantum complementarity:
• “There are three basic concepts that underlie human cognition:
granulation, organization and causation. Informally, granulation
involves decomposition of whole into parts; organization involves
integration of parts into whole; and causation involves association of
causes with effects” (Zadeh 1997)
• “Granulation of an object A leads to a collection of granules of A, with
a granule being a clump of points (objects) drawn together by
indistinguishability, similarity, proximity or functionality” (Zadeh
1997)
• Here is presented an theoretical and abstract approach to be
constructed the granules of meaning as signs in a non-Saussurian
semiotic scheme

5. From the Saussure scheme to inseparable
“granules” of meaning
• It can be also obtained from the classical Saussure scheme if the
signified and the signifier are complementary to each other
• Here is how:
The Saussure scheme supposed that the signified and signifier
correspond to each other, being absolutely independent of each
other, and their unity is just a sign. Thus the sign is their relation and
thus derivative from them
Granular semiotics postulates the sign as primary and furthermore as
an separable unit of meaning
Sign can be thought either as a signifier or as a signified, or even as
some fuzzy unity of both, but never as a certain correspondence
between them

6. The granules as quanta of being
• That granular semiotics allows of an ontological interpretation directly:
• The “twins” of language and reality are merged into a single ontology of
quanta, which can be interpreted complementarily either as “words”
(i.e. units of meanings in the language) or as “things” (i.e. units of
reality)
• This originates inherently from the identification of “sign” and
“meaning”
• One can say further that “sign” and “meaning” constitute the same
kind of inseparable unity of “signifier” and “signified” therefore
implying the unity of “thing” and “word” in any meaning

7. The model of granular semiotics in Hilbert
space
• That granular semiotics can be formalized by the formalism of
quantum information in Hilbert spaces whether non-entangled (and
thus equivalent to a single one) or entangled
• Both granular semiotics and quantum mechanics can be considered
as two interpretations of the one and the same mathematical
formalism: that of Hilbert space
• This allows of a very well developed theoretical language to be
utilized, and the conjugate quantities and their values in turn to be
interpreted as a kind of a numerical and quantitative version of
granular semiotics

8. The language unifying human beings
• One can compare the properties of the Saussure and granular
semiotics to each other
• The language in terms of ontological quanta abandons and darkens all
dividing the human beings unlike the Saussure one. Here is why:
• The latter suggests many languages as different sets of signifiers for
ones and same signified and thus misunderstanding and
disagreements, the tool of which is just language
• Unlike this, the ontological quanta shape the map of reality only by
their use as words: The words are things not less or more than the
things are words

9. The quanta of language invariant to
differences
• Those quanta might be called invariant to the different intellect and
experience of the humans
• Indeed the artificial language for any scientific or theoretical area is
quite complicated, sophisticated, and thus incomprehensible for the
almost all people
• On the contrary, real language has been being created for the
communication of all people and thus does not excludes anybody in
definition
• Its model in terms of ontological quanta is able to recreate that
property for words, which are not used often enough, cannot be
being because language is immediately reality

10. The meaning in terms of quanta
• The linguistic “atoms” are able to concentrate themselves only on a few
unifying features of reality constituting a meaning
• The numerous uses of words in fact create reality. Indeed if a word exists,
this means that many, many people have been used it many, many times
and only thus the word outlines a thing, which is granted as its meaning
• However, the distinction between the word and thing at issue does not
make much sense since the thing is a word used many enough times and
this is nonsense to be divided and even opposed to the word itself as the
Saussure semiotics does interpreting them as a signifier and another
signified
• That artificial opposition is impossible for granular semiotics as it considers
the things and words as a whole speaking of ontology rather than of reality

11. A metaphor for linguistic quanta
• Those linguistic units are “live beings” “fed” by consensus and therefore
created to search for it and find its “deposits”
• Indeed they exist just as the metaphors: only while they are used
• The interpretation of that metaphor of “live beings” can be the following:
• The ontological and linguistic quanta change their meaning, which seems
as a motion on the map of reality, which represents in fact them as a whole
• They move from a deposit of consensus to another just as the live beings
move from a deposit of food to another
• They are fed by the consensus of the people

12. The language as a “map of consensus”
• Consequently the language is a map of “treasures” of consensus
elaborated by living linguistic “cells”
• First of all, this means that reality is a result of the action of
ontological quanta and the agreement between the people
• Reality can be consider as a particular case of ontology: namely that
ontology, which is both old enough and static enough so that it can be
represented as a map with immovable outlines
• Representation is the way for a map including the kind of “map of
reality” to exist
• Being too dynamical in general, ontology sees the representations of
reality rather as movable metaphors

13. The ontological quanta and the map of
consensus
• The ontological quanta are those “living words” “fed” by consensus
and creating the map of reality as the locations of its deposits
• The locations of consensus frame both map of reality and the
understanding of human beings
• The change of language, e.g. in the course of history, results into the
change of reality
• Speaking of “language as ontology”, one is concentrated on its
dynamics, change, variability
• Ontological quanta are a possible theoretical instrument for language
as ontology to be described both in a relevant, even metaphorical
way and by an explicit mathematical model, that of Hilbert space

14. The uncertainty of any meaning
• Any meaning consists in the optimal proportion between its
unclearness and exactness
• The Saussure semantics generates an alleged ideal of absolute
transparency: Language interpreted as a collection of signifiers should
be only an exact image of reality
• However real language is rather opaque: It maintains some fruitful
unclearness
• That uncertainty of language is not at all some deficiency or
disadvantage, which the artificial language of science overcomes
• Its unclearness is very fruitful in searching of consensus: Ontological
quanta help for the constitutive uncertainty of language

15. The principle of granular “picture”
• The existence of ontological quanta forces the picture to be granular
as a principle
• This means, that if one tries to represent the ontology of quanta in
terms or usual metaphors of reality such as “picture” or “image”, they
will seem to be granular, consisting of granules, sells, quanta, ...
• However in terms of ontology, this granular picture, furthermore even
movable, is the reality itself, which cannot be divided from language
• Language is the space and way, by which reality exists
• Ontology in turn can be understood as all realities, which language
can create

16. The indivisibility of ontological quanta
• The indivisibility of the ontological quanta is the condition for them to
behavior as “living” and searching for “deposits” of consensus
• The classical division of sign into two absolutely independent parts of
signifier and signified guarantees for it to be “dead”: immovable
• On the contrary, the words of real language are movable. What
moves them is their use and dependence on the context of use
• The frequency use allows of probabilities to be associated to different
ways for them to be connected to each other in the frame of their
understanding in language
• In turn, this allows of a wave function, i.e. of a vector or a point in
Hilbert space, to be assigned to the meaning and thus to any
ontological quantum

17. Granularity and visibility
• The ontological quanta are bigger, the “picture” is grainier, but the
attraction between the quanta is stronger and the “deposits” of
consensus are more visible
• Thus there is a certain optimal proportion of the degrees of
consensus and exactness of that “picture”: The uses of terms in
science tend to the pole of exactness. On the contrary, those in
everyday language tend to consensus but not to certainty
• The model by wave functions allows of to be quantitatively described
the attraction and mutual restriction in their use, as entanglement
• The bigger granules correspond to higher degree of entanglement

18. The dynamics of language
• The ontological quanta are “living” and “moving” thus re-outlining
new “deposits” of consensus, i.e. new meanings
• The granules are elementary units of meaning by themselves. They
constitute complex meanings as well as complex signs grouping and
organizing themselves
• The constituted complex meaning can be considered in turn as a
whole and thus represented by a single wave function, which refers to
the system consisting of entangled subsystems
• Though the ontological quanta seem to be re-configured and re-
outlined outside they conserve one and the same internal structure
of a single wave function corresponding to a set of entangled wave
function of each separated ontological quanta

19. Conclusions:
• Granular semiotics can be obtained from the Saussure one
considering both signifier and signified as complementary to each
other and each of them equivalent to the sign as a whole as well
• The indivisible unity of sign can be interpreted as the indivisible unity
ontological quantum being both “word” and “thing”
• A model in Hilbert space corresponding to that of quantum
mechanics can be assigned to granular semiotics
• Granular semiotic outlines much better a series of properties of real
language: partial uncertainty, addressing the consensus and
communication of people, granularity of meaning, and a series of
others

20. References:
• Lotfi A. Zadeh, Toward a theory of fuzzy information granulation and
its centrality in human reasoning and fuzzy logic. Fuzzy Sets and
Systems, 90(1997), 111-127.
• Burghard B. Rieger: Computing Fuzzy Semantic Granules from Natural
Language Texts. A computational semiotics approach to
understanding word meanings, in: Hamza, M.H. (ed.): Artificial
Intelligence and Soft Computing, Proceedings of the IASTED
International Conference, Anaheim/ Calgary/ Zürich (IASTED/ Acta
Press) 1999, 475–479.

21. Thank you for your kind
attention looking forward
to your comments or
questions!