Knowledge as a Complex Phenomenon
Rafal Maciag
Institute of Information Studies, Jagiellonian University, Lojasiewicza 4, 30-348 Krakow, Poland
Keywords: Knowledge, Discourse, Dynamical Space, Discursive Space, Complexity.
Abstract: The paper presents the construction of the discursive space, which is a representation of knowledge. It is a
multidimensional dynamic space crossed by discourses running along their specific trajectories. These
discourses remain in the relationship of supervenience with reality, which is interpreted as a world of facts
(state of affairs). Discourses inherit the complexity of the world, and because they are the articulation/retention
of knowledge, this knowledge also inherits this property. Discursive space is, therefore, a model of knowledge
of a complex nature.
This paper addresses the subject of knowledge in the
context of complexity. In particular, it presents a
knowledge representation model based on two main
ideas: discourse and dynamic space. The first idea
comes from the area of social sciences and
philosophy and uses the classical concept of discourse
presented by Michel Foucault (Foucault, 1966, 1969,
1971). The second idea comes from the area of
physics, where it is also a classic tool for representing
and describing various types of phenomena (Nolte,
2010, 2015). Thanks to this combination, it is possible
to find a junction between the existing formal
construction and the phenomenon which is very hard
to formalize, although such solutions have been
Dynamic space is a tool that can be used to
describe complex systems. However, the key place to
justify the use of the concept of complexity in the
proposed knowledge model is the mutual relation of
discourses and the world, which is based on the
relationship of supervenience (Armstrong, 1997),
which exists between discourses and the world
interpreted as a set of facts (world of affairs).
Armstrong, who develops the ideas of Wittgenstein
and Russell, is based on this interpretation (Russell,
1923; Wittgenstein, 1922). In this situation,
discourses must inherit the uncontroversial immanent
property of the world, which is its complexity.
Complexity, therefore, appears not as an assumption
but as a necessarily arising problem to be solved.
The immediate reason for taking up the described
problems is the phenomenon of knowledge and the
state of interpretation of this phenomenon, in
particular in the context of IT development.
Knowledge is treated in the IT field as an autonomous
resource that must be reconstructed in a computable
way. The effort involved has been going on since at
least the 1960s and is mainly associated with the so-
called artificial intelligence.
However, knowledge is a phenomenon whose
perception has undergone a broader, fundamental
revision in the 20th century. The classical definition
of knowledge puts at the center a man who is its only
subject (Pritchard, 2016, p. 3). It was given in Plato's
dialogue Theaetetus and functions as the basis for
understanding knowledge to the present. Its short
definition is Dóksa alethés metá lógu (Appiah, 2003),
in English translation by Waterfield: “true belief
accompanied by a rational account” (Plato, 1987, p.
115), usually shortened to justified true belief (Dancy
et al., 2010). It is a combination of three elements:
belief, true and justification (the so-called tripartite)
which “is a central philosophical claim [of
knowledge] of the Western tradition since Plato”
(Appiah, 2003, p. 43).
The revision was based on the deprivation of
knowledge of its transcendental nature, in particular,
the abandonment of the condition of truth and a
pragmatic approach in its understanding. This kind of
Maciag, R.
Knowledge as a Complex Phenomenon.
DOI: 10.5220/0009513201130119
In Proceedings of the 5th International Conference on Complexity, Future Information Systems and Risk (COMPLEXIS 2020), pages 113-119
ISBN: 978-989-758-427-5
2020 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
change was due to some fundamental changes in the
understanding of physics and mathematics in the
nineteenth century e.g. (Husserl, 2008; Russell,
1923). This leads to a functional and teleological
understanding of knowledge e.g. “as a generalized
capacity to act and as a model for reality” (Adolf &
Stehr, 2014, p. 22) and also to perceive it as the
separate and autonomous issue i.e. human-
independent phenomenon e.g. (Adolf & Stehr, 2014;
Burgin, 2015; Ibekwe-SanJuan & Dousa, 2014;
Pritchard, 2006; Tolksdorf, 2011).
The implementation of this pragmatic approach
had many variants. These include the emergence of a
modern philosophy of science that is based on
reflection as old as philosophy itself (Losee, 2001;
Machamer & Silberstein, 2002). The philosophy of
science in the twentieth century has become,
however, “the distinct yet central part of philosophy”
(Psillos & Curd, 2008, p. xxi) formulating
fundamental questions about the justification of the
scientific reasoning e.g. (Popper, 1935). One of the
branches of this philosophy even led to the
phenomenon of the so-called “historical turn” in the
understanding of science interpreted by researchers
like Kuhn, Lakatos, and Feyerabend as a product of
current historical and social circumstances (Bird,
2008, p. 21).
In the 20th century, this social context becomes
the most important circumstance of knowledge and
shows the way to its interpretation (Bloor, 1976;
Fleck, 1935; Knorr-Cetina, 1981; Latour & Woolgar,
1979; Mannheim, 1929). This interpretation may
have a more philosophical and speculative character,
as exemplified by the reflection of Foucault and
Lyotard (Foucault, 1966, 1969, 1971; Lyotard, 1979)
or based on a social, economic and political approach.
In the latter area, knowledge can be interpreted in at
least three ways: first, as the basis of management, the
main premise of political organization and a direct
resource, e.g. for business (Bell, 1973; Drucker,
1961; Machlup, 1962; Simon, 1971). Secondly, it can
be subject to instrumental economic management
(Nonaka & Takeuchi, 1991; Wiig, 1993) or thirdly, to
function as a resource that is subject to practical
human activities such as searching, acquiring and
organizing (Hjørland, 2016).
However, probably the most important way of
understanding knowledge in a pragmatic way is
associated with its use in the area of IT. Knowledge
perceived from this perspective is computable, i.e. it
is treated either as purposeful, intentional, explicit
knowledge bases or on the contrary as hidden,
spontaneous and random resources. Especially the
latter have gained in importance recently, leading to
generalized ways of interpreting knowledge e.g.
(Burgin, 2015; Moldoveanu & Baum, 2014; Weller,
2010; Zhuge, 2012).
Computing solutions aimed at formalizing
knowledge for broadly understood IT purposes have
their beginnings in the 1960s and 1970s e.g. (Collins
& Quillian, 1969; Minsky, 1974; Schank & Abelson,
1975; Sowa, 2000) and have developed many
practical solutions e.g. (Brachman & Levesque, 2004;
Van Harmelen et al., 2008). Recent rapid progress in
the field of neural networks has raised the importance
of solutions based on the non-symbolic, distributed
way of knowledge understanding e.g. (Bengio et al.,
2003; Goodfellow et al., 2014; LeCun et al., 1990;
Mikolov et al., 2013; Vaswani et al., 2017). Another
rapidly growing area of knowledge acquisition is
massive data repositories created spontaneously,
whose prototype is the WWW, explored through
several techniques known as mining: data mining or
particularly text mining (Bramer, 2016; Jo, 2019;
Kitchin, 2014).
The reasoning presented in this paper has a
conceptual character (Gilson & Goldberg 2015) since
it presents the metalevel type of reflection due to the
general problem of knowledge. Although it refers to
the numerous empirical reflections on particular
issues and solutions. Such reasoning maintains
coherence both on the level of deduction and
coherence of the adopted assumptions, fulfilling, on
the one hand, Popper's postulate (Popper, 1935) and
on the other assumption of the axiomatic approach
(Hilbert, 1899; Peano, 1889).
This paper proposes the discursive space construction
as a model of knowledge. The definition of the
discursive space is as follows: “the discursive space
(DS) […] is the method of the description of the
massive and ubiquitous phenomena like the internet
chosen as an example. This method could be also
treated as the model of knowledge about the chosen
phenomenon. This knowledge is understood from the
point of view brought by sociology and philosophy
which present the so-called constructivist attitude
which means that the knowledge is treated by them as
a social, temporary and spatially local creation. […]
Two essential ingredients appears as the base of DS:
COMPLEXIS 2020 - 5th International Conference on Complexity, Future Information Systems and Risk
complexity as a generic model and discourse as its
direct substance” (Maciag, 2018). The more formal
definition of it is as follows: discursive space is an n-
dimensional dynamical space in which discourses,
which are autonomous instances of knowledge, run in
time trajectories describing the real state of
knowledge in the subject they concern.
Such a definition brings instantly at least the
following two questions: first, about the nature of
discourses, second, about the conditions of the
building of the dynamical space i.e. its dimensions.
For the complexity the first is crucial. To establish
such a space the idea of discourse was based on the
theory by Michel Foucault (Foucault, 1971). Foucault
describes discourse as a retention/articulation of
knowledge, what is classical approach now, widely
presented in the current literature e.g. (Angermüller
et al., 2014, p. 6; Dijk, 2013, p. 592; Hyland &
Paltridge, 2011, p. 39; Jørgensen & Phillips, 2002, p.
Foucault characterizes discourse indirectly, by
formulating the rules of its analysis, which are the
only ways due to its character. This character is
fundamentally linguistic but discourse goes beyond
this level. Foucault proposes four rules that explain
this character. He names the reversal as the first rule
and opts for the rejection of such classical subjects as
the author, the discipline, the will to truth. They are
recognized as “the negative action of a cutting-up and
a rarefaction of discourse” (Foucault, 1981, p. 67).
The second is the discontinuity which qualifies
discourse as “discontinuous practices, which cross
each other” (ibidem). The third rule: specifity, maybe
the most difficult, which underlines the influence of
discourse on things, discourse through the violence
becomes operational. The fourth rule is the
exteriority, which refers to the conditions of the
existence of discourse which are always external.
Discourse presents then the autonomous entity of
the uncertain identity. This uncertainty defines it. The
only way to recognize discourse is to observe its
impact on things what means that this identity is
invisible by itself by the usual modes of cognition.
Foucault calls it “practices” (pratiques) what heading
towards certain human actions and also towards their
dynamic form of existence. The rule of exteriority
excludes the existence of kernel, the overriding
principle of the discourses which “cross each other,
are sometimes juxtaposed with one another, but can
just as well exclude or be unaware of each other”
(Foucault, 1981, p. 67). Such a set of properties lets
understand discourse as potentially complex.
However, the main premise for the claim of the
complex nature of discourse comes from the
assumption about the ontological establishment of the
discourse. This establishment assumes the relation of
supervenience between the space of discourses and
the world. Armstrong defines the supervenience
which is as follows: “We shall say that entity Q
supervenes upon entity P if and only if it is impossible
that P should exist and Q not exist, where P is
possible” (Armstrong, 1997, p. 11). The general
character of this definition neither doesn’t exclude the
particular kinds of relations nor determines the
direction of them what allows the presence of circular
relations instead of the simple casual ones. At the
same time, Armstrong doesn’t exclude the factor of
time which means that supervenience relation can
develop over time i.e. is a dynamic process.
The second side of the relation (besides the
discourses): the reality is interpreted by Armstrong
who names it in terms of a state of affairs. He defines
it as follows: “The general structure of states of affairs
will be argued to be this. A state of affairs exists if
and only if a particular (at a later point to be dubbed
a thin particular) has a property or, instead, a relation
holds between two or more particulars. Each state of
affairs, and each constituent of each state of affairs,
meaning by their constituents the particulars,
properties, relations and, in the case of higher-order
states of affairs, lower-order states of affairs, is a
contingent existent. The properties and the relations
are universals, not particulars. The relations are all
external relations” (Armstrong, 1997, p. 1).
Armstrong relies on the idea proposed earlier by
Wittgenstein and Russell (Russell, 1923;
Wittgenstein, 1922).
Russell describes the idea of the structure of the
world in a text from 1911: „I believe there are simple
beings in the universe, and that these beings have
relations in virtue of which complex beings are
composed.” (Russell, 2003, p. 94). For this text is the
indication of the relational character of the world is
most important. Russell composed his structure of the
world of the two elements representing on one side
the simplest parts of it and the relations between them
on the other (Russell, 2003, p. 95). He calls them “the
stuff” and “the structure” (Russell, 2003, p. 276) and
names them “particulars” and “universals”.
Wittgenstein published Tractatus in 1921, but the
first draft entitled Notes on Logic he presented to
Russell in 1913 whose student he became in 1912.
Wittgenstein created the visionary idea of the world
structure based on the idea of the facts: “1.1 The
world is the totality of facts, not of things. […] 2.
What is the casea factis the existence of states of
affairs. 2.1 A state of affairs (a state of things) is a
combination of objects (things)” (Wittgenstein, 2002,
Knowledge as a Complex Phenomenon
p. 5). Such a world is the base of the language. There
is a clear connection between them that uses well-
defined intermediaries: facts, a logical picture,
thoughts, and propositions. There is no place here to
develop a detailed justification, so let us remain with
the statement that this is the clear manifestation of the
complex nature of the world understood in terms of
the network (Wittgenstein, 2002, p. 59).
The last component of reasoning is the mode of
the representation of the whole concept which is
based on the idea of the dynamical space. Nolte refers
the fundamental nature of this construction as
follows: “A unifying viewpoint of physics has
emerged, over the past century, that studying the
geometric properties of special points and curves
within dynamical spaces makes it possible to gain a
global view of the dynamical behavior, rather than
focusing on individual trajectories. Dynamical spaces
can have many different dimensions and many
different symmetries” (Nolte, 2015, p. 2).
Discursive space is built of the unlimited set of
dimensions which have primordially the qualitative
character. They are the result of the qualitative
(semantical) analysis of the discourses regarding the
issue under consideration. Infinitely many discourses
can run usually trajectories in such a space since there
are many interpretations i.e. the manifestations of
knowledge concerning every subject. Due to the
constructivist nature of such knowledge the category
of truth is irrelevant. In the example of the discursive
space, the subject of the study was the Internet, which
was presented as the value of 19 variables of various
types observed in time (Maciag, 2017, 2018). The
status of these values has been visualized as a chart
on the coordinate system parallel (Inselberg &
Shneiderman, 2009). The idea of space can be
extended by the introduction of the idea of manifold
invented by Riemann, who didn’t understand
manifold as formally as modern topology (Torretti,
1978). Manifold has been understood in a more
general way also by the Husserl (Smith, 2002).
The application of the idea of complexity to the social
and humanistic field which is the case of the idea of
the discursive space is not new. Preiser and Cilliers
writes that attempts to combine social sciences and
humanities with complexity science emerged in the
1990s and point to publications by Byrne and by
Luhman as examples (Preiser & Cilliers, 2010, p. 95).
In 2005, John Urry called the application of this idea
in social research "the complexity turn" and
compared it to other, similar alterations of the
paradigmatic research approaches and mentions
„Marxism in the 1970s, the linguistic turn and
postmodernism in the 1980s, the body, performative
and global culture turns in the 1990s” (Urry, 2005, p.
Castellani and Hafferty very widely justify the
need to apply the idea of complexity in sociology
(Castellani & Hafferty, 2010). Social, humanistic and
philosophical aspects of complexity are also the
subject of numerous literature e.g. (D. Byrne, 1998,
1998; D. S. Byrne & Callaghan, 2014; Cilliers &
Bruce, 1998; Jörg, 2011; Preiser & Cilliers, 2010;
Youngman & Hadzikadic, 2014). Complexity was
also applied extensively in the field of science of
organizations e.g. (Anderson, 1999; Burnes, 2005;
Griffin & Stacey, 2005). Routledge even devoted two
publishing series to this issue: Complexity and
Emergence in Organizations in 2002 and Complexity
as the Experience of Organizing in 2005. There are
also many textbooks introducing the problematics of
the complexity e.g. (Beautement & Broenner, 2011;
Downey, 2012; Holland, 2014; Johnson, 2007;
Mitchell, 2011).
The way in which complexity appears here is the
closest to Byrne and Callaghan's conception (D. S.
Byrne & Callaghan, 2014). They perceive the theory
of complexity as „an ontologically founded
framework of understanding” (D. S. Byrne &
Callaghan, 2014, p. 8). They devote a special analysis
to the phase space and the state space which are the
realizations of the dynamical space construction in
the context of the complex adaptive systems they
choose as a model (D. S. Byrne & Callaghan, 2014,
p. 27). They write that the dimensions of this space
are not necessarily mathematical. In the justification,
they refer to the difference that separates the so-called
metric space and topological space, described by
DeLanda (Delanda, 2002, p. 23). In that way, they
dismiss the methodological problem of research in
social sciences that results from the conflict between
the qualitative and quantitative approaches (D. S.
Byrne & Callaghan, 2014, p. 38).
The idea of the multidimensional space despite its
quantitative nature was also used by Gärdenfors in his
idea of the conceptual spaces (Gärdenfors, 2000,
2004; Zenker & Gärdenfors, 2015). The notion of the
dynamical system has its strict physical interpretation
proposed by Poincaré and developed in a classical
work by Birkhoff, who is considered an inventor of
this notion (Abraham et al., 1980; Birkhoff, 1966
(1927); Nolte, 2015). Nevertheless, a concept of that
system was proposed by Poincaré as a combination of
COMPLEXIS 2020 - 5th International Conference on Complexity, Future Information Systems and Risk
the qualitative and quantitative approaches in a
geometric concept (Abraham et al., 1980, p. xviii).
An approach based on the construction of dynamic
space allows the creation of a knowledge model that
is represented by discourse trajectories. Discourses
are considered articulations/retention of knowledge
as interpreted by Michel Foucault, which is one of the
foundations of reasoning. These discourses remain in
the relationship of supervenience with reality, which
is interpreted as a world of facts (state of affairs). The
key property of such a world is its relational
character, which is an analog of a dynamic network
This structure reflects the complex nature of the
world, which is otherwise its non-controversial
property. This structure plays the role of a conceptual
interpretation of this complexity. Thanks to the
relationship of supervenience, discourses as
articulations/retention of knowledge about this world
inherit its complexity. Dynamic space allows
modeling the state of discourses over time and thus
modeling the dynamic state of knowledge.
Knowledge presented in this way also acquires the
character of a complex phenomenon.
The paper was created as a result of the realization of
the research project financed from the grant number
2018/29/B/HS1/01882 awarded by the National
Science Centre, Poland.
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