Rafał Maciąg

The subject of this paper is the problem of knowledge revealed by the emergence of advanced natural language processing technology, called large language models (LLMs). It proposes an interpretation of the appearance of this phenomenon as an emergent effect of a complex system, such as LLMs. The meaning of this interpretation is based on the observation of the computational trajectory of computational units (vectors) which, on the other hand, represent discrete semantic units, tokens. To justify the autonomy and relevance of this interpretation of knowledge, the paper invokes the concept of discursive space, which allows, in particular, for the reliance on language as a container of knowledge and for the generalization of the idea of knowledge to other semantic environments. To describe more general units of knowledge, the strong version of the theory proposes the introduction of the institution of gnosemes, of which discourse is a special case. Gnosemes find application in the case of LLMs. Due to the different ontical contexts of the entities described, the paper proposes a transdisciplinary approach, the axis of which is the field of social sciences.

The chapter describes the rapid development of digital technologies and their universality, which makes them a lever for economic development. This is also how digital transformation was interpreted. The chapter contains a detailed analysis of this process, which is a source of economic development and profits. This development has led to the emergence of great economic and social projects. Industry 4.0, Cyber-Physical Systems, 4th Revolution. Each of them concerned a slightly different sphere and was governed by a different logic. The first was the area of economy, the second was the organization of large technological processes, such as energy distribution or transport organization. The third project was the most general attempt to formulate social change, commissioned by the major global political and economic stakeholders. Digital transformation is proving to be a large-scale process, leading to the development of the most advanced artificial intelligence technology. The latter can also be understood as a specific and innovative way of managing knowledge, which complements the epistemic transformations described in the previous chapter. At the same time, its most spectacular development takes place in the area of language manipulation. In this way, the final shape of the so-called digital transformation is revealed: as a process of changing the understanding, describing and organizing the world, in which knowledge becomes the key field, the background and course of which are described in the following chapters.

The chapter contains an extended definition of the concept of transformation, the starting point of which is a description of the meaning of the words that make up this concept: transformation and digitization. This analysis follows two paths. First of all, it shows its unknown and deep mathematical background. The history of the idea of number, beginning around the fourth century BC, leads to an extremely turbulent period in mathematics at the turn of the nineteenth and twentieth centuries, from which the idea of a machine emerged, which was a conceptual model for the computer, i.e. the Turing machine. During this period, very basic questions about number and mathematics were asked, and novel approaches were proposed, like Peano and Hilbert, that liberated mathematics and its sister, geometry, from the obligation to represent reality. They became purely speculative and probably therefore extremely rich fields of thought that led to philosophical questions. Such questions about ontology of mathematical entities like number were asked, for example, by Alain Badiou. This part is complemented and developed by a description of the contemporary digitization process as a key element of digital transformation into social reality. This process concerns both economic phenomena and deeper anthropological processes, described i.a. by Luciano Floridi.

The protagonist of the chapter is Henri Poincaré, an outstanding French mathematician whose contribution to the development of mathematics is extremely rich. For the argument presented in the book, however, his understanding of the idea of space, presented by him at the beginning of the twentieth century, is of the most important significance. The chapter discusses the development of understanding the phenomenon of space that takes place not only within geometry but also in art. The history of geometry is also the story of the development of the idea of space since Euclid. This idea turned out to be necessary for the creation of the image of the world, and this belief appeared about a whole range of philosophers such as Giordano Bruno, Isaac Newton, Gottfried Leibniz, and Immanuel Kant. The breakthrough took place in the nineteenth century, when geometry, and with it space, were completely deprived of the obligation to represent the world and become completely autonomous. The chapter goes on to describe Poincaré’s idea of space as part of his overall approach to geometry. He constructed an image of a completely abstract and speculative space. At the same time, Poincaré introduces the concept of a qualitative approach, i.e. without the need for metric coordinate systems, which inaugurates a new field of geometry: topology. Poincaré also interpreted space as a dynamic structure, which introduced one of the most important constructions of modern physics, also used in other sciences, known by names such as configuration space, state space, phase space or space-time. In this way, a cognitive category was created, which enabled a possibility of the universal and abstract description for a selected phenomenon, in our case, knowledge.

The patron of this chapter is Michel Foucault, an eminent French philosopher, author of one of the most important books of the twentieth century, Les mots et les choses. Une archéologie des sciences humaines (The Order of Things: An Archaeology of the Human Sciences). For Foucault, the two most important axes of thought were knowledge and power, whose dynamics were social, local, and historical, and the medium in which they both express themselves was language. The period of the second half of the twentieth century brought great interest in the phenomenon of language understood in this way. Foucault gave his reasoning, as Deleuze argued, a general dimension, which brought him closer to the construction of manifold. This construction, described at length, is crucial, giving reasoning an overarching and abstract order. Although it was proposed by the mathematician Bernhardt Riemann, it was also understood, for example by Edmund Husserl, as a much more general category. This allows one to understand the proper level of Foucault’s thought as well as the level of his understanding of language. The same level also appeared in Wittgenstein. The chapter goes on to describe the linguistic construction for the retention and articulation of knowledge (and power) proposed by Foucault, which is a discourse. It is the culmination of reasoning, which accepts language as the mediator that binds social structures and, at the same time, stores knowledge. At the same time, discourse is a phenomenon to which Foucault devoted most space, creating it ontological portrait. Discourse retroactively also gives a special role to language, which becomes a source of social reality.

This chapter does not have, like the previous ones, a main character whose work marked the essential milestone for the reasoning being conducted here. Instead, it is the culmination of this process, presenting the final construction, which is the idea of discursive space. The chapter describes and justifies this construction in the following steps. Step one introduces the ontological interpretation of the elements of the world proposed by David Malet Armstrong, inspired by the contributions of Bertrand Russell and Ludwig Wittgenstein, allowing for an appropriate level of unification of concepts needed to understand the level of functioning of discourse as a phenomenon of knowledge. The second step describes the dispersion of knowledge, which results from exogenous factors, e.g. the development of technology and social and endogenous changes related to the processes of knowledge accumulation and storage. The third step recalls the role and way of existence of discourse, which is interpreted as constantly emerging reasoning, leading to knowledge. This step can assume such a role thanks to the reconfiguration of the role of man, on the one hand thrown into the changing world of social determinations and, on the other freed and able to produce arbitrary interpretations of the reality that surrounds him. The knowledge that is the product of this process is dispersed in a completely arbitrary, random way. Its existence is dynamic and multiple. As such, it lends itself to modeling by means of the phase space in which discourses traverse multidimensional spaces, materializing according to the logic of discourse: as utterances. The multiplicity of discourses creates the need for a structure more general than space, that is, a manifold. At the same time, the example of discourse open up the possibility of the existence of the higher order of knowledge, which can also include other, also unknown forms of it, going beyond the language. The units of knowledge moving along trajectories then would have a different character, and a new concept would become necessary to name them. The author proposes the word of gnosem, which allows one to cover every form of knowledge, closing the book’s reasoning with this proposal.

The patron of the chapter is Edmund Gettier, who almost by accident, due to the circumstances of the creation of the groundbreaking article, presents a critique of the definition of knowledge given by Plato and valid until modern times. This attack provokes a discussion that continues, which is understandable because Plato’s definition has shaped the understanding of knowledge for millennia. The chapter contains a description and analysis of the reasoning used by Gettier, and which similar themes also appeared in other philosophers, e.g. Bertrand Russell. The chapter proposes to rely on the concept of Alfred Tarski, which concerns a certain essential property of natural language. Natural language combines levels of utterance without distinguishing direct predication of the world from predication of this predication, which leads to paradoxes. The distinction between these levels allows one to understand the essence of Gettier’s allegations. In the case of the Gettier article, the language is realized as text. The rest of the chapter describes the specificity of the latter phenomenon, based on the concept of Umberto Eco, which emphasizes its contextual, systemic determination of a very complex nature. In this way, the knowledge contained in this text is also determined. This thread was extensively analyzed by Jacques Derrida, who went back to the phenomenon of writing in order to understand the cognitive dynamics and epistemic circumstances of writing, i.e. this mode of existence of language, which is the basis of modern civilization, as well as—let us remind—digital technologies. The chapter provides an extensive description of Derrida’s reasoning, which extends the previously introduced meta descriptive mode of understanding language and its implementation.

The patron of the chapter is Ludwig Wittgenstein, who was one of the first, and certainly the one who proposed the still valid approach, to work on the mutual relations of language and the world, understood as knowledge. His subtle analyses, referring to the classics of philosophy, led to a new understanding of knowledge as an autonomous and spread substance. Wittgenstein deconstructed the image of language as a logically coherent structure, which he initially believed, in favor of free and dynamic play. The world thus viewed revealed itself in a completely new order, which was explained by new structures such as a network, a system, or a general idea of complexity. These ideas resonated with the idea of the dynamics of language, as described by Michel Foucault, as well as John Langshaw Austin and Jacques Derrida. Complexity turned out to be a paradigmatically new way of perceiving and describing the world, liberated from a naive causal order. This way reveals the necessity of reasoning both at the level of direct insight into the world and at the level of the conditions and circumstances of this insight. Such an approach, on the one hand, shows the relativization of knowledge in relation to the research context, i.e., the potential dispersion and differentiation of knowledge, while, on the other hand, it makes knowledge an equal subject of contextual research reflection. At the same time, complex systems exhibit specific emerging effects to understand phenomena such as digital transformation.

The patron of the chapter is Yoneji Masuda, who is also considered the author of the concept of the information society, according to the title of his book, which was published in 1981. However, this concept appeared earlier in Japan, which was racing against the United States in this field. Masuda had no doubt that the axis of transformations concerning social organization, especially in the context of the economy, is the computer and the technology associated with it. These were the times of the formation of a new way of defining society and new definitions of society were emerging, such as post-industrial society. The chapter seeks to organize this issue by describing extensively the ideas of two of its most important legislators: Fritz Machlup and Graham Bell. Machlup’s idea refered to the phenomenon of information as the basis of social processes, which led him to formulate the important role of knowledge. In a comprehensive book, Graham Bell addressed the subject of knowledge, making it the basis of the existence of post-industrial society. The problem of knowledge thus becomes a social and economic problem, without the need to derive its philosophical definition, as well as the direct presence of man as an instance of knowledge. It appeared as an autonomous social phenomenon that also become an important political context because it served the distribution of power. This aspect of knowledge was already described by Plato, followed by Francis Bacon and Thomas Hobbes. The latter formulated a maxim known to this day: scientia potentia est. This means opening the problem of knowledge to a new level: knowledge becomes the basic variable of social structures such as the state. The mutual relationship of knowledge and power would be ordered by Michel Foucault.

The patron of the chapter is Ludwik Fleck, a Polish physician of Jewish origin, who published a book in Basel in 1935, which shocked the certainty of scientific procedures and opened up the problems of the social context of scientific research. Thomas Kuhn, creating his idea of scientific revolutions, and Bruno Latour, discussing the sociology of science, as well as the sociology of knowledge more broadly, were based on Fleck’s observations, widely discussed in the chapter. The chapter contains an introduction to this issue, covering researchers as Max Scheler and Karl Mannheim, whose views become the starting point for the analysis of Fleck’s concepts. The next part of the chapter deals with knowledge as a social entity, referring i.a. to François Lyotard and his book on postmodern condition, and David Bloor, the creator of the so-called strong programme, directly deriving the social basis of knowledge from Plato’s definition. In the following part, there is a description of the understanding of the sociology of knowledge proposed by Bruno Latour, who deals with knowledge in this context in a fundamental way, e.g. formulates a specific ontology explaining the mutual relation of the world of things and the world of their social presence. This ontology, known as ANT—Actor-Network-Theory, goes far beyond linguistic issues, but at the same time reminds us of the basic nature of the relationships studied. Their ancient character is reminded by the distinction: Logos vs. Mythos, described by Władysław Stróżewski.

The patron of the chapter is Jean-François Lyotard, who appears here as the author of another groundbreaking book in the twentieth century: La condition postmoderne. Rapport sur le savoir (The postmodern condition: A report on knowledge) published in 1979. Its title refers directly to the problem of knowledge, which, as is to justify the reasoning contained in the chapter, Lyotard treats as a pragmatic social phenomenon, removed from man. At the same time, Lyotard places his perception of knowledge in the context of digital technologies, which is often forgotten, since the book is mainly considered the inauguration of the concept of postmodernism. For Lyotard, knowledge assumes the role of a social resource that shapes the historical social reality, and then takes on the role of narratives, created, and changed depending on the circumstances. This resource is strictly linguistic and is based on the phenomenon of discourse. In the chapter there is an extensive explanation of the indicated elements of Lyotard’s reasoning, which leads to a strictly pragmatic treatment of knowledge as an autonomous phenomenon, which can also directly assume the roles of a resource or even a product. The final objectification of knowledge appears in the 1990s as knowledge management, i.e. a very practical business strategy, as well as knowledge organization, i.e. reducing knowledge to its documentary form, which involves direct ordering and searching processes. In this way, the vision described by Machlup and Bell is realized, to which Lyotard gave a historiosophical dynamic. He placed the problem of knowledge directly in the context of such issues as the organization of social and political order and power.

The protagonist of the chapter is George Boole, who played a fundamental role in both the development of the idea of discourse, the description of which fills most of the chapter, and the logic underlying the functioning of digital technologies. The chapter justifies, at the beginning, the legitimate reason for their coexistence, which is realized through language. Again, Foucault appears at the beginning of the reasoning, but he uses the notion of discourse introduced by Boole. Language appears as a dialectical connection between the representation of the world and an arbitrary, artificial system, which is done by, among others, Alain Badiou. Boole, who created logical calculus, chose the other side at the same time, preceding a similar breakthrough that appeared in mathematics at the turn of the nineteenth and twentieth centuries. The next part of the chapter presents an analysis of the similarity of natural language and mathematics as parallel symbolic systems. Boole introduces the concept of the universe of discourse, which evokes an artificial reductionist descriptive system, which is an inspiration for the concept of discourse transferred into the area of social and philosophical entities. Zelig Harris sets out these two paths of development of the idea of discourse in the twentieth century. Discourse as a social phenomenon becomes the basis of extensive studies, providing both insight into the nature and dynamics of language and social reality. This chapter describes the development of these studies and their tool, which was discourse. They provide justification for the constructivist role of language, reinforcing its arbitrary and autonomous status. On the other hand, they justify the heteromorphy of language games, using the concept of Lyotard, i.e. the different interpretations of reality, leading to the different instances of knowledge and even different knowledges. This construction simultaneously implements the idea of the universe of Boolean discourse.

This text describes the process that led to knowledge becoming the most important modern good and a complex phenomenon beginning at the end of the 19th century. It was a change in the way of understanding the world proposed by mathematics and geometry. This volume reveals how the paradigm shift, still in progress, is gradually transforming less obvious fields of science, such as the humanities and social sciences while affecting the phenomenon of knowledge. Firstly, meta-analysis gained importance, and secondly, it became natural to perceive knowledge in a social context, showing its diverse and multi-cause dispersion, leading to the phenomenon of knowledge. Due to the interpretation of knowledge as a complex social phenomenon, the author proposes a new model of knowledge description, called the theory of discursive space, making it possible to describe the role and meaning of knowledge as a component of modern civilization that is all-encompassing. This text appeals to students and researchers working in the philosophy of technology.

The article presents and justifies the thesis that the way of understanding knowledge has changed significantly over the last century. This change consists in departing from the classic definition of knowledge formulated by Plato, and in particular in questioning the subjective role of man as the holder of knowledge and abandoning claims to the truthfulness of knowledge. This process was an intensive evolution; its elements are given and justified in the text. Its source was a deep reconstruction of the mode of creating epistemic structures in mathematics and geometry, based on the abandonment of the principle of representation. Knowledge turned out to be determined by the social context, it became dispersed, decentralized, which led to the rejection of the condition of its truthfulness. The last phase of this evolution is knowledge as a phenomenon in the area of digital technologies, in particular artificial intelligence. This evolution has led to the emergence of many variants of knowledge that act as local knowledge, which justifies the use of the plural in this case.

The paper describes the circumstances in which digital technology arises; the change is recognized in the literature as the basis of digital transformation. This transformation is understood as a deterministic economic process. However, the analysis of the deeper circumstances of this process shows that we are dealing with a vast change in the ways of understanding and describing the world, i.e. with an epistemological change. This change concerns, on the one hand, the method of creating general mathematical (including geometric) structures that are the basis of models used to describe the world, and on the other hand—tools for its description, e.g. network theory, systems theory, complexity theory. Such a broadly understood change makes the deterministic description proposed by the digital transformation too simple and shallow. Instead, the concept of predigital transformation is proposed. It includes not only the omitted historical part but also creates better and richer conditions for understanding the digital transformation process, as well as for developing appropriate conceptual tools for its use.

This paper discusses the theory of knowledge based on the idea of dynamical space. The goal of this effort is to comprehend the knowledge that remains beyond the human domain, e.g., of the artificial cognitive systems. This theory occurs in two versions, weak and strong. The weak version is limited to knowledge in which retention and articulation are performed through the discourse. The strong version is general and is not limited in any way. In the weak version, knowledge is represented by the trajectories of discourses in time, in a dynamical space called the discursive space, which has an arbitrary number of dimensions. Given space is used to represent a given part of knowledge. A manifold is introduced to represent knowledge with a wider scope (all knowledge). The strong version is an extrapolation of the weak version to cover all forms of knowledge, not necessarily human or manifesting in language. The use of dynamical space construction allows one to formalize knowledge as such. Such an effort requires us to initially consider knowledge as mainly a social and linguistic phenomenon, which also could be presented as a result of the evolution of the understanding of knowledge that took place in the 20th century.

The article presents and justifies the thesis that the way of understanding knowledge has changed significantly over the last century. This change consists in departing from the classic definition of knowledge formulated by Plato, and in particular in questioning the subjective role of man as the holder of knowledge and abandoning claims to the truthfulness of knowledge. This process was an intensive evolution; its elements are given and justified in the text. Its source was a deep reconstruction of the mode of creating epistemic structures in mathematics and geometry, based on the abandonment of the principle of representation. Knowledge turned out to be determined by the social context, it became dispersed, decentralized, which led to the rejection of the condition of its truthfulness. The last phase of this evolution is knowledge as a phenomenon in the area of digital technologies, in particular artificial intelligence. This evolution has led to the emergence of many variants of knowledge that act as local knowledge, which justifies the use of the plural in this case.

The paper develops the idea of discursive space by describing the manner of existence of this space and the world of facts. The ontology of discursive space is based on the idea of discourse by Foucault. Discourse, being a language phenomenon, is a form of existence of knowledge. The discursive space is a representation of knowledge and can be interpreted as the system of acquiring this knowledge. This space is connected with the world of facts by a relationship of supervenience, which can be interpreted as a flow of knowledge. At the same time, the existence of the world of facts (world of affairs) assumes that it covers all phenomena and processes, and therefore, necessarily, also the discursive space. Hence, this space is not a separate system but a system that emerges from the world in order to allow the gathering of specific knowledge about it. Treating the discursive space as one of the possible cognitive systems, one can imagine other systems of knowledge that emerge from the world (the whole), as parts subordinated to particular goals (the use of knowledge), which can have a multilevel character. The flow of knowledge on the border of such a system and the whole of it can be interpreted as information. This paper tries to justify this possibility, which could lead to a general model of the flow of the knowledge.