A. Newell and H. A. Simon were two of the most influential scientists in the emerging field of artificial intelligence (AI) in the late 1950s through to the early 1990s. This paper reviews their crucial contribution to this field, namely to symbolic AI. This contribution was constituted mostly by their quest for the implementation of general intelligence and (commonsense) knowledge in artificial thinking or reasoning artifacts, a project they shared with many other scientists but that in their case was theoretically (...) based on the idiosyncratic notions of symbol systems and the representational abilities they give rise to, in particular with respect to knowledge. While focusing on the period 1956-1982, this review cites both earlier and later literature and it attempts to make visible their potential relevance to today's greatest unifying AI challenge, to wit, the design of wholly autonomous artificial agents (a.k.a. robots) that are not only rational and ethical, but also self-conscious. (shrink)

In this paper, we recall and study the new type of algebraic structures called Symbolic Plithogenic Algebraic Structures. Their operations are given under the Absorbance Law and the Prevalence Order.

In this paper, we extend the mathematical framework of **non-commutative scalar fields** and numerical techniques discussed previously to build a foundation for **AI-based reasoning systems**. The goal is to enable AI to operate over **symbolic hierarchies, semantic transformations**, and **large-scale infinite or non-commutative domains**. Inspired by quantum tensor field operations, we integrate reasoning over symbolic, numeric, and approximate representations into machine learning pipelines. This work leverages concepts from numerical techniques for non-commutative mixed derivatives, recur- sive tensor calculus, and symbolic transformation (...) logic to build **deep learning architectures** capable of representing and reasoning with structured, hierarchical complexity. (shrink)

A ring is said to be clean if every element of the ring can be written as a sum of an idempotent element and a unit element of the ring and a ring is said to be nil-clean if every element of the ring can be written as a sum of an idempotent element and a nilpotent element of the ring. In this paper, we generalize these arguments to symbolic 2-plithogenic structure. We introduce the structure of clean and nil-clean symbolic (...) 2-plithogenic rings and some of its elementary properties are presented. Also, we have found the equivalence between classical clean(nil-clean) ring R and the corresponding symbolic 2-plithogenic ring 2-SPR. (shrink)

This paper is devoted to Plithogeny, Plithogenic Set, and its extensions. These concepts are branches of uncertainty and indeterminacy instruments of practical and theoretical interest. Starting with some examples, we proceed towards general structures. Then we present definitions and applications of the principal concepts derived from plithogeny, and relate them to complex problems.

Although formal thought disorder (FTD) has been for long a clinical label in the assessment of some psychiatric disorders, in particular of schizophrenia, it remains a source of controversy, mostly because it is hard to say what exactly the “formal” in FTD refers to. We see anomalous processing of terminological knowledge, a core construct of human knowledge in general, behind FTD symptoms and we approach this anomaly from a strictly formal perspective. More specifically, we present here a symbolic computational model (...) of storage in, and activation of, a human semantic network, or semantic memory, whose core element is logical form; this is normalized by description logic (DL), namely by CL, a DL-based language – Conception Language – designed to formalize conceptualization from the viewpoint of individual cognitive agency. In this model, disruptions in the rule-based implementation of the logical form account for the apparently semantic anomalies symptomatic of FTD, which are detected by means of a CL-based algorithmic assessment. (shrink)

This paper attempts to illustrate a process of analysis that will hopefully open a path to more complete and useful definitions of sign and symbol. It applies a form-content analysis to the metaphysical properties of these two concepts. The objective is to locate criteria necessary and sufficient to derive formal definitions for these terms. Wittgenstein’s concept of “forms of representation” is analyzed and applied to the topic. Criteria are outlined that determine the appropriateness of the sign and symbol (...) to be applied as labels. Criteria of definition are then developed using gesture, metaphor, and several other example types to illustrate the use of the criteria in distinguishing between sign and symbol. The structural organization of these two concepts proved to be especially complex and led to what some readers may find somewhat obscure. It is not our intention to be purposefully obscure. (shrink)

The study of culture and cultural selection from a biological perspective has been hampered by the lack of any firm theoretical basis for how the information for cultural traits is stored and transmitted. In addition, the study of any living system with a decentralized or multi-level information structure has been somewhat restricted due to the focus in genetics on the gene and the particular hereditary structure of multicellular organisms. Here a different perspective is used, one which regards living systems as (...) self-constructing energy users that utilize their genome as a library of information, making the genetic system just another component that adds fitness to the overall integrated unit. In this framework, basic fitness is measured as the ability to gather energy for growth and reproduction, and the fitness of the genetic system is broken down into two aspects: first, the effectiveness in searching for new somatic functional information, and second, the effectiveness in searching for better structures to store and process information. With this more generalized perspective, major evolutionary transitions to higher levels of organization become competitions between different information structures; furthermore the functioning and fitness of cultural systems can be more easily described and compared with other modes of information storage within biological systems. Modern technological societies are self-constructing systems that rely on written (symbolic) information storage and very complex algorithms that effectively search for variation with a high probability of successful selection. These systems are currently competing with traditional organic systems, and this competition constitutes the latest major evolutionary transition. Upon comparison of the energy-gathering potential of symbolic-based systems with DNA-based life, it appears that symbolic systems have a tremendous fitness potential and the current shift to a higher level of selection may be as significant and far-reaching as any of the previous major evolutionary transitions. (shrink)

This paper presents an original dialectical logic symbol system designed to transcend the limitations of traditional logical symbols in capturing subjectivity, qualitative aspects, and contradictions inherent in the human mind. By introducing new symbols, such as “ὄ” (being) and “⌀” (nothing), and arranging them based on principles of symmetry, the system’s operations capture complex dialectical relationships essential to both Hegelian philosophy and Buddhist thought. The operations of this system are primarily structured around the categories found in Hegel’s (...) Logic, and it allows users to incorporate their own subjectivity into the logical processes, opening up new possibilities in the philosophy of subjectivity. This symbol system also has the potential to help us explore fundamental questions of language and to precisely describe processes of consciousness transformation through symbols. This form of logic offers a new, irreducible tool for qualitative methods, and it will spark a new philosophical reflection on its relationship with traditional logic and mathematical symbols. (shrink)

Older siblings play a role in their younger siblings’ language socialization by ratifying or rejecting linguistic behavior. In addition, older siblings may engage in a struggle to maintain their dominant position in the family hierarchy. This struggle is seen through the lens of language and political economy as a struggle for symbolic capital. Bilingual adolescent sibling interactions are analyzed as expressions both of identity and of symbolic power. This paper proposes a theory of political micro-economy, by which analysts may trace (...) connections between broad societal structures and structures of face-to-face interaction. (shrink)

In the present book, the starting line is defined by a morphogenetic perspective on human communication and culture. The focus is on visual communication, music, religion (myth), and language, i.e., on the “symbolic forms” at the heart of human cultures (Ernst Cassirer). The term “morphogenesis” has more precisely the meaning given by René Thom (1923-2002) in his book “Morphogenesis and Structural Stability” (1972) and the notions of “self-organization” and cooperation of subsystems in the “Synergetics” of Hermann Haken (1927- ). The (...) naturalization of communication and cultural phenomena is the favored strategy, but the major results of the involved disciplines (art history, music theory, religious science, and linguistics) are respected. Visual art from the Paleolithic to modernity stands for visual communication. The present book focuses on studies of classical painting and sculpture (e.g., Leonardo da Vinci, William Turner, and Henry Moore) and modern art (e.g., Jackson Pollock and Joseph Beuys). Musical morphogenesis embraces classical music (from J. S. Bach to Arnold Schönberg) and political songwriting (Bob Dylan, Leonhard Cohen). The myths of pre-literary societies show the effects of self-organization in the re-assembly (bricolage) of traditions. Classical polytheistic and monotheistic religions demonstrate the unfolding of basic germs (religious attractors) and their reduction in periods of crisis, the self-organization of complex religious networks, and rationalized macro-structures (in theologies). Significant tendencies are analyzed in the case of Buddhism and Christianism. Eventually, a holistic view of symbolic communication and human culture emerges based on state-of-the-art in evolutionary biology, cognitive science, linguistics, and semiotics (philosophy of symbolic forms). (shrink)

The main aim of this article is to present and defend a thesis according to which conceptual representations of some types of mental states are encoded in the same neural structures that underlie the first-personal experience of those states. To support this proposal here, I will put forth a novel account of the cognitive function played by ‘shared representations’ of emotions and bodily sensations, i.e. neural structures that are active when one experiences a mental state of a certain (...) type as well as when one observes someone else experiencing a state of the same type. I will argue that shared representations in fact constitute vehicles of certain mental state concepts (more precisely, concepts of specific types of emotions and somatosensory states). The main line of arguing for this will consist in showing that shared representations exhibit specific, ‘conceptual’ functional properties:(1) causal effect on forming metacognitive judgments, (2) cognitive penetrability, (3) diversity of input types. (shrink)

This essay centers on the notion of the symbolic and its impact as developed by Claude Lévi-Strauss in his Introduction to the Work of Marcel Mauss. I examine Lévi-Strauss’ formulation of the “floating signifier” and its influence in French thought, particularly in the work of Jacques Lacan and Jacques Derrida. In doing so, I argue that Lévi-Strauss’ notion may be a misreading of the structural linguistics of Ferdinand de Saussure that has important implications for contemporary political issues on the left (...) in both theory and practice. (shrink)

Thirty years ago, I elaborated on a position that could be seen as a compromise between an "extreme," symbol-based AI, and a "neurochemical reductionism" in AI. The present article recalls aspects of the espoused framework of schema theory that, it suggested, could provide a better bridge from human psychology to brain theory than that offered by the symbol systems of A. Newell and H. A. Simon.

The purpose of this paper is to understand if and how interactions with Sexual Robots will modify users’ relational abilities in human-human relations. We first underline that, in today’s scholar discussion on the ‘symbolic argument’, there is no theoretical framework explaining the process of symbolic shift between human-robot interactions (HRI) and human-human interactions (HHI). To clarify the symbolic shift mechanism, we propose the concept of objectual mediation. Moreover, under the lens of Winnicott’s object-relation theory, we argue that HRI can structurally (...) modify users relationality, degrading intersubjective abilities: Sexual Robots may blurry the limit between the ‘internal object’ and the external one. We conclude that, under certain conditions, interactions with Sexual Robots may bring the user back to an infantile object-relation setting, worsening the user ability to manage relational frustration. This will negatively impact on human-human interactions and social values in general. -/- . (shrink)

The paper discusses a few tensions “crucifying” the works and even personality of the great Georgian philosopher Merab Mamardashvili: East and West; human being and thought, symbol and consciousness, infinity and finiteness, similarity and differences. The observer can be involved as the correlative counterpart of the totality: An observer opposed to the totality externalizes an internal part outside. Thus the phenomena of an observer and the totality turn out to converge to each other or to be one and the (...) same. In other words, the phenomenon of an observer includes the singularity of the solipsistic Self, which (or “who”) is the same as that of the totality. Furthermore, observation can be thought as that primary and initial action underlain by the phenomenon of an observer. That action of observation consists in the externalization of the solipsistic Self outside as some external reality. It is both a zero action and the singularity of the phenomenon of action. The main conclusions are: Mamardashvili’s philosophy can be thought both as the suffering effort to be a human being again and again as well as the philosophical reflection on the genesis of thought from itself by the same effort. Thus it can be recognized as a powerful tension between signs and symbol, between conscious structures and consciousness, between the syncretism of the East and the discursiveness of the West crucifying spiritually Georgia. (shrink)

On the example of the analysis of the content of films-leaders of the box office box office, the value dynamics of the symbols of success is revealed as an objectively occurring sociocultural process in film communication. Cultural production and consumption are being rethought as the self-communication of society, which has sustainable trends. The connections of the sociocultural process of symbolizing success with communicative, semantic and semiotic processes have been studied. The specificity of the dialectical contradiction between sociocentric and personocentric (...) symbols of success is described. The theoretical provisions that reveal the structural and functional side of the socio-cultural process of symbolizing success are presented, its objectivity is proved on the example of the analysis of an array of films, the dominant tendencies in the halo of the cultural space of the general film market are determined. The book is addressed to scientists, students and teachers interested in cultural dynamics, social communication, the role of cinema in modern society. (shrink)

The objective of this paper is to introduce, into the English scientific-philosophical literature of Genetic Epistemology, a model called the Model of the System of Schemes of Actions and Operations on Symbols and Signs (MoSSAOSS), and summarize its results, so far. MoSSAOSS articulates some of the principal theoretical and experimental results obtained by Piaget and his coworkers, in a systemic, systematic and synthetic view. Here, the term model means a schematic representation of experience, in which the relation of elements (...) can be explored by means of logic and mathematics in order to deduce properties that correspond to direct observable empirical properties, in a sufficiently accurate form. Through explicit definitions and hypotheses, MoSSAOSS intends to reveal, in an abstract and simplified form, the general structure and functioning of the System of Schemes of Actions and Operations on Symbols and Signs. This system makes explicit the necessary elements for the acquisition of knowledge by the epistemic subject (the knower subject), allowing for the explanation of its developmental stages, as well as the attribution of meaning to objects and situations, and to the subject’s actions and operations. Conceived in 1992 and introduced in Portuguese scientific-philosophical literature in 2014, MoSSAOSS has been used in a research program to study the necessary structures for knowledge acquisition, particularly scientific-philosophical knowledge. Its main results are summarized here. (shrink)

This paper discusses similarities of both form and meaning between two symbolic structures: the Diagram of the Supreme Pole of Song Neo-Confucianism and the Kabbalistic Tree of medieval Jewish mysticism. These similarities are remarkable in the light of the many differences that exist between Chinese and Judaic thought, which also manifest in the two symbols. Intercultural influence might account for the similarities, but there is no historical evidence for such influence. An alternative explanation would attribute the similarities to (...) the ubiquity of religious-philosophical ideas about hierarchy, polarity, and macrocosm-microcosm parallelism, but this does not adequately account for the similar overall structure of the symbols. The question of how to understand these similarities remains open. (shrink)

My paper was commissioned by Journal of Philosophy to provide a piece adequately explaining the significance of the Lacanian Mirror stage within Lacan's larger work. -/- I focus on the transition from the mirror stage to the incorporation of the subject into the symbolic order. I argue that the mirror stage is transitional and that its significance lies in what of it is incorporated into and transformed within the more complex structures of the subject and the unconscious. -/- Implicit (...) in my claim is that "lacanian" theories which hypostatize the mirror stage into a determinate structure of adult consciousness are misinterpreting Lacan. I use Seminars 1 and 2 to make fuller sense the mirror stage as presented in his Ecrits. (shrink)

This paper develops a theory of analog representation. We first argue that the mark of the analog is to be found in the nature of a representational system’s interpretation function, rather than in its vehicles or contents alone. We then develop the rulebound structure theory of analog representation, according to which analog systems are those that use interpretive rules to map syntactic structural features onto semantic structural features. The theory involves three degree-theoretic measures that capture three independent ways in which (...) a system can be more or less analog. We explain how our theory improves upon prior accounts of analog representation, provides plausible diagnoses for novel challenge cases, extends to hybrid systems that are partially analog and partially symbolic, and accounts for some of the advantages and disadvantages of representing analogically versus symbolically. (shrink)

By comparing some founding concepts underlying developing interest in the role of signs and symbols in social life, such as the nature of the sign in Charles Peirce and Ferdinand de Saussure and in Emile Durkheim and George Herbert Mead, and then exploring recent developments in structuralism and symbolic interactionism, a critical appraisal of their theories of meaning is made in the context of an emerging semiotic sociology.

In this paper I aim to show that the philosophy of Mihai Şora can both be seen as a phenomenological treatment of being and as a general theory of being in its most rigorous sense. At least, this philosophy could be designated as a phenomenological ontology which opens up itself towards an originally metaphysical perspective based on a specific type of knowledge of the sort of “global disclosure”. I will argue too that within Şora's philosophy one can have a twofold (...) approach: one starts from what we could call the phenomenology of the “common givenness” (“ordinary/ quotidian givenness”) and then proceeds (in a phenomenological manner) to a general theory of being, which is represented in Şora's philosophy by the constitution of the model of the “sphere with the null ray”; the second commences with the treatment of the ontological model as such (the model, which is already formed, represents in the end the symbolic structure of reality), that is, from this “general theory of being” (or of the constitution of being) and then advances step by step towards various (phenomenological) applications of this ontological model to the multifaceted spheres of the domain of being (the sphere of language, of temporality, of ethics, of the social, of politics, etc.). (shrink)

This paper takes up the challenge which Carnap poses in his Aufbau: to make of it a basis for continued epistemological research. I try to close some gaps in Carnap’s original presentation and to make at least the first few steps of his constructional outline more accessible to the modern reader. Particularly emphasized is Carnap’s implicit recognition that, to be effective, “structural” models of epistemology (using logical symbols) must be complemented with “procedural” models (his “fictitious operations”). The paper shows (...) how a procedural model, a computer program,can “bypass” Nelson Goodman’s counter example to Carnap’s logical construction of “similarity circles”. (shrink)

Recent accounts of actual causation are stated in terms of extended causal models. These extended causal models contain two elements representing two seemingly distinct modalities. The first element are structural equations which represent the or mechanisms of the model, just as ordinary causal models do. The second element are ranking functions which represent normality or typicality. The aim of this paper is to show that these two modalities can be unified. I do so by formulating two constraints under which extended (...) causal models with their two modalities can be subsumed under so called which contain just one modality. These two constraints will be formally precise versions of Lewissystem of weights or priorities” governing overall similarity between possible worlds. (shrink)

In this paper the class of Fidel-structures for the paraconsistent logic mbC is studied from the point of view of Model Theory and Category Theory. The basic point is that Fidel-structures for mbC (or mbC-structures) can be seen as first-order structures over the signature of Boolean algebras expanded by two binary predicate symbols N (for negation) and O (for the consistency connective) satisfying certain Horn sentences. This perspective allows us to consider notions and results from (...) Model Theory in order to analyze the class of mbC-structures. Thus, substructures, union of chains, direct products, direct limits, congruences and quotient structures can be analyzed under this perspective. In particular, a Birkhoff-like representation theorem for mbC-structures as subdirect poducts in terms of subdirectly irreducible mbC-structures is obtained by adapting a general result for first-order structures due to Caicedo. Moreover, a characterization of all the subdirectly irreducible mbC-structures is also given. An alternative decomposition theorem is obtained by using the notions of weak substructure and weak isomorphism considered by Fidel for Cn-structures. (shrink)

The paper aims to show that by abstracting from a specific mythical historical- stylistic context and “ideation” of the notion of the Proto-Slavic deities Perun and Veles, especially in Croatian tradition, symbolic archetypes and abstract notions of form and primordial matter (materia prima) can be extracted from mythical content. We refer to mythical texts and contents according to the reconstructions and materials brought by Radoslav Katičić, and comparative analysis by Mislav Ježić. We distinguish form (1) as that in which identity (...) and possibility of a thing consists, (2) as the reasonableness of judgment and the form of existence, and (3) as the specific structure of a thing, which unites its parts and aspects as a whole and constitutes its internal necessity. These formative notions are relativized and nullified in Veles’ appearances, in which the archetypal notion of primordial matter is encoded. Examples of Platō’s dialogues historically confirm certain aspects of decoding myth as constitutive of philosophy. The above approach also opens a view of the roots of Croatian philosophical thought, which in its genesis can be traced back to Proto-Slavic mythical archetypes. With the implementation of Christianity, the questions of identity, reason and the structure of the whole are raised radically and sharply, as shown by the text of Trpimir’s grant (852). (shrink)

Wolfgang Pauli was influenced by Carl Jung and the Platonism of Arnold Sommerfeld, who introduced the fine-structure constant. Pauli’s vision of a World Clock is related to the symbolic form of the Emerald Tablet of Hermes and Plato’s geometric allegory otherwise known as the Cosmological Circle attributed to ancient tradition. With this vision Pauli revealed geometric clues to the mystery of the fine-structure constant that determines the strength of the electromagnetic interaction. A Platonic interpretation of the World Clock and the (...) Cosmological Circle provides an explanation that includes the geometric structure of the pineal gland described by the golden ratio. In his experience of archetypal images Pauli encounters the synchronicity of events that contribute to his quest for physical symmetry relevant to the development of quantum electrodynamics. (shrink)

The discrete–structural structure of the world is described. In comparison with the idea of Heraclitus about an indissoluble world, preference is given to the discrete world of Democritus. It is noted that if the discrete atoms of Democritus were simple and indivisible, the atoms of the modern world indicated in the article would possess, rather, a structural structure. The article proves the problem of how the mutual connection of mathematics and philosophy influences cognition, which creates a discrete–structural worldview. The author (...) notes that the appearance of writing, symbolic language and the depiction of the picture of the world through mathematics, led us into the sphere of discrete mathematical mathematics. (shrink)

The aim of this study is to stylistically analyze the common symbols in Charles Dickens’s Christmas Books, which revived the Christmas spirit in the dark Victorian era. Experiencing the vast impacts of Industrial Revolution, people in Dickens’s time were suffering from the consequences of industrialism, poverty, class distinctions and shifting values within a dark world. Upon combining sentimentality towards human nature, Dickens, in his Christmas stories, revived a festival which faded away from English life during the 19th c. Through (...) this blending of a Christmas spirit in the dark Victorian era, Dickens drew the desired picture of a better future for his readers. His ‘Dickensian’ style enables questioning and judging the discrepancies in the society and the defects of humanity while entertaining the reader with the concerns of family harmony, forgiveness, charity, happiness, compassion and Christmas joy. Yet instead of presenting his messages explicitly, in the deeper structure, Charles Dickens directs his readers through the messages with the use of symbols in his five Christmas stories. To this end, this study aims at clarifying the common symbols in the stories of Christmas Books to suggest that Dickens lights a candle via his stories for his readers who were imprisoned in the dark Victorian age. (shrink)

The aim of this work is to develop a comparative analysis of the discursive structures that underlie the socialized formation of the interpretative paradigms of reality. We analyse how both political ideologies and the so-called “conspiracy theories” can be understood starting from the structure and functioning of Marc Augè's ideo-logic, namely the systemic-discursive device that defines the field of all possible sentences defining the real. -/- .

After a brief review of the golden ratio in history and our previous exposition of the fine-structure constant and equations with the exponential function, the fine-structure constant is studied in the context of other research calculating the fine-structure constant from the golden ratio geometry of the hydrogen atom. This research is extended and the fine-structure constant is then calculated in powers of the golden ratio to an accuracy consistent with the most recent publications. The mathematical constants associated with the golden (...) ratio are also involved in both the calculation of the fine-structure constant and the proton-electron mass ratio. These constants are included in symbolic geometry of historical relevance in the science of the ancients. (shrink)

Despite some notable similarities between the scientific realisms of Sellars and Peirce (such as both being anti-representationalist, and future-directed), in his mature work Science and Metaphysics Sellars explicitly critiqued Peirce’s account of truth, as lacking “an intelligible foundation” (Sellars 1968: vii). In this paper, I explore Sellars’ proposed remedy to Peirce’s purported lack, in his complex and enigmatic account of picturing – a non-discursive ‘mapping’ of the world. I argue that although Sellars’ development of this idea is largely sound, much (...) of what he charges Peirce’s philosophy with missing is actually present there. By means of his semiotic icon / index / symbol distinction, Peirce manages to develop a philosophy of language which effectively coordinates the real order and the order of signification within the very structure of the proposition as he understands it, by contrast to Sellars’ claim that the two orders are merely connected by ‘analogy’. I also argue that in between Sellars’ ambitious account of veridicality, which appears to anticipate a form of scientific self-mensuration, and the dismissive ‘anti-truth’ quietism of neopragmatists such as Rorty, Peirce’s “contrite fallibilism” (Peirce CP 1.14) charts a wise middle path. (shrink)

This article is a commentary on Machery (2009) Doing without Concepts. Concepts are mental symbols that have semantic structure and processing structure. This approach (1) allows for different disciplines to converge on a common subject matter; (2) it promotes theoretical unification; and (3) it accommodates the varied processes that preoccupy Machery. It also avoids problems that go with his eliminativism, including the explanation of how fundamentally different types of concepts can be co-referential.

This article makes the case for the necessity of a multi-focal conception of violence in religion and peacebuilding. I first trace the emergence and development of the analytical concepts of structural and cultural violence in peace studies, demonstrating how these lenses both draw central insights from, but also differ from and improve upon, critical theory and reflexive sociology. I argue that addressing structural and cultural forms of violence are concerns as central as addressing direct (explicit, personal) forms of violence for (...) purposes of building just and sustainable peace. Moreover, religiously informed and/or motivated peacebuilders are especially well-appointed and equipped to identify and address violence in its structural and cultural manifestations. I the examine how concepts of structural and cultural violence, in effect, centrally inform the efforts of Martin Luther King and Cornel West to cultivate just and sustainable peace in a context as putatively peaceful and prosperous as the United States. (shrink)

What does it look like when a group of scientists set out to re-envision an entire field of biology in symbolic and formal terms? I analyze the founding and articulation of Numerical Taxonomy between 1950 and 1970, the period when it set out a radical new approach to classification and founded a tradition of mathematics in systematic biology. I argue that introducing mathematics in a comprehensive way also requires re-organizing the daily work of scientists in the field. Numerical taxonomists sought (...) to establish a mathematical method for classification that was universal to every type of organism, and I argue this intrinsically implicated them in a qualitative re-organization of the work of all systematists. I also discuss how Numerical Taxonomy’s re-organization of practice became entrenched across systematic biology even as opposing schools produced their own competing mathematical methods. In this way, the structure of the work process became more fundamental than the methodological theories that motivated it. (shrink)

This paper presents a critical analysis of dual-class share structures (DCSS) within an ethical and logical framework for ownership and control. Moreover, it contends that the existence of DCSS constitutes a de facto infringement on the ownership rights of shareholders. By adopting a conceptual approach rooted in symbolic logic, the paper demonstrates that DCSS falls short of the ethical precept of “one share, one vote” and is therefore an unjust and inefficient equity arrangement. The paper contributes to the existing (...) literature on DCSS by focusing on the ethical and logical basis of such share structures. (shrink)

The perceptual symbol system view assumes that perceptual representations have a role-argument structure. A role-argument structure is often incorporated into amodal symbol systems in order to explain conceptual functions like abstraction and rule use. The power of perceptual symbol systems to support conceptual functions is likewise rooted in its use of structure. On Barsalou's account, this capacity to use structure (in the form of frames) must be innate.

This paper offers both a theoretical and an experimental perspective on the relationship between connectionist and Classical (symbol-processing) models. Firstly, a serious flaw in Fodor and Pylyshyn’s argument against connectionism is pointed out: if, in fact, a part of their argument is valid, then it establishes a conclusion quite different from that which they intend, a conclusion which is demonstrably false. The source of this flaw is traced to an underestimation of the differences between localist and distributed representation. It (...) has been claimed that distributed representations cannot support systematic operations, or that if they can, then they will be mere implementations of traditional ideas. This paper presents experimental evidence against this conclusion: distributed representations can be used to support direct structure-sensitive operations, in a man- ner quite unlike the Classical approach. Finally, it is argued that even if Fodor and Pylyshyn’s argument that connectionist models of compositionality must be mere implementations were correct, then this would still not be a serious argument against connectionism as a theory of mind. (shrink)

Husserl's Phenomenology: A Lacanian and Feminist Reappraisal -/- This study undertakes a comprehensive critique of Edmund Husserl's phenomenology, highlighting its limitations and omissions. Through Lacanian psychoanalysis, feminist perspectives, and intersubjective theories, this analysis challenges Husserl's notions of bracketing, reduction, and absolute givenness. Key concerns include the neglect of unconscious dynamics, symbolic structures, embodied experience, and cultural contexts. Critics such as Zizek, Sartre, Quine, and Rorty are engaged in addressing issues of solipsism, truth, and ideology. This evaluation underscores the need (...) for phenomenology to integrate diverse perspectives, ensuring a more inclusive and nuanced understanding of human experience. -/- Keywords: Husserl, Phenomenology, Lacanian Psychoanalysis, Feminist Theory, Intersubjectivity, Critical Evaluation. (shrink)

Metaphors allow us to come to terms with abstract and complex information, by comparing it to something which is structured, familiar and concrete. Although modern science is “iconoclastic”, as Gaston Bachelard phrases it, scientists are at the same time prolific producers of metaphoric images themselves. Synthetic biology is an outstanding example of a technoscientific discourse replete with metaphors, including textual metaphors such as the “Morse code” of life, the “barcode” of life and the “book” of life. This paper focuses on (...) a different type of metaphor, however, namely on the archetypal metaphor of the mandala as a symbol of restored unity and wholeness. Notably, mandala images emerge in textual materials related to one of the new “frontiers” of contemporary technoscience, namely the building of a synthetic cell: a laboratory artefact that functions like a cell and is even able to replicate itself. The mandala symbol suggests that, after living systems have been successfully reduced to the elementary building blocks and barcodes of life, the time has now come to put these fragments together again. We can only claim to understand life, synthetic cell experts argue, if we are able to technically reproduce a fully functioning cell. This holistic turn towards the cell as a meaningful whole also requires convergence at the “subject pole”: the building of a synthetic cell as a practice of the self, representing a turn towards integration, of multiple perspectives and various forms of expertise. (shrink)

Abstract The Greek composer and architect Iannis Xenakis has shown in Formalized Music (1963) how it is possible to compose or describe music and sound by means of probabilistic laws from mathematics, information theory and statistical mechanics. In his theory, scientific concepts and properties such as entropy take on a musical meaning in that they become also properties structurally instantiable by music. Philosophically speaking, this raises many important questions about the relation between science and the arts. One of these questions (...) concerns in particular the possibility for aesthetic symbols (like musical compositions) to convey scientific understanding, and understanding in general. In the present work, I claim that this question can be answered positively. In general, understanding does not necessarily depend on truth, explanation and propositionality (non-factualism, non-reductivism). Understanding can be conveyed also in non-propositional domains, in particular by means of exemplification. Since aesthetic and musical symbols are non-propositional, they can advance understanding possibly by exemplification, and in particular scientific understanding as long as they exemplify scientific concepts and properties. I moreover substantiate my claim by taking a case study: the concept of entropy in music. On the basis of Xenakis’ stochastic theory of music, I show how by exemplifying this concept, music can advance understanding of it. (shrink)

Conscious states—state that there is something it is like to be in—seem both rich or full of detail and ineffable or hard to fully describe or recall. The problem of ineffability, in particular, is a longstanding issue in philosophy that partly motivates the explanatory gap: the belief that consciousness cannot be reduced to underlying physical processes. Here, we provide an information theoretic dynamical systems perspective on the richness and ineffability of consciousness. In our framework, the richness of conscious experience corresponds (...) to the amount of information in a conscious state and ineffability corresponds to the amount of information lost at different stages of processing. We describe how attractor dynamics in working memory would induce impoverished recollections of our original experiences, how the discrete symbolic nature of language is insufficient for describing the rich and high-dimensional structure of experiences, and how similarity in the cognitive function of two individuals relates to improved communicability of their experiences to each other. While our model may not settle all questions relating to the explanatory gap, it makes progress toward a fully physicalist explanation of the richness and ineffability of conscious experience—two important aspects that seem to be part of what makes qualitative character so puzzling. (shrink)

This paper argues against definitions of depiction in terms of the syntactic and semantic properties of symbol systems. In particular, it is argued that John Kulvicki's definition of depictive symbol systems in terms of relative repleteness, semantic richness, syntactic sensitivity and transparency is susceptible to similar counterexamples as Nelson Goodman's in terms of syntactic density, semantic density and relative repleteness. The general moral drawn is that defining depiction requires attention not merely to descriptive questions about syntax and semantics, (...) but also to foundational questions about what makes it the case that depictions have the syntactic and semantic properties they do. (shrink)

We introduce two notions–the shadows and the shallows of explanation–in opening up explanation to broader, interdisciplinary investigation. The shadows of explanation refer to past philosophical efforts to provide either a conceptual analysis of explanation or in some other way to pinpoint the essence of explanation. The shallows of explanation refer to the phenomenon of having surprisingly limited everyday, individual cognitive abilities when it comes to explanation. Explanations are ubiquitous, but they typically are not accompanied by the depth that we might, (...) prima facie, expect. We explain the existence of the shadows and shallows of explanation in terms of there being a theoretical abyss between explanation and richer, theoretical structures that are often attributed to people. We offer an account of the shallows, in particular, both in terms of shorn-down, internal, mental machinery, and in terms of an enriched, public symbolic environment, relative to the currently dominant ways of thinking about cognition and the world. (shrink)

The relationship between the One and the Multiple in mystic philosophy is a profound and central theme that explores the nature of existence, the cosmos, and the divine. This theme is present in various mystical traditions, including those of the East and West, and it addresses the paradoxical coexistence of the unity and multiplicity of all things. -/- In mystic philosophy, the **One** often represents the ultimate reality, the source from which all things emanate and to which all things return. (...) It is the absolute, the infinite, and the unchanging. The One is beyond all attributes and is often associated with the divine or the absolute truth. -/- The **Multiple**, on the other hand, represents the manifest world, the diversity of forms, and the realm of change and plurality. It is the world we experience through our senses, the domain of time and space, where differentiation and individuality are apparent. -/- The relationship between the One and the Multiple is not one of opposition but of emanation and unity. The Multiple is seen as a reflection, expression, or manifestation of the One. In this sense, the diversity of the world doesn’t contradict the unity of the One but rather demonstrates it in a myriad of forms. -/- Mystics seek to understand and experience this relationship through various practices and insights. They aim to transcend the illusion of separation and duality to experience the non-dual reality where the One and the Multiple are recognized as inseparable. -/- This concept can be illustrated by the metaphor of the ocean and its waves. The ocean represents the One—vast, deep, and all-encompassing—while the waves represent the Multiple—distinct, diverse, and ever-changing. Each wave is unique, yet it is not separate from the ocean. The wave’s existence is dependent on and made of the same substance as the ocean. In the same way, each individual entity in the Multiple is an expression of the One. -/- In summary, the relationship between the One and the Multiple in mystic philosophy is a dynamic interplay that challenges the conventional understanding of separation. It invites a deeper exploration of reality, where the apparent multiplicity of the world is a direct expression of the singular, underlying essence of all that is. -/- The relationship between the One and the Multiple in the context of mathematical philosophy is a profound topic that touches upon the very foundations of existence and knowledge. It’s a theme that has been explored by philosophers and mathematicians alike, often leading to the contemplation of unity and diversity within the structures of reality. -/- In mathematics, the concept of the One can be seen as the basis of unity from which all numbers derive. It’s the identity element in multiplication, the starting point in counting, and the foundation of dimension in geometry. The One is often associated with the concept of monism in philosophy, which posits that there is a single, underlying substance or principle that constitutes reality. -/- On the other hand, the Multiple represents the infinite variety and diversity of forms and numbers that arise from the One. It’s the embodiment of plurality and the complex interplay of different entities that mathematics seeks to understand and describe. This reflects the philosophical stance of pluralism, which acknowledges the existence of multiple realities or truths. -/- The interplay between the One and the Multiple can be seen in the mathematical concept of sets. A set can be thought of as a unity, a whole composed of distinct elements. Yet, each element within the set also retains its individuality, contributing to the diversity of the set’s composition. This duality is mirrored in the philosophical exploration of the universal and the particular, where the universal represents the One, and the particulars represent the Multiple. -/- In the realm of mathematical philosophy, this relationship often leads to questions about the nature of mathematical objects: Are they discovered as part of an objective reality (the One), or are they constructed by the human mind from a multitude of experiences (the Multiple)? This debate resonates with the philosophical inquiry into the nature of truth and reality. -/- Reflecting on the One and the Multiple can also lead to a deeper understanding of the self and the cosmos. Just as the number one is integral to the existence of all other numbers, the individual self can be seen as a unique expression of the universal whole. Similarly, the cosmos can be viewed as a grand unity composed of a multiplicity of forms and phenomena. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers⁴. -/- The **first incompleteness theorem** reveals that within any such consistent system, there are propositions that are true but cannot be proven within the system itself. This reflects the idea of the Multiple in that there is an abundance of mathematical truths, a multiplicity that exceeds the unifying framework of any one system. It suggests that the realm of mathematical truth is more extensive than any single formal system can fully capture. -/- The **second incompleteness theorem** extends this by showing that a system cannot prove its own consistency. This relates to the concept of the One, as it implies that a system’s complete self-understanding, its unity and coherence, is unattainable from within. It must look beyond itself, to an external vantage point, to ascertain its consistency. -/- In the context of the One and the Multiple, Gödel’s theorems imply that the One (a consistent formal system) is inherently incomplete and cannot encompass the Multiple (the totality of mathematical truths). This resonates with philosophical discussions about the relationship between unity and plurality. Just as a single philosophical system cannot capture the entirety of truth, a single formal mathematical system cannot encapsulate all mathematical truths. -/- Moreover, Gödel’s work suggests that the pursuit of a single, unified theory of everything in mathematics—a One that encompasses all Multiples—is an inherently Sisyphean task. There will always be more truths (Multiples) than can be derived from any given set of axioms (the One). -/- In essence, Gödel’s incompleteness theorems provide a formal underpinning to the philosophical notion that the One cannot exist without the Multiple, and vice versa. They are interdependent, with the One giving rise to the Multiple, and the Multiple necessitating the One for its expression and comprehension. This interplay is a dance of limitations and possibilities, where the boundaries of logic, mathematics, and philosophy blur into one another. -/- The relationship between the One and the Multiple in the context of the mathematics of zero is a deeply philosophical inquiry that bridges the abstract world of numbers with the existential questions of being and non-being. -/- Zero, in mathematics, is a symbol of absence, a representation of nothingness, yet it holds a pivotal position as a number. It is the void from which all things emerge and to which they return. In the philosophy of mathematics, zero is the paradoxical junction where the One and the Multiple converge and diverge. -/- From the perspective of the One, zero can be seen as the origin—the singular point that precedes the existence of numbers. It is the empty set, the foundation upon which the edifice of mathematics is constructed. As the identity element in addition, zero maintains the integrity of numbers, for adding zero to any number leaves it unchanged, reflecting the immutable nature of the One. -/- Conversely, when we consider the Multiple, zero represents the infinite potentiality of creation. It is the canvas upon which the integers, both positive and negative, express their multitude. Zero is the balance point, the fulcrum around which the symphony of numbers dances. It embodies the plurality of possibilities, the beginning of the number line that stretches infinitely in both directions. -/- Philosophically, zero challenges our understanding of existence. It is both something and nothing—a number that quantifies the absence of quantity. This duality echoes the philosophical struggle to comprehend how the One gives rise to the Multiple. How does the unity of being manifest the diversity of the cosmos? Zero offers a mathematical metaphor for this mystery, as it encapsulates the transition from non-existence to existence, from the undifferentiated One to the differentiated Multiple. -/- In the realm of set theory, zero corresponds to the empty set—a set with no elements. This set is unique in that it is the only set that contains nothing, yet it is the foundation upon which all other sets are built. The empty set is the mathematical embodiment of the One, and all other sets, containing multiple elements, arise from it. -/- Reflecting on zero in the context of Gödel’s incompleteness theorems, we find a resonance with the idea that the One (a consistent formal system) cannot capture the entirety of the Multiple (the totality of mathematical truths). Zero, as the foundation of numbers, similarly suggests that from the nothingness of the One, the infinite complexity of the Multiple emerges—yet it can never be fully encompassed or expressed by any single system. -/- In conclusion, the mathematics of zero offers a profound reflection on the relationship between the One and the Multiple. It serves as a bridge between the abstract and the concrete, the known and the unknowable, challenging us to ponder the origins of existence and the nature of reality itself. -/- . (shrink)

Apparency and actuality are discussed with respect to science, genetics, evolution, cognition and perception. Rules for a (sub)set of actual/allowable sets of entities and objects from a total set that is based on differences and contrasts extracted from perceptual experience of the world elucidate tenable combinations/recombinations from a total of the transparent(history/past dependant) and the apparent as they can be construed to comprise the actual/real faces of perception. The elements of dreams, language, symbolisms, abstractions are proposed to encompass to encompass (...) a total set of plausible apparencies. Nature from which both internal and external life is mirrored at the simplest structural level is propose to be constructed similarly-to physically possess also concepts and abstractions as states that reflect differences/combinations/recombinations parametrically that are emerged from the parameters associated with particular circumstances. This view is dependant upon, for its' conceptual soundness, a total construction of the world that descends, rather than ascends, in structural complexity and diversity and which is innately divided and compartmentalized in sequence from a more complex uniquely existing state describable singularly as a place of force and proximities form which all processes ensue. Integration of sound, light, into sensory experience and language is proposed to be a natural process of the accomplishment of new proximities/states from total apparent plausibility’s (past and actual combined) verses the actually(past and present) existing. Two potential important aspects of this scheme exist with regards to evolution theory: 1) a very relative dynamic state of change and emergence is plausible 2) a consistent identity of objects and entities is resolvable that is not based on apparent observations or partial history of events but on a set of total states and processes occurred during the progression to an actual condition. This is suggested to be unique for each and every actual situation as an identifier and is proposed to account for allowances with respect to new potentials. "Self" in this sense can assume more involved relations with self more than with the more distant, hence alien, otherwise arrived at proximal components, components of the environment, inert or otherwise. An example is presented with respect to solar energies and their toxicity to cause disturbances/disease upon internal exposure-as an unnaturally arrived imbalance/proximity between the transparent (history dependant) and the apparent-together comprising, in this situation, a disturbed actual state that can encompass also distortions in the perception of time. Time is proposed to be delineated as a contrast of proximal and distal factors mutually involved with both transparent (genealogically) oriented parameters, and empirically apparent factors that together comprise the actual, as well as those more immediate proximal and distal components(e.g. solar radiation, light-the less structured ambient verse those elements that comprise visual perceptions) as they influence the senses. Each entity species in this scheme possesses its’ own characteristic sense of time along with contemporary factors that influence the perception of time state, state of health and disturbance. (shrink)

This chapter focuses on picture theory, which is sometimes spoken of as a theory of the proposition. By a proposition, Wittgenstein like Frege means something that determines its sense by means of a correlation between the mode of combination of its constituent symbols and the structure of its sense. It has been an orthodoxy amongst Tractatus interpreters, and continues to be such in the wider philosophical community, that Wittgenstein follows the Russell in offering a correspondence theory of truth. The (...) expression of a Tractarian fact provides that fact's mode of combination, and from here there can be no further question as to the ontological types of its constituents. Tractarian facts, it is however added, are not truth conditions but items whose existence explains the obtaining of truth conditions: a Tractarian atomic fact is not a truth condition but a truthmaker. (shrink)

While this article sets out to advance our knowledge about the characteristics of Nigerian cybercriminals (Yahoo-Boys), it is also the first study to explore the narratives of the Economic and Financial Crimes Commission (EFCC) officers concerning them. It appraises symbolic interactionist insights to consider the ways in which contextual factors and worldview may help to illuminate officers’ narratives of cybercriminals and the interpretations and implications of such accounts. Semi-structured interviews of forty frontline EFCC officers formed the empirical basis of this (...) study and were subjected to a directed approach of qualitative content analysis. While prior studies, for example, indicated that only a group of cybercriminals deploy spiritual and magical powers to defraud victims (i.e. modus operandi), our data analysis extended this classification into more refined levels involving multiple features. In particular, analysis bifurcates cybercriminals and their operations based on three factors: [a] educational-attainment, [b] modus-operandi, and [c] networks-collaborators. Results also suggest that these cybercriminals and their operations are embedded in “masculinity-and-material-wealth”. These contributions thus have implications for a range of generally accepted viewpoints about these cybercriminals previously taken-for-granted. Since these criminals have victims all over the world, insights from our study may help various local and international agencies [a] to understand the actions/features of these two groups of cybercriminals better and develop more effective response strategies. [b] to appreciate the vulnerabilities of their victims better and develop more adequate support schemes. We also consider the limitations of social control agents’ narratives on criminals. (shrink)