The Newman problem is a fundamental problem that threatens to undermine structural assumptions and structural theories throughout philosophy and science. Here, we consider the problem in the context of consciousness science. We introduce and discuss the problem, and explain why it is detrimental not only to structuralist assumptions, but also to theories of consciousness, if left unconsidered. However, we show that if phenomenal spaces, and mathematical structures of conscious experience more generally, are understood in the (...) right way, the Newman problem does not arise. The upshot of our paper is that consciousness science needs to be careful in which definition of structure to consider, but if it is, the Newman problem disappears. (shrink)

Every scientific theory is a simulacrum of reality, every written story a simulacrum of the canon, and every conceptualization of a subjective perspective a simulacrum of the consciousness behind it—but is there a shared essence to these simulacra? The pursuit of answering seemingly disparate fundamental questions across different disciplines may ultimately converge into a single solution: a single ontological answer underlying grand unified theory, hard problem of consciousness, and the foundation of mathematics. I provide a hypothesis, a speculative (...) approximation, supported by a comprehensive overview of scientific evidence and philosophical literature, of a unified epistemic and phenomenological model and, in doing so, propose a parsimonious solution to the hard problem of consciousness. -/- The proposition of the hypothesis bears important implications for cross-disciplinary study between linguistics, mathematics, physics, and computer science, and offers new epistemic, ontological, and ethical propositions about the nature of AI consciousness, as well as existential risk mitigation. (shrink)

In recent years, the science and the philosophy of consciousness has seen growing interest in structural questions about consciousness. This is the Editorial Introduction for a special volume for Philosophy and the Mind Sciences on “Structuralism in Consciousness Studies.”.

Quantum theory can be regarded as a rationally coherent theory of the interaction of mind and matter and it allows our conscious thoughts to play a causally e cacious and necessary role in brain dynamics It therefore provides a natural basis created by scientists for the science of consciousness As an illustration it is explained how the interaction of brain and consciousness can speed up brain processing and thereby enhance the survival prospects of conscious organisms as compared (...) to similar organisms that lack consciousness As a second illustration it is explained how within the quantum framework the consciously experi enced I directs the actions of a human being It is concluded that contemporary science already has an adequate framework for incorporat ing causally e cacious experiential events into the physical universe in a manner that puts the neural correlates of consciousness into the theory in a well de ned way explains in principle how the e ects of consciousness per se can enhance the survival prospects of organisms that possess it allows this survival e ect to feed into phylogenetic de velopment and explains how the consciously experienced I can direct human behaviour.. (shrink)

Several promising approaches have been developed to represent conscious experience in terms of mathematical spaces and structures. What is missing, however, is an explicit definition of what a ‘mathematical structure of conscious experience’ is. Here, we propose such a definition. This definition provides a link between the abstract formal entities of mathematics and the concreta of conscious experience; it complements recent approaches that study quality spaces, qualia spaces, or phenomenal spaces; and it provides a general method to identify (...) and investigate structures of conscious experience. We hope that ultimately this work provides a basis for developing a common formal language to study consciousness. (shrink)

This book presents consciousness models from Eastern and Western perspectives that accommodate current scientific research in the natural sciences and humanities, from neurological experiments through philosophical enquiries to spiritual approaches. It offers up to date research from key disciplines in consciousness studies ranging from neurology, quantum mechanics, algorithmic science, mathematics, and astrophysics to literary studies, philosophy, and (comparative) theology. The volume examines the dichotomy between Western and Eastern perceptions of consciousness – where consciousness is perceived (...) as brain activity by Western scientists, and as a divine presence by various religions, especially in the East. The essays contextualize each other and reciprocally illuminate the potential and limits of the respective approaches. The texts aim at a transdisciplinary and transcultural exchange of ideas in consciousness studies and address a readership from interested lay-readers to experts of the field. The volume is of interest to researchers of consciousness studies. (shrink)

Maurits Cornelis Escher’s 1938 lithograph, Cycle, illustrates what mathematical physicist Roger Penrose calls ‘impossible objects’. The illusion of three-dimensionality, the innovative use of tessellation, and the incorporation of traditionally figurative elements induce the viewer to perceive the lithographic print as depicting a visually plausible reality built on the deconstructive metamorphosis of man into cube. It is Escher’s ability to paradoxically combine the radical oppositions of man and cube, landscape and geometric abstraction into an apparently harmonious composition where shapes repeat (...) with subtle variation and almost imperceptibly transition into radically different shapes that I want to use as a visual paradigm for conceptualizing the shifts in human consciousness in the digital age. Roger Penrose, path-breaking theorist of consciousness as a physical but non-computational process, was inspired by and inspired Escher. Penrose’s provisional concepts of consciousness, time and space can be visually compared to Escher’s earlier man-cube renderings, where each of these individual design elements allows the transition to another shape. In other words, Penrose’s theories, like Escher’s design concepts, illustrate a moment of transition in consciousness theory. As in Escher’s Cycle, the individual elements are being continually redefined, reshaped and revealed. Each may be a unique distortion of the previous, but this does not mean that it is disconnected or independent of the final outcome. These distortions are transitional elements that lead us visually to the other side of the composition. Radical transformations and developing connectedness in the boundaries between art, technology and science function like the individual elements in Escher’s Cycle. As we try to define the shifts in human consciousness occurring in the digital age, visually speaking, we are focusing on only one element right in the middle of an Escher metamorphosis, unable to see exactly how this element will be part of the completed design. This thought can be both frightening and liberating: frightening because we humans are used to relying on boundaries and predictable outcomes to feel a sense of control, liberating because anything and everything is possible and the changes will occur naturally as part of the transition. If Escher teaches us anything, it is that each piece in the meta-morphosis is needed to complete the big picture. (shrink)

This book proposes a new phenomenological analysis of the questions of perception and cognition which are of paramount importance for a better understanding of those processes which underlies the formation of knowledge and consciousness. It presents many clear arguments showing how a phenomenological perspective helps to deeply interpret most fundamental findings of current research in neurosciences and also in mathematical and physical sciences.

Let a smooth experience be an experience with perfectly gradual changes in phenomenal character. Consider, as examples, your visual experience of a blue sky or your auditory experience of a rising pitch. Do the phenomenal characters of smooth experiences have continuous or discrete structures? If we appeal merely to introspection, then it may seem that we should think that smooth experiences are continuous. This paper (1) uses formal tools to clarify what it means to say that an experience is continuous (...) or discrete, and (2) develops a discrete model of the phenomenal characters of smooth experiences. As a result, I'll argue that introspection leaves open whether smooth experiences are continuous or discrete. Yet I’ll also argue—perhaps surprisingly—that the discrete theory may better fit our introspective evidence. (shrink)

This volume presents the proceedings from the Eleventh Brazilian Logic Conference on Mathematical Logic held by the Brazilian Logic Society in Salvador, Bahia, Brazil. The conference and the volume are dedicated to the memory of professor Mario Tourasse Teixeira, an educator and researcher who contributed to the formation of several generations of Brazilian logicians. Contributions were made from leading Brazilian logicians and their Latin-American and European colleagues. All papers were selected by a careful refereeing processs and were revised and (...) updated by their authors for publication in this volume. There are three sections: Advances in Logic, Advances in Theoretical Computer Science, and Advances in Philosophical Logic. Well-known specialists present original research on several aspects of model theory, proof theory, algebraic logic, category theory, connections between logic and computer science, and topics of philosophical logic of current interest. Topics interweave proof-theoretical, semantical, foundational, and philosophical aspects with algorithmic and algebraic views, offering lively high-level research results. (shrink)

Then involvement is essential. You cannot stand aside as a member of a community. The real involvement presupposes first a connection at the level of understanding the phenomenon, an empathic relationship with the studied phenomena and processes, relationship that generate intuitions, leaps in understanding and knowledge, discoveries, revelations. The paper is based on the idea that information technology and communications today generate a global interaction based on a complex computer network, which forms a sphere that covers the planet, assimilated with (...) a global intelligence, to which we can consciously adhere becoming a synapse. a global neural network. (shrink)

Progress in neuroscience has left a central question of psychism unanswered: what is consciousness? Modeling the psyche from a computational perspective has helped to develop cognitive neurosciences, but it has also shown their limits, of which the definition, description and functioning of consciousness remain essential. From Rene Descartes, who tackled the issue of psychism as the brain-mind dualism, to Chambers, who defined qualia as the tough, difficult problem of research in neuroscience, many hypotheses and theories have been issued (...) to encompass the phenomenon of consciousness. Neuroscience specialists, such as Giulio Tononi or David Eagleman, consider consciousness as a phenomenon of emergence of all processes that take place in the brain. This hypothesis has the advantage of being supported by progress made in the study of complex systems in which the issue of emergence can be mathematically formalized and analyzed by physical-mathematical models. The current tendency to associate neural networks within the broad scope of network science also allows for a physical-mathematical formalization of phenomenology in neural networks and the construction of information-symbolic models. The extrapolation of emergence at the level of physical systems, biological systems and psychic systems can bring new models that can also be applied to the concept of consciousness. The meaning and significance that seem to structure the nature of consciousness is found as direction of evolution and teleological finality, of integration in the whole system and in any complex system at all scales. Starting from the wave-corpuscle duality in quantum physics, we can propose a model for structuring reality, based on the emergence of systems that contribute to the integration and coherence of the entire reality. Physical-mathematical models based mainly on topology can provide a mathematical formalization path, and the paradigm of information could allow the development of a pattern of emergence, that is common to all systems, including the psychic system, the difference being given only by the degree of information complexity. Thus, the mind-brain duality, which has been dominating the representation on psychism for a few centuries, could be solved by an informational approach, describing the connection between object and subject, reality and human consciousness, between mind and brain, thus unifying the perspective on natural sciences and humanities. (shrink)

A principle, according to which any scientific theory can be mathematized, is investigated. Social science, liberal arts, history, and philosophy are meant first of all. That kind of theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be (...) accepted rather a metamathematical axiom about the relation of mathematics and reality. The main statement is formulated as follows: Any scientific theory admits isomorphism to some mathematical structure in a way constructive. Its investigation needs philosophical means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. The sketch of the proof is organized in five steps: a generalization of epoché; involving transfinite induction in the transition between Peano arithmetic and set theory; discussing the finiteness of Peano arithmetic; applying transfinite induction to Peano arithmetic; discussing an arithmetical model of reality. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. The present paper follows a pathway grounded on Husserl’s phenomenology and “bracketing reality” to achieve the generalized arithmetic necessary for the principle to be founded in alternative ontology, in which there is no reality external to mathematics: reality is included within mathematics. That latter mathematics is able to self-found itself and can be called Hilbert mathematics in honour of Hilbert’s program for self-founding mathematics on the base of arithmetic. The principle of universal mathematizability is consistent to Hilbert mathematics, but not to Gödel mathematics. Consequently, its validity or rejection would resolve the problem which mathematics refers to our being; and vice versa: the choice between them for different reasons would confirm or refuse the principle as to the being. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. The Schrödinger equation in quantum mechanics is involved to illustrate that ontology. Thus the problem which of the two mathematics is more relevant to our being is discussed again in a new way A few directions for future work can be: a rigorous formal proof of the principle as an independent axiom; the further development of information ontology consistent to both kinds of mathematics, but much more natural for Hilbert mathematics; the development of the information interpretation of quantum mechanics as a mathematical one for information ontology and thus Hilbert mathematics; the description of consciousness in terms of information ontology. (shrink)

The Upanishads reveal that in the beginning, nothing existed: “This was but non-existence in the beginning. That became existence. That became ready to be manifest”. (Chandogya Upanishad 3.15.1) The creation began from this state of non-existence or nonduality, a state comparable to (0). One can add any number of zeros to (0), but there will be nothing except a big (0) because (0) is a neutral number. If we take (0) as Nirguna Brahman (God without any form and attributes), then (...) from where and how did the universe come into existence? -/- The neutral power (0) cannot produce anything without having an element of duality in it. Although Nirguna Brahman is neutral, it has a positive, negative, and neutral pole, constituting its Prakriti or nature. Prakriti has three latent Gunas (modes or qualities): Satva, Rajas, and Tamas. They are related to Gyana Shakti (the power of knowledge) Sankalpa Shakti (the power of ideation), and Kriya Shakti (the power of action). Science says that Atom is the basic element from which the universe evolved. The Atom has three nuclei- electron, pluton, and neutron. The Satva, Rajas, and Tamas in Indian spirituality are nothing but the mystical names for the nuclei of an atom. -/- According to Bhagavata Purana, Prakriti is also constituted of the elements of Time, Karma (action/destiny) and Swabhava (innate nature). Time disturbs the equilibrium of Gunas. From the aspect of Karma is produced an entity called Mahat, in the form of intelligence. Mahat is dominated by Satva and Rajas. From Mahat manifests the next evolute dominated by Tamas with three predominant qualities – Dravya (substance), Kriya (action), as well as intelligence. It forms to become the Ego principle (Ahamkara). -/- Ahamkara has three modes – Satvic, Rajasic and Tamasic. Satvic is Jnana oriented, Rajasic action-oriented and Tamasic Dravya (substance) oriented. From the Tamasic Ahankara, five gross elements are produced (ether, air, fire, water, and earth - Akash, Vayu, Agni, Jal and Prithvi). From the Satvic Ahamkara, guardian deities (the sun and moon, deities of sense organs, and organs of action) and from Rajasic Ahamkara, ten senses (Indriyas), five senses of perception, five organs of action, the faculties of intellect and Prana (life breath) are produced. -/- Bhagavata says that since these energies, elements, and faculties remained disassociated, they were combined to form a Cosmic Egg. The egg floats in the primal waters for a thousand years. Then God enters this Cosmic Egg and manifests himself as the Cosmic Purusha. He is the first nucleus, the God particle equivalent to the number (1) which is the embodiment of everything in the universe. The concept of creation and dissolution in Hinduism can be compared to the waves in an ocean that appear and disappear incessantly. The Manvantaras are such successive episodes of creation emerging from the Cosmic Person, the Manu who is embodied God-Consciousness, God himself. These episodes of creation are measured in Hinduism in terms of Manvantaras, the epochs of Manus. -/- Manu is the ‘First-Born’ (1) of God, the Cosmic Purusha from whom the world has originated. This Cosmic Person (Purusha) has been described as having fourteen biospheres (heavens) that are inhabited by various life forms in the order of evolution of consciousness. If we begin from the human biosphere (Bhuloka), there are ten astral biospheres that a man must transcend to attain liberation or Mukti from the cycle of births and deaths. -/- The number (1) produces the primary numbers up to (9) through the transmutation of the creational energies and qualities. The process can be related to the descent and cyclical evolution of (1) through ten spiritual stages, finally merging with the nondual (0). The number (10) marks the merger of (1) with (0). The Hindu worldview is that all life forms in an episode of creation must evolve to become one with the non-dual state (0) to attain liberation from the cycle of births and deaths in a cyclical process. -/- . (shrink)

I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, (...) parallel universes and Gödel incompleteness. I hypothesize that only computable and decidable (in Gödel’s sense) structures exist, which alleviates the cosmological measure problem and may help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems. (shrink)

Consciousness-based education and Maharishi Vedic science -- Consciousness-based education and education -- Consciousness-based education and physiology and health -- Consciousness-based education and physics -- Consciousness-based education and mathematics -- Consciousness-based education and literature -- Consciousness-based education and art -- Consciousness-based education and management -- Consciousness-based education and government -- Consciousness-based education and computer science -- Consciousness-based education and sustainability -- Consciousness-based education and world peace.

In lieu of an abstract, here is a brief excerpt of the content:Symbolic Mathematics and the Intellect Militant: On Modern Philosophy’s Revolutionary SpiritCarl PageWhat makes modern philosophy different? My question presupposes the legitimacy of calling part of philosophy “modern.” That presupposition is in turn open to question as regards its meaning, its warrant, and the conditions of its applicability. 1 Importance notwithstanding, such further inquiries all start out from the phenomenon upon which everyone agrees: philosophy running through Plato and Aristotle (...) looks significantly different from philosophy running from Descartes to Kant.My concern in this essay is with the phenomenon of the difference itself, rather than with the second-order questions associated with how properly to assign it historical meaning. I take the difference between ancient and modern philosophy to be as significant as differences in philosophy’s history can be: modern philosophy rests on a new interpretation of the nature and fulfillment of human reason, and disputes about the nature of human reason are the ultimate battles of philosophy. But the general thesis is not my main point. 2 The focus of this essay falls on what may be called the integrity of the phenomenon, on the specific interpretation of human reason that lends modern philosophy its peculiar face. [End Page 233]Modern philosophy’s strikingly revolutionary spirit is my point of departure. When Descartes writes in the first of his Meditations that “it was necessary, once in the course of my life, to demolish everything completely and start again right from the foundations if I wanted to establish anything at all in the sciences that was stable and likely to last,” 3 he reveals the same enthusiasm for total reform later found in Kant: “This attempt to alter the procedure which has hitherto prevailed in metaphysics, by completely revolutionizing it in accordance with the example set by the geometers and physicists, forms indeed the main purpose of this critique of pure speculative reason.” 4 How exactly did philosophy become so convinced that its central tradition—a sprawling, disorganized, ugly city, as Descartes has it in the Discourse (I:116)—needed razing to the ground in the interest of some rational town-planning? Moreover, the calls for revolution have not abated, despite contemporary disillusionment with both Cartesian rationalism and Enlightenment philosophy in general; they have grown more shrill. The confidence with which rationalism, foundationalism, universalism, logocentrism, Platonism, and so on are currently set at naught for the sake of contingency, particularity, and difference reveals the same revolutionary and totalizing spirit that marks the earlier phase of philosophy’s modernity. Such enthusiasm is reason’s freedom taken to an extreme. 5 What inspires this march of the intellect militant? What, if anything, justifies its hubristic self-assertions in the domain of philosophy? These are the questions I address.Descartes is commonly identified as the father of modern philosophy. While the full story of modern philosophy’s parentage is more complicated than this, it is fair to say that in Descartes self-consciousness of a new mode of doing philosophy emerges with a focus and revolutionary sense of purpose that caught philosophical imagination in his own time and continues to do so in ours. 6 Motifs of modern philosophy may be found in many places—Machiavelli, Hobbes, Francis Bacon, Nicholas of Cusa, Giordano Bruno, Jakob Boehme—nonetheless, Descartes’s intensely single-minded, even jealous advocacy commends itself to all but the most stubborn antiquarian mentality as modernity’s almost perfect philosophical representative. [End Page 234]That Descartes stands on a remarkable philosophical cusp is apparent in the contrast between the title and the subject matter of his most influential philosophical work: Meditationes de Prima Philosophiae (1641). To that point prima philosophia or First Philosophy had been construed as the metaphysics. It was not concerned with the critical question of how metaphysical sciences are possible and was not directly related to any doctrine of the human soul—except perhaps on the one point of the divinity of nous, the human soul’s highest part. In Descartes’s Meditations, on the other hand, the landscape has altered. Doubt, certainty, knowledge, the ego cogitans and its stream of representations are the new subject matter. What is first in philosophy is no longer what... (shrink)

Advances in artificial intelligence and neuroscience claim to have begun to undermine the assumptions of the arts and educational theory community by explaining consciousness through either a reduction to mathematical functionalism or an excrescence of brain biology. I suggest that the worldview behind such reductionism is opposed to the worldview assumed by many educational practitioners and theorists. I then go on to outline a few common positions taken in the burgeoning field of consciousness studies that suggest that—though (...) many attributes of consciousness have been identified and explained—individual consciousness itself remains as much of an enigma to scientists as to the rest of us who experience it. However, I do suggest the necessity of intersubjectivity for conscious evolution. (shrink)

Platonism is the most pervasive philosophy of mathematics. Indeed, it can be argued that an inarticulate, half-conscious Platonism is nearly universal among mathematicians. The basic idea is that mathematical entities exist outside space and time, outside thought and matter, in an abstract realm. In the more eloquent words of Edward Everett, a distinguished nineteenth-century American scholar, "in pure mathematics we contemplate absolute truths which existed in the divine mind before the morning stars sang together, and which will continue to (...) exist there when the last of their radiant host shall have fallen from heaven." In What is Mathematics, Really?, renowned mathematician Rueben Hersh takes these eloquent words and this pervasive philosophy to task, in a subversive attack on traditional philosophies of mathematics, most notably, Platonism and formalism. Virtually all philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Mathematical objects are created by humans, not arbitrarily, but from activity with existing mathematical objects, and from the needs of science and daily life. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of the book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Plato, Descartes, Spinoza, and Kant, to Bertrand Russell, David Hilbert, Rudolph Carnap, and Willard V.O. Quine--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, Peirce, Dewey, and Lakatos. In his epilogue, Hersh reveals that this is no mere armchair debate, of little consequence to the outside world. He contends that Platonism and elitism fit well together, that Platonism in fact is used to justify the claim that "some people just can't learn math." The humanist philosophy, on the other hand, links mathematics with geople, with society, and with history. It fits with liberal anti-elitism and its historical striving for universal literacy, universal higher education, and universal access to knowledge and culture. Thus Hersh's argument has educational and political ramifications. Written by the co-author of The Mathematical Experience, which won the American Book Award in 1983, this volume reflects an insider's view of mathematical life, based on twenty years of doing research on advanced mathematical problems, thirty-five years of teaching graduates and undergraduates, and many long hours of listening, talking to, and reading philosophers. A clearly written and highly iconoclastic book, it is sure to be hotly debated by anyone with a passionate interest in mathematics or the philosophy of science. (shrink)

Growing up, I was a mathematics and science geek. I read everything I could in these areas. Every now and then, something would point in a philosophical direction. Perhaps my most important influence was reading Hofstadter’s Gödel, Escher, Bach as a teenager. I read it initially for the mathematical parts, but it planted a seed for thinking about the mind. Later, Hofstadter and Dennett’s The Mind’s I got me thinking more about the mind–body problem in particular.

This paper explores a remarkable convergence of ideas and evidence, previously presented in separate places by its authors. That convergence has now become so persuasive that we believe we are working within substantially the same broad framework. Taylor's mathematical papers on neuronal systems involved in consciousness dovetail well with work by Newman and Baars on the thalamocortical system, suggesting a brain mechanism much like the global workspace architecture developed by Baars (see references below). This architecture is relational, in (...) the sense that it continuously mediates the interaction of input with memory. While our approaches overlap in a number of ways, each of us tends to focus on different areas of detail. What is most striking, and we believe significant, is the extent of consensus, which we believe to be consistent with other contemporary approaches by Weiskrantz, Gray, Crick and Koch, Edelman, Gazzaniga, Newell and colleagues, Posner, Baddeley, and a number of others. We suggest that cognitive neuroscience is moving toward a shared understanding of consciousness in the brain. (shrink)

Summary A new culture of mathematics was developed in sixteenth-century England, the culture of ?the mathematicalls?. Its representatives were the self-styled mathematical practitioners who presented their art as a practical and worldly activity. The careers of two practitioners, Thomas Bedwell and Thomas Hood, are used as case studies to examine the establishment of this culture of the mathematicalls. Both practitioners self-consciously used mathematical instruments as key resources in negotiating their own roles. Bedwell defined his role in contrast to (...) mechanicians and he secured patronage in military engineering and the service of the commonwealth; Hood worked in the commercial setting of London as a teacher, author, chartmaker, and retailer. Working in new contexts and dealing with new audiences of gentlemen and mechanicians, Bedwell and Hood used instruments to construct a public consensus on the status and aims of mathematics. (shrink)

In this wide-ranging book, Brian Davies discusses the basis for scientists' claims to knowledge about the world. He looks at science historically, emphasizing not only the achievements of scientists from Galileo onwards, but also their mistakes. He rejects the claim that all scientific knowledge is provisional, by citing examples from chemistry, biology and geology. A major feature of the book is its defense of the view that mathematics was invented rather than discovered. A large number of examples are used (...) to illustrate these points, and many of the deep issues in today's world discussed-from psychology and evolution to quantum theory, consciousness and even religious belief. Disentangling knowledge from opinion and aspiration is a hard task, but this book provided a clear guide to the difficulties. (shrink)

Science as a Spiritual Practice is in three parts. In the first part the author argues that there are problems with materialism and that self-transformation could lead individual scientists to more comprehensive ways of understanding reality. In the second part he takes on the contentious notion of inner knowledge and shows how access to inner knowledge could be possible in some altered states of consciousness. The third part is an analysis of the philosophy of Franklin Wolff, who claimed (...) that the transcendent states of consciousness which occurred for him resulted from his mathematical approach to spirituality. (shrink)

This book addresses the fascinating cross-disciplinary field of quantum information theory applied to the study of brain function. It offers a self-study guide to probe the problems of consciousness, including a concise but rigorous introduction to classical and quantum information theory, theoretical neuroscience, and philosophy of the mind. It aims to address long-standing problems related to consciousness within the framework of modern theoretical physics in a comprehensible manner that elucidates the nature of the mind-body relationship. The reader also (...) gains an overview of methods for constructing and testing quantum informational theories of consciousness. (shrink)

It can not be our purpose to give here a complete account of the phenomenological history of mathematical doctrine. It will be enough to refer to the battle of opinions in mathematical theory which was waged within the last eighty-five years, since Riemann's inaugural lecture on Non-Euclidean Geometry. Furthermore, the revolution which Einstein's theory of general relativity created is indicative of the complete absence of any general awareness that mathematics as a science has any relation to social (...) reality. If we are going to establish such relations, we are conscious of the fact that they would be hotly contended by many mathematicians. (shrink)

In this article we present and compare two early attempts to establish psychology as an independent scientific discipline that had considerable influence in central Europe: the theories of Johann Friedrich Herbart (1776—1841) and Franz Brentano (1838—1917). While both of them emphasize that psychology ought to be conceived as an empirical science, their conceptions show revealing differences. Herbart starts with metaphysical principles and aims at mathematizing psychology, whereas Brentano rejects all metaphysics and bases his method on a conception of inner (...) perception (as opposed to inner observation) as a secondary consciousness, by means of which one gets to be aware of all of one’s own conscious phenomena. Brentano’s focus on inner perception brings him to deny the claim that there could be unconscious mental phenomena — a view that stands in sharp contrast to Herbart’s emphasis on unconscious, ‘repressed’ presentations as a core element of his mechanics of mind. Herbart, on the other hand, denies any role for psychological experiments, while Brentano encouraged laboratory work, thus paving the road for the more experimental work of his students like Stumpf and Meinong. By briefly tracing the fate of the schools of Herbart and Brentano, respectively, we aim to illustrate their impact on the development of psychological research, mainly in central Europe. (shrink)

A fundamental problem in science is how to make logical inferences from scientific data. Mere data does not suffice since additional information is necessary to select a domain of models or hypotheses and thus determine the likelihood of each model or hypothesis. Thomas Bayes’ Theorem relates the data and prior information to posterior probabilities associated with differing models or hypotheses and thus is useful in identifying the roles played by the known data and the assumed prior information when making (...) inferences. Scientists, philosophers, and theologians accumulate knowledge when analyzing different aspects of reality and search for particular hypotheses or models to fit their respective subject matters. Of course, a main goal is then to integrate all kinds of knowledge into an all-encompassing worldview that would describe the whole of reality. A generous description of the whole of reality would span, in the order of complexity, from the purely physical to the supernatural. These two extreme aspects of reality are bridged by a nonphysical realm, which would include elements of life, man, consciousness, rationality, mental and mathematical abstractions, etc. An urgent problem in the theory of knowledge is what science is and what it is not. Albert Einstein’s notion of science in terms of sense perception is refined by defining operationally the data that makes up the subject matter of science. It is shown, for instance, that theological considerations included in the prior information assumed by Isaac Newton is irrelevant in relating the data logically to the model or hypothesis. In addition, the concepts of naturalism, intelligent design, and evolutionary theory are critically analyzed. Finally, Eugene P. Wigner’s suggestions concerning the nature of human consciousness, life, and the success of mathematics in the natural sciences is considered in the context of the creative power endowed in humans by God. (shrink)

This open access book chronicles the rise of a new scientific paradigm offering novel insights into the age-old enigmas of existence. Over 300 years ago, the human mind discovered the machine code of reality: mathematics. By utilizing abstract thought systems, humans began to decode the workings of the cosmos. From this understanding, the current scientific paradigm emerged, ultimately discovering the gift of technology. Today, however, our island of knowledge is surrounded by ever longer shores of ignorance. Science appears to (...) have hit a dead end when confronted with the nature of reality and consciousness. In this fascinating and accessible volume, James Glattfelder explores a radical paradigm shift uncovering the ontology of reality. It is found to be information-theoretic and participatory, yielding a computational and programmable universe. (shrink)

In recent decades, the scientific study of consciousness has significantly increased our understanding of this elusive phenomenon. Yet, despite critical development in our understanding of the functional side of consciousness, we still lack a fundamental theory regarding its phenomenal aspect. There is an “explanatory gap” between our scientific knowledge of functional consciousness and its “subjective,” phenomenal aspects, referred to as the “hard problem” of consciousness. The phenomenal aspect of consciousness is the first-person answer to “what (...) it’s like” question, and it has thus far proved recalcitrant to direct scientific investigation. Naturalistic dualists argue that it is composed of a primitive, private, non-reductive element of reality that is independent from the functional and physical aspects of consciousness. Illusionists, on the other hand, argue that it is merely a cognitive illusion, and that all that exists are ultimately physical, non-phenomenal properties. We contend that both the dualist and illusionist positions are flawed because they tacitly assume consciousness to be an absolute property that doesn’t depend on the observer. We develop a conceptual and a mathematical argument for a relativistic theory of consciousness in which a system either has or doesn’t have phenomenal consciousness with respect to some observer. Phenomenal consciousness is neither private nor delusional, just relativistic. In the frame of reference of the cognitive system, it will be observable and in other frame of reference it will not. These two cognitive frames of reference are both correct, just as in the case of an observer that claims to be at rest while another will claim that the observer has constant velocity. Given that consciousness is a relativistic phenomenon, neither observer position can be privileged, as they both describe the same underlying reality. Based on relativistic phenomena in physics we developed a mathematical formalization for consciousness which bridges the explanatory gap and dissolves the hard problem. Given that the first-person cognitive frame of reference also offers legitimate observations on consciousness, we conclude by arguing that philosophers can usefully contribute to the science of consciousness by collaborating with neuroscientists to explore the neural basis of phenomenal structures. (shrink)

Mathematical practitioners in seventeenth-century London formed a cohesive knowledge community that intersected closely with instrument-makers, printers and booksellers. Many wrote books for an increasingly numerate metropolitan market on topics covering a wide range of mathematical disciplines, ranging from algebra to arithmetic, from merchants’ accounts to the art of surveying. They were also teachers of mathematics like John Kersey or Euclid Speidell who would use their own rooms or the premises of instrument-makers for instruction. There was a high degree (...) of interdependency even beyond their immediate milieu. Authors would cite not only each other, but also practitioners of other professions, especially those artisans with whom they collaborated closely. Practical mathematical books effectively served as an advertising medium for the increasingly self-conscious members of a new emerging professional class. Contemporaries would talk explicitly of ‘the London mathematicians’ in distinction to their academic counterparts at Oxford or Cambridge. The article takes a closer look at this metropolitan knowledge culture during the second half of the century, considering its locations, its meeting places and the mathematical clubs which helped forge the identity of its practitioners. It discusses their backgrounds, teaching practices and relations to the London book trade, which supplied inexpensive practical mathematical books to a seemingly insatiable public. (shrink)

The ‘hard problem’ is hard because of the special epistemological status of consciousness, which does not, however, preclude its scientific investigation. Data from phenomenologically trained observers can be combined with neurological investigations to establish the relation between experience and neurodynamics. Although experience cannot be reduced to physical phenomena, parallel phenomenological and neurological analyses allow the structure of experience to be related to the structure of the brain. Such an analysis suggests a theoretical entity, an elementary unit of experience, the (...) protophenomenon, which corresponds to an activity site in the brain. The structure of experience is determined by connections between these activity sites; the connections correspond to temporal patterns among the elementary units of experience, which can be expressed mathematically. This theoretical framework illuminates several issues, including degrees of consciousness, nonbiological consciousness, sensory inversions, unity of consciousness and the unconscious mind. (shrink)

Objective. Conceptualization of the definition of space as a semantic unit of language consciousness. -/- Materials & Methods. A structural-ontological approach is used in the work, the methodology of which has been tested and applied in order to analyze the subject matter area of psychology, psycholinguistics and other social sciences, as well as in interdisciplinary studies of complex systems. Mathematical representations of space as a set of parallel series of events (Alexandrov) were used as the initial theoretical basis (...) of the structural-ontological analysis. In this case, understanding of an event was considered in the context of the definition adopted in computer science – a change in the object properties registered by the observer. -/- Results. The negative nature of space realizes itself in the subject-object structure, the components interaction of which is characterized by a change – a key property of the system under study. Observer’s registration of changes is accompanied by spatial focusing (situational concretization of the field of changes) and relating of its results with the field of potentially distinguishable changes (subjective knowledge about «changing world»). The indicated correlation performs the function of space identification in terms of recognizing its properties and their subjective significance, depending on the features of the observer`s motivational sphere. As a result, the correction of the actual affective dynamics of the observer is carried out, which structures the current perception of space according to principle of the semantic fractal. Fractalization is a formation of such a subjective perception of space, which supposes the establishment of semantic accordance between the situational field of changes, on the one hand, and the worldview, as well as the motivational characteristics of the observer, on the other. -/- Conclusions. Performed structural-ontological analysis of the system formed by the interaction of the perceptual function of the psyche and the semantic field of the language made it possible to conceptualize the space as a field of changes potentially distinguishable by the observer, structurally organized according to the principle of the semantic fractal. The compositional features of the fractalization process consist in fact that the semantic fractal of space is relevant to the product of the difference between the situational field of changes and the field of potentially distinguishable changes, adjusted by the current configuration of the observer`s value-needs hierarchy and reduced by his actual affective dynamics. (shrink)

In his stimulating book SHADOWS OF THE MIND, Roger Penrose presents arguments, based on Gödel's theorem, for the conclusion that human thought is uncomputable. There are actually two separate arguments in Penrose's book. The second has been widely ignored, but seems to me to be much more interesting and novel than the first. I will address both forms of the argument in some detail. Toward the end, I will also comment on Penrose's proposals for a "new science of (...) class='Hi'>consciousness". (shrink)

This book constitutes the first treatment of C. S. Peirce’s unique concept of habit. Habit animated the pragmatists of the 19th and early 20th centuries, who picked up the baton from classical scholars, principally Aristotle. Most prominent among the pragmatists thereafter is Charles Sanders Peirce. In our vernacular, habit connotes a pattern of conduct. Nonetheless, Peirce’s concept transcends application to mere regularity or to human conduct; it extends into natural and social phenomena, making cohesive inner and outer worlds. Chapters in (...) this anthology define and amplify Peircean habit; as such, they highlight the dialectic between doubt and belief. Doubt destabilizes habit, leaving open the possibility for new beliefs in the form of habit-change; and without habit-change, the regularity would fall short of habit – conforming to automatic/mechanistic systems. This treatment of habit showcases how, through human agency, innovative regularities of behavior and thought advance the process of making the unconscious conscious. The latter materializes when affordances form the basis for modifications in action schemas and modes of reasoning. Further, the book charts how indexical signs in language and action are pivotal in establishing attentional patterns; and how these habits accommodate novel orientations within event templates. It is intended for those interested in Peirce’s metaphysic or semiotic, including both senior scholars and students of philosophy and religion, psychology, sociology and anthropology, as well as mathematics, and the natural sciences. (shrink)

In this paper we provide a philosophical analysis of the Hard Problem of consciousness and the implications of conceivability scenarios for current neuroscientific research. In particular, we focus on one of the most prominent neuroscientific theories of consciousness, integrated information theory (IIT). After a brief introduction on IIT, we present Chalmers’ original formulation and propose our own layered view of the hard problem, showing how 2 separate issues can be distinguished. More specifically, we argue that it’s possible to (...) disentangle a core problem of consciousness from a layered hard problem, the latter being essentially connected to Chalmers’ conceivability argument. We then assess the relation between the Hard Problem and IIT, showing how the theory resists conceivability scenarios, and how it is equipped to face up to the hard problem in its broadest acceptation. (shrink)

The theory suggests that quantum computations in brain neuronal dendritic-somatic microtubules regulate axonal firings to control conscious behavior. Within microtubule subunit proteins, collective dipoles in arrays of contiguous amino acid electron clouds enable suitable for topological dipole able to physically represent cognitive values, for example, those portrayed by Pothos & Busemeyer (P&B) as projections in abstract Hilbert space.

While practical efforts in the field of artificial intelligence grow exponentially, the truly scientific and mathematically exact understanding of the underlying phenomena of intelligence and consciousness is still missing in the conventional science framework. The inevitably dominating empirical, trial-and-error approach has vanishing efficiency for those extremely complicated phenomena, ending up in fundamentally limited imitations of intelligent behaviour. We provide the first-principle analysis of unreduced many-body interaction process in the brain revealing its qualitatively new features, which give rise to (...) rigorously defined chaotic, noncomputable, intelligent and conscious behaviour. Based on the obtained universal concepts of unreduced dynamic complexity, intelligence and consciousness, we derive the universal laws of intelligence applicable to any kind of intelligent system interacting with the environment. We finally show why and how these fundamentally substantiated and therefore practically efficient laws of intelligent system dynamics are indispensable for correct AI design and training, which is urgently needed in this time of critical global change towards the truly sustainable development. (shrink)

Temporal consciousness is philosophically problematic because it appears to have features that cannot be analyzed in a way compatible with the fundamental view of time as a one-dimensional order of events. For example, it seems to be a manifest fact of experience that within a strictly present state of consciousness one can be immediately aware of a succession of events, yet the standard view of time denies that successive events can co-exist, so how can they be given together (...) in a present perceptual state? Such puzzles have occasionally led philosophers to reject scientific or mathematical theories of time. Some time ago C. D. Broad developed a largely unappreciated theory of temporal cognition to cope with these puzzles. In this paper the evolution of Broad’s theory is traced, and it is defended from the misinterpretations of later critics. Finally, it is suggested that a modification of Broad’s theory, which frees it from the trappings of sense-data epistemology, shows it to be compatible with sane current naturalistic approaches to experience that also would need to account for temporal experience within the framework of scientific time. (shrink)

After an undergraduate degree with a major in mathematics, I turned to philosophy—in part because philosophy had all the interest of math (and logic) plus an indefinitely wide range of subject matter. I began philosophy at an intersection of metaphysics and philosophy of science. My dissertation, Ontological and Linguistic Aspects of Temporal Becoming, was on the philosophy of time. A convinced physicalist, I defended the idea that past, present and future (the A-series) are merely “mind-dependent.” I spent a year (...) as a Mellon postdoctoral fellow at the University of Pittsburgh, working mainly with Adolf Grünbaum, who was very generous to me with his time. Other members of the philosophical community in Pittsburgh suggested that there was no philosophical interest in nowness; the word ‘now’ exhausted whatever there was of real interest concerning the status of the present. I therefore turned my attention from the status of the present (nowness) to the word ‘now’. (shrink)

In this paper we provide a philosophical analysis of the Hard Problem of consciousness and the implications of conceivability scenarios for current neuroscientific research. In particular, we focus on one of the most prominent neuroscientific theories of consciousness, integrated information theory (IIT). After a brief introduction on IIT, we present Chalmers’ original formulation and propose our own layered view of the hard problem, showing how 2 separate issues can be distinguished. More specifically, we argue that it’s possible to (...) disentangle a core problem of consciousness from a layered hard problem, the latter being essentially connected to Chalmers’ conceivability argument. We then assess the relation between the Hard Problem and IIT, showing how the theory resists conceivability scenarios, and how it is equipped to face up to the hard problem in its broadest acceptation. (shrink)

One of the outstanding problems in the cognitive sciences is to understand how ongoing conscious experience is related to the workings of the brain and nervous system. Neurodynamics offers a powerful approach to this problem because it provides a coherent framework for investigating change, variability, complex spatiotemporal patterns of activity, and multiscale processes (among others). In this chapter, we advocate a neurodynamical approach to consciousness that integrates mathematical tools of analysis and modeling, sophisticated physiological data recordings, and detailed (...) phenomenological descriptions. We begin by stating the basic intuition: Consciousness is an intrinsically dynamic phenomenon and must therefore be studied within a framework that is capable of rendering its dynamics intelligible. We then discuss some of the formal, analytical features of dynamical systems theory, with particular reference to neurodynamics. We then review several neuroscientific proposals that make use of dynamical systems theory in characterizing the neurophysiologi-. (shrink)

Fifty years ago when Jacques Hadamard set out to explore how mathematicians invent new ideas, he considered the creative experiences of some of the greatest thinkers of his generation, such as George Polya, Claude Le;vi-Strauss, and Albert Einstein. It appeared that inspiration could strike anytime, particularly after an individual had worked hard on a problem for days and then turned attention to another activity. In exploring this phenomenon, Hadamard produced one of the most famous and cogent cases for the existence (...) of unconscious mental processes in mathematical invention and other forms of creativity. Written before the explosion of research in computers and cognitive science, his book, originally titled The Psychology of Invention in the Mathematical Field , remains an important tool for exploring the increasingly complex problem of mental life. The roots of creativity for Hadamard lie not in consciousness, but in the long unconscious work of incubation, and in the unconscious aesthetic selection of ideas that thereby pass into consciousness. His discussion of this process comprises a wide range of topics, including the use of mental images or symbols, visualized or auditory words, "meaningless" words, logic, and intuition. Among the important documents collected is a letter from Albert Einstein analyzing his own mechanism of thought. (shrink)

We argue that the projective geometrical component of the Projective Consciousness Model can account for key aspects of pre-reflective self-consciousness and can relate PRSC intelligibly to another signal feature of subjectivity: perspectival character or point of view. We illustrate how the projective geometrical versions of the concepts of duality, reciprocity, polarity, closedness, closure, and unboundedness answer to salient aspects of the phenomenology of PRSC. We thus show that the same mathematics that accounts for the statics and dynamics of (...) perspectival character also accounts for PRSC. More generally, we argue that introducing higher-level geometrical concepts into the theory of PRSC, and into the theory of consciousness broadly, as the PCM does, promises to break longstanding theoretical impasses and dialectical stalemates. (shrink)