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A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (28 February 2020) | Viewed by 107942

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Prof. Dr. Ian T. Durham

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Department of Physics, Saint Anselm College, Manchester, NH 03102, USA
Interests: relativistic quantum information; quantum foundations; formal models of consciousness and free will

Dr. Johannes Kleiner

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1. Munich Center for Mathematical Philosophy, Ludwig Maximilian University of Munich, 80539 Munich, Germany
2. Graduate School of Systemic Neurosciences, Ludwig Maximilian University of Munich, 82152 Planegg-Martinsried, Germany
3. Institute for Psychology, University of Bamberg, 96047 Bamberg, Germany
Interests: mathematical consciousness science; mathematical physics; calculus of variations
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Prof. Dr. Yakov Kremnitzer

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Mathematical Institute, University of Oxford, OX2 6GG Oxford, UK
Interests: Geometric representation theory; analytic and arithmetic geometry; mathematical physics; formal models of consciousness

Dr. Jonathan Mason

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Mathematical Institute, University of Oxford, OX2 6GG Oxford, UK
Interests: Spaces and algebras of functions; mathematical theories of consciousness involving relationships

Dr. Robert Prentner

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Guest Editor

Department of Cognitive Sciences, University of California, Irvine, CA 92627, USA
Interests: Core concepts for a science of consciousness; philosophy of mind; molecular quantum mechanics

Special Issue Information

Dear Colleagues,

The field ‘Scientific Study of Consciousness’ emerged in the early 1990s as a response to groundbreaking developments in neuroscience, cognitive psychology, and analytic philosophy. In the 25 years of its existence, it has become a major part of these disciplines and has made numerous discoveries that illuminate the relation between consciousness, cognition, and the brain.

From the very beginning, a large part of the research activity was aimed at discovering laws or regularities that describe how consciousness relates to the physical domain. Much like fundamental physics, the goal was to understand a part of reality using formal mathematical tools.

Thus, it is not surprising that in the past few years the activities of this field have attracted increasing attention from mathematicians, physicists and others who work with formal methods.

In order to bring those researchers together, we have organized the international conference ‘Models of Consciousness’ at the University of Oxford’s Mathematical Institute. On the occasion of this conference, we are very happy to call for submissions to this Entropy Special Issue dedicated to formal models of consciousness.

Complementing the excellent pool of journals in this area, this call is restricted to formal or mathematical approaches to the topic (please see the ‘Criteria for acceptance’ below).

Our hope in announcing this Special Issue is to facilitate the creation of a community of researchers who strive to investigate the theoretical and mathematical side of consciousness studies in a collaborative and open-minded manner. We believe that in cooperation with the important experimental work being done around the globe, a formal perspective might make valuable contributions to the scientific study of consciousness.

In joyful anticipation of your submission,

Prof. Dr. Ian Durham
Dr. Johannes Kleiner
Prof. Yakov Kremnitzer
Dr. Jonathan Mason
Dr. Dr. Robert Prentner
Guest Editors

Criteria for Acceptance

This call for submissions is open to everyone. We note that only submissions that satisfy the following criteria can be accepted for peer review:

The submission is either a research article that presents novel research or a comprehensive review article. Comments, re-submissions or minor modifications of previously published articles will not be accepted.
The submission is concerned with formal models of consciousness, experience, awareness, or the mind–matter relationship. Submissions focused on other topics (e.g., pure cognitive neuroscience) cannot be accepted.
Submissions need to specify clearly in what sense terms such as consciousness or experience are being used, as well as the long-term goal of the research project to which the submission belongs.
The presentation of essential mathematical details is strongly encouraged, as is the explanation of why a specific mathematical structure is being chosen. Submissions which merely gesture at some general mathematical structure cannot be accepted.
The submission needs to be comprehensible to anyone with an MA degree in mathematics or theoretical physics. We ask that non-trivial philosophical notions are introduced in a concise manner.
The submission needs to conform to Entropy’s criteria for scholarly publication, including word lengths and citation style. Please carefully read Entropy’s guide for authors linked below before submission. Proofreading cannot be provided.

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

Formal models of consciousness
Theoretical consciousness studies
Mathematical models of the mind-matter relation
Mathematics of consciousness
Experience and qualia space
Scientific study of consciousness

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Published Papers (13 papers)

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18 pages, 375 KiB

Open AccessArticle

A Compositional Model of Consciousness Based on Consciousness-Only

by Camilo Miguel Signorelli, Quanlong Wang and Ilyas Khan

Entropy 2021, 23(3), 308; https://doi.org/10.3390/e23030308 - 5 Mar 2021

Cited by 11 | Viewed by 4269

Abstract

Scientific studies of consciousness rely on objects whose existence is assumed to be independent of any consciousness. On the contrary, we assume consciousness to be fundamental, and that one of the main features of consciousness is characterized as being other-dependent. We set up a framework which naturally subsumes this feature by defining a compact closed category where morphisms represent conscious processes. These morphisms are a composition of a set of generators, each being specified by their relations with other generators, and therefore co-dependent. The framework is general enough and fits well into a compositional model of consciousness. Interestingly, we also show how our proposal may become a step towards avoiding the hard problem of consciousness, and thereby address the combination problem of conscious experiences. Full article

(This article belongs to the Special Issue Models of Consciousness)

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13 pages, 235 KiB

Open AccessArticle

An ESR Framework for the Study of Consciousness

by Diana Stanciu

Entropy 2021, 23(1), 97; https://doi.org/10.3390/e23010097 - 11 Jan 2021

Cited by 1 | Viewed by 3194

Abstract

I will argue that, in an interdisciplinary study of consciousness, epistemic structural realism (ESR) can offer a feasible philosophical background for the study of consciousness and its associated neurophysiological phenomena in neuroscience and cognitive science while also taking into account the mathematical structures involved in this type of research. Applying the ESR principles also to the study of the neurophysiological phenomena associated with free will (or rather conscious free choice) and with various alterations of consciousness (AOCs) generated by various pathologies such as epilepsy would add explanatory value to the matter. This interdisciplinary approach would be in tune with Quine’s well known idea that philosophy is not simple conceptual analysis but is continuous with science and actually represents an abstract branch of the empirical research. The ESR could thus resonate with scientific models of consciousness such as the global neuronal workspace model (inspired by the global workspace theory—GWT) and the integrated information theory (IIT) model. While structural realism has already been employed in physics or biology, its application as a meta-theory contextualising and relating various scientific findings on consciousness is new indeed. Out of the two variants: ontic structural realism (OSR) and epistemic structural realism (ESR), the latter can be considered more suitable for the study of consciousness and its associated neurophysiological phenomena because it removes the pressure of the still unanswered ‘What is consciousness?’ ontological question and allows us to concentrate instead on the ‘What can we know about consciousness?’ epistemological question. Full article

(This article belongs to the Special Issue Models of Consciousness)

68 pages, 575 KiB

Open AccessArticle

The Meta-Dynamic Nature of Consciousness

by John A. Barnden

Entropy 2020, 22(12), 1433; https://doi.org/10.3390/e22121433 - 18 Dec 2020

Cited by 5 | Viewed by 3652

Abstract

How, if at all, consciousness can be part of the physical universe remains a baffling problem. This article outlines a new, developing philosophical theory of how it could do so, and offers a preliminary mathematical formulation of a physical grounding for key aspects of the theory. Because the philosophical side has radical elements, so does the physical-theory side. The philosophical side is radical, first, in proposing that the productivity or dynamism in the universe that many believe to be responsible for its systematic regularities is actually itself a physical constituent of the universe, along with more familiar entities. Indeed, it proposes that instances of dynamism can themselves take part in physical interactions with other entities, this interaction then being “meta-dynamism” (a type of meta-causation). Secondly, the theory is radical, and unique, in arguing that consciousness is necessarily partly constituted of meta-dynamic auto-sensitivity, in other words it must react via meta-dynamism to its own dynamism, and also in conjecturing that some specific form of this sensitivity is sufficient for and indeed constitutive of consciousness. The article proposes a way for physical laws to be modified to accommodate meta-dynamism, via the radical step of including elements that explicitly refer to dynamism itself. Additionally, laws become, explicitly, temporally non-local in referring directly to quantity values holding at times prior to a given instant of application of the law. The approach therefore implicitly brings in considerations about what information determines states. Because of the temporal non-locality, and also because of the deep connections between dynamism and time-flow, the approach also implicitly connects to the topic of entropy insofar as this is related to time. Full article

(This article belongs to the Special Issue Models of Consciousness)

11 pages, 3295 KiB

Open AccessArticle

Toy Models of Top Down Causation

by Adrian Kent

Entropy 2020, 22(11), 1224; https://doi.org/10.3390/e22111224 - 27 Oct 2020

Cited by 3 | Viewed by 2683

Abstract

Models in which causation arises from higher level structures as well as from microdynamics may be relevant to unifying quantum theory with classical physics or general relativity. They also give a way of defining a form of panprotopsychist property dualism, in which consciousness and material physics causally affect one another. I describe probabilistic toy models based on cellular automata that illustrate possibilities and difficulties with these ideas. Full article

(This article belongs to the Special Issue Models of Consciousness)

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32 pages, 3085 KiB

Open AccessArticle

Modelling Consciousness within Mental Monism: An Automata-Theoretic Approach

by Peter B. Lloyd

Entropy 2020, 22(6), 698; https://doi.org/10.3390/e22060698 - 22 Jun 2020

Cited by 2 | Viewed by 6630

Abstract

Models of consciousness are usually developed within physical monist or dualistic frameworks, in which the structure and dynamics of the mind are derived from the workings of the physical brain. Little attention has been given to modelling consciousness within a mental monist framework, deriving the structure and dynamics of the mental world from primitive mental constituents only—with no neural substrate. Mental monism is gaining attention as a candidate solution to Chalmers’ Hard Problem on philosophical grounds, and it is therefore timely to examine possible formal models of consciousness within it. Here, I argue that the austere ontology of mental monism places certain constraints on possible models of consciousness, and propose a minimal set of hypotheses that a model of consciousness (within mental monism) should respect. From those hypotheses, it would be possible to construct many formal models that permit universal computation in the mental world, through cellular automata. We need further hypotheses to define transition rules for particular models, and I propose a transition rule with the unusual property of deep copying in the time dimension. Full article

(This article belongs to the Special Issue Models of Consciousness)

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19 pages, 249 KiB

Open AccessArticle

Varieties Of Evolved Forms Of Consciousness, Including Mathematical Consciousness

by Aaron Sloman

Entropy 2020, 22(6), 615; https://doi.org/10.3390/e22060615 - 2 Jun 2020

Cited by 1 | Viewed by 4830

Abstract

I shall introduce a complex, apparently unique, cross-disciplinary approach to understanding consciousness, especially ancient forms of mathematical consciousness, based on joint work with Jackie Chappell (Birmingham Biosciences) on the Meta-Configured Genome (MCG) theory. All known forms of consciousness (apart from recent very simple AI forms) are products of biological evolution, in some cases augmented by products of social, or technological evolution. Forms of consciousness differ between organisms with different sensory mechanisms, needs and abilities; and in complex animals can vary across different stages of development before and after birth or hatching or pupation, and before or after sexual and other kinds of maturity (or senility). Those forms can differ across individuals with different natural talents and environments, some with and some without fully functional sense organs or motor control functions (in humans: hearing, sight, touch, taste, smell, proprioception and other senses), along with mechanisms supporting meta-cognitive functions such as recollection, expectation, foreboding, error correction, and so forth, and varying forms of conscious control differing partly because of physical differences, such as conjoined twins sharing body parts. Forms of consciousness can also differ across individuals in different cultures with different shared theories, and social practices (e.g., art-forms, musical traditions, religions, etc.). There are many unanswered questions about such varieties of consciousness in products of biological evolution. Most of the details are completely ignored by most philosophers and scientists who focus only on a small subset of types of human consciousness—resulting in shallow theories. Immanuel Kant was deeper than most, though his insights, especially insights into mathematical consciousness tend to be ignored by recent philosophers and scientists, for bad reasons. This paper, partly inspired by Turing’s 1952 paper on chemistry-based morphogenesis, supporting William James’ observation that all known forms of consciousness must have been products of biological evolution in combination with other influences, attempts to provide (still tentative and incomplete) foundations for a proper study of the variety of biological and non-biological forms of consciousness, including the types of mathematical consciousness identified by Kant in 1781. Full article

(This article belongs to the Special Issue Models of Consciousness)

53 pages, 574 KiB

Open AccessEditor’s ChoiceArticle

Mathematical Models of Consciousness

by Johannes Kleiner

Entropy 2020, 22(6), 609; https://doi.org/10.3390/e22060609 - 30 May 2020

Cited by 27 | Viewed by 11323

Abstract

In recent years, promising mathematical models have been proposed that aim to describe conscious experience and its relation to the physical domain. Whereas the axioms and metaphysical ideas of these theories have been carefully motivated, their mathematical formalism has not. In this article, we aim to remedy this situation. We give an account of what warrants mathematical representation of phenomenal experience, derive a general mathematical framework that takes into account consciousness’ epistemic context, and study which mathematical structures some of the key characteristics of conscious experience imply, showing precisely where mathematical approaches allow to go beyond what the standard methodology can do. The result is a general mathematical framework for models of consciousness that can be employed in the theory-building process. Full article

(This article belongs to the Special Issue Models of Consciousness)

12 pages, 352 KiB

Open AccessArticle

A Formal Model for Adaptive Free Choice in Complex Systems

by Ian Durham

Entropy 2020, 22(5), 568; https://doi.org/10.3390/e22050568 - 19 May 2020

Cited by 4 | Viewed by 3389

Abstract

In this article, I develop a formal model of free will for complex systems based on emergent properties and adaptive selection. The model is based on a process ontology in which a free choice is a singular process that takes a system from one macrostate to another. I quantify the model by introducing a formal measure of the ‘freedom’ of a singular choice. The ‘free will’ of a system, then, is emergent from the aggregate freedom of the choice processes carried out by the system. The focus in this model is on the actual choices themselves viewed in the context of processes. That is, the nature of the system making the choices is not considered. Nevertheless, my model does not necessarily conflict with models that are based on internal properties of the system. Rather it takes a behavioral approach by focusing on the externalities of the choice process. Full article

(This article belongs to the Special Issue Models of Consciousness)

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35 pages, 1693 KiB

Open AccessEditor’s ChoiceArticle

Re-Thinking the World with Neutral Monism:Removing the Boundaries Between Mind, Matter, and Spacetime

by Michael Silberstein and William Stuckey

Entropy 2020, 22(5), 551; https://doi.org/10.3390/e22050551 - 14 May 2020

Cited by 3 | Viewed by 11668

Abstract

Herein we are not interested in merely using dynamical systems theory, graph theory, information theory, etc., to model the relationship between brain dynamics and networks, and various states and degrees of conscious processes. We are interested in the question of how phenomenal conscious experience and fundamental physics are most deeply related. Any attempt to mathematically and formally model conscious experience and its relationship to physics must begin with some metaphysical assumption in mind about the nature of conscious experience, the nature of matter and the nature of the relationship between them. These days the most prominent metaphysical fixed points are strong emergence or some variant of panpsychism. In this paper we will detail another distinct metaphysical starting point known as neutral monism. In particular, we will focus on a variant of the neutral monism of William James and Bertrand Russell. Rather than starting with physics as fundamental, as both strong emergence and panpsychism do in their own way, our goal is to suggest how one might derive fundamental physics from neutral monism. Thus, starting with two axioms grounded in our characterization of neutral monism, we will sketch out a derivation of and explanation for some key features of relativity and quantum mechanics that suggest a unity between those two theories that is generally unappreciated. Our mode of explanation throughout will be of the principle as opposed to constructive variety in something like Einstein’s sense of those terms. We will argue throughout that a bias towards property dualism and a bias toward reductive dynamical and constructive explanation lead to the hard problem and the explanatory gap in consciousness studies, and lead to serious unresolved problems in fundamental physics, such as the measurement problem and the mystery of entanglement in quantum mechanics and lack of progress in producing an empirically well-grounded theory of quantum gravity. We hope to show that given our take on neutral monism and all that follows from it, the aforementioned problems can be satisfactorily resolved leaving us with a far more intuitive and commonsense model of the relationship between conscious experience and physics. Full article

(This article belongs to the Special Issue Models of Consciousness)

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31 pages, 2293 KiB

Open AccessArticle

Sentience and the Origins of Consciousness: From Cartesian Duality to Markovian Monism

by Karl J. Friston, Wanja Wiese and J. Allan Hobson

Entropy 2020, 22(5), 516; https://doi.org/10.3390/e22050516 - 30 Apr 2020

Cited by 152 | Viewed by 27646

Abstract

This essay addresses Cartesian duality and how its implicit dialectic might be repaired using physics and information theory. Our agenda is to describe a key distinction in the physical sciences that may provide a foundation for the distinction between mind and matter, and between sentient and intentional systems. From this perspective, it becomes tenable to talk about the physics of sentience and ‘forces’ that underwrite our beliefs (in the sense of probability distributions represented by our internal states), which may ground our mental states and consciousness. We will refer to this view as Markovian monism, which entails two claims: (1) fundamentally, there is only one type of thing and only one type of irreducible property (hence monism). (2) All systems possessing a Markov blanket have properties that are relevant for understanding the mind and consciousness: if such systems have mental properties, then they have them partly by virtue of possessing a Markov blanket (hence Markovian). Markovian monism rests upon the information geometry of random dynamic systems. In brief, the information geometry induced in any system—whose internal states can be distinguished from external states—must acquire a dual aspect. This dual aspect concerns the (intrinsic) information geometry of the probabilistic evolution of internal states and a separate (extrinsic) information geometry of probabilistic beliefs about external states that are parameterised by internal states. We call these intrinsic (i.e., mechanical, or state-based) and extrinsic (i.e., Markovian, or belief-based) information geometries, respectively. Although these mathematical notions may sound complicated, they are fairly straightforward to handle, and may offer a means through which to frame the origins of consciousness. Full article

(This article belongs to the Special Issue Models of Consciousness)

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23 pages, 605 KiB

Open AccessArticle

Fact, Fiction, and Fitness

by Chetan Prakash, Chris Fields, Donald D. Hoffman, Robert Prentner and Manish Singh

Entropy 2020, 22(5), 514; https://doi.org/10.3390/e22050514 - 30 Apr 2020

Cited by 37 | Viewed by 13643

Abstract

A theory of consciousness, whatever else it may do, must address the structure of experience. Our perceptual experiences are richly structured. Simply seeing a red apple, swaying between green leaves on a stout tree, involves symmetries, geometries, orders, topologies, and algebras of events. Are these structures also present in the world, fully independent of their observation? Perceptual theorists of many persuasions—from computational to radical embodied—say yes: perception veridically presents to observers structures that exist in an observer-independent world; and it does so because natural selection shapes perceptual systems to be increasingly veridical. Here we study four structures: total orders, permutation groups, cyclic groups, and measurable spaces. We ask whether the payoff functions that drive evolution by natural selection are homomorphisms of these structures. We prove, in each case, that generically the answer is no: as the number of world states and payoff values go to infinity, the probability that a payoff function is a homomorphism goes to zero. We conclude that natural selection almost surely shapes perceptions of these structures to be non-veridical. This is consistent with the interface theory of perception, which claims that natural selection shapes perceptual systems not to provide veridical perceptions, but to serve as species-specific interfaces that guide adaptive behavior. Our results present a constraint for any theory of consciousness which assumes that structure in perceptual experience is shaped by natural selection. Full article

(This article belongs to the Special Issue Models of Consciousness)

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11 pages, 238 KiB

Open AccessArticle

Human Creativity and Consciousness: Unintended Consequences of the Brain’s Extraordinary Energy Efficiency?

by Tim Palmer

Entropy 2020, 22(3), 281; https://doi.org/10.3390/e22030281 - 29 Feb 2020

Cited by 13 | Viewed by 6780

Abstract

It is proposed that both human creativity and human consciousness are (unintended) consequences of the human brain’s extraordinary energy efficiency. The topics of creativity and consciousness are treated separately, though have a common sub-structure. It is argued that creativity arises from a synergy between two cognitive modes of the human brain (which broadly coincide with Kahneman’s Systems 1 and 2). In the first, available energy is spread across a relatively large network of neurons, many of which are small enough to be susceptible to thermal (ultimately quantum decoherent) noise. In the second, available energy is focussed on a smaller subset of larger neurons whose action is deterministic. Possible implications for creative computing in silicon are discussed. Starting with a discussion of the concept of free will, the notion of consciousness is defined in terms of an awareness of what are perceived to be nearby counterfactual worlds in state space. It is argued that such awareness arises from an interplay between memories on the one hand, and quantum physical mechanisms (where, unlike in classical physics, nearby counterfactual worlds play an indispensable dynamical role) in the ion channels of neural networks, on the other. As with the brain’s susceptibility to noise, it is argued that in situations where quantum physics plays a role in the brain, it does so for reasons of energy efficiency. As an illustration of this definition of consciousness, a novel proposal is outlined as to why quantum entanglement appears to be so counter-intuitive. Full article

(This article belongs to the Special Issue Models of Consciousness)

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10 pages, 2224 KiB

Open AccessConcept Paper

Ecological Clues to the Nature of Consciousness

by Robert E. Ulanowicz

Entropy 2020, 22(6), 611; https://doi.org/10.3390/e22060611 - 30 May 2020

Cited by 1 | Viewed by 3078

Abstract

Some dynamics associated with consciousness are shared by other complex macroscopic living systems. For example, autocatalysis, an active agency in ecosystems, imparts to them a centripetality, the ability to attract resources that identifies the system as an agency apart from its surroundings. It is likely that autocatalysis in the central nervous system likewise gives rise to the phenomenon of selfhood, id or ego. Similarly, a coherence domain, as constituted in terms of complex bi-level coordination in ecosystems, stands as an analogy to the simultaneous access the mind has to assorted information available over different channels. The result is the feeling that various features of one’s surroundings are present to the individual all at once. Research on these phenomena in other fields may suggest empirical approaches to the study of consciousness in humans and other higher animals. Full article

(This article belongs to the Special Issue Models of Consciousness)

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