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The scientific study of consciousness has long been recognized as defying the borders of scientific disciplines. Joint efforts of philosophers, neuroscientists, physicists and computer scientists have advanced the field considerably in the past decades and resulted in a plethora of available data and numerous ...

The scientific study of consciousness has long been recognized as defying the borders of scientific disciplines. Joint efforts of philosophers, neuroscientists, physicists and computer scientists have advanced the field considerably in the past decades and resulted in a plethora of available data and numerous theoretical models.

However, what is currently missing is a comprehensive foundational framework that brings together mathematical and empirical approaches to consciousness, akin to the role that theoretical physics or computational biology plays in their respective disciplines. The goal of this Research Topic is to help bridge this gap by bringing together the growing number of researchers who are interested in formal and empirical approaches to the problem of consciousness. The underlying hope is that development of formal mathematical approaches can complement important experimental studies and vice-versa.

The following list of topics, far from being complete or exhaustive, is deliberately broad so as to give an impression of the general purpose of this research topic:

Formal Distinctions Between Models of Consciousness
Models of consciousness are hypotheses about how consciousness relates to the physical domain. Various different and competing models exist, for example Integrated Information Theory, Global Neuronal Workspace Theory, Predictive Processing Theory, Higher Order Theories or Orchestrated Objective Reduction Theory. Among other things, this research topic is intended to discuss mathematical structures as well as philosophical and empirical underpinnings of these models with the objective of highlighting similarities or differences between them. An important question is whether these various models are really adversarial or is there an underlying common framework behind them? How can theoretical and empirical tools be brought together to discern the scope of these models?

Mathematical Formalization of Experience and Qualia
Being hypotheses about consciousness and its relation to the physical domain, models of consciousness need to refer to both a formal description of a physical system and a formal description of experience. But what mathematical structure should the space of states of experience or qualia carry? How does this mathematical structure relate to philosophical conceptions of qualia? How does it represent the phenomenology of experience? In recent times, promising insights have emerged from the use of pure as well as applied mathematics in addressing the mind-matter relation. Methods coming from category theory, information theory, statistical physics, logic and geometry have been particularly useful in this regard. What is the current status and what are the prospects of research in this direction? Which new vistas exist, and how do these relate to cognitive, behavioral and philosophical insights about experience?

Empirical Approaches that Constrain Models of Consciousness
Numerous experiments in psychology and cognitive neuroscience have provided valuable constraints on the relation between experience and brain structure. This research topic intends to collate and analyze relevant phenomenological constraints that may serve as guiding principles for fine-tuning or falsifying theoretical approaches. In particular, what are the important cognitive and psychological paradigms that reveal phenomenological properties and structure of experience? Are there new promising experimental designs that may help validate or dismiss existing theories?

Philosophical Insights and Thought Experiments about the Metaphysical Origins of Consciousness
The scientific study of consciousness has its origins in philosophical questions, such as Thomas Nagel’s famous: “What it is like to be a bat?” and conceptualizations of the “hard problem” or the “explanatory gap”. This research topic intends to address how these, and other philosophical analyses relate to the mathematical structure of models of consciousness. Which constraints arise for model-building and how can the rich body of work in philosophy of mind be translated into theoretical models? This research topic also calls for new thought experiments that probe the metaphysical origins of consciousness, including the mind-matter relation. How do these philosophical analyses provide the conceptual framework for theoretical and empirical models?

Note from the Topic Editors: Selection Criteria for this Research Topic
This call for submissions is open to everyone. Kindly note however that only submissions that satisfy the following criteria can be considered as part of this Research Topic.
(If your work falls outside of these criteria, the Editorial Office invites the authors to consider submitting directly to the participating journals instead, outside of this Research Topic.)

i) The submission constitutes novel research contributions or a comprehensive review/perspective. Comments, re-submissions or minor modifications of previously published articles will not be considered.
ii) 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 considered, as other journals and Research Topics are already available to this end. Submissions bridging the gap between mathematical and philosophy/empirical approaches are especially welcome.
iii) 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.
iv) 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 as part of this Research Topic.
v) The submission needs to be comprehensible to anyone with a master's degree in mathematics or theoretical physics. We ask that non-trivial philosophical notions are introduced in a concise manner.

If you would like to contribute, you are cordially invited to submit an initial abstract prior to completing your paper. This will help us to give early feedback in case a submission does not fit the scope of the Research Topic.

We do realize that there is currently a large gap between mathematical approaches and philosophy of mind / empirical consciousness research. We sincerely hope that this Research Topic will help to start bridging this gap.

This Research Topic has been created in parallel to the Mathematical Consciousness Science online seminar series exploring the role of mathematics in the scientific study of consciousness.

The Topic Editors would like to express their profound gratitude to Ms. Joanna Szczotka for their valuable assistance in initiating this Research Topic and actively contributing to it.

Cover image (c) 2020. Created by Dr Johannes Kleiner based on Vincent van Gogh's "Almond Blossom".

Keywords: Mathematical and Empirical Foundations of Consciousness and Cognition, Theories of Consciousness, Dynamical Models of Brain and Cognition, Philosophy of Mind, Neural Correlates of Consciousness, Mathematical Consciousness Science

Important Note: All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.

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