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.
Highlights
Conscious experience and its relation to the physical domain have been studied by philosophers, theologians, and scientists over many centuries [1]
Great care has been taken to keep the mathematical structure of this formalism as general as possible and to provide operational justifications of all essential definitions, so as to ensure that the framework is compatible with all types of mathematical structure one would want to use in modeling consciousness, including category theory [11,26], information theory [27], or complex system approaches [28], among many others
Since the states that are accessible in the third-person perspective are physical states and the states that are accessible in the first-person perspective are aspects of experience, this implies that the dynamical variables of a formal model of consciousness are a subset of d= E×P, where E denotes the mathematical representation of conscious experience we have introduced above and where P denotes the state space of some physical theory TP
Summary
Conscious experience and its relation to the physical domain have been studied by philosophers, theologians, and scientists over many centuries [1]. Groundbreaking developments in neuroscience, cognitive psychology, and analytic philosophy lead to the emergence of a dedicated science of consciousness, whose aim is to develop a scientific account of conscious experience and its relation to the physical domain (e.g., brain processes). A model of consciousness is a hypothetical theory about how conscious experience and the physical domain relate [2]. Models of consciousness complement metaphysical theories of consciousness, such as the various forms of functionalism, identity theories, interactive dualisms, or neutral monisms. These theories are concerned primarily with ontological questions and address the general type of relation between consciousness and the physical domain
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