Mathematics and the Brain: A Category Theoretical Approach to Go Beyond the Neural Correlates of Consciousness

A mathematical framework called category theory (CT) can formally define and study the relationship between consciousness and its neural substrates. CT uses concepts such as category, inclusion functor, expansion functor, and natural transformation, each mapped to specific features in the neural correlates of consciousness (NCC). Applying CT to integrated information theory (IIT) and the temporospatial theory of consciousness (TTC) shows that natural transformation reveals the need to go beyond NCC and raises questions that any future neuroscientific theory of consciousness must address.

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Abstract

Consciousness is a central issue in neuroscience, however, we still lack a formal framework that can address the nature of the relationship between consciousness and its physical substrates. In this review, we provide a novel mathematical framework of category theory (CT), in which we can define and study the sameness between different domains of phenomena such as consciousness and its neural substrates. CT was designed and developed to deal with the relationships between various domains of phenomena. We introduce three concepts of CT which include (i) category; (ii) inclusion functor and expansion functor; and, most importantly, (iii) natural transformation between the functors. Each of these mathematical concepts is related to specific features in the neural correlates of consciousness (NCC). In this novel framework, we will examine two of the major theories of consciousness, integrated information theory (IIT) of consciousness and temporospatial theory of consciousness (TTC). We conclude that CT, especially the application of the notion of natural transformation, highlights that we need to go beyond NCC and unravels questions that need to be addressed by any future neuroscientific theory of consciousness.