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.
Highlights
Because the discussion of all these approaches is beyond the scope of this paper, we focus on two of the major theories, the integrated information theory (IIT) and temporospatial theory of consciousness (TTC)
Here, we do not go into details of IIT and TTC and instead we focus on those aspects that are relevant within the present category theoretical approach
In this paper, we will focus on how IIT treats the category of N through an IIT functor and a possible IIT natural transformation and demonstrate that rigorous, yet complex, operations of IIT [53] can be reinterpreted through category theory (CT), which eventually offers a fresh and interesting insight on a potential reverse reductionistic approach in IIT
Summary
Consciousness has long been regarded as a mysterious phenomenon, and it has been mainly dealt with in philosophy. There have been sporadic attempts to apply mathematical tools to bridge the gap between the physical and the mental domains [29,30,31,32,33,34,35] Tools such as graph theory, topology, algebra, and set theory are not sufficient to deal with the problem of consciousness. Consciousness, which extend and go beyond the traditional concept of the NCC
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