scholarly journals Mathematics and the brain –a category theoretic approach to go beyond the neural correlates of consciousness

2019 ◽  
Author(s):  
Georg Northoff ◽  
Naotsugu Tsuchiya ◽  
Hayato Saigo
Keyword(s):  
Information Theory ◽  
Category Theory ◽  
Neural Correlates ◽  
Spatial Theory ◽  
Neural Correlates Of Consciousness ◽  
Neuronal Mechanisms ◽  
Mathematical Formalization ◽  
The Relationship ◽  
Integrated Information Theory ◽  
Integrated Information

AbstractConsciousness is a central issue in cognitive neuroscience. To explain the relationship between consciousness and its neural correlates, various theories have been proposed. We still lack a formal framework that can address the nature of the relationship between consciousness and its physical substrates though. Here, 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 including (i) category; (ii) inclusion functor and expansion functor; and (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 temporo-spatial theory of consciousness (TTC). These theories concern the structural relationships among structures of physical substrates and subjective experiences. The three CT-based concepts, introduced in this paper, unravel some basic issues in our search for the NCC; while addressing the same questions, we show that IIT and TTC provide different albeit complementary answers. Importantly, our account suggests that we need to go beyond a traditional concept of NCC including both content-specific and full NCC. We need to shift our focus from the relationship between “one” neuronal and “one” phenomenal state to the relationship between a structure of neural states and a structure of phenomenal states. We conclude that CT unravels and highlights basic questions about the NCC in general which needs to be met and addressed by any future neuroscientific theory of consciousness.Author summaryNeuroscience has made considerable progress in uncovering the neural correlates of consciousness (NCC). At the same time, recent studies demonstrated the complexity of the neuronal mechanisms underlying consciousness. To make further progress in the neuroscience of consciousness, we need proper mathematical formalization of the neuronal mechanisms potentially underlying consciousness. Providing a first tentative attempt, our paper addresses both by (i) pointing out the specific problems of and proposing a new approach to go beyond the traditional approach of the neural correlates of consciousness, and (ii) by recruiting a recently popular mathematical formalization, category theory (CT). With CT, we provide mathematical formalization of the broader neural correlates of consciousness by its application to two of the major theories, integrated information theory (IIT) and temporo-spatial theory of consciousness (TTC). Together, our CT-based mathematical formalization of the neural correlates of consciousness including its specification in the terms of IIT and TTC allows to go beyond the current concept of NCC in both mathematical and neural terms.

scholarly journals On the dangers of conflating strong and weak versions of a theory of consciousness

2020 ◽  
Vol 1 (II) ◽  
Author(s):  
Matthias Michel ◽  
Hakwan Lau
Keyword(s):  
Information Theory ◽  
Limbic System ◽  
Neural Correlates ◽  
Neural Correlates Of Consciousness ◽  
Sensory Cortices ◽  
Integrated Information Theory ◽  
Integrated Information

Some proponents of the Integrated Information Theory (IIT) of consciousness profess strong views on the Neural Correlates of Consciousness (NCC), namely that large swathes of the neocortex, the cerebellum, at least some sensory cortices, and the so-called limbic system are all not essential for any form of conscious experiences. We argue that this connection is not incidental. Conflation between strong and weak versions of the theory has led these researchers to adopt definitions of NCC that are inconsistent with their own previous definitions, inadvertently betraying the promises of an otherwise fruitful empirical endeavour.

scholarly journals On the dangers of conflating strong and weak versions of a theory of consciousness

2019 ◽  
Author(s):  
Hakwan Lau ◽  
Matthias Michel
Keyword(s):  
Information Theory ◽  
Limbic System ◽  
Neural Correlates ◽  
Neural Correlates Of Consciousness ◽  
Sensory Cortices ◽  
Integrated Information Theory ◽  
Integrated Information

Some proponents of the Integrated Information Theory (IIT) of consciousness profess strong views on the Neural Correlates of Consciousness (NCC), namely that large swathes of the neocortex, the cerebellum, at least some sensory cortices, and the so-called limbic system are all not essential for any form of conscious experiences. We argue that this connection is not incidental. Conflation between strong and weak versions of the theory has led these researchers to adopt definitions of NCC that are inconsistent with their own previous definitions, inadvertently betraying the promises of an otherwise fruitful empirical endeavour.

scholarly journals Exclusion and Underdetermined Qualia

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 405 ◽  
Author(s):  
Kyumin Moon
Keyword(s):  
Information Theory ◽  
Theoretical Foundation ◽  
Practical Application ◽  
Scientific Content ◽  
Physical Systems ◽  
Theoretical Structure ◽  
The Relationship ◽  
Integrated Information Theory ◽  
Integrated Information

Integrated information theory (IIT) asserts that both the level and the quality of consciousness can be explained by the ability of physical systems to integrate information. Although the scientific content and empirical prospects of IIT have attracted interest, this paper focuses on another aspect of IIT, its unique theoretical structure, which relates the phenomenological axioms with the ontological postulates. In particular, the relationship between the exclusion axiom and the exclusion postulate is unclear. Moreover, the exclusion postulate leads to a serious problem in IIT: the quale underdetermination problem. Therefore, in this paper, I will explore answers to the following three questions: (1) how does the exclusion axiom lead to the exclusion postulate? (2) How does the exclusion postulate cause the qualia underdetermination problem? (3) Is there a solution to this problem? I will provide proposals and arguments for each question. If successful, IIT can be confirmed with respect to, not only its theoretical foundation, but also its practical application.

scholarly journals Entropic Integrated Information Theory-Theory of Consciousness

2020 ◽  
Author(s):  
Siddharth Sharma
Keyword(s):  
Information Theory ◽  
Distance Function ◽  
Theory Theory ◽  
Conceptual Information ◽  
Information Distance ◽  
And Topology ◽  
Relationship Of ◽  
The Relationship ◽  
Integrated Information Theory ◽  
Integrated Information

In this paper I am going to give a mathematical theory of Integrated Information Theory, using entropy as measure of information and hence, as the information distance function. Also, we will consider a set, whose open subsets are mechanisms and topology is the system, we use these two modification in the structure of Integrated Information Theory [2] and Quantum Integrated Information theory [3], to define Entropic Integrated Information Theory, we will also justify our claims to use why entropy should be use as a measure of cause/effect information and as information distance function using [1]. We will also see the relationship of entanglement with concept and conceptual information. This paper is an attempt to binds consciousness, quantum information, entanglement and quantum mechanics together.

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

Entropy ◽  
2019 ◽  
Vol 21 (12) ◽  
pp. 1234 ◽  
Author(s):  
Georg Northoff ◽  
Naotsugu Tsuchiya ◽  
Hayato Saigo
Keyword(s):  
Natural Transformation ◽  
Neural Substrates ◽  
Neural Correlates ◽  
Mathematical Framework ◽  
Mathematical Concepts ◽  
Neural Correlates Of Consciousness ◽  
Formal Framework ◽  
The Relationship ◽  
The Brain ◽  
Integrated Information Theory

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.

scholarly journals Awareness and integrated information theory identify plant meristems as sites of conscious activity

PROTOPLASMA ◽  
2021 ◽  
Author(s):  
Anthony Trewavas
Keyword(s):  
Information Theory ◽  
Nervous System ◽  
Complex Networks ◽  
Environmental Changes ◽  
Biological Function ◽  
Human Consciousness ◽  
Extrinsic Information ◽  
Integrated Information Theory ◽  
Conscious Activity ◽  
Integrated Information

AbstractLacking an anatomical brain/nervous system, it is assumed plants are not conscious. The biological function of consciousness is an input to behaviour; it is adaptive (subject to selection) and based on information. Complex language makes human consciousness unique. Consciousness is equated to awareness. All organisms are aware of their surroundings, modifying their behaviour to improve survival. Awareness requires assessment too. The mechanisms of animal assessment are neural while molecular and electrical in plants. Awareness of plants being also consciousness may resolve controversy. The integrated information theory (IIT), a leading theory of consciousness, is also blind to brains, nerves and synapses. The integrated information theory indicates plant awareness involves information of two kinds: (1) communicative, extrinsic information as a result of the perception of environmental changes and (2) integrated intrinsic information located in the shoot and root meristems and possibly cambium. The combination of information constructs an information nexus in the meristems leading to assessment and behaviour. The interpretation of integrated information in meristems probably involves the complex networks built around [Ca2+]i that also enable plant learning, memory and intelligent activities. A mature plant contains a large number of conjoined, conscious or aware, meristems possibly unique in the living kingdom.

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