The objective of this paper is to show that non-constructive mathematics is incapable as a framework for research on consciousness. Indeed, we shall discuss how non-constructive mathematics is inconsistent with the physics of consciousness which deals with quantumness. This inconsistency implies the incapability of non-constructive mathematics to represent the free will of a conscious agent. Furthermore, we shall suggest Constructive mathematics (and topos theory which is one of its models) as an alternative framework to study consciousness. The pivotal role of the excluded middle law in our discussion will be addressed in detail.
The objective of this paper is to show that non-constructive mathematics is incapable as a framework for research on consciousness. Indeed, we shall discuss how non-constructive mathematics is inconsistent with the physics of consciousness which deals with quantumness. This inconsistency implies the incapability of non-constructive mathematics to represent the free will of a conscious agent. Furthermore, we shall suggest Constructive mathematics (and topos theory which is one of its models) as an alternative framework to study consciousness. The pivotal role of the excluded middle law in our discussion will be addressed in detail.
We argue that limitations arise when using non-constructive mathematics (NCM) as a foundation for quantum mechanics, since the Boolean logical substrate of NCM fits a distributive propositional structure, but fits less naturally into the non-distributive lattice of quantum propositions. We distinguish three logical structures relevant to this discussion: Boolean algebras (classical, distributive, complemented), Heyting algebras (constructive, distributive, not necessarily complemented), and orthomodular lattices (quantum, non-distributive). The linear structure of quantum state space is compatible with NCM, but the propositional structure of quantum mechanics forms a non-distributive lattice rather than a Boolean algebra. Topos theory, one of the models of constructive mathematics, offers a way forward: the Döring–Isham framework provides an explicit bridge—the daseinization map—from quantum propositions to a topos whose internal logic is intuitionistic. Although some topoi carry Boolean logic, in general, topoi are not constrained to it. We argue that this bridged framework is more suitable for the mathematical foundation of quantum mechanics than one that retains the law of excluded middle (LEM) without such a bridge. Our discussion centers on the pivotal role of the LEM.
The hard problem in consciousness is the problem of understanding how physical processes in the brain could give rise to subjective conscious experience. In this paper, I suggest that in order to understand the relationship between consciousness and the physical world, we need to probe deeply into the nature of physical reality. This leads us to quantum physics and to a second explanatory gap: that between quantum and classical reality. I will seek a philosophical framework that can address these two gaps simultaneously. Our analysis of quantum mechanics will naturally lead us to the notion of a hidden reality and to the postulate that consciousness is an integral component of this reality. The framework proposed in the paper provides the philosophical underpinnings for a theory of consciousness while satisfactorily resolving the interpretation problem in quantum mechanics without the need to alter its mathematical structure. I also discuss some implications for a scientific theory of consciousness.
Scientific investigation of the classic mind-body problem has failed to produce a viable theory. As McGinn puts it, We know that brains are the de facto causal basis of consciousness, but we have, it seems, no understanding whatever of how this can be. I propose that the obstruction is commitment to a physicalist ontology: It is not possible to obtain consciousness from unconscious ingredients. I propose instead the ontology of conscious realism: Consciousness and its contents are all that exists. Matter, brains, and space-time are among the contents of consciousness, dependent on it for their existence. For a conscious realist the mind-body problem is to show precisely how conscious agents construct the macroscopic and microscopic physical world. I propose a mathematically rigorous account of conscious agents and their dynamics, and of their construction of the physical world. In particular, I propose that the physical world is a species-specific user interface, and that quantum physics represents properties of the stable dynamics of conscious agents. Symmetries of these stable dynamics are the source of the symmetries studied in quantum physics. I present a concrete dynamics for pairs of conscious agents that exhibits SL(2,C) symmetry, and from this obtain a physical representation of the dynamics in terms of relativistic spin half particles. This representation allows one to canonically associate a discrete patch of Minkowski space-time to each such pair of conscious agents, and suggests that, at the smallest scale, space-time is discrete. This suggestion comports well with current approaches to quantum gravity.
Science is learning more about the brain activity necessary for consciousness, but has not identified any mechanisms for how it could actually arise through neural processes. Here I present ways to build consciousness into the mathematics of quantum mechanics for use in the growing area of quantum neurology. Quantum waves are not physical in the sense of forces acting on particles through cause and effect, and they are expressed using mathematical placeholders that do not have agreed-upon real-world representations. These can be used to represent consciousness. Quantum mechanics has shown how the traditional aspects of the physical world emerge from non-physical quantum information through a combination of mathematical, not causal, determinism, and stochastic interactions. The modeling methods here could help account for how the mental world could also emerge from information fields. Neural interactions for mental experiences are complex, so it is reasonable to expect that consciousness is an emergent property of neural networks. But emergent properties are not magic – they work through procedural mechanisms – in this case for how neural processes generate experiences. No steps for how consciousness could be manufactured in this way are apparent, and philosophers have strong arguments for such not being possible. An alternative is to model consciousness as part of quantum waves, so it is accessed, not created, by the brain. This is a form of neutral monism – the idea that the physical and mental worlds both come from a single underlying source – in this case quantum waves. The classical physical picture of particles and forces acting under cause and effect has developed into a belief system, not just a theory, and this has created difficulties in taking quantum mechanics itself at face value. The result has been the creation of numerous “interpretations” of quantum mechanics that seek to frame it within these philosophical presuppositions. The conceptual framework of Cartesian dualism provides a platform for analysis of the related philosophical issues of consciousness and of quantum mechanics itself.
Creating machines that are conscious is a long term objective of research in artificial intelligence. This paper look at this idea with new arguments from physics and logic. Observers have no place in classical physics, and although they play a role in measurement in quantum physics there is no explanation for their emergence within the framework. There is suggestion that consciousness, which is implicitly a property of the observer, is a consequence of the complexity of specific brain structures, but this is problematic because one associates free will with consciousness, which goes counter to causal closure of physics. Considering a nested physical system, we argue that even if the system were assumed to have agency, observers cannot exist within it. Since complex systems can be viewed in nested hierarchies, this constitutes a proof against consciousness as a product of complexity, for then we will have nested system of conscious agents. As the existence of consciousness in cognitive agents cannot be denied, the implication is that consciousness belongs to a dimension that is not physical and machine consciousness is unattainable. These ideas are used to take a fresh look at two well-known paradoxes of quantum theory that are important in quantum information theory.
In this paper, I propose a set of ideas to explain the phenomena of life and consciousness in the universe and their relation to the interpretation of quantum mechanics. Consciousness is described as a result of specific dynamical configurations of matter and fields aided by fundamental properties of nature proposed in this paper. First, I review the various theories of consciousness in current literature and come up with various hypotheses, definitions, and propositions to build a physical theory of consciousness. I introduce the concept of interaction binding of consciousness and discuss in detail how the brain gives rise to consciousness. I propose three sets of postulates on the physical foundations of consciousness from a quantum general relativistic background using the Quantum General Relativistic Framework, 5 proposals to understand time and reduction. A Quantum Reduction Free Will Equivalence Principle is discussed to link quantum reduction to conscious free will. I discuss the potential possibility of retrocausal effects on consciousness-influenced reduction probability. I discuss the concept of conscious being as a more general concept than conscious identity, as separate from conscious content, and its nature. I introduce the concept of classicum as an analog of the quantum, and discuss its relation to consciousness. I discuss mathematical measures to calculate the complexity of harmonic relational structures. I put these together in a set of propositions on the nature of consciousness and its relation to the nature of quantum phenomena. I discuss a mathematical model of interaction binding, and free will. I discuss theory and experiments to verify these