In this paper, we propose a mathematical model of subjective experience in terms of classes of hierarchical geometries of representations (“n-awareness”). We first outline a general framework by recalling concepts from higher category theory, homotopy theory, and the theory of (infinity,1)-topoi. We then state three conjectures that enrich this framework. We first propose that the (infinity,1)-category of a geometric structure known as perfectoid diamond is an (infinity,1)-topos. In order to construct a topology on the (infinity,1)-category of diamonds we then propose (...) that topological localization, in the sense of Grothendieck-Rezk-Lurie (infinity,1)-topoi, extends to the (infinity,1)-category of diamonds. We provide a small-scale model using triangulated categories. Finally, our meta-model takes the form of Efimov K-theory of the (infinity,1)-category of perfectoid diamonds, which illustrates structural equivalences between the category of diamonds and subjective experience (i.e.its privacy, self-containedness, and self-reflexivity). Based on this, we investigate implications of the model. We posit a grammar (“n-declension”) for a novel language to express n-awareness, accompanied by a new temporal scheme (“n-time”). Our framework allows us to revisit old problems in the philosophy of time: how is change possible and what do we mean by simultaneity and coincidence? We also examine the notion of “self” within our framework. A new model of personal identity is introduced which resembles a categorical version of the “bundle theory”: selves are not substances in which properties inhere but (weakly) persistent moduli spaces in the K-theory of perfectoid diamonds. (shrink)

Context: The evolution of perceptual systems and hence of observers remains largely disconnected from the question of the emergence of classical objects and spacetime. This disconnection between the biosciences and physics impedes progress toward understanding the role of the “observer” in physical theory. Problem: In this article we consider the problem of how to understand objects and spacetime in observer-relative evolutionary terms. Method: We rely on a comparative analysis using multiple formal frameworks. Results: The eigenform construct of von Foerster is (...) compared to other formal representations of observer-environment interactions. Eigenforms are shown to be encoded on observer-environment interfaces and to encode fitness consequences of actions. Space and time are components of observational outcomes in this framework; it is suggested that spacetime constitutes an error-correcting code for fitness consequences. Implications: Our results contribute to an understanding of the world in which neither objects nor spacetime are observer-independent. Constructivist content: The eigenform concept of von Foerster is linked to the concepts of decoherence and holographic encoding from physics and the concept of fitness from evolutionary biology. (shrink)

In this paper we wish to raise the following question: which conceptual obstacles need to be overcome to arrive at a scientific and theoretical understanding of the mind? In the course of this examination, we shall encounter methodological and explanatory challenges and discuss them from the point of view of the philosophy of chemistry and quantum mechanics. This will eventually lead us to a discussion of emergence and metaphysics, thereby focusing on the status of objects. The question remains whether this (...) could be interpreted in terms of a re-description or dissolution of seemingly troubling problems in the philosophy of mind, or whether it further emphasizes the problematic: the ubiquitous and irreducible role of mind and consciousness in scientific activities. (shrink)

In this paper, we develop a mathematical model of awareness based on the idea of plurality. Instead of positing a singular principle, telos, or essence as noumenon, we model it as plurality accessible through multiple forms of awareness (“n-awareness”). In contrast to many other approaches, our model is committed to pluralist thinking. The noumenon is plural, and reality is neither reducible nor irreducible. Nothing dies out in meaning making. We begin by mathematizing the concept of awareness by appealing to the (...) mathematical formalism of higher category theory. The beauty of higher category theory lies in its universality. Pluralism is categorical. In particular, we model awareness using the theories of derived categories and (infinity, 1)-topoi which will give rise to our meta-language. We then posit a “grammar” (“n-declension”) which could express n-awareness, accompanied by a new temporal ontology (“n-time”). Our framework allows us to revisit old problems in the philosophy of time: how is change possible and what do we mean by simultaneity and coincidence? Another question which could be re-conceptualized in our model is one of soteriology related to this pluralism: what is a self in this context? A new model of “personal identity over time” is thus introduced. (shrink)

In this article, we look at the hard problem of consciousness from the perspective of process metaphysics. We thereby identify three problematic premises of the problem that pertain to the constitution of consciousness and its causal relation to the world. We argue for the necessity of re-thinking the corresponding phenomena in terms of internally-structured processes. The hard problem would then cease to be an insurmountable obstacle to a science of consciousness. Furthermore, this line of reasoning is shown to be continuous (...) with philosophical projects from the early 20th century that preceded the contemporary philosophy of mind. Specifically, we investigate the relationship of parts and wholes, and translate metaphysical problems of consciousness into mereological language. Despite this being a philosophical project, we frequently note and discuss links to the empirical sciences, in particular those of quantum mechanics, systems theory and the embodied cognition framework. (shrink)

This contribution discusses a materialist framework for addressing conscious experience. In the first part of the paper the structure of this framework is laid out. Several explananda of consciousness are identified that materialists should try to relate to an under- lying substrate by identity statements, reductions, or functional descriptions. Most important for giving a satisfactory explanation of consciousness are accounts of why these relations hold (e.g., by nomological necessity) or how they can be embedded in a part- whole ontology (mereology). (...) A way to achieve this is discussed in the second part of the paper. Drawing from the philosophy of science, the importance of model building is stressed. Analogies play a crucial role here. A position in the philosophy of mind for which analogies seem particularly important is panpsychism. The relation between analogies and arguments for panpsychism is studied systematically and with respect to historical examples. It will be argued that a particular class of analogies is important, not only for panpsychism, but for a science of consciousness as such. The two-step argument presented in favor of such analogies roughly reads: (i) some analogies are important for any kind of model in science, and (ii) such analogies must therefore not be neglected. In the philosophy of mind, those are identified to be structural ones. The article concludes with a formulation of research questions for the future. Emphasis is placed on the necessity to formalize the explananda of consciousness, as well as mereological and analogical arguments to arrive at a coherent concept of mind-matter relations. (shrink)

This perspective examines the role of chemistry and molecular biology for a science of consciousness. Opposed to the consensus view, we argue that the molecular organization of biological systems is key to arrive at a thorough understanding of the dynamics correlated to the phenomenology of consciousness in complex organisms. This is indicated by the fact that the molecular sciences either provide one or more mechanisms directly related to phenomenology or otherwise describe the dynamics of the underlying substrate. In addition, we (...) discuss substrate-independence in information-processing theories of consciousness and the issue of combination in panpsychist theories of consciousness, both from the angle of the molecular sciences. In any case, molecular details matter. (shrink)

In his book “Galileo’s Error”, Philip Goff lays out what he calls “foundations for a new science of consciousness”, which are decidedly anti-physicalist (panpsychist), motivated by a critique of Galileo’s distinction into knowable objective and unknowable subjective properties and Arthur Eddington’s argument for the limitation of purely structural (physical) knowledge. Here we outline an alternative theory, premised on the Interface Theory of Perception, that too subscribes to a “post-Galilean” research programme. However, interface theorists disagree along several lines. 1. They note (...) that Galileo’s distinction should be replaced by a truly non-dual account, referring to a difference of degree only. 2. They highly appreciate the role of mathematics, in particular when it comes to actually engage scientifically with consciousness. Some notable features of the interface theory are its skepticism towards our epistemic capacities and its rejection of the existence of a public, mind-independent reality. In addition, some interface theorists further employ a thin concept of “conscious agency” to ground their theory. The interface theory leaves open many of the problems of consciousness science (e.g. what is a “self”?) as questions for further (scientific, mathematical) research. (shrink)

The relationship between philosophy and research on artificial intelligence (AI) has been difficult since its beginning, with mutual misunderstanding and sometimes even hostility. By contrast, we show how an approach informed by both philosophy and AI can be productive. After reviewing some popular frameworks for computation and learning, we apply the AI methodology of “build it and see” to tackle the philosophical and psychological problem of characterizing perception as distinct from sensation. Our model comprises a network of very simple, but (...) interacting agents which have binary experiences of the “yes/no”-type and communicate their experiences with each other. When does such a network refer to a single agent instead of a distributed network of entities? We apply machine learning techniques to address the following related questions: i) how can the model explain stability of compound entities, and ii) how could the model implement a single task such as perceptual inference? We thereby find consistency with previous work on “interface” strategies from perception research. While this reflects some necessary conditions for the ascription of agency, we suggest that it is not sufficient. Here, AI research, if it is intended to contribute to conceptual understanding, would benefit from issues previously raised by philosophy. We thus conclude the article with a discussion of action-selection, the role of embodiment, and consciousness to make this more explicit. We conjecture that a combination of AI research and philosophy allows general principles of mind and being to emerge from a “quasi-empirical” investigation. (shrink)

We discuss the potential of applying category theory to the study of consciousness. We first review a recent proposal from the neurosciences of consciousness to illustrate the “correlational project”, using the integrated information theory of consciousness as an example. We then discuss some technical preliminaries related to categories and in particular to the notion of a functor, which carries the bulk of conceptual weight in many current discussions. We then look at possible payoffs of this project—getting to grips with the (...) hard problem, theory integration, and exploiting explanatory dualities—and discuss possible avenues for further research, stressing the need to better develop the categorical representation of consciousness, in particular its phenomenological structure. A better understanding of consciousness cannot be achieved by merely studying the physical brain. By contrast, the categorical treatment even suggests application beyond the domain of neuroscience, for example in computer science and artificial intelligence research, while also emphasizing the primacy of (phenomenal) experience. (shrink)

Mathematics has a long track record of refining the concepts by which we make sense of the world. For example, mathematics allows one to speak about different senses of "sameness", depending on the larger context. Phenomenology is the name of a philosophical discipline that tries to systematically investigate the first-personal perspective on reality and how it is constituted. Together, mathematics and phenomenology seem to be a good fit to derive statements about our experience that are, at the same time, well-defined, (...) precise, and significant to our inner lives. However, there are difficulties stemming from the fact that phenomenology deals with inherently subjective things. Phenomenological investigations seem to lose their appeal when trying to approach them in the clear-cut way afforded by mathematics. How to overcome this obstacle? We argue that the Arts play a special role in mediating between the precise statements of mathematics and the sometimes fuzzy nature of our experience. Mathematics and art are complementary ways to come to a comprehensive understanding of reality. (shrink)

A new philosophy of nature is urgently needed. The received ontological view, physicalism, is unable to account for experiential phenomena and in particular for consciousness in all its varieties. We shall outline the concept of experiencing which should figure as a new conceptual primitive in natural philosophy. Experiencing refers to a process which comprises the interaction of an agent with its world through action based on phenomenal experience. This process can be viewed under two different aspects. One regards the subjective (...) aspect of experiencing, the other one regards it in terms of physical objects. The first case illustrates the “what-it-is-likeness„ of experiencing, the second illustrates how experiencing gets “objectified„ in nature. We furthermore wish to delineate our concept of experiencing from the concept of (meta-cognitive) awareness. Scientific theories that explain how awareness comes about in sufficiently organized brains should respect the distinction between experiencing and awareness. We also sketch how experiencing could be related to theoretical biology in terms of information processing by organisms. Experiencing is non-exclusive; it refers to a primitive and a-personal natural process and not to a property possessed only by humans or other persons. (shrink)

Formal models lead beyond ordinary experience to abstractions such as black holes and quantum entanglement. Applying such models to experience itself makes it seem unfamiliar and even paradoxical. We suggest, however, that doing so also leads to insights. It shows, in particular, that the “view from nowhere” employed by the theorist is both essential and deeply paradoxical, and it suggests that experience has an unrecorded, non-reportable component in addition to its remembered, reportable component.

Bewusstsein äußert sich als System von Beziehungen. Unsere Welt entspricht einem Netzwerk von Akteuren und deren Verhältnissen. Gleichzeitig können wir Bewusstsein in unserer Wahrnehmung als Verweis auf eine Ganzheit erfahren – etwas, das wir in diesem Buch als Herausbildung eines Zeichens auffassen wollen. Die Aufgabe der Wissenschaften wird dann darin bestehen, dieses doppelte Erscheinen (einmal objektiv als System von Beziehungen, einmal subjektiv als Zeichen) zueinander in Relation zu setzen.

Open peer commentary on the article “Conflatingion with Empirical Observation: The False Mind-Matter Dichotomy” by Bernardo Kastrup. Upshot: Based on epistemological considerations, the author of the target article proposes an idealist solution to the mind-body problem. But is such a transition from epistemology to ontology justified? This commentary briefly asks about the historical motives underlying the dichotomy of mind/matter and argues that science requires metaphysical commitments. This gets illustrated with respect to some of the material mentioned at the end of (...) the target article. (shrink)