Philosophy and the Mind Sciences
January 30, 2026
Johannes Kleiner
The Newman problem is a fundamental problem that threatens to undermine structural assumptions and structural theories throughout philosophy and science. Here, we consider the problem in the context of consciousness science. We introduce and discuss the problem, and explain why it is detrimental not only to structuralist assumptions, but also to theories of consciousness, if left unconsidered....
2025
Johannes Kleiner
It is perhaps somewhat surprising, from an external point of view, that the scientifc study of consciousness, also known as consciousness science, comprises a host of mathematical models, methods, and questions.This is the case, on the one hand, because it builds on mathematical models and mathematical methods developed in other sciences, for example models of the brain, analysis techniques,...
arXiv Preprint Archive
March 6, 2024
Johannes Kleiner
Computational functionalism posits that consciousness is a computation. Here we show, perhaps surprisingly, that it cannot be a Turing computation. Rather, computational functionalism implies that consciousness is a novel type of computation that has recently been proposed by Geoffrey Hinton, called mortal computation.
Consciousness and Cognition
February 28, 2024
Johannes Kleiner
Recent activities in virtually all fields engaged in consciousness studies indicate early signs of a structural turn, where verbal descriptions or simple formalisations of conscious experiences are replaced by structural tools, most notably mathematical spaces. My goal here is to offer three comments that, in my opinion, are essential to avoid misunderstandings in these developments early on....
arXiv (Cornell University)
April 11, 2023
Johannes Kleiner, Tim A. Ludwig
We demonstrate that if consciousness is relevant for the temporal evolution of a system's states--that is, if it is dynamically relevant--then AI systems cannot be conscious. That is because AI systems run on CPUs, GPUs, TPUs or other processors which have been designed and verified to adhere to computational dynamics that systematically preclude or suppress deviations. The design and...
arXiv Preprint Archive
January 26, 2023
Johannes Kleiner, Tim A. Ludwig
In consciousness science, several promising approaches have been developed for how to represent conscious experience in terms of mathematical spaces and structures. What is missing, however, is an explicit definition of what a 'mathematical structure of conscious experience' is. Here, we propose such a definition. This definition provides a link between the abstract formal entities of...
Frontiers in Applied Mathematics and Statistics
June 4, 2021
Johannes Kleiner, Sean Tull
Integrated Information Theory is one of the leading models of consciousness. It aims to describe both the quality and quantity of the conscious experience of a physical system, such as the brain, in a particular state. In this contribution, we propound the mathematical structure of the theory, separating the essentials from auxiliary formal tools. We provide a definition of a generalized IIT...
Consciousness and Cognition
October 1, 2020
Johannes Kleiner
Recently, it has been claimed that Integrated Information Theory and other theories of its type cannot explain consciousness ("unfolding argument"). We unravel this argument mathematically and prove that the premises of the argument imply a much stronger result according to which the observed problem holds for almost all theories of consciousness. We find, however, that one of the premises is...
Entropy (Basel, Switzerland)
May 30, 2020
Johannes Kleiner
37 citations
In recent years, promising mathematical models have been proposed that aim to describe conscious experience and its relation to the physical domain. Whereas the axioms and metaphysical ideas of these theories have been carefully motivated, their mathematical formalism has not. In this article, we aim to remedy this situation. We give an account of what warrants mathematical representation of...
arXiv Preprint Archive
April 7, 2020
Johannes Kleiner, Erik Hoel
The search for a scientific theory of consciousness should result in theories that are falsifiable. However, here we show that falsification is especially problematic for theories of consciousness. We formally describe the standard experimental setup for testing these theories. Based on a theory's application to some physical system, such as the brain, testing requires comparing a theory's...