Entropy (Basel, Switzerland)
May 30, 2020
Johannes Kleiner
37 citations
Mathematical models of consciousness often lack a clear justification for their formal structure. This article provides that justification by examining what makes phenomenal experience suitable for mathematical representation. It derives a general mathematical framework grounded in the epistemic context of consciousness—specifically, the non-collatability of experience and the structure of phenomenal space. The framework shows how key characteristics of conscious experience imply particular mathematical structures, allowing theory-building to go beyond what standard philosophical methodology alone can achieve. The result is a formal foundation that can guide the development and evaluation of specific mathematical models of consciousness.
Philosophy and the Mind Sciences
January 30, 2026
Johannes Kleiner
The Newman problem threatens structural assumptions and theories across philosophy and science. In consciousness science, it undermines structuralist approaches and theories of consciousness if not properly addressed. However, when phenomenal spaces and mathematical structures of conscious experience are correctly understood, the Newman problem does not arise. Consciousness science must carefully choose which definition of structure to adopt; doing so makes the problem disappear.
arXiv (Cornell University)
April 11, 2023
Johannes Kleiner, Tim A. Ludwig
If consciousness influences how a system's states change over time—if it has dynamical relevance—then artificial intelligence systems cannot be conscious. This is because AI systems run on processors like CPUs, GPUs, and TPUs that are designed and verified to follow strict computational dynamics. This design and verification systematically prevent or suppress any deviations, including potential effects that consciousness would have on dynamics. Therefore, if consciousness were dynamically relevant, AI systems would be incapable of being conscious.
arXiv Preprint Archive
March 6, 2024
Johannes Kleiner
Computational functionalism holds that consciousness is a form of computation. This paper demonstrates that consciousness cannot be a Turing computation, but instead aligns with a type of computation proposed by Geoffrey Hinton called mortal computation.
Consciousness and Cognition
February 28, 2024
Johannes Kleiner
A structural turn is emerging across consciousness studies, replacing verbal descriptions of conscious experience with mathematical spaces and other structural tools. The author offers three essential comments to prevent early misunderstandings: metaphysical premises underlying structural approaches, the viability of structure-preserving mappings, and clarifying what a structure of conscious experience actually is. The piece also explains the great promises of structural methodologies and their potential impact on consciousness science.
arXiv Preprint Archive
January 26, 2023
Johannes Kleiner, Tim A. Ludwig
A definition is proposed for what a 'mathematical structure of conscious experience' is, linking abstract mathematical entities to the concrete aspects of conscious experience. This definition complements existing approaches that study quality spaces, qualia spaces, or phenomenal spaces. It offers a general method for identifying and investigating structures of conscious experience and may serve as a unifying framework for diverse approaches across fields. The work aims to provide a basis for developing a common formal language to study consciousness.
Frontiers in Applied Mathematics and Statistics
June 4, 2021
Johannes Kleiner, Sean Tull
Integrated Information Theory (IIT) is a leading model of consciousness that aims to describe both the quality and quantity of conscious experience in a physical system like the brain. This paper presents the mathematical structure of the theory, separating core principles from auxiliary tools. It provides a definition of a generalized IIT that includes both IIT 3.0 and Quantum IIT as special cases, offering an axiomatic foundation for future formal research and serving as an introduction for researchers with a formal background.
Consciousness and Cognition
October 1, 2020
Johannes Kleiner
A recent argument claimed that Integrated Information Theory and similar theories cannot explain consciousness (the 'unfolding argument'). A mathematical analysis proves that the argument's premises, if accepted, would imply the same problem for almost all theories of consciousness. However, one premise—that measures of brain activity cannot be used in empirical tests of consciousness theories—is unwarranted. When this premise is dropped, the argument no longer holds. Thus the unfolding argument is not valid.
arXiv Preprint Archive
April 7, 2020
Johannes Kleiner, Erik Hoel
Falsification, a cornerstone of scientific testing, is especially problematic for theories of consciousness. In the standard experimental setup, a theory's predicted experience (based on brain data) is compared with an inferred experience (based on report or behavior). If inference and prediction are independent, any minimally informative theory is automatically falsified—a dilemma for many current theories that rely on report to infer conscious experience. If inference and prediction are strictly dependent, the theory becomes unfalsifiable. The paper explores potential ways out of this dilemma, highlighting a fundamental challenge for empirical testing in consciousness research.