A mathematical framework using the graphical calculus of process theories (symmetric monoidal categories with Frobenius algebras) provides an ontologically neutral language to model aspects of consciousness. A toy example demonstrates how this axiomatic approach recovers features of conscious experience, including the distinction between external and internal subjective perspectives, the privacy or unreadability of personal subjective experience, and phenomenal unity—a key challenge for scientific studies of consciousness. These features emerge naturally from the compositional structure of the calculus.
Consciousness can be described using a mathematical language called process theory, which uses diagrams to represent how experiences combine. This approach treats consciousness as a compositional system, where basic elements combine to create complex experiences. The mathematical framework naturally explains several features of conscious experience, including the distinction between external and internal subjective experience, the privacy of personal experience, and phenomenal unity—how different sensations feel like they belong to one unified experience. A toy example demonstrates how this axiomatic approach recovers these features without needing to add them separately. The work suggests that these puzzling aspects of consciousness may arise naturally from the compositional structure of experience itself.