Sketches of a Mathematical Theory of Qualia

Explore a mathematical approach to defining qualia and developing a toy model of consciousness in this 20-minute conference talk from the Models of Consciousness Conferences. Delve into Pedro Resende's attempt to mathematically formulate C.I. Lewis's 1929 theory of qualia and concepts. Examine the basic principles that abstract the behavior of physical qualia-detecting devices, such as animal brains. Discover how the proposed space of qualia is constructed as a topological space with additional algebraic structure, forming a stably Gelfand quantale. Investigate the conceptual consequences, including the emergence of "stable observers" and their relation to space perception. Explore the logical versions of quantum superposition and complementarity that arise from this model. Learn about the mathematical connection to quantum theory through operator algebras and how the space of qualia can be interpreted as an algebraic and topological model of quantum measurements.

Intro
What is qualia
qualia form a set
structure
logic
fuzzy sets
qualia and concepts
geometric logic
sober spaces
quantal
binary joints
quantum superposition
logical superpositions
sister algebra
spin case
partial isometry
embedded pseudogroups
systems of symmetries
qualia compositions
mappings
conclusion
intersubjectivity