Phi-monads are conceptually problematic and mathematically undefined in Integrated Information Theory 4.0
Ignacio Cea, Niccolò Negro, Pedro A. M. Mediano, Camilo Miguel Signorelli
Summary
AI-generated from the abstractThe Integrated Information Theory (IIT) 4.0 defines minimal conscious entities called 'monads' as single-unit systems with maximal integrated information (phi_s*). This paper argues that IIT's own formalism cannot apply to monads because it requires any candidate substrate of consciousness to consist of at least two non-overlapping, non-empty, jointly exhaustive parts—the Plurality requirement. Monads violate this requirement, making the equations for calculating system integrated information undefined. The authors call for clarification or revision from IIT proponents regarding the status of phi-monads as ontologically fundamental building blocks and minimal substrates of consciousness.
Study at a glance
| Characteristics | Theoretical or philosophical paper |
|---|---|
| Key finding | Argues that IIT 4.0's formalism cannot be applied to monads because they violate the Plurality requirement, making the calculation of system integrated information undefined. |
Abstract
The Integrated Information Theory (IIT) 4.0 is an influential framework aiming to explain consciousness mathematically in terms of intrinsic existence, namely what exists for itself in a specific, maximally irreducible, structured form. IIT thus posits that the minimal substrates of consciousness are also the ultimate building blocks of what exists. These are called ‘monads’, and are defined as self-connected, single-unit systems purportedly specifying maximal values of IIT’s measure of conscious irreducible existence, namely system integrated information phi_s* (i.e., phi-monads). In this paper, we argue that IIT 4.0’s formalism cannot be applied to monads, thus threatening the theory’s own ontological ground. We show that IIT’s formalism requires that any candidate substrate of consciousness must be constituted by at least two non-overlapping, non-empty, and jointly exhaustive parts, which we refer to as the Plurality requirement. We then show that monads violate this requirement, which leads to serious mathematical and conceptual problems, since the equations needed to calculate system integrated information become undefined. Thus, our paper calls for urgent clarification and/or revision by IIT proponents concerning the status of phi-monads as ontologically fundamental building blocks and minimal substrates of consciousness.