This paper presents Integrated Information Theory (IIT) 4.0. IIT aims to account for the properties of experience in physical (operational) terms. It identifies the essential properties of experience (axioms), infers the necessary and sufficient properties that its substrate must satisfy (postulates), and expresses them in mathematical terms. In principle, the postulates can be applied to any system of units in a state to determine whether it is conscious, to what degree, and in what way. IIT offers a parsimonious explanation of empirical evidence, makes testable predictions concerning both the presence and the quality of experience, and permits inferences and extrapolations. IIT 4.0 incorporates several developments of the past ten years, including a more accurate formulation of the axioms as postulates and mathematical expressions, the introduction of a unique measure of intrinsic information that is consistent with the postulates, and an explicit assessment of causal relations. By fully unfolding a system’s irreducible cause–effect power, the distinctions and relations specified by a substrate can account for the quality of experience.

Objective correlates—behavioral, functional, and neural—provide essential tools for the scientific study of consciousness. But reliance on these correlates should not lead to the ‘fallacy of misplaced objectivity’: the assumption that only objective properties should and can be accounted for objectively through science. Instead, what needs to be explained scientifically is what experience is intrinsically—its subjective properties—not just what we can do with it extrinsically. And it must be explained; otherwise the way experience feels would turn out to be magical rather than physical. We argue that it is possible to account for subjective properties objectively once we move beyond cognitive functions and realize what experience is and how it is structured. Drawing on integrated information theory, we show how an objective science of the subjective can account, in strictly physical terms, for both the essential properties of every experience and the specific properties that make particular experiences feel the way they do.

Integrated information theory (IIT) starts from consciousness itself and identifies a set of properties (axioms) that are true of every conceivable experience. The axioms are translated into a set of postulates about the substrate of consciousness (called a complex), which are then used to formulate a mathematical framework for assessing both the quality and quantity of experience. The explanatory identity proposed by IIT is that an experience is identical to the cause–effect structure unfolded from a maximally irreducible substrate (a $\mathsf{\Phi }$-structure). In this work we introduce a definition for the integrated information of a system (${\phi }_s$) that is based on the existence, intrinsicality, information, and integration postulates of IIT. We explore how notions of determinism, degeneracy, and fault lines in the connectivity impact system-integrated information. We then demonstrate how the proposed measure identifies complexes as systems, the ${\phi }_s$ of which is greater than the ${\phi }_s$ of any overlapping candidate systems.

Neuroscience has made remarkable advances in accounting for how the brain performs its various functions. Consciousness, too, is usually approached in functional terms: the goal is to understand how the brain represents information, accesses that information, and acts on it. While useful for prediction, this functional, information-processing approach leaves out the subjective structure of experience: it does not account for how experience feels. Here, we consider a simple model of how a “grid-like” network meant to resemble posterior cortical areas can represent spatial information and act on it to perform a simple “fixation” function. Using standard neuroscience tools, we show how the model represents topographically the retinal position of a stimulus and triggers eye muscles to fixate or follow it. Encoding, decoding, and tuning functions of model units illustrate the working of the model in a way that fully explains what the model does. However, these functional properties have nothing to say about the fact that a human fixating a stimulus would also “see” it—experience it at a location in space. Using the tools of Integrated Information Theory, we then show how the subjective properties of experienced space—its extendedness—can be accounted for in objective, neuroscientific terms by the “cause-effect structure” specified by the grid-like cortical area. By contrast, a “map-like” network without lateral connections, meant to resemble a pretectal circuit, is functionally equivalent to the grid-like system with respect to representation, action, and fixation but cannot account for the phenomenal properties of space.

The target article misrepresents the foundations of integrated information theory (IIT) and ignores many essential publications. It, thus, falls to this lead commentary to outline the axioms and postulates of IIT and correct major misconceptions. The commentary also explains why IIT starts from phenomenology and why it predicts that only select physical substrates can support consciousness. Finally, it highlights that IIT's account of experience – a cause–effect structure quantified by integrated information – has nothing to do with “information transfer.”