Integrated Information Theory 4.0 (IIT) is one of the leading frameworks in the neuroscience of consciousness (Consortium et al., 2023; Seth and Bayne, 2022; Signorelli et al., 2021). It aims to explain consciousness by mathematically formalizing its relation to cause-effect power and existence, while employing computational tools to investigate this experimentally (Zaeemzadeh and Tononi, 2024; Albantakis et al., 2023; Ellia et al., 2021). In principle, IIT can be used to assess both the level and content of consciousness in any physical system, such as the brain of a comatose patient or under anesthesia (Albantakis et al., 2023; Tononi et al., 2016).

More specifically, IIT conceives consciousness as an intrinsic structure of cause-effect powers, proposing that any conscious system exists for itself as a maximally unitary whole, irreducible to its parts (Albantakis et al., 2023; Ellia et al., 2021). This is mathematically formalized and computationally analyzed in terms of several measures of “integrated information.” In this article, we focus specifically on maximal system integrated information (φs*). This is used by IIT to identify, among a set of candidate systems, the one(s) that supports consciousness, and hence “exists for itself” subjectively and irreducibly. In contrast, according to IIT's assumptions, systems that do not specify φs*, at best, only “exist” from the perspective of another conscious entity, and hence do not “truly exist” (Albantakis et al., 2023; Koch, 2024; Tononi et al., 2022). In this way, IIT's measure of φs* is conceptually tied to both consciousness and an absolute, intrinsic form of existence, thus providing a computational neuroscience framework to quantitatively address questions related to both consciousness and ontology (i.e., about existence) that have been relegated to centuries of endless philosophical debates. At the same time, we acknowledge that, unlike familiar physical frameworks (like classical mechanics or thermodynamics) which can be introduced at progressive levels of mathematical detail and complexity (e.g., from F = ma to more advanced vectorial formulations), IIT's formalism remains comparatively opaque and harder to grasp.

Nevertheless, IIT still holds the potential to advance our understanding of questions related to ontology and consciousness through mathematical and computational means. But this potential is hindered by some key ontological assumptions of IIT, which lead to a problematic conceptual interpretation of its mathematical formalism, computational simulation results, and hypothetical scenarios allowed by the theory (Cea et al., 2024b,a, 2023). This underscores the crucial role that conceptual interpretation plays in scientific theories employing mathematical formalisms. History shows that reinterpreting pre-existing formalisms can be crucial for scientific advancement. For example, non-Euclidean geometry, developed by Gauss and later generalized by Riemann into higher-dimensional spaces, was conceptually reinterpreted by Einstein in his general relativity to describe the curvature of spacetime, addressing the limitations of Newtonian gravity, including its assumption of instantaneous information transfer in gravitational fields (Renn, 2007; Torretti, 1996). While our aims are far more modest and we are not comparing our work to Einstein's monumental achievements, reconsidering IIT's mathematical formalism from a new conceptual perspective might help address current limitations and enhance its explanatory power concerning the relationship between brain activity, consciousness, and ultimately, the concept of existence.

In the following, we first introduce the main principles of IIT (Section 2), focusing on the mathematical formalization of the theory's proposed marker of intrinsic, conscious existence (i.e., maximal system integrated information φs∗, and IIT's associated conceptual interpretation based on the ontological principles of (i) being, (ii) true existence, (iii) maximal existence, and (iv) “Great Divide of Being.” Next (Section 3), we briefly explain why these ontological assumptions are troublesome and motivate revision. Then (Section 4), we propose specific amendments to these ontological assumptions to improve the theory's overall theoretical robustness and thus, its capacity to address issues about consciousness and existence from a computational neuroscience perspective. We end with concluding remarks and propose directions for future research (Section 5).

Grounded in the purportedly essential properties of experience (i.e., the “phenomenal axioms”), IIT proposes six “postulates of physical existence,” which, according to the theory, define the necessary and sufficient conditions for any physical substrate to instantiate consciousness. In line with IIT's Principle of Being (PB), which states that “to be is to have cause–effect power” (Albantakis et al., 2023, p. 11), these postulates are framed in terms of cause-effect power that must satisfy: (i) existence, (ii) intrinsicality, (iii) information, (iv) integration, (v) exclusion, and (vi) composition.

The theory then mathematically formalizes these causal-physical postulates and applies them to simulated neural networks (i.e., candidate substrates/systems).¹ As anticipated, we will focus on maximal system integrated information φs*, which is based on system integrated information φ_s, a quantity that computes the cause-effect power of a system as an irreducible whole (Albantakis et al., 2023; Marshall et al., 2023).²

Mathematically, φ_s is computed as the minimum between a substrate's integrated cause information (φ_c), and integrated effect information (φ_e), according to the formalism (Albantakis et al., 2023, p. 17, Equations 19–21):

While φ_c and φ_e are computed as follows:

Integrated effect information (φ_e):

Integrated cause information (φ_c):

Both φ_c and φ_e quantify the difference that a partition θ of the system makes, with respect to the probability with which the entire unpartitioned system specifies its past/cause state sc′ (for φ_c), and its future/effect state se′ (for φ_e), given its current state s. The greater the cause/effect probabilities pe(se′|s) and pc←(sc′|s) specified by the unpartitioned system, and the greater the difference when partitioned (evaluated by the logarithmic terms), the greater the integrated cause/effect information, and hence, its overall φ_s.³

Given that IIT endorses the principle of maximal existence (PME), which posits that “what exists is what exists the most” (Albantakis et al., 2023, p. 11), the complex (i.e., consciousness substrate) is identified as the subset of interconnected units within a universe U_k with maximal system integrated information (φs*), as formalized below (Albantakis et al., 2023, p. 19, Equation 24):

where U_k represents the set of units available at iteration k, and S denotes a candidate subset. The subset achieving the maximum value, φs*, is selected as the complex for that iteration, consistent with the PME. Iteratively, once a complex is identified, its units are removed from the universe U_k, and the search continues within the remaining units to identify the next, non-overlapping, maximal subset. This process ensures that at the end of the iterative search, “overlapping substrates with lower φ_s are thus excluded from existence” (Albantakis et al., 2023, p. 18). Crucially, according to IIT's ontological interpretation, this “exclusion from existence” is literal: systems that don't specify maximal φ_s (i.e., φs*) don't exist “for themselves” in the irrefutable, self-evidencing, experiential sense; and hence, according to IIT, do not truly exist. Thus, only maximal φ_s complexes truly exist, as they exist for themselves as subjective experiences (Tononi et al., 2022; Albantakis et al., 2023; Koch, 2024).⁴

Accordingly, IIT assumes what Cea et al. (2023) call IIT's principle of true existence, namely that “only phenomenal existence is true existence” (p. 4), as well as an eliminative stance that denies mind-independent existence to all physical entities that do not maximize φ_s and hence are non-conscious. This is closely related to IIT's “Great Divide of Being” (Koch, 2024; Tononi et al., 2022; Tononi, 2017), which is “the divide between what truly exists in an absolute sense, in and of itself—namely conscious, intrinsic entities—and what only exist in a relative sense, for something else” (Tononi et al., 2022, p. 8). This entails that familiar physical objects that do not instantiate φs*, and hence are non-conscious, like “bodies and organs, tables and rocks. . . do not truly exist” (Tononi et al., 2022, p. 8, italics added).⁵ In other words, since our bodies presumably do not specify maximal φ_s (i.e., φs*) and therefore do not qualify as additional substrates of consciousness besides the main complex in our brains, IIT's ontological interpretation implies that our own bodies do not truly exist. At best, they merely exist as objects for some consciousness observing them: “since my body is a superset of my true PSC (i.e., neural complex), it is excluded from it—relegated to the realm of entities that only exist relatively, for an observer” (Tononi et al., 2022, p. 8).

In previous works, we have examined the problematic implications of these radical assumptions in detail (Cea et al., 2024a,b,c, 2023; Signorelli et al., 2023). Here, we will briefly introduce them and direct the reader to that literature for further details. First, IIT's ontological commitments create an explanatory tension with both common neuroscientific practice and IIT's own declared goal of explaining consciousness in physical terms: why attempt to explain consciousness in neuroscientific terms if it is considered ontologically primitive, while, in contrast, any non-conscious physical entity is deemed mind-dependent?(Signorelli et al., 2023). Second, IIT's ontology seems to entail that truly existing, conscious systems, can (i) be eliminated from existence solely by altering external, non-existent entities; (ii) be engineered out of nothing; and (iii) either phylogenetically originate from nothing or have existed since the beginning of the universe (Cea et al., 2024b,a).

Now, IIT could prima facie address these issues by invoking an “ontological dust” (Tononi et al., 2022) ultimately composed of minimally conscious monads (indivisible units) (Hendren et al., 2024). However, there are several problems with the latter (Cea et al., 2024a,c). First, there are compelling reasons to think of a deep link between life and consciousness (Cea and Martínez-Pernía, 2023; Damasio and Damasio, 2024; Seth, 2024; Thompson, 2007), and thus against the idea of non-living, minimally conscious, indivisible particles of intrinsic existence. Second, the notion of monads seems to contradict IIT's own formalism (Cea et al., 2024c), which requires–to apply the integration postulate–that valid partitions of a system into at least two non-overlapping, non-empty parts, are possible (Albantakis et al., 2023). Otherwise, φ_s is not computable as such, but has to be replaced in practice by the measure of intrinsic information, which is insufficient for consciousness according to IIT's postulates (Cea et al., 2024c).

In sum, IIT's Great Divide of Being, along with its principles of true existence and eliminativism regarding non-conscious entities, raises several important issues.⁶ To address these concerns and align better with neuroscience practice, we propose minimal conceptual adjustments for IIT to adopt causal-physical realism, which asserts that non-φs*, non-conscious systems may also truly exist if they have cause-effect power. This conceptual revision allows a reinterpretation of IIT's formalism such that maximal φ_s (i.e., φs*) is no longer the exclusionary marker of a truly existent entity, but just the marker of consciousness, while causally powerful non-conscious entities may also be acknowledged to exist.

In the following, we propose that for IIT to endorse causal-physical realism and overcome the many problems we briefly sketched in the previous section, the theory should: (i) reject the principle of true existence (PTE; and associated Great Divide of Being) (Section 4.1), (ii) modify the principle of maximal existence (PME) (Section 4.2), and (iii) endorse a realistic, not merely operational, principle of being (PB) (Section 4.3).

In sum, our analysis suggests that IIT needs to endorse causal-physical realism, and to achieve that, (i) reject the principle of true existence (PTE) (and associated Great Divide of Being); (ii) endorse the revised principle of maximal conscious existence: “what exists consciously is what holistically exists the most” (PMCE); and (iii) endorse the revised principle of realistic being (“PRB”), according to which “to truly exist is to have causal power.” This would allow IIT theorists to pursue their current neuroscientific methodology and computational framework to find the physical substrate of consciousness (i.e., complex) and unfold its cause-effect structure, without conceptually entailing the rejection of the mind-independent, genuine existence of the non-conscious parts of their own brains and bodies.

Future theoretical research should assess the types of entities allowed by IIT's formalism, once the “Great Divide of Being” is overcome. For instance, what is the ontological difference between entities that only specify positive values of intrinsic information but zero system integrated information, compared to entities that do specify positive values of the latter? Presumably, both exist in virtue of having cause-effect power, but only the latter present causal emergence (Hoel et al., 2013; Mediano et al., 2022; Hoel et al., 2016).

Additionally, future research could explore IIT's potential to integrate theoretical insights and empirical findings from embodied approaches, which propose that the non-neural body, far from “existing” solely from the perspective of the conscious brain, is structurally and dynamically intertwined with it (Thompson and Cosmelli, 2012; Thompson and Varela, 2001) and fundamental to understanding both the origins of our mathematical capacities (Lakoff and Nunez, 2000) and the very feeling of existence at the root of all consciousness (Thompson and Cosmelli, 2012; Seth, 2021, 2024; Damasio and Damasio, 2023, 2024; Thompson and Varela, 2001; Cea and Martínez-Pernía, 2023; Ratcliffe, 2020).