Half masked and half disfigured, how could its identity not be mistaken? For such is the portrait of integrated information theory (IIT) painted by the target article. Our main task here will, thus, be to sketch a picture of IIT that is at least recognizable (for a proper introduction, see Haun & Tononi [Reference Haun and Tononi2019]; Oizumi, Albantakis, & Tononi [Reference Oizumi, Albantakis and Tononi2014]; Tononi [Reference Tononi2015]), focusing on a few key points.Footnote ¹

IIT addresses consciousness starting not, as is usually done in neuroscience, from its behavioral, functional, or neural correlates, but from phenomenology – the existence of one's own experience, which is immediate and indubitable. IIT then identifies the properties of consciousness that are essential – immediate, indubitable, and true of every conceivable experience – namely intrinsicality, composition, information, integration, and exclusion (Fig. 1). These properties, which have always been at the core of IIT, were more recently codified as “axioms” (Oizumi et al., Reference Oizumi, Albantakis and Tononi2014; Tononi, Reference Tononi2012) because nothing can be more axiomatic as a starting point than what is true of every conceivable experience.

Fig. 1 The essential properties of experience (axioms of IIT).

Because the axioms capture properties that are essential, it should be obvious that none of them can be left out without destroying the whole edifice. Yet Merker et al. only consider information and integration, virtually ignore intrinsicality and composition, and dismiss exclusion by claiming (gratuitously) that it was added “ad hoc” to fix unpleasant consequences of information and integration. Not even Euclid's venerable geometry would survive without three of its five axioms, nor would physical theories without half the terms in the defining equations. Hence, this response must begin by restating the five axioms of IIT (adapted from Haun & Tononi [Reference Haun and Tononi2019]).

Intrinsicality means that every experience is subjective – it is for the subject of experience, from its own private, intrinsic perspective, rather than for something extrinsic to it. Using spatial experiences as an example, if I experience the sight of my bedroom, the canvas of phenomenal space is experienced by me, not by somebody else. Composition means that every experience is structured, being composed of phenomenal distinctions and relations. In the case of spatial experiences, distinctions can be taken as “spots” (areas of space of any size and shape), and their relations as the way spots connect, fuse, and include each other. Information means that every experience is the specific way it is. For example, the canvas of space may be homogeneous, or embossed by inhomogeneities such as a body, a book, a bed, in countless possible configurations. Integration means that every experience is unitary, being irreducible to separate components. Thus, the canvas of space cannot be reduced to a left side and a right side that are experienced independently – if it were so, there would be two independent consciousnesses rather than one. Finally, exclusion means that every experience is definite – it contains what it contains, neither less nor more. In the case of space, the canvas contains all the spots and relations it contains – not just the left or the right side, or just a single spot in the middle or in the periphery – but it does not extend beyond its borders, such as behind one's head. Importantly, these five essential properties are true of every conceivable experience, not just of spatial ones. They also delineate what must be accounted for by a satisfactory explanation of consciousness.

To provide an explanation for experience in physical terms, every phenomenal property must be accounted for by the causal properties of the physical substrate of consciousness (PSC). Therefore, the next step of IIT is to “translate” the essential phenomenal properties into essential physical properties (called “postulates”). In IIT, “physical” is defined in purely operational terms as cause–effect power – being able to take and make a difference – whether we are dealing with a Higgs boson, a stone, a computer, a body, or a brain. In principle, the cause–effect power of a physical system is characterized in full by its transition probability matrix (TPM) – how it responds to all possible perturbations of its state. From the TPM of a system, say, the one characterizing a portion of our cerebral cortex, we can then unfold all its causal properties and assess whether it satisfies the five essential properties required for a PSC. If so, unfolding yields a maximally irreducible cause–effect structure composed of causal distinctions and relations that capture all the physical properties of the PSC.

IIT then proposes its fundamental, explanatory identity, according to which the components of the cause–effect structure correspond one-to-one to the components of experience – to the quality of a specific experience. Thus, every content of an experience “here and now,” including not just space and objects, but also memories and expectations, correspond to sub-structures in a cause–effect structure. Furthermore, the quantity of experience – how much one exists phenomenally – is measured by the irreducibility Φ of the cause–effect structure.Footnote ²

The explanatory and predictive validity of IIT can be assessed by considering whether the PSC satisfies the five physical properties that the theory considers essential, but other regions do not. Moreover, the PSC should cease to satisfy these properties when consciousness vanishes in dreamless sleep or under anesthesia, as confirmed by studies explicitly designed to test this prediction of IIT with transcranial magnetic stimulation and electroencephalography (TMS-EEG) (Tononi, Boly, Massimini, & Koch, Reference Tononi, Boly, Massimini and Koch2016). The explanatory identity of IIT also predicts that the cause–effect structure unfolded from the PSC should account for the specific properties of specific experiences. For example, Haun and Tononi (Reference Haun and Tononi2019) demonstrate how the phenomenal properties that make space feel extended (reflexivity, connection, fusion, and inclusion) can be accounted for in the cause–effect structures unfolded from neural units with grid-like connectivity, as evident in topographically organized areas of posterior cortex. We encourage the reader to consult this paper because it represents the first attempt to apply IIT to account for the quality of experience from first principles. It also demonstrates IIT's explanatory and predictive power with respect to a large body of neurological evidence concerning the perception of space. Ironically, completely ignoring this account, Merker et al. single out “the geometries of visual space” as something that should one day be explained.Footnote ³

After this all-too-short summary of IIT, let us consider just some major ways in which Merker et al. make the theory unrecognizable by ignoring or misinterpreting the axioms. Let us briefly illustrate this by delving a bit deeper into the axiom of exclusion, whose sidelining leads to all kinds of erroneous inferences.

As stated above, exclusion means that every experience is definite – it contains what it contains, neither less nor more: For example, I experience the entire visual field, not just one half or any smaller (or larger) portion of it. Being definite is taken as an axiomatic property because, first, it is immediately given – I do not have to infer that my experience contains what it contains; it just does. Second, that an experience is definite is indubitable – an experience that contained, say, less than it contains, such as the left half of the visual field only, would simply be another experience that contains exactly what it contains, thus reaffirming the validity of the axiom. Finally, being definite is true of every conceivable experience.

As with all the other axioms, exclusion is translated in physical terms – namely cause–effect power. Accordingly, the PSC must have cause–effect power that is also definite, in the sense of having a border: Its cause–effect structure must be specified by a definite set of units – neither less nor more. The border is established by assessing which set of units unfolds into a cause–effect structure that is maximally irreducible, as measured by Φ = Φ^max. In IIT, Φ is the quantifier of existence (to exist, something must be irreducible to independent components), so ultimately the border of the PSC is defined by which set of units “exists the most” among competing sets.Footnote ⁴ But, if having Φ = Φ^max defines the set of units constituting the PSC, it also excludes any overlapping set having Φ < Φ^max.

A direct consequence of IIT is then that only maxima of Φ correspond to conscious entities (more or less conscious depending on their Φ value). This excludes all kinds of things Merker et al. erroneously list as IIT-conscious. For example, a society to which I belong cannot be conscious simply because I am conscious, which excludes from existence any superset that includes my PSC (no “group mind”). Digital computers cannot be conscious, even if they were functionally equivalent to us, because their physical substrate, unlike ours, disintegrates into trivially small units of minimal Φ.Footnote ⁵ For the same reason, the internet or any network of computers cannot be conscious. Expander graphs are not conscious because they are not physical systems, but mathematical abstractions (Aaronson, Reference Aaronson2014). As for physical “grids,” it all depends on the nature of the units, on their fan-in and fan-out, and on the level of noise. Most likely, power grids should harbor little hope of being conscious. In short, Merker et al. express their own misconceived assumptions, rather than conclusions based on IIT and its axioms.

In fact, unlike Merker et al., at this stage we prefer not to speculate. As argued in various papers (Hoel, Albantakis, Marshall, & Tononi, Reference Hoel, Albantakis, Marshall and Tononi2016; Hoel, Albantakis, & Tononi, Reference Hoel, Albantakis and Tononi2013; Marshall, Albantakis, & Tononi, Reference Marshall, Albantakis and Tononi2018), also ignored by Merker et al., to draw any conclusion about a candidate substrate of consciousness, one should first establish at which grain that physical substrate allows for maximum Φ (another consequence of exclusion). Consider the grain of our own PSC: is it neurons, micro-columns, or mini-columns? Is it over microseconds, milliseconds, or seconds (Tononi et al., Reference Tononi, Boly, Massimini and Koch2016)? Indeed, predictions about grain and borders are, in principle, testable: If it turns out that the units of our PSC are not at the grain that allows for maximum Φ, IIT is wrong. Similarly, IIT is wrong if the theoretical PSC – the set of brain units yielding maximum Φ – does not correspond to the empirical PSC.

A critical point here is that the predictions of IIT must be validated in us, because only in us can phenomenology and physics be directly compared. It is only on the strength of that validation that we can venture inferences about consciousness outside us. Unfortunately, this realization eludes Merker et al., as revealed by this quote: “the claim of sufficiency would require independent evidence that…all…natural and artificial systems that…combine integration with differentiation…are in fact conscious.” One wonders what they have in mind, for what could possibly count as “independent evidence” for phenomenology? What makes consciousness special, and different from any other object of scientific inquiry, is precisely that it is subjective and private. As captured by the intrinsicality axiom, immediate evidence for phenomenology is only available from the intrinsic perspective of the subject of experience.Footnote ⁶ Therefore, the only viable scientific avenue is to develop a theory that adequately accounts for the presence and properties of our consciousness – for its quality and quantity – based on its physical substrate in our brain, and to extrapolate from there (inference from a good explanation, Ellia et al., Reference Ellia, Hendren, Grasso, Kozma, Mindt, Lang and Tononi2021). Conversely, inferences based on intuitive, unexamined assumptions of anatomical or functional complexity, on pre-theoretical notions, or on “gut feelings” (Aaronson, Reference Aaronson2014), should be considered with great skepticism. In fact, a highly “complex” neural architecture or an involvement in “complex” cognitive functions is no guarantee of consciousness.Footnote ⁷

Let us now briefly examine the two postulates actually considered by Merker et al. In the target article, the main refrain is that although integration and information may well be necessary requirements for consciousness, they are not sufficient.Footnote ⁸ But who said they would be? As summarized above, IIT explicitly says the PSC must satisfy all five postulates, not just two. Therefore, countless substrates may score high on information integration, but only maxima of Φ can be a PSC.

Furthermore, even integration and information are misrepresented in critical ways. The integrated information of IIT is explicitly not (Tononi et al., Reference Tononi, Boly, Massimini and Koch2016), as assumed by Merker et al., a purported “high capacity for efficient global information transfer” of a network. The informativeness of a specific experience – what the experience means – corresponds to a specific cause–effect structure – not to a message to be “transferred” across a channel.Footnote ⁹ In fact, one of the counterintuitive predictions of IIT is that a neural substrate might be conscious even in the absence of neural activity, with no function being performed and no information being transferred in the Shannon sense. Indeed, if IIT is correct, seeing a “blank screen” corresponds to a cause–effect structure of immense richness (informativeness), even though the experience can be roughly described and communicated to another human being in just two words (Haun & Tononi, Reference Haun and Tononi2019).Footnote ¹⁰ Related predictions are that changes in connectivity, in the absence of changes in activity, can be associated with changes in experience, as can be tested with psychophysical experiments (Song, Haun, & Tononi, Reference Song, Haun and Tononi2017; Tononi et al., Reference Tononi, Boly, Massimini and Koch2016).

Before ending, we can only touch upon two additional criticisms. Throughout their article, Merker et al. emphasize that we typically feel as if we were “looking out” at the world from a “perspective” located ~4 cm behind the bridge of the nose, which they call the “ego-center.” They complain that the “intrinsic perspective” of IIT does not account for this prominent “point of view.” Indeed, the intrinsic perspective of IIT expresses the axiom of intrinsicality – a property that is true not just of viewer-centered experiences but of every conceivable experience: It means “from the inside” – for the subject of experience – as opposed to the extrinsic perspective of an observer – “from the outside.” Nonetheless, the feeling of a perspectival “center” of space is an intriguing phenomenal property that should be eventually explained in physical terms. To quote from IIT's account of spatial experience (Haun & Tononi, Reference Haun and Tononi2019): “Apart from some asymmetries due to border effects…, a natural center may be provided by grids specifying body space, which would be heavily bound by relations to the middle of visual space, and by grids responsible for initiating movements near the body midline.”

Merker et al. also complain that proxies for Φ proposed by different groups can lead to different results, and they argue that “integrated information itself is a hypothetical construct in search of a unique and well-defined formal definition and measure.”Footnote ¹¹ This too is ironic because recent papers from our group (also not cited) have done just that. By formalizing all the postulates of IIT, we demonstrated that it is possible to obtain a measure of intrinsic integrated information that is in fact unique (Barbosa, Marshall, Albantakis, & Tononi, Reference Barbosa, Marshall, Albantakis and Tononi2021; Barbosa, Marshall, Streipert, Albantakis, & Tononi, Reference Barbosa, Marshall, Streipert, Albantakis and Tononi2020). Uniqueness is important to IIT because an experience is the way it is, and so should be its physical correspondent (rather than varying with different measures of irreducibility). Admittedly, before this theoretical development, IIT deliberately made do with provisional measures that captured at least some of the essential properties of experience. In fact, IIT remains “work in progress.” The first attempt to account for the quality of experience – specifically of spatial extendedness – is comparatively recent (Haun & Tononi, Reference Haun and Tononi2019). Ongoing work aims at accounting for the feeling of temporal flow and of objects, at revealing the borders of the PSC through explicit approximations of Φ from functional magnetic resonance imaging (fMRI) time series, and at assessing how intrinsic meanings – substructures in a cause–effect structure – can match causal regularities in the environment. Although these are incremental steps, they are principled steps, and hopefully steps in the right direction.

In fact, it is one of the key consequences of IIT – that all meaning is intrinsic – which may provide an apt conclusion to this response. And meanings such as existence, subjectivity, information, space, and time, and of course consciousness itself, are likely to be highly entrenched sub-structures. Therefore, in the end it is not surprising that the theory Merker et al. decry is one they think they see, rather than the one that is actually there. Theirs is, indeed, a case of mistaken identity.