The fundamental identity of IIT states that an experience is identical to the Φ-structure unfolded from a complex: every property of the experience should be accounted for by a corresponding property of the Φ-structure. 

[The figure below] shows a schematic depiction of the identity. The left side shows a snapshot of the experience that served to illustrate the essential properties of every experience—namely, that every experience is intrinsic, specific, unitary, definite, and structured. Of course, this representative experience also has its particular, accidental properties, which give it its specific content and make it different from countless other experiences: the room, the bed, my body, a blue book in the middle, and so on.  The right side of the figure shows the intrinsic entity that corresponds to the experience—a Φ-structure unfolded from a complex constituted of active and inactive neurons in the back of the cerebral cortex (blue outline). By definition, a complex is a substrate whose cause–effect power is characterized in physical terms in accordance with the essential properties of phenomenal existence. Furthermore, according to the fundamental identity, the Φ-structure specified by a complex must also account for all accidental properties: my particular experience of the bed, my body, the blue book, and so on should correspond to the particular properties of the Φ-structure specified by my substrate in the brain. 

The goal of the identity proposal is to put forth a complete account of consciousness in terms of natural science. Complete means that the account must ultimately explain all aspects of consciousness: under what conditions it is present, to what degree it is present (its quantity), and the particular ways it is present (its quality). In terms of natural science means that the explanation must be based on properties of a universe that exists independently of individual experience and can be investigated in physical terms—that is, operationally [...]. 

According to the fundamental identity, consciousness should be present if a substrate is a maximum of irreducible, intrinsic cause–effect power and absent otherwise. The degree to which consciousness is present—its quantity—is given by the Φ value of the Φ-structure specified by the substrate. It follows that every time consciousness vanishes and returns, its substrate and associated Φ-structure should disintegrate and reintegrate, as reflected by its Φ value. Similarly, the degree to which phenomenal components exist within an experience is given by the φ values of the corresponding distinctions and relations within the Φ-structure. 

The particular way an experience feels—its quality—must also be accounted for by the properties of the corresponding Φ-structure. The essential properties of experience are accounted for explicitly through the requirements that the postulates of IIT impose on the substrate of consciousness. But the fundamental identity of IIT requires that all the accidental properties that make an experience that specific experience can be accounted for by the substrate’s Φ-structure, with no additional ingredients. In other words, all qualitative properties of an experience that make it feel the way it does must be accounted for by corresponding properties of the Φ-structure. In short, quality is structure. 

The identity also implies that the degree to which a content exists within an experience should be accounted for by the degree to which a sub-structure exists within the Φ-structure. For example, when I see a face and then the face vanishes from experience, a corresponding, highly interrelated Φ-fold should do the same (as measured by ΦR). Similarly, the phenomenal grain of the experience should be accounted for by the causal grain of the Φ-structure.

Properties summarizing overall features of the experience—such as its richness, its vividness, the number of distinct contents, modalities, sub-modalities, and so on—should also be accounted for by corresponding features of the Φ-structure. Finally, the similarity and dissimilarity of contents within an experience should be accounted for by the similarity or dissimilarity of their respective Φ-folds. The same holds for similarities and dissimilarities between experiences, which should be accounted for by similarities and dissimilarities between the corresponding Φ-structures. 

In short, a Φ-structure should account for the corresponding experience in both quantity and quality—an identity that, in principle, should leave nothing unexplained [1]. The explanatory completeness of the identity becomes especially clear in accounting for why specific experiences feel the way they do—that is, in substantiating the claim that “quality is structure.” Hence, [the Contents of Experience section presents] a first attempt at accounting for some paradigmatic qualitative properties of experience in terms of structural properties of Φ-structures. For example, the “extendedness” that characterizes spatial aspects of an experience can be accounted for by extendedness of Φ-folds; the “flowing” that characterizes temporal aspects of an experience can be accounted for by the directed flowing of corresponding Φ-folds; and the “object-like” nature of certain contents of experience, such as an apple, can be accounted for by the hierarchical arrangement of corresponding Φ-folds. 

The specific experiences of space, time, and objects were chosen as natural starting points because the structure of these experiences can be at least partially decomposed through introspection. If this approach is successful, however, it may then be justifiable to probe the identity in the reverse direction as well—from the properties of Φ-structures to those of experiences. In other words, we may then use “inference from a good explanation” to reason about accidental properties of experience that are difficult or impossible to decompose through introspection. By reasoning in both directions in this way, the completeness of the identity can be progressively established. 

Identity is a fraught notion [1], so it is important to clarify what is meant here by explanatory identity [2]. By Leibniz’s law, an identity requires that each property of one object is a property of the other and vice versa. Strictly speaking, then, something can only be identical to itself, which is utterly uninformative. In the present case, this would amount to stating that the current experience is identical to itself. An identity statement can become explanatory when its terms differ in sense [3].

Classic identity explanations in science are of this sort, such as the identity between temperature and mean kinetic energy or between water and H2O. Typically, the domain that does the explaining is more general than the one being explained. Moreover, a satisfactory scientific explanation is often reductive, in that coarser properties in one domain are decomposed into finer properties in another domain. For example, in the domain of things that can be observed by the eyes and manipulated by the hands, “water” is characterized as a transparent liquid that boils and freezes at certain temperatures. Science can explain the properties of water through those of H2O, characterized in the broader domain of physics and chemistry as properties of fine-grained molecules, their interactions, and their susceptibility to phase transitions. In this case, it is reasonable to conclude that water and H2O refer to the same “thing,” while using different kinds of observations and manipulations to characterize it. 

In the case of IIT, the identity is explanatory in a similar way because it tries to account for one sense of existence—phenomenal existence, understood as experience—through another sense of existence—physical existence, understood as cause–effect power. If experiences turn out to be identical to Φ-structures, they would be accounted for through a principle that is not private but publicly available—namely, cause–effect power (the principle of being). This principle is fully general and potentially capable of accounting for all of nature. Furthermore, the properties of Φ-structures offer the prospect of decomposing the properties of experience in a way that is as fine-grained as possible and much finer than what can be done by introspection alone. This is because, at least in principle, we could characterize cause–effect power down to the atomic level, unfolding the powers of a substrate with an objective, shared methodology based on public observations and manipulations.

Thus, the explanatory identity proposed by IIT is similar to other identities in science in accounting for one domain through another that is accessible in a more general and fine-grained way. It is unique, however, because the identity of IIT is between a subjective and an objective domain, whereas explanatory identities elsewhere in science are between two objective domains. Most importantly, in IIT the physical domain is not primary (in fact, not even co-primary), but an explanatory inference made from within the phenomenal domain. As we saw in [the 0th axiom], IIT takes the existence of experience as primary: it is immediate and irrefutable, rather than being inferred through observations and manipulations [...]. By contrast, the existence of an independent, atomic world of cause–effect power—the physical world—is explicitly treated as an inference from within experience to explain its regularities. 

Two further remarks about the explanatory identity of IIT are in order. First, identity must be distinguished from isomorphism [4]. Isomorphism typically implies a one-to-one correspondence between two different things. Unlike an isomorphism, IIT’s identity does not need to explain why there should be such a “lovely” correspondence between two different things: Φ-structures are meant as an explanation of phenomenal properties in terms of physical properties, not as something that happens to be correlated with them.  

Second, an explanatory identity must be distinguished from a causal explanation. The identity of IIT does not claim that the phenomenal is caused by the physical, but rather that the phenomenal can be explained in physical terms. If the identity holds, the question of how a substrate would “cause,” “generate,” or “give rise to” experience is ill-posed, as is the question of how phenomenal, subjective properties would mysteriously “emerge” out of physical, objective properties [see FAQ: Is IIT an emergentist theory of consciousness?]. 

[If] we take the existence of the physical world as primary, explaining how it would be correlated with phenomenal experience, or even cause it, becomes not just hard but impossibly hard. 

To qualify as an explanation of experience, the explanatory identity of IIT should satisfy the criteria of inferences to a good explanation [...]: scope, synthesis, specificity, self-consistency, system consistency, simplicity, and scientific validation. By analogy, consider again the classic example of the identity between water and H20 proposed by contemporary physics and chemistry. The explanation covers a full scope in that every feature of water can be accounted for in terms of properties of H20; it would not be enough, for example, to account for its liquidity but not for the fact that it can freeze. It is synthetic by providing a unifying explanation for its behavior in its solid, liquid, and gaseous phase. It is specific in that it predicts, for example, the exact temperature of freezing. It is also reasonably simple, self-consistent, systematically consistent with the rest of science, and empirically testable. In a similar vein, IIT proposes that the properties of Φ-structures can provide a good explanation for all the properties of experience. 

To do so, the identity proposed by IIT should be validated with wide scope, in many different situations. For example, it should explain and predict the presence or absence of consciousness and, more generally, its quantity, not only during wakefulness and sleep but also in cases of anesthesia, brain damage, or epileptic seizures. Moreover, it should explain and predict many of the qualitative features of consciousness—how space feels extended, time flowing, objects at once general and particular, local qualities colored or pitched, and so on [see Contents of Experience].

It should do so in a synthetic manner, by providing a “deep” explanation that unifies these various, seemingly disparate manifestations using the same set of principles. In principle, IIT’s identity lets us account for every conceivable property of experience—essential and accidental—through the single, parsimonious principle of cause–effect power, with no further ingredients or ad hoc explanations. This is especially demonstrated in [the Contents of Experience section], where we will see how the identity can account for accidental properties of various kinds of experiences without invoking any domain-specific “bridging principles.” Moreover, [...] the identity might offer a unifying foundation for ontology and metaphysics—for defining macro-units; characterizing different types of entities; and providing an account of meaning, reference, and knowledge, as well as causation and free will.

The scope of the explanation should be not just broad and deep, but also highly specific. This means it must encompass the minutest components of experience, so that nothing is left unaccounted for. The identity of IIT is highly specific in demanding that every phenomenal distinction and relation correspond one-to-one with their physical counterpart. The identity should further satisfy specificity by making detailed predictions. In practice, of course, broader predictions come before highly specific ones. But, like in other areas of science, a theory should offer increasingly specific predictions as the evidence accumulates, and ideally some counterintuitive ones [...].

The identity already satisfies simplicity. This would certainly be the case if one were indeed able to characterize the properties of all that exists based on just five axioms introspected from phenomenology, and on their translation into five operational postulates, all based on the notion of cause–effect power, and complemented by four basic principles (of being, becoming, and maximal and minimal existence), and a few auxiliary assumptions. 

Self-consistency is evident in the way the explanatory identity accounts for every aspect of consciousness in a systematic, internally coherent way. There is not one set of principles to explain the quantity of consciousness and another for explaining its content, one for explaining the experience of time and another for that of color. Rather, the identity between experience and the structure of cause–effect power permits a self-consistent account of everything that needs to be explained. This consistency is rooted in how the axioms are formulated as postulates, which can in turn be formalized as mathematical expressions [2]. It is also evident in the way the postulates build upon one another—existence, intrinsicality, specificity, integration, exclusion, and composition—to yield such expressions in a transparent manner. Finally, it is reflected in the mathematical symmetry between the expressions for identifying the substrate of entities (φs) and those for identifying the distinctions and relations that compose them (φd and φr). 

The explanatory identity also satisfies system consistency because it does not require mysterious new physical “forces” or “laws” but fits within the natural sciences. In fact, it emphasizes the unity of science by claiming that experience is part of nature, unified by the notion of cause–effect power as the definition of the physical. Though the identity fits with the way science attempts to characterize nature objectively, through observations and manipulations, it also reveals, within a unitary, natural explanation of all that exists, a great divide of being—the divide between existence that is intrinsic and existence that is merely extrinsic [...] [3]. 

Finally, the criteria for assessing the identity are objective: [...] IIT can be scientifically validated against the necessary and sufficient conditions for our own consciousness. Of course, validation is not possible in one fell swoop but only through the accumulation of evidence of many kinds. As evidence mounts, however, the identity may provide a good enough explanation from which to extrapolate to difficult cases (inference from a good explanation), such as establishing the quantity and quality of consciousness in newborns, animals, and machines.

[...]