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Summary
Summary
Composition is an essential property of experience (an axiom) and, by inference, also an essential property of the substrate of consciousness (a postulate).
The axiom states that experience is structured: it is composed of distinctions and relations that bind them together, yielding a phenomenal structure that feels the way it feels. Formulated in physical terms, the postulate states that the cause–effect power of the substrate of consciousness must be structured: subsets of its units must specify cause–effects over subsets of units (distinctions) that can overlap with one another (relations), yielding a cause–effect structure that is the way it is.
Composition Axiom
Composition Axiom
Experience is structured: it is composed of distinctions and the relations that bind them together, yielding a phenomenal structure that feels the way it feels.
Experience is structured: it is composed of distinctions and the relations that bind them together, yielding a phenomenal structure that feels the way it feels.
[This excerpt is taken from Tononi, G. (forthcoming). On Being.
Ch. 2: The axioms of phenomenal existence.]
Ch. 2: The axioms of phenomenal existence.]
Within my experience I can distinguish many components, corresponding to phenomenal distinctions and relations. For example, looking at the image [here], I can pick out the bed, the body, the book, the color blue, and so on. But I can equally well pick out larger components, such as "the left side of space" or the room, as well as smaller components—for example, the corner of the bed, the leg of the body, and so on. Furthermore, the components of an experience are related to one another. The color blue is bound to the cover of the book, the book to the region of space it occupies in my experience, that region of space to neighboring and overlapping regions, and all regions of space to one another to compose the extended canvas in front of my eyes [1]. Together, the distinctions and relations that compose this particular experience are what make it feel the way it feels.
Introspection allows me to analyze the structure of an experience—its phenomenal structure—by dissecting it into coarse components, let’s call them compound distinctions, and the way these distinctions are bound, corresponding to compound relations. However, introspection alone is hardly adequate to the task of dissecting an experience down to what I might consider to be elementary distinctions and relations. For example, I can distinguish the book and my left hand, and see they are related—the hand lies on the book. I can also distinguish the book’s cover, its top and bottom edges, and its title, just as I can distinguish my thumb and index finger. I can also see that the two fingers are related to a different region of the book. But I cannot possibly hope to dissect my experience all the way down, or to count the innumerable ways in which the contents of my experience are related [2].
Composition is immediate because I do not need to infer the structure of experience, the way the experience feels. It is already there, the way it is, "in front of my eyes"—the book bound to its shape, color, and position in space; my body lying over my bed within the room; and so on. Composition is also irrefutable, in the sense that its negation is self-contradictory or absurd. Try to think of an experience that had no components at all, not even a single distinction. The structure of the experience would be composed of nothing, which is the same as saying that there would be no experience [3]. And while I can conceive of an experience structured in a different way, it would remain true that when I experience it, it would be structured in its particular way—it would feel the way it feels—reaffirming the validity of the axiom. Moreover, composition is true not just of the experience I am having now, but it must be true of every conceivable experience, which makes it an essential property of phenomenal existence.
Footnotes
[1] [The section on space] will illustrate how the structure of the "extended canvas of space" comes about.[2] [An] introspectable, compound phenomenal distinction should ultimately correspond to a compound physical distinction (which includes a number of elementary distinctions), and a compound phenomenal relation to a compound physical relation (which includes many elementary relations). Nevertheless, the term distinction appropriately captures the idea that we "pick out" or "single out" (which is to say, "distinguish") some component of experience, and the term relation captures the idea that when we do so, we typically pick out other distinctions that are "bound" to it. More generally, any composition of distinctions and relations—a sub-structure within the phenomenal structure—can be considered a content of the experience.[3] A truly “minimal experience” would be composed of just one distinction related to itself. It would correspond to the simplest possible structure but still be a structure and thus still an experience. In mereology, a whole can be considered as a part of itself, including the only part of itself (a so-called improper part). A self-consistent axiomatic system can be constructed assuming proper or improper parts.
Composition Postulate
Composition Postulate
The cause–effect power of the substrate of consciousness must be structured: subsets of its units must specify cause–effects over subsets of units (distinctions) that can overlap with one another (relations),
yielding a cause–effect structure that is the way it is.
The cause–effect power of the substrate of consciousness must be structured: subsets of its units must specify cause–effects over subsets of units (distinctions) that can overlap with one another (relations),
yielding a cause–effect structure that is the way it is.
[This excerpt is taken from Tononi, G. (forthcoming). On Being.
Ch. 4: The postulates of physical existence II.]
Ch. 4: The postulates of physical existence II.]
How can we formulate the phenomenal property of composition in physical terms? Phenomenally, composition means that every experience is structured, being composed of phenomenal distinctions bound by phenomenal relations to form a phenomenal structure that is the way it is. Therefore, the substrate of consciousness must have cause–effect power that is structured in a particular way. We can reveal this internal structure by considering, first, whether and how subsets of units take and make a difference over subsets of units within a complex, specifying their own cause–effect states and yielding causal distinctions. Second, we must consider how these distinctions’ causes and effects overlap over subsets of units, yielding causal relations. Altogether, causal distinctions and relations form a cause–effect structure, also called a Φ-structure.
Distinctions
Distinctions
[This excerpt is taken from Tononi, G. (forthcoming). On Being.
Ch. 4: The postulates of physical existence II.]
Ch. 4: The postulates of physical existence II.]
We saw in the previous postulates that the complex as a whole must specify both a cause and an effect over itself. Likewise, a subset of its units can only exert cause–effect power within the complex if it specifies a cause–effect (a cause and an effect) within the complex, called a causal distinction. A distinction comprises a mechanism, a cause purview, and an effect purview: a mechanism is a subset of units within a complex that can take and make a difference within it, its cause purview is the subset of units from which the mechanism takes a difference, and its effect purview is the subset of units to which it makes a difference. The link between cause and effect provided by a mechanism can be roughly expressed as “given this cause, then this effect.” [In the figures], distinctions are illustrated by orange lines connecting a mechanism and its cause and effect purviews.
As a simple analogy—albeit imperfect—think of a distinction as comprising a pulley (the mechanism) and two weights attached to the two ends of a cable (the cause and effect purviews). Alone, the mechanism is simply a wheel with a cable around it. To exert causal power, it must link weights at both ends of the cable.
The crucial feature of composition is that, in principle, any subset of units of a complex can constitute a mechanism or a purview. This is illustrated [in the slides above] by the powersets of mechanisms, causes, and effects, any of which may be combined to form a candidate distinction. Note that the mechanisms “inherit” their state (which units are ON and OFF) from the system’s current state and the cause–effect purviews from the system’s cause–effect state. Within each powerset, the mechanisms and purviews that make up distinctions that are maximally irreducible are highlighted in bold. Two distinctions, referred to by their respective mechanisms ("distinction b" and "distinction cd"), are singled out in the [slides above]: first-order distinction b specifying cause purview a and effect purview d, and second-order distinction cd specifying cause purview a and effect purview ad.
For a substrate constituted of n units, there are 2n–1 combinations of units (the powerset of the n units, excluding the empty set [1]), so the substrate could specify up to 2n–1 distinctions. In a given mechanism or purview, the term order refers to the number of units involved. In the example here, the mechanisms and effect purviews are both second order, while the cause purviews are first order.
As components of the cause–effect power of the complex, distinctions—like the complex as a whole—must be characterized in accordance with the postulates of physical existence (save for composition because, being components themselves, they do not have components). Recall that the complex as a whole must be able to take and make a difference (existence) and do so within itself (intrinsicality). It must also select a specific cause and effect state (information). Similarly, a distinction can only exist for the complex if it can make and take a difference. For this, it needs a mechanism that links a cause with an effect. Distinctions must also comply with the intrinsicality postulate: their cause–effect power must be exerted within a system, and from the intrinsic perspective of the mechanism. Likewise, they must comply with the information postulate: a mechanism in its specific current state must select a specific cause–effect state. As for the system, this is the state for which intrinsic information is maximal (indicated by the red and green squares on the TPM in [the slides above]) [2].
Finally, distinctions must comply with the integration and exclusion postulates. A distinction’s integrated information is measured by φd (“phi” with subscript d for distinction), which quantifies how much specific cause–effect power a mechanism has over its purviews as one mechanism. As with the system, and in line with the principle of minimal existence, we assess integration by considering the partition for which the difference is minimal, relative to the maximum possible integrated information for that partition. We also take the minimum between the cause and the effect sides [3]. To comply with the exclusion postulate, we follow the principle of maximal existence and establish the border of a distinction by determining the cause–effect purview over which a mechanism achieves maximal integrated information, excluding any purview with lower φd [4].
Note that when assessing integrated information of higher-order mechanisms, φd is not a measure of how much additional effects (or causes) a higher-order mechanism (say, Abcd) specifies over first-order mechanisms (say, A, b, c, d). Additional effects, say, due to non-linear interactions, may be relevant from an extrinsic perspective. Yet from the intrinsic perspective of an entity, what matters with respect to structure is whether the mechanism Abcd has an effect (and cause) in a way that is maximally irreducible. In other words, does the complex have at its disposal the integrated "pulley" or "handle" Abcd to specify a certain effect (and cause) within itself? [For more, see FAQ: Why do we assess the causal power of all orders of mechanisms? Why not simply assess the causal power of the individual units alone?]
Footnotes
[1] Subsets are any combination of units of the complex (its powerset). Because the subject is existence, the empty set is not considered as a legitimate subset.[2] As for the system as a whole, the maximum operator ensures that the mechanism takes or makes a difference that, compared to chance, increases the probability of occurrence of the purview state it specifies. The reason is that the phenomenal distinctions that compose an experience are actual—they actually exist (intrinsically and in the specific way they do). Physically, the intrinsic cause or effect specified by a distinction must be not only specific but also such that their probability of occurrence—of being actual (existing)—is increased by a mechanism, not decreased (or left unchanged).[3] The procedure is described in detail in Albantakis et al., 2022.[4] Maximal irreducibility will typically be sensitive to the presence of minimum partitions that cut across a fault line of a purview, such as units connected to a mechanism with low strength. Moreover, φd is based on intrinsic information, which is sensitive to the tension between expansion and dilution. Therefore, φd will typically be higher for a smaller purview that can be specified with high selectivity than for a larger purview that can be specified with much lower selectivity.
Relations
Relations
[This excerpt is taken from Tononi, G. (forthcoming). On Being.
Ch. 4: The postulates of physical existence II.]
Ch. 4: The postulates of physical existence II.]
Relations capture how a set of distinctions are bound together because they specify their cause and/or effect purviews over the same units in the same state—they have a congruent overlap. Just as a distinction links a cause and an effect purview by specifying their states, a relation binds a set of distinctions by specifying which units and states correspond to which across distinctions. Relations thus reflect how the cause–effect power of a set of distinctions is bound together irreducibly within a complex, as measured by the relation’s φr (“phi” with subscript r for relation). As congruent overlaps among causes or effects of various distinctions, relations are just as important to the structure of the substrate’s cause–effect power as the causes and effects of each distinction. [This can be] illustrated by the ropes from two pulleys converging on the same weight. Clearly, the fact that two pulleys are pulling on the same weight is just as important for a system as the fact that each pulley is pulling on its weight.
In principle, a complex constituted of n units can specify a very large number of relations, up to n*22^n. A relation is composed of one or more distinctions (the relation’s degree) [1]. Each relation has one or more faces (the face’s degree), each of which corresponds to a distinct combination of causes and/or effects of the participating distinctions. Each face has a corresponding face purview—the maximal congruent overlap shared by two or more causes and/or effects. For example, a relation between distinctions b and cd is indicated [in the slides above] by a dark line “binding” two labels in the mechanism powerset; the respective relation faces are shown as blue lines (for second degree) and a plane (for third degree) connecting the specified causes and effects in the cause and effect powersets.
The union of all face purviews is called the relation purview, or joint purview. [In the slides above], for example, the relation purview of distinctions b and cd comprises purview elements a and d. The particular combination of faces that constitute a relation characterize its type. For example, a self-relation is reflexive, a relation where all causes and effects are maximally congruent with one another is a complete relation (which is necessarily reflexive), a relation where the effects of one set of distinctions overlap congruently with the causes of the remaining distinctions (but not the other way around) is a directed relation, and so on. The type of relations will become important when accounting for the quality of experience [...].
Like distinctions, relations must be characterized according to the postulates of physical existence. Relations inherit existence from the cause–effect power of the distinctions that compose them. They inherit intrinsicality because the causes and effects that compose their faces are specified within the substrate. Moreover, relations are specific because their face purviews must be congruent for all causes and effects.
Relations satisfy integration because they capture the irreducibility of cause–effect power due to the overlap among distinctions [2]. The irreducibility of a relation (φr) is measured by “unbinding” distinctions from their joint purviews, one by one. By the principle of minimal existence, a relation can only be as irreducible as the minimal amount of irreducible information specified by any one distinction in the relation. Therefore, the relation integrated information (φr) is given by the minimum φd value scaled by the number of unique units over the face purviews of all faces in the relation [3].
Finally, a relation complies with exclusion in that its integrated information is naturally maximized over the maximally congruent overlap for each relation face (taking subsets of these overlaps could only reduce the integrated information of the relation).
In sum, for both distinctions and relations, φ is again a quantifier of integrated existence: a distinction or relation only exists as one distinction or relation to the extent that it is causally irreducible.
Relations also serve to “relate” the identity and state of the units of a complex from its intrinsic perspective. Needless to say, intrinsically, neither the units in a purview nor their states come with a label (such as unit A or B, state ON or OFF). It is relations that specify which purview units in one distinction correspond to which purview units in another, and which states correspond to which states. In this way, relations can uniquely specify (or “lock in”) the identity of both the units and of the states from the intrinsic perspective of the complex [4].
Footnotes
[1] An individual distinction whose cause and effect overlap congruently specifies a first-degree “self-relation.”[2] Accordingly, in IIT, relations do add to being. [...][3] Details are in Albantakis et al., 2022.[4] The way IIT characterizes relations—from an intrinsic, causal perspective—differs from the way the term is used in everyday language, in philosophy, and even in mathematics. Relations in everyday language, as well as in philosophy, are typically of this kind: Billy is taller than Susy, Billy is married to Susy, or Billy is near Susy. Relations are often subdivided into internal and external. An internal relation, say, Billy is taller than Susy, only depends on the intrinsic properties of the things that are related: if Billy and Susy exist, with their respective properties such as height, then the relation is supposed to follow necessarily. An external relation, say, Billy is near Susy, does not follow necessarily. But there is much disagreement on the definition of internal and external relations, even whether they should be thought to exist at all. Clearly, the causal relations defined by the postulates of IIT are meant to capture something else—namely, irreducible overlaps among causal distinctions. In this sense, IIT relations are not only causal but also always internal. However, they are always internal to an individual complex, not to the universe as a whole. So what does IIT have to say about the ontological status of the relations of everyday language and philosophy? Do they exist, and, if so, how? As we will briefly see in Part III (see Box: IIT and Platonic realism), relations such as “taller than,” “married to,” “near to,” and many others should be thought of as high-level concepts. The same way that high-level concepts—such as “Billy,” “Susy,” “tall,” “marriage,” “near”—pick out disjunctions of conjunctions (see Objects), relations such as “taller than,” “married to,” and “near to” pick out conjunctions of other concepts. Like other concepts, they truly exist, but only as contents of experience—as intrinsic meanings. And, like other concepts, they may or may not correspond to objective properties of extrinsic entities, such as Billy and Susy.
Φ-structures and Φ
Φ-structures and Φ
[This excerpt is taken from Tononi, G. (forthcoming). On Being.
Ch. 4: The postulates of physical existence II.]
Ch. 4: The postulates of physical existence II.]
To make fully explicit the internal structure of the cause–effect power specified by a complex, we need to unfold all the distinctions it supports, of any order, and all the relations that bind them together, of any degree. However, in line with intrinsicality and information, from the intrinsic perspective of the complex, the only distinctions and relations that truly exists are those that are congruent with its own cause–effect state. A distinction’s mechanism must be constituted by units of the complex, whose current state is a subset of the state of the complex as a whole. Likewise, the cause purview of any distinction must be in the same state as the cause state of the complex as a whole, and similarly for the effect purviews and the joint purviews of relations. This can be seen in [the slides above], where the three powersets [...] are always congruent with the cause–effect state of the complex. The complete set of distinctions and the associated relations specified by the complex compose a cause–effect structure—or, for brevity, a Φ-structure [1]. A Φ-structure thus captures the fully ‘unfolded’ cause–effect power of a complex in its current state [2].
In the Φ-structure depicted [in the slides], mechanisms are represented by black letters, cause purviews by red letters, and effect purviews by green letters. The order of the mechanism or purview is the number of units that constitute it, which corresponds to the z-axis “level” in the figure. Distinctions are depicted by orange lines linking a cause purview (left side) and an effect purview (right side) through a mechanism (middle), and the thickness of the line reflects the φd value. Relation faces are depicted as lines (for second degree) and planes (for third degree), whose color intensity reflects the value of φr (the large number of relation faces higher than third degree cannot be visualized). Note that the Φ-structure is “planted” on the complex through its first-order mechanisms and, like the complex, it is depicted in a blue palette. This is to indicate that a Φ-structure is not a mathematical abstraction, disconnected from the substrate; it is rather the fully unfolded cause–effect power of that substrate.
Together, a complex and the Φ-structure unfolded from it comprise an intrinsic entity. The distinctions and relations that compose the Φ-structure characterize what exists, and the way they are organized characterize which way it exists—what it is like. The φd and φr values measure how much the distinctions and relations exist within the structure. The sum of their φd and φr values is the Φ value (“big phi”) of the Φ-structure, which measures its total structure integrated information—how much the entity exists.
Footnotes
[1] In the context of composition, it is useful to clearly distinguish among constitution, combination, and superposition.Constitution. A component’s mechanism and purviews are constituted of one or more units from a substrate.Combination. A component’s mechanism and purviews can be constituted of any combination of units from a substrate. Given a substrate constituted of n units, the number of possible combinations or subsets of units (its powerset) is 2n-1 (-1 is due to the empty set, which cannot constitute a mechanism or purview).Superposition. The mechanisms and purviews of different components can overlap within the substrate. On the mechanism side, this means that a substrate constituted of n units can potentially support up to 2n-1 different mechanisms, as long as they exert cause–effect power within the system. These combinatorial mechanisms come for free, as it were. On the purview side, this means that the cause and effect purviews of different mechanisms will overlap over various subsets of units, composing candidate relations.[2] An important consequence of the intrinsic perspective is that many causal powers that can be demonstrated extrinsically do not exist intrinsically. Based on the exclusion postulate, causal interactions across the border of a complex can be demonstrated extrinsically, but do not exist intrinsically. The same is true for causal interactions within a complex but across the borders of a purview, or across the border of a macro-unit. Similarly, extrinsically we may be able to demonstrate that the causal power of a mechanism in a state extends to many more units and states that those of its intrinsic cause and effect purviews, but those causes and effects do not exist intrinsically.
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For the composition axiom, please cite Tononi, Giulio. Forthcoming. On Being. Chapter 2: The axioms of phenomenal existence.For the composition postulate, please cite Tononi, Giulio. Forthcoming. On Being. Chapter 4: The postulates of physical existence II.
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