FAQs
The Axioms of Integrated Information Theory
These FAQs presume familiarity with the axioms of IIT. If you have a question about the axioms that is yet not covered here, please add or upvote a new question on the comment thread of the respective page: Intrinsicality, Information, Integration, Exclusion, Composition.
What is meant by the term axiom in IIT?
The term axiom has different meanings. In regular speech, it refers to statements that are taken to be true because they are self-evident or obvious, and thus accepted without question. In modern logic and mathematics, it usually refers to an assumption that is true by stipulation—that is, a premise that is assumed to be true within a given formal system.
In all these uses, an axiom is a starting assertion that requires no further justification. IIT shares this basic meaning of axiom, but it grounds the truth of its axioms not by stipulation but in experience itself—in phenomenal existence (see 0th axiom). Phenomenal existence is immediate, and the five axioms proposed by IIT aim to capture its essential properties—those that are irrefutably true of every conceivable experience. Let’s examine these key notions in turn.
Experience is immediate: I have “direct” or “unmediated” access to my own experience (you to yours, and ditto for everyone). In this sense, every property of experience is immediate—both its essential properties (axioms) and its accidental ones. Consider the mundane experience of seeing a red apple. To what should I appeal to be sure that I see red? Should I appeal to my knowledge of electromagnetic wavelengths or of area V4 in the brain? Of course not. My experience of red is immediate and unmediated—I simply experience it. This holds even if it turns out the apple is actually a green granny smith that was made to look red through a trick in lighting, or even if there is no apple whatsoever and I am hallucinating it. In such a case, it is still true for me that I see the granny smith as red, in an immediate, unmediated sense.
The notion of immediacy is crucial since the axioms are often misinterpreted as being logical “propositions.” They are not propositions to parse and interpret; they are rather insights to experience and confirm through your own process of introspection.
The axioms express properties that are irrefutably true of every conceivable experience—and hence essential properties. To say they are irrefutable does not mean I cannot try to doubt and refute them; it rather means that through the act of doubting, I will confirm them. There is a clear historical precedent for this type of reasoning, namely, Descartes’s cogito: if there is one thing I cannot be mistaken about, it is the fact that I am having an experience right now. If I doubt this, the act of doubting confirms it because doubting, too, is an experience.
In math and logic, this form of reasoning is known as proof by contradiction or reductio ad impossibile. It may be helpful to think of IIT’s axioms as being established in this way; it is certainly a useful way to draw the line between what should and should not be considered an essential property of experience (see FAQ: Why aren’t the experiences of space and time considered axioms in IIT?). Again, however, keep in mind the immediacy of the axioms: even though you can establish them using the proof-by-contradiction method, it is best to think of them not as formal propositions but as immediate, experiential insights that arise through this reflection and reasoning process.
The immediacy and irrefutability of the axioms of IIT distinguish them from the axioms of mathematics. Mathematical axioms are true by stipulation: they are the foundation of a particular axiomatic system, and it makes no sense to ask whether they are true outside of the system. To the contrary, axioms of experience cannot be arbitrary. They are not relative to an axiomatic system; they are either true or false depending on whether they reflect a fact of our own experience.
For these reasons, IIT’s axioms of experience are more fundamental than the axioms of mathematics: they are grounded in phenomenal facts rather than stipulation. Moreover, an axiomatic approach is not only fruitful but necessary in consciousness science. Contrary to natural science and (in some cases) mathematics, consciousness science must start from truths about experience discovered through introspective techniques. Those truths, however, can then serve as an inferential basis to investigate the corresponding properties of the substrate of consciousness (in IIT terms, the postulates).
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If the axioms are “immediate” and “irrefutably true,” shouldn’t they also be self-evident?
Ch. 1: Phenomenal and physical existence.]
If the essential properties of consciousness are indeed immediate and irrefutably true of every conceivable experience, we might think that they should be self-evident, as axioms are often supposed to be. And yet to see what they really mean seems to require some effort, for several reasons.
First, the axioms can only be established, understood, and confirmed if some prerequisites are met. I need to be conscious in the first place—I must be able to start from my own experience. An unconscious computer could spit out “experience exists” and claim it is an axiom—immediate and irrefutable—yet it would neither hear nor understand what it is talking about. Furthermore, to see the axioms as essential properties of experience, I must also be able to think consciously about my experiences—that is, I must have the capacity for reflective consciousness [1]. I should also be endowed with sufficient rational powers, including the capacity to ask “why” and avoid contradiction, as well as the power to conceive various scenarios.
Finally, as mentioned at the start, to see the axioms as essential properties of every experience, I must be able to step back and realize that their true meaning may be hard to grasp precisely because they are “right in front of my nose”—characterizing existence itself. They may also sound almost trivial, precisely because they spell out what is so obvious that I fail to notice it. The difficulty in recognizing the axioms is like the difficulty in seeing a perfectly transparent window through which I view everything else: the axioms may be self-evident, but only once I see them for what they are—not before.
[Moreover], the axioms come in a single package. While each spells out a distinct property of experience, to properly characterize phenomenal existence, the axioms must be considered together. There is also a sequence to the axioms, in the sense that they build upon one another. Obviously, the five essential properties of experience only make sense if there is such a thing as experience—phenomenal existence (0th axiom). I must then first have the experience intrinsically, for myself, before realizing that it is in a specific way [information]. Only then can I judge that the experience is a whole [integration] and that it is this whole [exclusion]. Finally, only after establishing that the experience exists, is mine, is the way it is, is unitary, and is definite can I delve into its internal structure and characterize its distinctions and relations [composition] [2].
Footnotes
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Why aren’t the experiences of space and time considered axioms in IIT?
The five axioms of IIT capture essential properties of experience—called essential because they are irrefutably true of every conceivable experience: there is no possible counterexample of an experience that lacks any of them. What about the experience of space and time? Indeed, most experiences feel spatial and temporal: visual scenes feel extended as a canvas before our eyes and our bodies feel to be spatially extended; events feel like they inexorably flow from one moment to the next. Though extendedness and flow are true of nearly every human experience, they are not essential properties of every experience.
Try to imagine an experience without space or time. Even if this feels extremely difficult to do, such an experience is not “irrefutably true of every conceivable experience” (see FAQ: What is meant by the term axiom in IIT?). For example, if we try to refute the axiom of integration by conceiving of an “unintegrated experience,” we end up with two experiences, each of which is integrated; hence we demonstrate that integration is irrefutable because we end up with an absurdity or a contradiction. The same cannot be done for space or time. If we try, for example, to conceive of an experience without space, we don’t inadvertently end up with an experience that is necessarily spatial. For example, we might conceive of a solely olfactory experience—say, of pure lavender—with no sense of extendedness. And even if this is difficult to imagine—nearly impossible even—it does not lead to absurdity or contradiction if you try. Hence, the feeling of space (or extendedness) is not irrefutably true of every conceivable experience. And the same reasoning holds for the feeling of time (or temporal flow).
Furthermore, in the IIT framework, the experience of space can be accounted for based on IIT’s five postulates alone—with no additional ingredients needed. This is not the reason why space should be excluded as an axiom, but it is another clue that there’s no need for a space axiom. More precisely, it is possible to show that the distinctions and relations in the Φ-structures specified by grid-like substrates have properties that fully explain the feeling of spatial extendedness [1]. Considering that large parts of our brain are grid-like, if IIT is right, it is no wonder that we easily feel space to be always present. A similar story likely holds for the feeling of temporal flow—whose neural mechanisms are, however, less understood than those for space [2].
For more, see
Footnotes
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Does intrinsicality imply an ego, self, self-awareness or self-report?
When we reflect on our own experience, it is difficult to do so without some concept of self-awareness or self-report—without somehow thinking “I” am thinking about “my experience.” Is it even possible to introspect our experience without creating some conceptualization of ourselves as individuals? Probably not. Of course when we describe our reflection—inwardly or outwardly—we can try to erase the pronouns to say something like “thinking is happening.” But this is likely mere wordplay; when we reflect on experience, we inevitably have some sense of a self being aware of or reporting to itself [1].
The intrinsicality axiom, however, implies none of this: neither a sense of “mineness” of the experience, nor a notion of ourselves as selves or individuals, nor a process of self-reporting (e.g., through inner dialogue). This axiom merely states that experience inherently has a subjective point of view, rather than, say, a “view from nowhere.”
Intrinsicality may be best illustrated by “flow states”—when we are fully absorbed in an experience precisely because we are not self-aware. For example, when an accomplished musician plays a solo, she is not thinking, “I am soloing now”; she is not actively constructing some inner image of herself as a great rock star. Of course these self-aware thoughts may rush in later, but during the solo, she is rather fully in it. In fact, if self-awareness or “self-consciousness” were to creep in while playing, which it might, it would likely make the solo worse and put a damper on the soloist’s experience.
In true flow states like this, self-awareness is absent, and many would say the sense of self dissolves completely. But an experiential perspective is undoubtedly there. This perspective may even be accentuated in a flow state because no attention is given to objectifying the self—because “you” are not a content of your awareness. The fact of this experiential perspective is what the intrinsicality axiom points out, and it is true not just of flow states but of every conceivable experience.
Of course, we can only identify flow states through reflection, which inevitably involves self-awareness or -report. But this does not negate intrinsicality. It simply points to a cognitive deficit—that we struggle to reflect on experience without smuggling in a sense of self. This notion of the “self” is like the light in the refrigerator: every time the door is open, the light is on. So one might assume it must be on all the time, not realizing that opening the fridge is what causes it to come on. (For more, see FAQ: If introspection requires reflection, how can we be sure that non-reflective experiences exist at all?)
Some may argue that a minimal notion of “self” always persists—not only in flow states but even for animals that don’t pass the “mirror self-recognition test.” Such counterarguments may be more about terminology and not necessarily in contradiction to the present argument [1]. Regardless, the key point here is that intrinsicality in IIT has nothing to do with being aware of oneself or inwardly “representing” oneself. Intrinsicality simply means that experience always exists from the experiencer’s first-person or subjective perspective—it is for the experiencer.
For more, see
Footnotes
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Can't I have a vague or generic experience, which isn't "specific"?
The information axiom states that every experience is specific. Some may try to argue that some experiences are “generic,” but this is not the case.
Take visual experience. You have been moving your eyes on this page. At each moment, you are having an experience that is specific: you are experiencing “this” image, even if you cannot introspect (let alone report) precisely how each image differs from the others. You might shift your eyes to a completely white wall and relax your focus to experience it as a “ganzfeld,” with no sense of depth, movement, texture, shape, and so on—what could be more “vague” than that? But this too is the specific experience of hazy whiteness.
You may also taste something and be unsure about the name of the flavor, but that is not because you are having a vague experience: you are tasting a specific taste that you can’t place. You think it is some kind of spice, but the fact that you can’t recognize it as, say, cloves does not mean you are having a generic experience, an experience of a phenomenally unspecific taste. The taste is there, strong and present even before you understand what it is (even though discovering what it is might change your experience by triggering associations).
Can there be experiences that are unspecific in themselves, without comparison with anything else? Consider the experience of seeing a color that is both blue and yellow at the same time, attainable by crossing your eyes as you look at this image, so that the two crosses overlap:
The resulting experience is either of alternating blue and yellow (as in binocular rivalry), or of blue-here and yellow-there, or of a strange green, or of a yellowish-blue or bluish-yellow (“blellow”?). In no case do you have a generic or unspecific hue (neither blue, nor yellow, nor any other color).
That you are unable to specifically describe your experience does not mean that your experience is not specific. Even the mesmerizing experience you may have staring at the Milky Way on a dark, moonless night is fully specific, with its myriad specs and clouds of light, which you can admire but would never be able to count. Experience is “what it is like to be” you, and the “what” is always specific—always a particular way.
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Is my experience "specific" owing to the potential experiences I could be having?
The information axiom states that every experience is specific. It is tempting to describe an experience as “specific” through the concept of differentiation—that is, by contrasting it with other possible experiences I could be having. (In fact, previous iterations of IIT did this [1].) This means claiming, for example, that yellow is yellow because it is not blue (or any other color); a major chord is what it is because it is not a minor chord (or any other musical interval). These statements could be true, but they are not immediately true of the experience itself. Rather, they require counterfactual reasoning.
As an axiom, information states only what can be said of the experience within the experience itself—in other words, without counterfactual reasoning. Red is simply red, and the major chord is simply that chord. We may indeed consider counterfactuals to confirm the axiom for ourselves (as we did above), but the axiom itself simply states that “experience is specific” in the sense that “it is the way it is.”
Remember our criterion for an axiom is whether it is possible to conceive of an experience lacking the given property without falling into absurdity or contradiction. Differentiation is not axiomatic because it requires us to think that my present experience is “one of many possible experiences.” This is indeed possible to doubt; it is conceivable that my momentary experience is the only possible experience. Though highly unlikely, this thought is not self-contradictory or absurd.
That said, differentiation is a consequence of the information axiom—that is, since an experience is “this one,” it also differs from other possible experiences. Differentiation is a useful concept in an explanatory sense, especially when we move from phenomenology to physics: when we analyze a given Φ-structure, it is illuminating to contrast it with other possible structures—to make sense of why it is “that one.” But this use of differentiation is based on inference; it is not immediate in the experience itself.
What if we see various colors next to one another in the same experience—a sort of “differentiation within”? These colors are indeed different components of your experience, but it is not that, say, the pink in your experience exists because of its contrast with the blue or yellow. The pink, again, simply is what it is in your experience, as is the blue. It is true that the experience of pink changes somewhat if the experience of yellow or blue is present—as illustrated by the Munker-White illusion here [2]. Yet these unique contrasts themselves are new specific components in your experience. Any experience of “differentiation within” is also always specific, and by inference, therefore, also differentiated from other possible experiences.
Footnotes
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If I have two unrelated contents of experience, doesn't this mean my experience is not "unitary"?
The integration axiom states that experience is unitary. This was illustrated in the integration section, where we saw the example of experiencing the flash of a camera and the bang of a car back-firing at the same time. Some may describe the flash–bang as an experience of two things that are not integrated. This objection is largely semantic. Recall that introspection in IIT is applied to a unique “moment” of experience. We would thus describe the flash and the bang as “unrelated,” yet they are integrated because these components occur in the same moment of experience—they are co-experienced within the same unitary whole.
As another example, consider listening to a person speak and watching their mouth at the same time. The auditory and visual components are clearly integrated and, incidentally, also highly related. Then consider watching a film in which the audio and video are out of sync. You hear a word but see a closed mouth, and you immediately feel the asynchrony. If a neuroscientist were looking at your brain at that moment, they might even say that the asynchrony broke the neural “sensory integration” that occurs when the sound and image are in sync. Yet your experience here, too, is an integrated whole. The feeling of asynchrony itself is a component of that integrated experience.
We may use words like “fragmented” or “unintegrated” to describe an experience. But we mustn’t let semantics obscure the meaning of the axiom. This face by Picasso, for example, we might describe as “unintegrated.” But this experience is only possible because it comprises facial components that we feel do not “hang together” the way they should. Ironically, perhaps, these “unintegrated” components must be co-experienced—or integrated—for that experience to feel “unintegrated.”
Consider the more complicated case of staring at a sunset while pondering democracy. One would be hard-pressed to find any relation between sunsets and democracy, yet this experience too is an integrated whole. The moment includes all the immensely rich components of the visual scene along with the many abstract associations included in your conception of democracy.
Finally, what about when our thoughts are racing or we struggle to focus? Again, we may use terms like “fragmented” or “chaotic” to describe the state of mind. But, again, the feeling of fragmentation—a single moment of that experience—is still a unitary experience.
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Isn't "definiteness" in the exclusion axiom the same thing as "specificity" in the information axiom?
The exclusion axiom states that every experience is definite. But how is this different from what was already established with the information axiom, saying that every experience is specific? IIT sees these essential properties of experience as tightly related but distinct. Information states that an experience is specific in the sense that it is not vague or generic—it is this experience. Exclusion adds to this by saying that an experience is exclusively this experience—not a greater or lesser one. Put another way, information establishes that an experience is always exactly what it is, while exclusion adds the fact that it contains what it contains—that there is a boundary to the experience, with specific contents in and others out.
The etymology of definite should help make this distinction memorable in that the “fin” root means “boundary.”
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Aren’t there some experiences that have no structure?
The composition axiom states that every experience is structured. Some people may claim to have experiences with no structure, often citing states of deep meditation or those induced by psychedelics. Some meditators, for example, describe a state in which there are no thoughts, no sounds, no bodily sensations, no objects in the visual field, no self. They describe this experience as pure “vastness,” “limitlessness,” or “openness.” Even these experiences, however, are highly structured in that they include extendedness: space has a right and a left half, which in turn contain a great number of regions of different sizes, all at some distance from one another (and much more). Even an experience of pure “emptiness” must include some sense of space that is empty. In sum, it is extremely difficult to have or conceive of an experience that does not somehow feel spatial. And when we introspect the feeling of space (both visual and somatosensory), we discover a strikingly rich internal structure (see Contents of experience: Space).
Let us grant, however, that an experience without spatial extendedness may be possible. Imagine, for example, the taste of grapefruit filling your experience in its entirety, with all other modalities gone. Even such a paradigmatic case of a simple, atomic quale—a pure gustatory experience—also has structured content: it feels like the taste of grapefruit—it is sour, bitter, and sweet at the same time. Could you experience the taste of grapefruit without that experience having a sour, bitter, and sweet component? If it didn’t, how could it be an experience of that taste anymore? The same goes for an experience of pure bitterness: how could it possibly feel different from other experiences if it weren’t because it has different components, structured in a different way?
We can go even further: can you conceive of the experience of a non-further-specified atomic quality—a “this”? This limit case challenges our imagination and marks the territory where our introspection cannot help anymore. We can at least notice, however, that the more we strip structure out of experience, the harder it becomes to conceive of such an experience. Most importantly, it is impossible to conceive of an experience devoid of all components, a contentless experience. An experience without content cannot be an experience at all. And an experience of “nothingness” is merely a play on words, for it must be distinguishable from “somethingness”—it must have minimal structure.
Experience is “what it is like to be,” and any experience will necessarily contain structured content—a “what” that “it is like to be.”
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What counts as a "component" of experience?
The composition axiom states that every experience is structured by many components, which we call phenomenal distinctions bound by phenomenal relations. Let us revisit the main example here. Imagine that is you, lying on the bed holding the book. Your experience has countless components—the most obvious ones being your body, the bed, the book, your hands, your shoes, the floor, the walls, the windows, and so on. Any one of these components comprises sub-components: Your body includes your hand, which includes your fingers, which include your fingernails, etc. The book comprises its oblong cubic shape; hues of blue, gray, and white; the words in the title, which themselves comprise letters, which again comprise their own unique shapes; and so forth.
Why do these various combinations feel clearly to be components, while others do not? Why does book shape+blue+letters feel like a component, while bed+shoe does not? IIT aims to give a complete answer on the physics side of the ledger—in terms of cause–effect power. But for now, how can we answer this question in phenomenological terms only?
Perhaps the best we can say is that book shape+blue+letters “hangs together”; these elements feel bound to one another in the experience in a way that bed+shoe does not. Phenomenal components are not arbitrary subsets; rather, they are whatever hangs together well in our experience. And when we speak of the “structure” of an experience, we refer to the myriad, yet specific, ways in which the experience feels to hang together.
This definition may appear to point out the obvious, but imagine if you had apperceptive visual agnosia. The low-level features of the visual scene would be identical (colors, lines, basic shapes, etc.), and you would still be able to steer your attention to the various elements, but the scene would not hang together the same way, or at all. The grouping book shape+blue+letters may feel just as arbitrary as bed+shoe.
If you were to catalog everything that hangs together well in this scene, the list would feel endless. Components would be formed through all senses, and often combinations of senses. They would also include abstractions such as center, periphery, left side, or top half. These are not objects, like our other examples, but they are essential components in that they give spatial structure to the scene. If they weren’t there, the scene would feel collapsed in on itself.
Isn’t this definition of components highly subjective? Yes, and it should be. In phenomenology, we talk about how things feel (how we experience them). And the feeling of what hangs together differs somewhat from person to person, and even for the same person over time. Through modulating your attention, you may even create components where there were none. You do this all the time as you learn or gain expertise through focusing attention. For example, the two sticks to the right might appear to be just that—two sticks. For a percussionist, however, they are a single instrument called the clave. In this sense, bed+shoe may start feeling more and more like a quasi-component the more this text talks about it.
The examples of components we have given so far have been quite coarse—they are thus called compound distinctions bound by compound relations. What are the lowest-level components of experience? There is clearly a limit to how far down we can decompose bundles of components. The blue of the book, for example, cannot be dissected further through introspection—it feels monolithically blue. But the book shape can be subdivided into individual lines related in specific ways. If we zoom in through our mind’s eye on one of these lines, they too can be further subdivided as a finite string of overlapping spots. And here, our ability to introspect bottoms out.
Nevertheless, given that decomposition is possible, it is reasonable to infer that there must be an atomic level of phenomenal components and the ways they are bound together. In IIT, we refer to this atomic level as elementary distinctions, which are bound by elementary relations. These are assumed to be the building blocks of all the components that structure our experience.
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