Axioms & Postulates
From Phenomenology to Physics
Summary
The five axioms of integrated information theory (IIT) express the essential properties of experience, discovered through introspection and reasoning. In the IIT method, we then ask, What physical properties of the substrate of consciousness might account for these five properties of experience? The answer is found by formulating each of the phenomenal axioms as a physical postulate that the substrate of consciousness must fulfill—that is, by formulating each axiom as a postulate in terms of cause–effect power.
This page offers a succinct overview of the axioms and postulates. Detailed explanations of each axiom–postulate pair can be found on the linked pages.
Five Axioms: Essential properties of every experience
What are the differences between hearing a Bach fugue, feeling a toothache, dreaming of flying, and resting in deep meditative absorption? Try to list them out. You could spend the rest of your life on this list, and there would still be more to say. But what if you were to describe what these experiences have in common? This list would be short and pithy—getting to the heart of what it means to have any experience whatsoever.
You might begin by observing that in each case, there is “something it is like” to experience them [1]. The something is what varies, but the fact that they feel like something is shared across these and every other experience—otherwise, it wouldn’t be an experience at all. Your own experience requires no proof: you know you are conscious. Likewise, experience is the single thing you cannot deny “from within” either. Paraphrasing Descartes’s cogito argument, the presence of your experience is irrefutable and thus proof that something exists (see 0th Axiom) [2].
The five axioms of IIT begin where Nagel and Descartes leave off. They characterize the essential properties of all experiences from the only authoritative perspective—yours and mine as experiencing subjects. This step is necessary to study consciousness scientifically: before we develop hypotheses and enter the lab, we must agree on and thoroughly describe the object of study—in this case, the properties of experience. Though we must use introspection in this step, the result is nevertheless a set of axioms that are universal in the sense that they can (and should) be confirmed by each person independently. This step of characterizing experience has been often ignored in the science of consciousness, yet only by first characterizing experience precisely can we then account for it precisely.
The five axioms are essential properties of experience because they characterize what experience is—or the nature of experience—and because they are irrefutably true of every conceivable experience, as confirmed through introspection and reflection alone. The axioms can be most succinctly stated as follows (the links offer extended explanations):
Existence (0th axiom): Experience exists: there is something.
Intrinsicality: Experience is intrinsic: it exists for itself.
Information: Experience is specific: it is this one.
Integration: Experience is unitary: it is a whole, irreducible to separate experiences.
Exclusion: Experience is definite: it is this whole.
Composition: 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.
In characterizing experience, the axioms characterize phenomenal existence. In line with Descartes’s cogito, the existence of one’s own experience is, strictly speaking, the only irrefutable truth. For IIT, this has not only epistemological but also ontological import: to reflect on the properties of experience is to reflect on the properties of existence.
The axioms of IIT are not necessarily self-evident, but they are indeed irrefutable. This means that one can try to doubt them, but through the process of doubting them, we necessarily confirm them [3]. They are also immediate in experience: just as Descartes needed no proof for his cogito, the axioms of IIT can only be discovered (and confirmed) through introspection and reflection.
In compiling a list of essential properties of consciousness, we should also consider what should be left off the list. Non-essential properties of consciousness are accidental (or “contingent”) if they may apply to some experiences but not others. Some obvious candidates are color and pain because we can easily imagine experiences without them. Less obvious candidates might be space and time, yet, in IIT, these are not axioms as they are not essential properties of every conceivable experience.
As you grapple with the five axioms, keep in mind that you may at times feel like a fish trying to make sense of water: they aim to describe facts about every experience of your life—features that are omnipresent and thus challenging to recognize. In this sense, a given axiom may even appear trivial at points. The importance of each axiom, however, will become clearer once it is paired with its respective postulate, or essential property of the substrate of consciousness.
Footnotes
Five Postulates: Essential properties of the substrate of consciousness
The five essential properties of experience outlined above must have an explanation—how might we account for them in physical terms? Based on minimal methodological assumptions, IIT answers this question by formulating each of the five axioms above as a postulate about the substrate of consciousness.
Why not just look directly at the brain to account for the axioms? Isn’t first “formulating” the axioms as postulates a roundabout approach? A more complete response is given here. But, in short, we don’t start from the brain because we have little idea what we’re looking for. The human brain is, by many measures, the most complex known object in the universe, with approximately 80 billion neurons and 100 trillion synapses. We need guidance on what aspect of this sublime jumble might let us account for the two why questions that IIT aims to answer as a theory of consciousness.
IIT constrains the search in three ways. First, we look specifically for physical properties that correspond to the essential properties of experience (axioms). Second, we start from a highly parsimonious notion of the physical as cause–effect power—the ability to “take and make a difference,” as demonstrated through operational interventions (see 0th postulate.) And third, we deliberately work with idealized systems of a few units, so that we can characterize cause–effect power as exhaustively as possible in a controlled setting. This approach does not mean that we ignore all we know about neurons and synapses, and about the neural, functional, and behavioral correlates of consciousness. Rather, we first use the postulates to establish a principled explanation of consciousness in physical terms, and then turn to empirical neuroscience to validate this explanation.
We saw above that each axiom characterizes an essential property of experience—one that defines what experience is. Each postulate, in turn, characterizes how the cause–effect power of a substrate of consciousness must be to account for the respective axiom. Thus they are called postulates because they are postulated based on what we know about the essential properties of experience.
The postulates can be most succinctly stated as follows (the links offer extended explanations):
Existence (0th postulate): The substrate of consciousness can be characterized operationally by cause–effect power: its units must take and make a difference.
Intrinsicality: Its cause–effect power must be intrinsic: it must take and make a difference within itself.
Information: Its cause–effect power must be specific: it must be in this state and select this cause–effect state.
Integration: Its cause–effect power must be unitary: it must specify its cause–effect state as a whole set of units, irreducible to separate subsets.
Exclusion: Its cause–effect power must be definite: it must specify its cause–effect state as this whole set of units.
Composition: Its cause–effect power must be structured: subsets of 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.
As a reminder, the postulates do not presume a substrate to exist as such. We rather treat the substrate as our operational basis to assess the physical properties in question. Only by applying all postulated properties together can we determine and characterize the substrate of consciousness. By IIT, what truly exists in the end is not the simple substrate of units per se, but rather a complex unfolded as a cause–effect structure (or Φ-structure). This is what truly exists because its properties are what correspond one-to-one with the properties of experience—the existence of which is immediate and irrefutable. For more, see the explanatory identity of IIT.
Axiom → Postulate Summary
Below is a synopsis of how each axiom is formulated as its corresponding postulate. This overview is meant to serve more as an abridged reference than as a learning tool; we suggest you click on the individual axiom–postulate pages to explore them more thoroughly.
Given that my experience exists, immediately and irrefutably (left), I infer that the substrate of consciousness can be characterized operationally by cause–effect power, which I can probe by observing and manipulating (eye & hand on brain) the states of its units. Its cause–effect power can be captured in a transition probability matrix (not shown) and depicted as a substrate graph (middle).
Just as my experience exists for itself (left), the cause–effect power of its substrate must be intrinsic—it must take and make a difference within itself (right). The dotted blue line on the substrate indicates a candidate substrate (ABCD), whose causal powers may be analyzed within itself, holding background conditions fixed (pins).
Just as my experience is specific (left), the cause–effect power of its substrate must be specific (right): it must be in a specific state (Abcd, uppercase ON, lowercase OFF) and select a specific cause–effect state (aBcd–abCd). And just as my experience—by virtue of being specific—differs from countless other experiences (left), the cause–effect state of its substrate is also differentiated from a repertoire of alternative states (right).
Just as my experience is unitary (left), the cause–effect power of its substrate must be unitary (right). This can be evaluated by finding the system’s minimum partition (orange), which yields its integrated information (φs): the degree to which the cause–effect state specified by its current state (Abcd) cannot be reduced to that specified by separate parts (here, Ab, c, & d).
Just as my experience is definite (left), the cause–effect power of its substrate must be definite (right). A complex (Abcd) is the set of units that exists the most (for which φs is maximal), excluding all smaller or larger overlapping sets. Here Abcd exists the most (blue area), thus excluding, for example, Abc and iAbcdo (dashed gray lines).
Just as my experience is structured by phenomenal distinctions and relations (left), the cause–effect power of the complex must be structured by causal distinctions and relations specified by subsets of units over subsets of units (right). Together, distinctions and relations compose the Φ-structure unfolded from a complex, which captures the quality and quantity of experience.
Frequently Asked Questions
If you would like to ask or upvote a new question, please see the discussion threads at the bottom of each specific axiom/postulate page.
Axioms/Postulates in General
What is meant by the term axiom in IIT?
If the axioms are “immediate” and “irrefutably true,” shouldn’t they also be self-evident?
Why aren’t the experiences of space and time considered axioms in IIT?
Why are the postulates so important in IIT?
If IIT starts from experience, isn't this method "subjective" and thus unscientific?
What is the meaning of cause–effect power in light of other notions of “causal power”?
How does intrinsic in IIT relate to the notion as used in philosophy (e.g. Lewis)?
Is my experience "specific" owing to the potential experiences I could be having?
Can't I have a vague or generic experience, which isn't "specific"?
How is information in IIT different from "Shannon information"?
If I have two unrelated contents of experience, doesn't this mean my experience is not "unitary"?
Aren’t there some experiences that have no structure?