# Glossary of IIT Terms *Source: https://www.iit.wiki/glossary* Note that IIT's terminology has grown more precise as the theory has developed. This glossary corresponds to the terminology in [IIT 4.0](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1011465). Entries will be refined and new terms added as needed. Cite the glossary: Grasso, Matteo, Bjørn Erik Juel, Jeremiah Hendren, and Giulio Tononi. "Glossary of IIT Terms." In *Integrated Information Theory Wiki*. Center for Sleep and Consciousness, University of Wisconsin–Madison. Last modified 30 June 2024. DOI: 10.5281/zenodo.14160283. . ### BibTeX ```bibtex @misc{grasso2024glossary, author={Grasso, Matteo and Juel, Bj{\o}rn Erik and Hendren, Jeremiah and Tononi, Giulio}, title={Glossary of IIT Terms}, howpublished={In {\em{Integrated Information Theory Wiki}}}, year={2024}, publisher={Center for Sleep and Consciousness, University of Wisconsin--Madison}, note={Last modified 30 June 2024. DOI: 10.5281/zenodo.14160283}, url={https://www.iit.wiki/glossary} } ``` - 0th axiom - 0th postulate - accidental properties - activation function - actual causation - atomism - axioms - background conditions - candidate - causal conditioning - causal marginalization - unconditional causal marginalization - conditional causal marginalization ("pinning") - causal power - cause–effect - cause–effect power - cause–effect state - cause–effect structure - complex - composition - compound distinction - compound relation - concept - conceptual structure - congruent - consciousness - cut - degree - differentiation - distinction - Eleatic principle - elementary distinction - elementary relation - entity - essential properties of experience - exclusion - existence - experience - explanatory identity - extrinsic - fault line - grain - identity - immediate - inference from a good explanation - inference to a good explanation - information - informativeness - integration - integrated information - φs – “system phi” - φd – “distinction phi” - φr – “relation phi” - φu – “unit phi” - Φ – “big phi” - ΦR – “Φ-fold phi” - intrinsicality - intrinsic difference - intrinsic entity - intrinsic information - Informativeness - Selectivity - intrinsic perspective - introspection - irreducible - irrefutable - manipulate and observe - marginalization - matching - meaning - mechanism - minimum partition - monad - network - neural correlates of consciousness (NCCs) - neural substrate of consciousness (NSC) - noising - operational - order - part - partition - perturbational approach - perturbational complexity index (PCI) - phenomenology - phenomenal existence - phenomenal structure - Φ ("big phi") - φ ("small phi") - Φ-fold - Φ-structure - physicalism - physical existence - physical substrate of consciousness (PSC) - pinning - posterior hot zone - postulates - powerset - principle of being - principle of maximal existence - principle of minimal existence - purview - realism - relation - relation face - repertoire - selectivity - self-loop - spot - state - substrate - substrate graph - substrate of consciousness - system - transition probability matrix (TPM) - state-by-node TPM - cause TPM - effect TPM - unbinding - unfolding - unit ## **0th axiom** The 0th [axiom](https://www.iit.wiki/glossary#h.qdzuf1i5vio4) of IIT is that *experience exists*. This insight is [immediate](https://www.iit.wiki/glossary#h.mtq44ohzelsq) and [irrefutable](https://www.iit.wiki/glossary#h.lfstqcfh9gsn), and the starting point of IIT, estamblishing the primacy of [experience](https://www.iit.wiki/glossary#h.97uzewmap754) in both an epistemological and ontological sense. Building from this ground truth, IIT then characterizes the essential properties of every experience (the [five axioms of IIT](https://www.iit.wiki/overview/axioms-and-postulates#h.gh95zjki6tz4)) and the [accidental properties](https://www.iit.wiki/glossary#h.5ec6914i1gwq) of specific experiences. For more, see * [Foundations: 0th Axiom](https://www.iit.wiki/overview/foundations#h.o56f0fhw0252) * [FAQ: What is meant by the term *axiom* in IIT?](https://www.iit.wiki/faqs/axioms#h.qusvdrxctnxr) * [Paper: Consciousness and the Fallacy of Misplaced Objectivity](https://doi.org/10.1093/nc/niab032) (an academic paper on the “phenomenology-first” approach of IIT) ## **0th postulate** The 0th [postulate](https://www.iit.wiki/glossary#h.irdac769fidh) of IIT—also called the *existence postulate*—is that the [substrate of consciousness](https://www.iit.wiki/glossary#h.j5clb514qcec) can be characterized operationally by [cause–effect power](https://www.iit.wiki/glossary#h.vlk7u52cim8x): its units must *take and make a difference*. The 0th postulate is the physical counterpart of IIT’s [0th axiom](https://www.iit.wiki/glossary#h.ihc2d4eaahbj). In other words, it is IIT’s starting point in its attempt to account for [experience](https://www.iit.wiki/glossary#h.97uzewmap754) in physical terms: it guides us to analyze the substrate of consciousness purely in terms of cause–effect power. The 0th postulate is supported by IIT’s [three methodological assumptions](https://www.iit.wiki/overview/foundations#h.8rzkbmyfu80) of *realism*, *physicalism*, and *atomism*. For more, see * [Foundations: 0th Postulate](https://www.iit.wiki/overview/foundations#h.5h9ssjclzgt9) * [FAQ: What is the meaning of cause–effect power in light of other notions of “causal power”?](https://www.iit.wiki/faqs/postulates#h.nh5gykv9jnng) ## **accidental properties** The *accidental* properties of an [experience](https://www.iit.wiki/glossary#h.97uzewmap754) are those that are true of some experiences, but—contrary to the [essential properties of experience](https://www.iit.wiki/glossary#h.qdzuf1i5vio4)—they are not [irrefutably true](https://www.iit.wiki/glossary#h.lfstqcfh9gsn) of every conceivable experience (hence they’re accidental and not essential). For instance, even if most of the time we hear sounds, auditory contents are accidental because there can clearly be experiences with no sound (e.g., when we are in a perfectly silent room). The research program of IIT aims to account for accidental properties of experience including [space, time, objects, and local qualities](https://www.iit.wiki/contents) such as color, pain, etc., whose underlying neural mechanisms may correspond to [content-specific NCCs](https://www.iit.wiki/glossary#h.hqe2k9cdzma0). Though accidental, these properties must nonetheless be [accounted for by a theory of consciousness](https://www.iit.wiki/overview#h.qvp0etiy6a1z). ## **activation function** The activation function of a [unit](https://www.iit.wiki/glossary#h.y4l991ydyf0n) expresses its probability of transitioning to a particular [state](https://www.iit.wiki/glossary#h.hnb1zhy1izf8) (e.g., ON) as a function of inputs. It can be obtained by controlled experiments—by providing all possible inputs and measuring the subsequent output—or by mathematically modelling it based on our best knowledge of the units in question. In IIT, we often model systems using sigmoid functions since they are thought to be a good approximation in modeling neural activity at the relevant [grain](https://www.iit.wiki/glossary#h.wecg9hts0fae). For sigmoid functions, the input is given as a sum of the states of input units multiplied by their connection strength to the unit in question. In the example below, the probability of the modeled binary unit to turn ON is represented on the y-axis, and the sum of its inputs on the x-axis. For this particular function, when the sum of the inputs is 1, the probability of the node turning on is roughly 0.95. Note that the activation function is a mathematical model of the unit and is used to construct its [TPM](https://www.iit.wiki/glossary#h.rgqyfluj1zit) when we model a [substrate](https://www.iit.wiki/glossary#h.63hvurupgbzf) of interest (as opposed to experimentally assessing its powers using the [perturbational approach](https://www.iit.wiki/glossary#h.urmduwg8ibdt)). Activation functions can be constructed to model any kind of unit to any level of precision, but they always remain mathematical models of the unit in question. ## **actual causation** The *actual causation* framework was developed following the [postulates](https://www.iit.wiki/glossary#h.irdac769fidh) and principles of IIT. However, rather than describing the [intrinsic](https://www.iit.wiki/glossary#h.2w4jmrulzrgg) causal powers of a [substrate](https://www.iit.wiki/glossary#h.63hvurupgbzf) in a [state](https://www.iit.wiki/glossary#h.hnb1zhy1izf8) (*potential* causes and effects), it was designed to uncover extrinsic, *actual* causes and effects of a substrate in a state. That is, given that a physical substrate (constituted of a set of [operationally](https://www.iit.wiki/glossary#h.vztp822ktk99) defined [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n) at a particular [grain](https://www.iit.wiki/glossary#h.wecg9hts0fae)) has dynamically transitioned through an actual series of states, we can use the substrate’s [TPM](https://www.iit.wiki/glossary#h.rgqyfluj1zit) and the actual causation framework to uncover the actual causes and effects of any occurrence (a set of units in a state) within the series of observed states. For example, the figure below depicts a substrate observed to have transitioned through the series of states (*t0*: ***Abc***, *t1*: ***ABc***, *t2*: ***abC***, *t3*: ***aBc***). Using actual causation, we can get quantitative answers to questions such as “What was the actual cause in *t1* of the occurrence ***bC*** at *t2*?” Was it ***ABc*** as a whole, or perhaps only ***A*** alone, or ***Ac*** together? Likewise, the framework could help us answer “What was the actual effect of unit ***A*** (ON) at *t0*?” or “What was the chain of occurrences that actually caused ***c*** (OFF) at *t3*?” or “What is the structure of actual causes and effects that bind *t2* to *t1* and *t3*, respectively?” ![](/corpus/figures/iit-wiki-glossary/glossary-image1.png) For details on the framework, see [Albantakis, L., Marshall, W., Hoel, E., & Tononi, G. (2019). What caused what? A quantitative account of actual causation using dynamical causal networks. *Entropy*, *21*(5), 459](https://www.mdpi.com/1099-4300/21/5/459). For applications of actual causation, see, for example, - Mayner, W., Juel, BE., Tononi, G. (Forthcoming). Meaning, perception, and matching: Quantifying how the structure of experience matches the environment. - [Juel, B. E., Comolatti, R., Tononi, G., & Albantakis, L. (2019, July). When is an action caused from within? Quantifying the causal chain leading to actions in simulated agents. In *Artificial Life Conference Proceedings* (pp. 477-484)](https://direct.mit.edu/isal/proceedings/isal2019/31/477/99174). - [Tononi, G., Albantakis, L., Boly, M., Cirelli, C., & Koch, C. (2022). Only what exists can cause: An intrinsic view of free will. *arXiv preprint arXiv:2206.02069*](https://arxiv.org/ftp/arxiv/papers/2206/2206.02069.pdf). ## **atomism** *Atomism* states that to provide an explanation that is as complete as possible, we ought to assess [cause–effect power](https://www.iit.wiki/glossary#h.vlk7u52cim8x) down to the smallest constituents (“atoms”) that we can [observe and manipulate](https://www.iit.wiki/glossary#h.urmduwg8ibdt). Together with [realism](https://www.iit.wiki/glossary#h.2v5fky6ntlfw) and [physicalism](https://www.iit.wiki/glossary#h.jtbdxiwp9igh), atomism is one of [three methodological assumptions](https://www.iit.wiki/overview/foundations#h.8rzkbmyfu80) of IIT. Note that atomism in IIT is an [operational](https://www.iit.wiki/glossary#h.vztp822ktk99) assumption, not a reductionist ontological position. For more, see * [Foundations of IIT](https://www.iit.wiki/overview/foundations) * [FAQ: If IIT assumes "atomism," does this make it a reductionist theory of consciousness?](https://www.iit.wiki/faqs/philosophy#h.p8d3ayub7a3f) ## **axioms** The axioms of IIT capture the essential properties of [experience](https://www.iit.wiki/glossary#h.97uzewmap754) (i.e., of [consciousness](https://www.iit.wiki/glossary#h.mnf6qtn02rcp)). They are not logical “propositions” but rather [phenomenological](https://www.iit.wiki/glossary#h.8j4o0g5ssetv) properties that are [immediate](https://www.iit.wiki/glossary#h.mtq44ohzelsq) and [irrefutably true](https://www.iit.wiki/glossary#h.lfstqcfh9gsn) of every conceivable experience. Starting from the fact that experience exists ([0th axiom](https://www.iit.wiki/overview/foundations#h.o56f0fhw0252)), the axioms express five properties essential to every experience: [intrinsicality](https://www.iit.wiki/glossary#h.2w4jmrulzrgg), [information](https://www.iit.wiki/glossary#h.9xr7m5huna7m), [integration](https://www.iit.wiki/glossary#h.cpmqk4mzfdb9), [exclusion](https://www.iit.wiki/glossary#h.wk5hvdb57mru), and [composition](https://www.iit.wiki/glossary#h.j0xivbr6tr10). IIT aims to account for each of these properties by formulating them as a corresponding [postulate](https://www.iit.wiki/glossary#h.irdac769fidh)—that is, an essential property of the [substrate of consciousness](https://www.iit.wiki/glossary#h.j5clb514qcec). For more, see * [Five Axioms: Essential Properties of Every Experience](https://www.iit.wiki/overview/axioms-and-postulates#h.gh95zjki6tz4) * [FAQ: What is meant by the term *axiom* in IIT?](https://www.iit.wiki/faqs/axioms#h.qusvdrxctnxr) ## **background conditions** The term *background conditions* refers to the current state of the [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n) that are outside the [candidate](https://www.iit.wiki/glossary#h.8mzotxp600xu) [substrate of consciousness](https://www.iit.wiki/glossary#h.j5clb514qcec). Operationally, these units are made causally inert through [causal marginalization](https://www.iit.wiki/glossary#h.4917uuub4bb2). Background conditions can be thought of as the “context” in which the substrate is situated. In the case of the substrate of consciousness in the brain, likely background conditions include the particular [state](https://www.iit.wiki/glossary#h.hnb1zhy1izf8) of subcortical activation, the provision of oxygenated blood, and the state of sensory relay cells in the thalamus. For more, see * [Intrinsicality Postulate](https://www.iit.wiki/axioms-and-postulates/intrinsicality#h.ffm1nm3ehxmu) * [FAQ: Does intrinsicality mean that the substrate of consciousness is not influenced by its environment?](https://www.iit.wiki/faqs/postulates#h.xhp2q0xa2bgh) * [FAQ: What would be considered background conditions in the human brain?](https://www.iit.wiki/faqs/postulates#h.93bxz5sygqri) * [Koch et al. 2016](https://doi.org/10.1038/nrn.2016.22) (where the term was first used in NCC research) ## **candidate** The term *candidate* is used to describe a [unit](https://www.iit.wiki/glossary#h.y4l991ydyf0n), [substrate](https://www.iit.wiki/glossary#h.63hvurupgbzf), [distinction](https://www.iit.wiki/glossary#h.ixtdw1emrvga), etc. until it is confirmed that it satisfies the relevant [postulates](https://www.iit.wiki/glossary#h.irdac769fidh). For instance, in the operations to identify the [main complex](https://www.iit.wiki/glossary#h.b6fxhbe1r3re), an early step is to define our substrate as a set of units and apply the [intrinsicality postulate](https://www.iit.wiki/glossary#h.2w4jmrulzrgg) (by treating the remaining units as background conditions). The substrate we define in this step is a mere *candidate* because it might turn out that it is [reducible](https://www.iit.wiki/glossary#h.sw1ddv976914) (if it doesn’t satisfy the [integration postulate](https://www.iit.wiki/glossary#h.cpmqk4mzfdb9)). ## **causal conditioning** This was an operation (and term) used in earlier IIT publications. This operation is now covered by [conditional causal marginalization](https://www.iit.wiki/glossary#h.4917uuub4bb2). ## **causal marginalization** *Marginalization* is a standard mathematical operation from probability theory: averaging over the possible values of one set of variables to determine the marginal contribution of another. In IIT, we apply *causal marginalization*, which just means that it is applied to probabilities obtained from causal interventions (see [perturbational approach](https://www.iit.wiki/glossary#h.urmduwg8ibdt) & [TPM](https://www.iit.wiki/glossary#h.rgqyfluj1zit)). That is, when assessing the causal powers of a [substrate](https://www.iit.wiki/glossary#h.63hvurupgbzf), a certain set of [unit](https://www.iit.wiki/glossary#h.y4l991ydyf0n) [states](https://www.iit.wiki/glossary#h.hnb1zhy1izf8) is averaged over (marginalized out) to leave only the contribution of the remaining unit states. This method is used to “screen off” some [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n) (those that are averaged out) in order to isolate the causal powers among the remaining units. In IIT, marginalization is applied with either conditional or uniform distributions, depending on what we aim to quantify: ### **unconditional causal marginalization** To evaluate [candidate](https://www.iit.wiki/glossary#h.8mzotxp600xu) [distinctions](https://www.iit.wiki/glossary#h.ixtdw1emrvga) (see [Computing *Φ*: Step 6.1—Distinctions](https://www.iit.wiki/unfolding#h.k3lm9nf12xz2)), we use the standard (unconditional) marginalization. Here, we marginalize out all units in the complex that are not part of the candidate [mechanism](https://www.iit.wiki/glossary#h.bdzvjltpbxqw) or [purview](https://www.iit.wiki/glossary#h.e5mwd8ynj4am), assuming a uniform distribution over their states. This ensures that any remaining causal power should indeed be *by* the mechanism and *over* the purview. Furthermore, using the uniform distribution ensures that we make no assumptions about the distribution of any relevant unit, as is required when taking the [intrinsic perspective](https://www.iit.wiki/glossary#h.lda1vi9ede5q). ### **conditional causal marginalization** We also use causal marginalization when applying the [intrinsicality postulate](https://www.iit.wiki/overview/axioms-and-postulates/intrinsicality) (see [Computing *Φ*: Step 2—Intrinsicality](http://www.iit.wiki/unfolding#h.5qi5tc64lye6)), where we obtain the (cause and effect) [TPM](https://www.iit.wiki/glossary#h.rgqyfluj1zit)s of a [candidate](https://www.iit.wiki/glossary#h.8mzotxp600xu) [complex](https://www.iit.wiki/glossary#h.b6fxhbe1r3re) and remove any causal influence of units outside the candidate. In this case, however, the marginalization is done using a conditional distribution of substrate states obtained by conditioning on the current state of the units outside of the complex (see [background conditions](https://www.iit.wiki/glossary#h.ot008m3n2clu)). Since the current state of the background units is informative of their previous state, when marginalizing out their contribution, it is important to use a distribution over their previous states conditioned on their current state. Note that conditional causal marginalization is sometimes called “pinning” for short. For more, see: * [Computing *Φ*: Step 2—intrinsicality](http://www.iit.wiki/unfolding#h.5qi5tc64lye6) * [Computing *Φ*: Step 6.1—Distinctions](https://www.iit.wiki/unfolding#h.k3lm9nf12xz2) * [IIT 4.0](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1011465) (for precise mathematical definitions) ## **causal power** The term *causal power* is generally used as a synonym for [cause–effect power](https://www.iit.wiki/glossary#h.vlk7u52cim8x) in IIT. However, it may occasionally appear in a more general, less technical sense—as simply the capacity to affect something or be affected by something. ## **cause–effect** A *cause–effect* is another word for a [distinction](https://www.iit.wiki/glossary#h.ixtdw1emrvga): a cause and an effect (i.e., a cause–effect) that are linked through a [mechanism](https://www.iit.wiki/glossary#h.bdzvjltpbxqw). ## **cause–effect power** *Cause–effect power* is the mark of the [physical](https://www.iit.wiki/glossary#h.jtbdxiwp9igh): the ability to “take and make a difference.” This notion is the starting point in characterizing the [substrate of consciousness](https://www.iit.wiki/glossary#h.j5clb514qcec) ([0th postulate](https://www.iit.wiki/glossary#h.ny792kcl3wmd)). Ultimately, for a candidate substrate to exist as a substrate of consciousness (i.e., [intrinsic entity](https://www.iit.wiki/glossary#h.dfvlx69kg5m4)), its cause–effect power must satisfy all five [postulates](https://www.iit.wiki/glossary#h.irdac769fidh)—that is, it must be intrinsic, specific, unitary, definite, and structured. For more, see: * [Foundations: Phenomenal & Physical Existence](https://www.iit.wiki/overview/foundations) * [FAQ: What is the meaning of cause–effect power in light of other notions of “causal power”?](https://www.iit.wiki/faqs/postulates#h.nh5gykv9jnng) ## **cause–effect state** The *cause–effect state* comprises the cause state and effect state selected by the [system](https://www.iit.wiki/glossary#h.4bdc61agv7oe) in its current state. Following the [information postulate](https://www.iit.wiki/overview/axioms-and-postulates/information), the cause and effect states selected are those that maximize [intrinsic information](https://www.iit.wiki/glossary#h.vkva0021by39). The cause–effect state of the system constrains which [distinctions](https://www.iit.wiki/glossary#h.ixtdw1emrvga) can exist in the [cause–effect structure](https://www.iit.wiki/glossary#h.u3dcbculq7ms) it specifies. That is, only distinctions whose [purviews](https://www.iit.wiki/glossary#h.e5mwd8ynj4am) are [congruent](https://www.iit.wiki/glossary#h.cm6by218tf7l) with the cause–effect state of the system can exist. For more, see * [Information postulate](https://www.iit.wiki/overview/axioms-and-postulates/information#h.lnlbeg807l4) * [Unfolding – Step 3: Apply information](https://colab.research.google.com/drive/17pNdp6HmQaYfh9DxUW0jhgaPFqGKJlf_#scrollTo=A7vxSeRcrnJK) ## **cause–effect structure** See [*Φ*\-structure](https://www.iit.wiki/glossary#h.u3dcbculq7ms). ## **complex** A *complex* (or *maximal substrate*) is a set of units that satisfies the [postulates](https://www.iit.wiki/overview/axioms-and-postulates#h.8d1ocowludyo). In other words, it is a substrate that lays a stronger claim to existence than any [candidate](https://www.iit.wiki/glossary#h.8mzotxp600xu) [substrate](https://www.iit.wiki/glossary#h.63hvurupgbzf) it overlaps with. In IIT’s ontology, a complex is a [substrate of consciousness](https://www.iit.wiki/glossary#h.j5clb514qcec), which—fully unfolded as a [*Φ*\-structure](https://www.iit.wiki/glossary#h.u3dcbculq7ms)—exists as an [intrinsic entity](https://www.iit.wiki/glossary#h.dfvlx69kg5m4). A given substrate of units may “condense” into various complexes. To identify their borders, we apply the postulates systematically (see [Computing *Φ*](https://www.iit.wiki/unfolding)): we first identify the *major complex* (or “main complex,” “first complex”)—the candidate with the highest [*φs*](https://www.iit.wiki/glossary#h.lv95466kjojq)—then among the remaining units, we identify the *minor complexes* (“second,” “third,” etc.). In the human brain, the major complex is presumed to be the [neural substrate of consciousness](https://www.iit.wiki/glossary#h.j16zhlml4tz1). ## **composition** Composition is the 5th [axiom](https://www.iit.wiki/glossary#h.qdzuf1i5vio4) and [postulate](https://www.iit.wiki/glossary#h.irdac769fidh) of IIT. As an axiom, it states that “[experience](https://www.iit.wiki/glossary#h.97uzewmap754) is *structured*: it is composed of [*distinctions*](https://www.iit.wiki/glossary#h.ixtdw1emrvga) and the [*relations*](https://www.iit.wiki/glossary#h.yp1dkd8f7s8u) that bind them together, yielding a [*phenomenal structure*](https://www.iit.wiki/glossary#h.ci0yggunfaj4) that feels *the way it feels*.” Formulated as a postulate, it states that “the [substrate of consciousness](https://www.iit.wiki/glossary#h.j5clb514qcec) must have *structured* [cause–effect power](https://www.iit.wiki/glossary#h.vlk7u52cim8x): subsets of its [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n) must specify [cause–effect states](https://www.iit.wiki/glossary#h.tp4brteczc2p) over subsets of units (*distinctions*) that can overlap with one another (*relations*), yielding a *cause–effect structure* (or [*Φ*\-structure](https://www.iit.wiki/glossary#h.u3dcbculq7ms)) that *is the way it is*.” For more, see * [Composition page](https://www.iit.wiki/overview/axioms-and-postulates/composition) * [FAQ: Aren’t there some experiences that have no structure?](https://www.iit.wiki/faqs/axioms#h.17zjnui8dg24) * [FAQ: What counts as a "component" of experience?](https://www.iit.wiki/faqs/axioms#h.i91i1ri1z1kc) * [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?](https://www.iit.wiki/faqs/axioms#h.tf5ab6cetopu) ## **compound distinction** A compound distinction is an [introspectable](http://www.iit.wiki/glossary?authuser=0#h.iohmb4ut7uw0) component of a [phenomenal structure](http://www.iit.wiki/glossary?authuser=0#h.ci0yggunfaj4), which is itself composed of elementary distinctions, which are not always introspectable. In physical terms, a compound (causal) distinction is the set of all [distinctions](http://www.iit.wiki/glossary?authuser=0#h.ixtdw1emrvga) specified picked out by a set of [units](http://www.iit.wiki/glossary?authuser=0#h.y4l991ydyf0n). ## **compound relation** A compound relation is an [introspectable](http://www.iit.wiki/glossary?authuser=0#h.iohmb4ut7uw0) component of a [phenomenal structure](http://www.iit.wiki/glossary?authuser=0#h.ci0yggunfaj4), which is itself composed of elementary relations, which are not always introspectable. In physical terms, a compound (causal) relation is the set of all [relations](http://www.iit.wiki/glossary?authuser=0#h.yp1dkd8f7s8u) between [distinctions](http://www.iit.wiki/glossary?authuser=0#h.ixtdw1emrvga) specified by a set of [units](http://www.iit.wiki/glossary?authuser=0#h.y4l991ydyf0n). ## **concept** This term was used in earlier IIT publications for what is now called a [distinction](https://www.iit.wiki/glossary#h.ixtdw1emrvga). ## **conceptual structure** This term was used in earlier IIT publications for what is now called a [*Φ*\-structure](https://www.iit.wiki/glossary#h.u3dcbculq7ms) (or *cause–effect structure*). ## **congruent** The term *congruent* is used to indicate whether two [states](https://www.iit.wiki/glossary#h.hnb1zhy1izf8) are in agreement. It is especially important in two steps of [unfolding](https://www.iit.wiki/glossary#h.frg5mnvcsu7): * When assessing the existence of a candidate [distinction](https://www.iit.wiki/glossary#h.ixtdw1emrvga), we make sure that its cause and effect [purview](https://www.iit.wiki/glossary#h.e5mwd8ynj4am) states are congruent with the [cause–effect state](https://www.iit.wiki/glossary#h.tp4brteczc2p) of the [substrate](https://www.iit.wiki/glossary#h.63hvurupgbzf) as a whole. For example, if the substrate specifies cause state *aBc* (OFF, ON, OFF), and a candidate distinction has cause purview *B* (ON), these are congruent. * When assessing [relations](https://www.iit.wiki/glossary#h.yp1dkd8f7s8u), we determine two (or more) distinctions to be related only if their purviews overlap congruently. For example, if two distinctions share purview [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n) (e.g., unit A), the state of that shared purview unit must be the same (e.g., both specify *A,* “ON”). ## **consciousness** In IIT, we often use the terms *consciousness* and [*experience*](https://www.iit.wiki/glossary#h.97uzewmap754) interchangeably, in the sense that being conscious is synonymous with having an experience. Yet there are slight nuances. *Consciousness* refers to having experiences regardless of their content, while *experience* is always of something specific. Hence we describe a patient as “losing consciousness” but not as “losing experience,” and we might say “my experience changed” (from one content to another) but not “my consciousness changed.” For more, see * [FAQ: What do you mean by consciousness?](https://www.iit.wiki/faqs/method#h.lbk0cbu6w8aw) * [Overview: What does it mean to explain consciousness scientifically?](https://www.iit.wiki/overview#h.qvp0etiy6a1z) ## **cut** When we assess the [irreducibility](http://www.iit.wiki/glossary?authuser=0#h.sw1ddv976914) of a system or mechanism, we apply a [partition](http://www.iit.wiki/glossary?authuser=0#h.tbsgfc5m3fti), which comprises a set of specific *cuts* among parts. The way we apply cuts varies for systems or mechanisms. But in general, to *cut* means to eliminate the causal constraint of one set of units upon another. For example, for system ABCD, cutting units A and B from C and D can be achieved by eliminating the causal constraints that part AB has over CD, or those that CD has over AB, or both. For details, see * [FAQ: What is a valid partition?](https://www.iit.wiki/faqs/technical#h.2xou8qbtjul1) ## **degree** *Degree* is used to define the number of elements that are bound (i.e., overlapping) in a [relation](https://www.iit.wiki/glossary#h.yp1dkd8f7s8u) or [relation face](https://www.iit.wiki/glossary#h.jbpcsbi2vw6e). The degree of a relation reflects the number of overlapping [distinctions](https://www.iit.wiki/glossary#h.ixtdw1emrvga). For example, a relation that binds three distinctions is a 3rd-degree relation (or a 3-relation). The degree of a relation face reflects the number of overlapping [purviews](https://www.iit.wiki/glossary#h.e5mwd8ynj4am). A relation face that binds together all causes and effects of the distinctions making up that 3-relation—six purviews in total—would be a 6th-degree relation face. For more, see: [Composition: Relations](https://www.iit.wiki/overview/axioms-and-postulates/composition#h.u591dz8u0iby) ## **differentiation** *Differentiation* is a consequence of the [information axiom and postulate](https://www.iit.wiki/overview/axioms-and-postulates/information): * On the axiom side: by virtue of being specific, each [experience](https://www.iit.wiki/glossary#h.97uzewmap754) also differs from a large [repertoire](https://www.iit.wiki/glossary#h.yfbi5xohkxxw) of other possible experiences. * On the postulate side: by virtue of being in its specific current [state](https://www.iit.wiki/glossary#h.hnb1zhy1izf8)—and thus specifying a specific [cause–effect state](https://www.iit.wiki/glossary#h.tp4brteczc2p)—the [substrate of consciousness](https://www.iit.wiki/glossary#h.j5clb514qcec) may also be in different states, which also specify different cause-effect states among a repertoire of possible ones. A related notion is *neurophysiological differentiation*, which refers to the number of different [states](https://www.iit.wiki/glossary#h.hnb1zhy1izf8) available to a [substrate](https://www.iit.wiki/glossary#h.63hvurupgbzf). This notion has been used to devise practically applicable measures of consciousness—such as the [perturbational complexity index](https://www.iit.wiki/glossary?authuser=0#h.wqwrlp5bgkhu). Note that in IIT literature, the term *differentiation* has sometimes been used to help understand the axiom/postulate of *information*—and sometimes treated as a synonym. Most precisely, however, differentiation is not itself an essential property of experience (and thus of its substrate); it is rather a consequence of the essential property. For more, see: * [Information postulate](https://www.iit.wiki/overview/axioms-and-postulates/information#h.lnlbeg807l4) * [Marshall, W., Gomez-Ramirez, J., & Tononi, G. (2016). Integrated information and state differentiation. *Frontiers in psychology*, *7*, 926\.](https://www.frontiersin.org/articles/10.3389/fpsyg.2016.00926/full) ## **distinction** A *distinction* is a “difference that makes a difference.” Phenomenally, a distinction is any aspect of our [experience](https://www.iit.wiki/glossary#h.97uzewmap754) that we can “pick out” through [introspection](https://www.iit.wiki/glossary#h.iohmb4ut7uw0)—for example, my hand, a musical tone, or the left half of visual space \[1\]. Physically, a (causal) distinction is the [cause–effect power](https://www.iit.wiki/glossary#h.vlk7u52cim8x) exerted by one subset of [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n) over other subsets within the [complex](https://www.iit.wiki/glossary#h.b6fxhbe1r3re). It thus comprises a [mechanism](https://www.iit.wiki/glossary#h.bdzvjltpbxqw), a cause [purview](https://www.iit.wiki/glossary#h.e5mwd8ynj4am), and an effect purview. Like the [system](https://www.iit.wiki/glossary#h.4bdc61agv7oe) as a whole, distinctions must adhere to the [postulates](https://www.iit.wiki/glossary#h.irdac769fidh) (save composition)—that is, they must be intrinsic, specific, unitary, and definite. Distinctions, and the [relations](https://www.iit.wiki/glossary#h.yp1dkd8f7s8u) that bind them, make up the fundamental components of structures in IIT—both [phenomenal structures](https://www.iit.wiki/glossary#h.ci0yggunfaj4) and [*Φ*\-structures](https://www.iit.wiki/glossary#h.u3dcbculq7ms). For more, see [Composition: Distinctions](https://www.iit.wiki/overview/axioms-and-postulates/composition#h.jndby56e0826). \[1\] As explained in the [information axiom](https://www.iit.wiki/overview/axioms-and-postulates/information#h.oavpyn809wg2), strictly speaking, any phenomenal distinction we can pick out through introspection is a *compound distinction* (meaning a set of elementary distinctions) owing to the limits of introspection. ## **Eleatic principle** See [principle of being](https://www.iit.wiki/glossary#h.lar9suu74goc). ## **elementary distinction** In [phenomenal](http://www.iit.wiki/glossary#h.8j4o0g5ssetv) terms, elementary distinctions are assumed to be the most basic components of a [phenomenal structure](http://www.iit.wiki/glossary#h.ci0yggunfaj4), and as such are not introspectable. For example, if we use introspection to pick out the smallest patch of visual space we can discern—a “dot”—this patch is still not an elementary distinction because it is necessarily [extended in space](http://www.iitwiki/contents#h.gt6k1srewfj7), which means it must be structured by lower-level components. Despite the limits of introspection, IIT assumes that any distinction we can introspect must comprise lower-level distinctions, down to an elementary level (see the assumption of [methodological “atomism”](http://www.iit.wiki/foundations#h.gc7e9zm8e1ma)). In [physical](http://www.iit.wiki/glossary#h.jtbdxiwp9igh) terms, an elementary (causal) distinction is simply a [distinction](http://www.iit.wiki/glossary?authuser=0#h.ixtdw1emrvga). ## **elementary relation** Elementary relations are assumed to be the building blocks of the [introspectable](http://www.iit.wiki/glossary#h.iohmb4ut7uw0) components of a [phenomenal structure](http://www.iit.wiki/glossary#h.ci0yggunfaj4), and as such are not always introspectable. In physical terms, an elementary (causal) relation is just a [relation](http://www.iit.wiki/glossary#h.yp1dkd8f7s8u). ## **entity** In the ontology of IIT, *intrinsic entities* are [systems](https://www.iit.wiki/glossary#h.4bdc61agv7oe) that exist [*for themselves*](https://www.iit.wiki/overview/axioms-and-postulates/intrinsicality)—those for whom it [“feels like something to be.”](https://www.iit.wiki/faqs/method#h.lbk0cbu6w8aw) These systems are characterized by [cause–effect power](https://www.iit.wiki/glossary#h.vlk7u52cim8x) that is intrinsic, specific, unitary, definite, and structured (i.e., they are entities that fulfill the [five postulates](https://www.iit.wiki/glossary#h.irdac769fidh)). An example of an intrinsic entity is the [main complex](https://www.iit.wiki/glossary#h.b6fxhbe1r3re) in the brain (unfolded as a [*Φ*\-structure](https://www.iit.wiki/glossary#h.u3dcbculq7ms)). In everyday language, we refer to “entities” in a looser sense—for example, a rock or a cloud. In IIT, these are *extrinsic entities* because they do not exist for themselves (i.e., they do not fulfill the five postulates), yet they still may exist [phenomenally](https://www.iit.wiki/glossary#h.8j4o0g5ssetv)—as concepts in the mind (i.e., as [*Φ*\-folds](https://www.iit.wiki/glossary#h.m0n0mcke3qm5)). Some extrinsic entities—such as a rock—not only often exist phenomenally but also [physically](https://www.iit.wiki/glossary#h.jtbdxiwp9igh); this means that by [manipulating and observing](https://www.iit.wiki/glossary#h.urmduwg8ibdt) such systems, we may find that they indeed “hang together” as relative maxima of cause–effect power but not absolute maxima (i.e., they are not [complexes](https://www.iit.wiki/glossary#h.b6fxhbe1r3re); see [Exclusion Postulate](https://www.iit.wiki/overview/axioms-and-postulates/exclusion#h.pvmrhffvh06e)). In contrast, other extrinsic entities—such as a cloud—may be more difficult to define [operationally](https://www.iit.wiki/glossary#h.vztp822ktk99): if we manipulate and observe them, they might turn out to not even be relative maxima of cause–effect power, though they may still feel to “hang together” as concepts in the mind. ## **essential properties of experience** These refer to the [axioms](https://www.iit.wiki/glossary#h.qdzuf1i5vio4) of IIT. ## **exclusion** *Exclusion* is the 4th [axiom](https://www.iit.wiki/glossary#h.qdzuf1i5vio4) and [postulate](https://www.iit.wiki/glossary#h.irdac769fidh) of IIT. As an axiom, it states that “[experience](https://www.iit.wiki/glossary#h.97uzewmap754) is *definite*: it is *this whole*.” Formulated as a postulate, it states that “The [substrate of consciousness](https://www.iit.wiki/glossary#h.j5clb514qcec) must have *definite* [cause–effect power](https://www.iit.wiki/glossary#h.vlk7u52cim8x): it must specify its [cause–effect state](https://www.iit.wiki/glossary#h.tp4brteczc2p) as *this whole* set of [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n).” For more, see [Exclusion](https://www.iit.wiki/overview/axioms-and-postulates/exclusion). ## **existence** *Existence* refers to the “0th” [axiom](https://www.iit.wiki/glossary#h.qdzuf1i5vio4) and [postulate](https://www.iit.wiki/glossary#h.irdac769fidh) of IIT. As an axiom, it states that “[experience](https://www.iit.wiki/glossary#h.97uzewmap754) exists.” As a postulate, it states that “the [substrate of consciousness](https://www.iit.wiki/glossary#h.j5clb514qcec) can be characterized operationally by [cause–effect power](https://www.iit.wiki/glossary#h.vlk7u52cim8x): its [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n) must *take and make a difference*.” These form the starting point of the IIT method (see [Foundations](https://www.iit.wiki/overview/foundations)). The term *existence* also appears in the ontology of IIT. *Intrinsic existence* characterizes [entities](https://www.iit.wiki/glossary#h.dfvlx69kg5m4) that exist *for themselves* (i.e. intrinsic entities). In contrast, *extrinsic existence* characterizes entities that don’t exist for themselves, but may exist *for us* as experiencing subjects (i.e., extrinsic entities). For more, see [entity](https://www.iit.wiki/glossary#h.dfvlx69kg5m4). ## **experience** *Experience* refers to “what it is like to be” \[1\]. This includes what it *feels* like to be you—or any human—in any conscious moment, whether in regular waking states, dream states, or altered states of consciousness. But it also refers to the subjective state of any [intrinsic entity](https://www.iit.wiki/glossary#h.dfvlx69kg5m4)—whether non-human animals or potentially artificial systems. In IIT, *experience* is often used synonymously with *consciousness*; but while *consciousness* refers to having experiences regardless of their content, *experience* is always of something specific. In IIT, when we do a [phenomenological](https://www.iit.wiki/glossary#h.8j4o0g5ssetv) analysis of [essential](https://www.iit.wiki/glossary#h.qdzuf1i5vio4) and [accidental](https://www.iit.wiki/glossary#h.5ec6914i1gwq) properties of experience, we aim to dissect a single “moment” of experience—”right here, right now.” In other words, we do not use the term *experience* to describe processes or events that are more than a “timeslice” of experience. For more, see * [Overview: What does it mean to explain consciousness scientifically?](https://sites.google.com/d/1l8CfqlZHkjbTWjRjxrsILS__ZE0qRJAx/p/1Ow2S3Ti-evCBtITdtl5JxLkc8qcEtlgx/edit) * [FAQ: What do you mean by consciousness?](https://www.iit.wiki/faqs/method#h.lbk0cbu6w8aw) \[1\] [citation here](https://www.iit.wiki/faqs/method#h.lbk0cbu6w8aw) ## **explanatory identity** IIT’s *explanatory identity* (or *fundamental identity*) states that every property of an [experience](https://www.iit.wiki/glossary#h.97uzewmap754) is accounted for in full by the [physical](https://www.iit.wiki/glossary#h.jtbdxiwp9igh) properties of the [*Φ*\-structure](https://www.iit.wiki/glossary#h.u3dcbculq7ms) [unfolded](https://www.iit.wiki/glossary#h.frg5mnvcsu7) from a [complex](https://www.iit.wiki/glossary#h.b6fxhbe1r3re), with no additional or “ad hoc” ingredients. This means there must be a one-to-one correspondence between the way the experience feels and the way [distinctions](https://www.iit.wiki/glossary#h.ixtdw1emrvga) and [relations](https://www.iit.wiki/glossary#h.yp1dkd8f7s8u) of the corresponding [*Φ*\-structure](https://www.iit.wiki/glossary#h.u3dcbculq7ms) are structured. Importantly, the identity is not meant as a correspondence between the properties of two separate “things,” nor is it meant in a reductive or “eliminitivist” sense (e.g., experience is “nothing but” a *Φ*\-structure). The identity should rather be understood in an *explanatory* sense: Experience remains primary in IIT, both epistemologically and ontologically; nevertheless, the properties of experience can be accounted for in [operational](https://www.iit.wiki/glossary#h.vztp822ktk99) terms of [cause–effect power](https://www.iit.wiki/glossary#h.vztp822ktk99). * [The Fundamental Identity](https://www.iit.wiki/identity) * [FAQ: How is the fundamental identity of IIT different from classical identity theories?](https://www.iit.wiki/faqs/philosophy#h.3b5xs2uig7ap) * [FAQ: How does the fundamental identity of IIT compare to other standard approaches to explaining consciousness?](https://www.iit.wiki/faqs/philosophy#h.b3eyb4li4hli) * [FAQ: If IIT assumes *atomism*, does this make it a reductionist theory of consciousness?](https://www.iit.wiki/faqs/philosophy#h.p8d3ayub7a3f) ## **extrinsic** *Extrinsic* is a general term used in IIT in opposition to the notion of [intrinsicality](http://www.iit.wiki/glossary?authuser=0#h.2w4jmrulzrgg) and the [intrinsic perspective](http://www.iit.wiki/glossary?authuser=0#h.lda1vi9ede5q). When referring to [cause–effect power](http://www.iit.wiki/glossary?authuser=0#h.vlk7u52cim8x), *extrinsic* means cause–effect power that is not from the intrinsic perspective of the system (or mechanism)—its “raw power” (measured by [informativeness](http://www.iit.wiki/glossary?authuser=0#h.r3o5152kwaw8)). Cause–effect power can also be extrinsic in the sense that one entity has causal power over another (rather than over itself). When referring to an [entity](http://www.iit.wiki/glossary?authuser=0#h.dfvlx69kg5m4), *extrinsic* means a system does not exist for itself, i.e. it is not a complex. Extrinsic entities can still exist (extrinsically) as local maxima of [integrated information](http://www.iit.wiki/glossary?authuser=0#h.o07sudcaz3vq) (e.g., our body or a rock), or as concepts in the mind of an intrinsic entity or conscious being (e.g., a chess set or a sports team). When referring to a perspective, *extrinsic* means that we’re describing or analyzing something based on what we can [observe and manipulate](http://www.iit.wiki/glossary?authuser=0#h.ghhmthp1zqrp) (e.g., a scientist’s perspective on neurons). For more, see [entity](http://www.iit.wiki/glossary?authuser=0#h.dfvlx69kg5m4). ## **fault line** The *fault lines* of a [system](http://www.iit.wiki/glossary?authuser=0#h.4bdc61agv7oe) refer to “weak links” among its subsets. It is a metaphorical way to refer to areas of a system that are more weakly connected, which is where we expect to find the [minimum partition](http://www.iit.wiki/glossary?authuser=0#h.uxjtor35txjh). ## **grain** The term *grain* refers to the scale at which a [substrate](http://www.iit.wiki/glossary#h.63hvurupgbzf) is analyzed and operations are performed on it: * The *constituent grain* defines the “spatial scale” \[1\] of the [units](http://www.iit.wiki/glossary#h.y4l991ydyf0n)—whether molecules, neurons, minicolumns, etc. * The *update grain* defines the “temporal scale” \[1\] of the units’ [state](http://www.iit.wiki/glossary#h.hnb1zhy1izf8)—whether microseconds, milliseconds, seconds, etc. Grains can be further described as *micro*, *macro*, or *meso*: * The *micro* *grain* is that at which the units and their updates are [operationally](http://www.iit.wiki/glossary#h.vztp822ktk99) indivisible. Micro units cannot be [partitioned](http://www.iit.wiki/glossary#h.tbsgfc5m3fti) into finer constituents, and micro updates cannot be partitioned into finer updates. Micro units are essentially “atoms” of [cause–effect power](http://www.iit.wiki/glossary#h.vlk7u52cim8x). * A *macro* *grain* is any grain coarser than the micro grain. A macro unit consists of multiple micro units, and a macro update consists of multiple micro updates. * Because macro grains can be built hierarchically (macro units at a given grain can be constituted of macro units at a finer grain), it is often useful to refer to these intermediate grains as *meso* *grains*. In IIT, the grain that supports consciousness is determined following the [exclusion postulate](http://www.iit.wiki/axioms-and-postulates/exclusion): among all [candidate](http://www.iit.wiki/glossary#h.8mzotxp600xu) grains, the one that maximizes [system integrated information (*φs*)](http://www.iit.wiki/glossary#h.o07sudcaz3vq) is the one at which the [complex](http://www.iit.wiki/glossary#h.b6fxhbe1r3re) exists. We call the units at this grain the complex’s *intrinsic units*. For the mapping of *micro states* into binary *macro states*, and the justification for why states are binary, see [Marshall et al. (2024)](https://www.biorxiv.org/content/10.1101/2024.04.12.589163v1.full.pdf). For more, see * [Marshall, W., Findlay, G., Albantakis, L., & Tononi, G. (2024). From micro to macro units: a mathematical framework for identifying the causal grain of a system from its intrinsic perspective. *bioRxiv*, 2024-04.](https://www.biorxiv.org/content/10.1101/2024.04.12.589163v1.full.pdf) * [Glossary: unit](http://www.iit.wiki/glossary#h.y4l991ydyf0n) \[1\] Note that the terms “spatial” and “temporal” scale are used here for convenience, but the IIT framework does not require spacetime to be fundamental. For this reason, macro units are sometimes described as being constructed “over constituents” and “over updates” rather than “over space” and “over time.” ## **identity** See [explanatory identity](https://www.iit.wiki/glossary#h.74qzd0b3gsko). ## **immediate** In IIT, the term *immediate* is used to describe the way we as experiencing subjects relate to the properties of [experience](https://www.iit.wiki/glossary#h.97uzewmap754) (both [essential](https://www.iit.wiki/glossary#h.qdzuf1i5vio4) and [accidental](https://www.iit.wiki/glossary#h.5ec6914i1gwq) properties) and recognize the truth of these properties. The properties of experience are immediate because they are given in the experience itself \[1\]; they are not inferred or “mediated” by anything. Similarly, we know the truth of these properties *immediately* in the sense that we need not (and *can* not) appeal to any justification outside the experience itself. For more, see * [0th Axiom: *Experience exists*](https://www.iit.wiki/overview/foundations#h.o56f0fhw0252) * [FAQ: If the axioms are “immediate” and “irrefutably true,” shouldn’t they also be self-evident?](https://www.iit.wiki/faqs/axioms#h.2bt9b53t5uuv) \[1\] Another way of expressing *immediate* is “by direct acquaintance.” ## **inference from a good explanation** In the IIT method, the principle of *inference from a good explanation* works hand-in-hand with *inference to a good explanation*. The [IIT method](https://www.iit.wiki/overview#h.ni9r4oe72m9i) starts by using [introspection](https://www.iit.wiki/glossary#h.iohmb4ut7uw0) to identify properties of [experience](https://www.iit.wiki/glossary#h.97uzewmap754), and then uses [inference to a good explanation](https://www.iit.wiki/glossary#h.gw0vdngumyee) to account for these properties in [physical](https://www.iit.wiki/glossary#h.jtbdxiwp9igh) terms. This method allows us to bootstrap the [fundamental identity](https://www.iit.wiki/identity) of the theory, which offers a [good overall explanation of consciousness](https://www.iit.wiki/faqs/method#h.21d179x6ff7w). Though necessary, this “phenomenology-first” method has its limits. Some properties of experience are seemingly impossible to dissect through introspection—for instance, the experience of “redness” simply feels monolithically “red.” Yet these properties, too, must be accounted for if we are to have a complete explanation of [consciousness](https://www.iit.wiki/glossary#h.mnf6qtn02rcp) and its contents. In such cases, we may use *inference from a good explanation* to probe the identity in the reverse direction—to use what we know about the [neural substrate](https://www.iit.wiki/glossary#h.j16zhlml4tz1) of such experiences (e.g., of color) to consider what kinds of [*Φ*\-structures](https://www.iit.wiki/glossary#h.u3dcbculq7ms) this substrate would most likely unfold into, and then to check the results against our own [phenomenology](https://www.iit.wiki/glossary#h.8j4o0g5ssetv). Reasoning in both directions in this way is what allows us to firmly establish the identity as an overall good explanation of consciousness. *Inference from a good explanation* is also what lets us reason about consciousness beyond humans. The more IIT’s fundamental identity is [validated scientifically](https://www.iit.wiki/validation) in humans, the stronger our inferences become when reasoning about the quantity and quality of consciousness in, for example, newborns, animals, and machines. ## **inference to a good explanation** IIT uses *inference to a good explanation* to refer to various inferential steps made in the theory—especially the theory’s [methodological assumptions](https://www.iit.wiki/overview/foundations#h.8rzkbmyfu80) and the way we formulate the [postulates](https://www.iit.wiki/glossary#h.irdac769fidh) based on the [axioms](https://www.iit.wiki/glossary#h.qdzuf1i5vio4). The term is related to the more common “inference to the best explanation” (a type of [abductive reasoning](https://plato.stanford.edu/entries/abduction/)), which requires multiple options of explanation in order to judge what is “best.” In IIT, we emphasize *good* rather than *best* in an attempt to be more humble—to recognize that, when it comes to consciousness, there’s no “objective” standpoint from which to determine the options and judge which is “best.” With [consciousness](https://www.iit.wiki/glossary#h.mnf6qtn02rcp), we must bootstrap our explanation from the inside out. IIT aims for a “good” explanation, understood in terms of the [seven S’s presented here](https://www.iit.wiki/faqs/method#h.21d179x6ff7w). ## **information** *Information* is the 2nd [axiom](https://www.iit.wiki/glossary#h.qdzuf1i5vio4) and [postulate](https://www.iit.wiki/glossary#h.irdac769fidh) of IIT. As an axiom, it states that “[Experience](https://www.iit.wiki/glossary#h.97uzewmap754) is *specific*: it is *this one*.” Formulated as a postulate, it states that “The [substrate of consciousness](https://www.iit.wiki/glossary#h.j5clb514qcec) must have *specific* [cause–effect power](https://www.iit.wiki/glossary#h.vlk7u52cim8x): it must be in *this [state](https://www.iit.wiki/glossary#h.hnb1zhy1izf8)* and select *this [cause–effect state](https://www.iit.wiki/glossary#h.tp4brteczc2p)*.” For more, see * [Information page](https://www.iit.wiki/overview/axioms-and-postulates/information) * [FAQ: Can’t I have a vague or generic experience, which is not “specific”?](https://www.iit.wiki/faqs/axioms#h.uwzhz1n3mgvs) * [FAQ: How is *information* in IIT different from Shannon information?](https://www.iit.wiki/faqs/postulates#h.9agaor5xgkwb) * [FAQ: Is my experience specific owing to the potential experiences I could be having (differentiation)?](https://www.iit.wiki/faqs/axioms#h.uwzhz1n3mgvs) ## **informativeness** A factor in the formula for *intrinsic information.* See [intrinsic information](https://www.iit.wiki/glossary#h.vkva0021by39). ## **Integration** *Integration* is the 3rd [axiom](https://www.iit.wiki/glossary#h.qdzuf1i5vio4) and [postulate](https://www.iit.wiki/glossary#h.irdac769fidh) of IIT. As an axiom, it states that “[experience](https://www.iit.wiki/glossary#h.97uzewmap754) is *unitary*: it is *a whole*, [irreducible](https://www.iit.wiki/glossary#h.sw1ddv976914) to separate experiences.” Formulated as a postulate, it states that “the [substrate of consciousness](https://www.iit.wiki/glossary#h.j5clb514qcec) must have *unitary* [cause–effect power](https://www.iit.wiki/glossary#h.vlk7u52cim8x): it must specify its [cause–effect state](https://www.iit.wiki/glossary#h.tp4brteczc2p) as *a whole* set of [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n), irreducible to separate subsets of units.” For more, see * [Integration page](https://www.iit.wiki/overview/axioms-and-postulates/integration) * [FAQ: If I have two unrelated contents of experience, doesn't this mean my experience is not integrated?](https://www.iit.wiki/faqs/axioms#h.emrj5cauie8v) ## **integrated information** *Integrated information* is a measure of [irreducibility](https://www.iit.wiki/glossary#h.sw1ddv976914). Depending on what it is applied to, its exact definition and [operational](https://www.iit.wiki/glossary#h.vztp822ktk99) implementation varies. Broadly speaking, *integrated information* either refers to irreducible [cause–effect power](https://www.iit.wiki/glossary#h.vlk7u52cim8x) determined through [partitioning](https://www.iit.wiki/glossary#h.tbsgfc5m3fti) (denoted by *φ*, “small phi”), or it summarizes the overall existence of an [entity](https://www.iit.wiki/glossary#h.dfvlx69kg5m4) as the sum of the irreducibility of its components (denoted by *Φ*, “big phi”). Below are various ways that *integrated information* appears in IIT. #### ***φs – “system phi”*** Quantifies the irreducibility of the [cause–effect state](https://www.iit.wiki/glossary#h.tp4brteczc2p) specified by a [system](https://www.iit.wiki/glossary#h.4bdc61agv7oe): it measures to what extent a system as a whole specifies its cause and effect in a unitary way, which is not reducible to power specified by separate [parts](https://www.iit.wiki/glossary#h.n1vnhc7wgosr) of the system. For more, see the [Integration Postulate](https://www.iit.wiki/overview/axioms-and-postulates/integration#h.1019venrnats) and [FAQ: How do we calculate *φs*?](https://www.iit.wiki/faqs/technical#h.itm7yrxtv7qs) #### ***φd – “distinction phi”*** Quantifies the irreducibility of the cause–effect power a [mechanism](https://www.iit.wiki/glossary#h.bdzvjltpbxqw) specifies over its [purviews](https://www.iit.wiki/glossary#h.e5mwd8ynj4am): it measures to what extent a mechanism specifies its cause and effect within a [system](https://www.iit.wiki/glossary#h.4bdc61agv7oe) in a unitary way, which is not reducible to power specified by separate [parts](https://www.iit.wiki/glossary#h.n1vnhc7wgosr) of the mechanism over separate parts of the purviews. For more, see [Composition postulate: Distinctions](https://www.iit.wiki/overview/axioms-and-postulates/composition#h.jndby56e0826). #### ***φr – “relation phi”*** Quantifies the irreducibility of the cause–effect power specified by a set of distinctions by virtue of congruently overlapping on their cause or effect. That is, it measures to what extent a set of distinctions *jointly* specify their causes and effects in a unitary way, which is not reducible to power specified by separate subsets of the distinctions. For more, see * [Composition Postulate: Relations](https://www.iit.wiki/overview/axioms-and-postulates/composition#h.u591dz8u0iby) * [Computing *Φ*: Step 6.3: Relations](https://www.iit.wiki/unfolding#h.o46e0bp35vbh) (with simplified formulas) * [IIT 4.0 section](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1011465#sec044) (with complete formulas) #### ***φu –*** **“unit phi”** Quantifies the irreducibility of the [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n) constituting the [substrate](https://www.iit.wiki/glossary#h.63hvurupgbzf). *φu* is computed by treating units as [candidate systems](https://www.iit.wiki/glossary#h.8mzotxp600xu) and computing their [*φs*](https://www.iit.wiki/glossary#h.lv95466kjojq). However, as they are constituents of a system, units only have to be maximally irreducible “within” (among all their subsets)—unlike systems, which also have to be maximally irreducible “without” (among their supersets). For more, see [Exclusion Postulate](https://www.iit.wiki/overview/axioms-and-postulates/exclusion#h.pvmrhffvh06e). #### ***Φ*** **– “big phi”** Quantifies the irreducibility of all [distinctions](https://www.iit.wiki/glossary#h.ixtdw1emrvga) and [relations](https://www.iit.wiki/glossary#h.yp1dkd8f7s8u) in the [*Φ*\-structure](https://www.iit.wiki/glossary#h.u3dcbculq7ms) of an [intrinsic entity](https://www.iit.wiki/glossary#h.dfvlx69kg5m4); it is the sum of all *φd* and *φr* values. *Φ* is also referred to as *structure integrated information* and can be interpreted as the entity’s quantity of [experience](https://www.iit.wiki/glossary#h.97uzewmap754) and thus of its intrinsic existence. For more, see [Composition Postulate: *Φ*\-structures and *Φ*](https://www.iit.wiki/overview/axioms-and-postulates/composition#h.2verg4nkqj8a). #### *Φ**R*** Quantifies the value of interrelatedness of a [*Φ*\-fold](http://www.iit.wiki/glossary?authuser=0#h.m0n0mcke3qm5) (substructure of a [*Φ*\-structure](http://www.iit.wiki/glossary?authuser=0#h.u3dcbculq7ms), which corresponds to a content of experience). As a *local maximum* of integrated information, *Φ**R*** is computed by summing the [*φ*](http://www.iit.wiki/glossary?authuser=0#h.a21jy4rkis6) values of the distinctions and relations across a minimum partition. ## **intrinsicality** *Intrinsicality* is the 1st [axiom](https://www.iit.wiki/glossary#h.qdzuf1i5vio4) and [postulate](https://www.iit.wiki/glossary#h.irdac769fidh) of IIT. As an axiom, it states that “[experience](https://www.iit.wiki/glossary#h.97uzewmap754) is *intrinsic*: it exists *for itself*.” Formulated as a postulate, it states that “the [substrate of consciousness](https://www.iit.wiki/glossary#h.j5clb514qcec) must have *intrinsic* [cause–effect power](https://www.iit.wiki/glossary#h.vlk7u52cim8x): it must take and make a difference *within itself*.” For more, see * [Intrinsicality page](https://www.iit.wiki/overview/axioms-and-postulates/intrinsicality) * [FAQ: Does the *intrinsicality* axiom imply a self, self-awareness, or self-report?](https://www.iit.wiki/faqs/axioms#h.kgo1jjifucdq) * [FAQ: How does *intrinsic* in IIT relate to the notion as used in philosophy (e.g., Lewis)?](https://www.iit.wiki/faqs/axioms#h.4u3b3s693wrv) * [FAQ: Does *intrinsicality* postulate mean that the substrate of consciousness is not influenced by its environment?](https://www.iit.wiki/faqs/postulates#h.xhp2q0xa2bgh) ## **intrinsic difference** *Intrinsic difference* is a measure of information that reflects the [intrinsic perspective](http://www.iit.wiki/glossary?authuser=0#h.lda1vi9ede5q) of a set of [units](http://www.iit.wiki/glossary?authuser=0#h.y4l991ydyf0n), rather than the [extrinsic](http://www.iit.wiki/glossary?authuser=0#h.hcl3aviuu9ra) perspective of, for example, a channel designer. It is the difference measure used to calculate [intrinsic information](http://www.iit.wiki/glossary?authuser=0#h.vkva0021by39) in IIT. The measure was devised to satisfy IIT’s postulates of existence (causality), intrinsicality, and information (specificity). For more, see [Barbosa et al. 2020](https://www.nature.com/articles/s41598-020-75943-4). ## **intrinsic entity** See [entity](https://www.iit.wiki/glossary#h.dfvlx69kg5m4). ## **intrinsic information** *Intrinsic information* quantifies the specific, intrinsic [cause–effect power](https://www.iit.wiki/glossary#h.vlk7u52cim8x) of a [system](https://www.iit.wiki/glossary#h.4bdc61agv7oe) as a whole or of a [mechanism](https://www.iit.wiki/glossary#h.bdzvjltpbxqw) within a system. As such, it operationalizes the postulates of [existence](https://www.iit.wiki/glossary#h.hyln43vondn5), [intrinsicality](https://www.iit.wiki/glossary#h.2w4jmrulzrgg), and [information](https://www.iit.wiki/glossary#h.9xr7m5huna7m) in precise mathematical terms. Intrinsic information is quantified using the [intrinsic difference](https://www.iit.wiki/glossary?authuser=0#h.c22hb8v3lwir) formula, which is made up of two factors, **informativeness** and **selectivity**. Conceptually, *informativeness* can be thought of as quantifying causal “raw power,” and selectivity as quantifying “control”: from the outside, a system may appear to have power, but from its [intrinsic perspective](https://www.iit.wiki/glossary#h.lda1vi9ede5q), this power is weak if it is spread thinly across the whole system (diluted). Rather, as the product of selectivity and informativeness, intrinsic information captures the interplay between “power” and “control.” In ideal systems, these two may grow together. However, in most systems these factors introduce *a tension between “expansion” and “dilution”*: the more units a system has, the more “power” it may have, yet more units also introduces greater potential for degeneracy or overdetermination (less “control”), which “dilutes” this power. Here is a simple version of the formula (see [IIT 4.0](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1011465) for a more technical look): ![](/corpus/figures/iit-wiki-glossary/glossary-image2.png) ### **Informativeness** On the effect side, informativeness measures the “raw power” of the current [state](https://www.iit.wiki/glossary#h.hnb1zhy1izf8) over a specific [effect state](https://www.iit.wiki/glossary#h.tp4brteczc2p), and on the cause side, it measures the power of a specific [cause state](https://www.iit.wiki/glossary#h.tp4brteczc2p) over the current state. It is formalized as the log ratio of two probabilities: P*constrained* is the probability of a specific state transition (i.e., the number we read off of the relevant square of the cause or effect [TPM](https://www.iit.wiki/glossary#h.rgqyfluj1zit) \[see [this FAQ](https://www.iit.wiki/faqs/technical#h.jyr7728ukvsm)\]), and P*unconstrained* is the probability of the same cause or effect states independent of the current state (i.e., based on chance). ### **Selectivity** Selectivity is quantified as the pointwise probability of an occurrence (e.g., the probability of finding the outputs of a [system](https://www.iit.wiki/glossary#h.4bdc61agv7oe) or [mechanism](https://www.iit.wiki/glossary#h.bdzvjltpbxqw) in a given state) relative to the maximal possible probability of observing that state (necessarily 1). (Note that *P*′constrained is the same as *P*constrained on the effect side, but on the cause side, it is the “backwards” probability found by applying Bayes’ rule to the “forwards” probabilities in the TPM.) For more, see: * [Information Postulate](https://www.iit.wiki/axioms-and-postulates/information) * [FAQ: How do we calculate *intrinsic information*?](https://www.iit.wiki/faqs/technical#h.9l275fb8gp1v) * [FAQ: When we calculate *intrinsic information*, what operations do we perform on the TPM?](https://www.iit.wiki/faqs/technical#h.jyr7728ukvsm) * [FAQ: How is *information* in IIT different from "Shannon information"?](https://www.iit.wiki/faqs/postulates#h.9agaor5xgkwb) * Academic papers: * [Barbosa, L. S., Marshall, W., Albantakis, L., & Tononi, G. (2021). Mechanism integrated information. *Entropy*, 23(3), 362.](https://www.mdpi.com/1099-4300/23/3/362) * [Barbosa, L. S., Marshall, W., Streipert, S., Albantakis, L., & Tononi, G. (2020). A measure for intrinsic information. *Scientific Reports*, 10(1), 18803.](https://www.nature.com/articles/s41598-020-75943-4) * [Marshall, W., Grasso, M., Mayner, W. G., Zaeemzadeh, A., Barbosa, L. S., ... & Tononi, G. (2023). System Integrated Information. *Entropy*, 25(2), 334.](https://www.mdpi.com/1099-4300/25/2/334) * [Albantakis, L., ... & Tononi, G. (2023). Integrated information theory (IIT) 4.0: formulating the properties of phenomenal existence in physical terms. *PLoS Computational Biology*, *19*(10), e1011465.](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1011465) ## **intrinsic perspective** When accounting for [experience](http://www.iit.wiki/glossary#h.97uzewmap754) in [physical](http://www.iit.wiki/glossary#h.jtbdxiwp9igh) terms, physical existence should be evaluated from the intrinsic perspective of an [entity](http://www.iit.wiki/glossary#h.dfvlx69kg5m4)—from the perspective of what exists for the entity itself, not that of an external observer. This perspective is embedded in the [intrinsicality postulate](http://www.iit.wiki/glossary#h.2w4jmrulzrgg), and it has several consequences when accounting for experience in physical terms: 1. We must account for the quantity and quality of a system’s cause–effect power from its own perspective, in a way that is observer-independent and non-arbitrary. 2. We treat units outside of the system as [background conditions](http://www.iit.wiki/glossary#h.ot008m3n2clu) in that they do not contribute directly to what the system *is*. 3. We evaluate the cause–effect power of a system by considering as input states the uniform probability distribution (of possible [states](http://www.iit.wiki/glossary#h.hnb1zhy1izf8))—the one that assumes no extrinsic knowledge—rather than one that is observed or imposed extrinsically. 4. We evaluate the [cause–effect power](http://www.iit.wiki/glossary#h.vlk7u52cim8x) of a system by considering not only its “raw power” (informativeness) but also its degree of “control” (selectivity) from its own perspective, as captured by the [intrinsic information](http://www.iit.wiki/glossary#h.vkva0021by39) formula. For more, see * [Intrinsicality Axiom & Postulate](http://www.iit.wiki/axioms-and-postulates/intrinsicality) * [FAQ: How does *intrinsic* in IIT relate to the notion as used in philosophy (e.g. Lewis)?](http://www.iit.wiki/faqs/philosophy#h.ky7wm6ipobmt) ## **introspection** To *introspect* means to direct one’s attention to the content of one’s own [experience](https://www.iit.wiki/glossary#h.97uzewmap754). Together with reasoning, introspection is our principal tool to investigate the [essential](https://www.iit.wiki/glossary#h.qdzuf1i5vio4) and [accidental](https://www.iit.wiki/glossary#h.5ec6914i1gwq) properties of experience. In the [IIT method](https://www.iit.wiki/overview#h.ni9r4oe72m9i), introspection is the necessary first step because the properties of experience make up our *explanandum*—[what we aim to explain in a theory of consciousness](https://www.iit.wiki/overview#h.qvp0etiy6a1z). That said, introspection has its limits. For example, we may be able to [introspect the experience of spatial extendedness](https://www.iit.wiki/contents-of-experience/space#h.4dp42fwe3css) reasonably well, but we may struggle to decompose the experience of redness—it just seems monolithically “red.” For this reason, though introspection is necessary for initial bootstrapping, a mature theory can then take us beyond the limitations of introspection, letting us apply [inference from a good explanation](https://www.iit.wiki/glossary#h.3yigbtgkn59b) to fill in gaps in accounting for properties of experience that we struggle to introspect. For more, see * [FAQ: If IIT starts from experience, isn't this method "subjective" and thus unscientific?](https://www.iit.wiki/faqs/method#h.nhabl9hcqvg8) * [FAQ: If introspection requires reflection, how can we be sure that non-reflective experiences exist at all?](https://www.iit.wiki/faqs/method#h.wvzfs1ohtez6) * [Ellia, F., Hendren, J., Grasso, M., Kozma, C., Mindt, G., P. Lang, J., ... & Tononi, G. (2021). Consciousness and the fallacy of misplaced objectivity. *Neuroscience of Consciousness*, 2021(2), niab032.](https://academic.oup.com/nc/article/2021/2/niab032/6398202) ## **irreducible** In IIT, a [candidate](https://www.iit.wiki/glossary#h.8mzotxp600xu) [system](https://www.iit.wiki/glossary#h.4bdc61agv7oe), [distinction](https://www.iit.wiki/glossary#h.ixtdw1emrvga), or [relation](https://www.iit.wiki/glossary#h.yp1dkd8f7s8u) is *irreducible* if the [cause–effect power](https://www.iit.wiki/glossary#h.vlk7u52cim8x) it specifies cannot be *reduced* to that specified by its [parts](https://www.iit.wiki/glossary#h.n1vnhc7wgosr) separately. For example, if we [partition](https://www.iit.wiki/glossary#h.tbsgfc5m3fti) system AB into two causally isolated systems (A and B), and find that its cause–effect power is unaffected, then we say that AB is *reducible*. To the contrary, if even the least-disruptive partition ([MIP](https://www.iit.wiki/glossary#h.uxjtor35txjh)) makes a difference to AB’s cause–effect power, then AB is *irreducible*—its cause–effect power cannot be *reduced* to that of A and B. Irreducibility is measured by [integrated information](https://www.iit.wiki/glossary#h.o07sudcaz3vq) (*φ* – “small phi”). For more, see * [Integration Postulate](https://www.iit.wiki/overview/axioms-and-postulates/integration#h.1019venrnats) * [Integrated information (glossary)](https://www.iit.wiki/glossary#h.o07sudcaz3vq) * [FAQ: How do we calculate *φs*?](https://www.iit.wiki/faqs/technical#h.itm7yrxtv7qs) ## **irrefutable** In IIT, *irrefutable* is used to describe the [essential properties](https://www.iit.wiki/glossary#h.qdzuf1i5vio4) of [experience](https://www.iit.wiki/glossary#h.97uzewmap754) expressed by the [axioms](https://www.iit.wiki/glossary#h.qdzuf1i5vio4). These properties are irrefutable because if we imagine an experience lacking one of them, we end up confirming that the experience has that property. For instance, every experience is unitary—a whole, [irreducible](https://www.iit.wiki/glossary#h.sw1ddv976914) to separate experiences ([integration axiom](https://www.iit.wiki/glossary#h.cpmqk4mzfdb9)). If we try to refute this by imagining an experience that were not unitary, we end up imagining two or more experiences, each of which is indeed a whole, irreducible to separate experiences. IIT uses the term *irrefutable* much the way Descartes used “indubitable,” yet note that *irrefutable* is more precise since any property can indeed be doubted but perhaps not refuted. For more, see * [Five Axioms: Essential properties of every experience](https://www.iit.wiki/overview/axioms-and-postulates#h.gh95zjki6tz4) * [FAQ: What is meant by the term *axiom* in IIT?](https://www.iit.wiki/faqs/axioms#h.qusvdrxctnxr) * [FAQ: If the axioms are “immediate” and “irrefutably true,” shouldn’t they also be self-evident?](https://www.iit.wiki/faqs/axioms#h.2bt9b53t5uuv) ## **manipulate and observe** See [perturbational approach](https://www.iit.wiki/glossary#h.urmduwg8ibdt). ## **marginalization** Coming soon. ## **matching** Coming soon. For now, see: [Mayner, W., Juel, B.E., and Tononi, G. (2023) Meaning, perceiving, and matching: quantifying how the structure of experience matches the structure of the world. (2024). *arXiv*, 2024-12](https://arxiv.org/pdf/2412.21111) ## **meaning** In IIT, *meaning* corresponds to the content of [experience](https://www.iit.wiki/glossary#h.97uzewmap754), which can be expressed in the maxim, ”the meaning is the feeling.” As such, a meaning is always fully [intrinsic](https://www.iit.wiki/glossary#h.2w4jmrulzrgg): if I see an apple on the table, hallucinate the apple, or dream of the apple, the meaning “apple” is always *for me* as the experiencing subject. That said, a meaning often [matches](https://www.iit.wiki/glossary#h.5korjncphta9) the environment to some extent—that is, it often refers to external causal processes that are relevant to an organism. In physical terms, meanings correspond to [*Φ*\-folds](https://www.iit.wiki/glossary#h.m0n0mcke3qm5), typically composed of sets of highly interrelated [distinctions](https://www.iit.wiki/glossary#h.ixtdw1emrvga). IIT’s view of meaning as intrinsic contrasts with views that place meaning elsewhere—for example, in the world (externalism), in the relation between the subject and the world (intentionalism or representationalism), in the functional role played by neural mechanisms (functionalism), in the information passed from the world to the subject (information processing views), or in the capacity to act on the world (enactivist views). ## **mechanism** A *mechanism* is a subset of [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n) in a [complex](https://www.iit.wiki/glossary#h.b6fxhbe1r3re) that has maximally [irreducible](https://www.iit.wiki/glossary#h.sw1ddv976914) [cause–effect power](https://www.iit.wiki/glossary#h.vlk7u52cim8x) within the complex. Any set of units from the system’s [powerset](https://www.iit.wiki/glossary#h.of3eml7gj8qf) can be a [candidate](https://www.iit.wiki/glossary#h.8mzotxp600xu) mechanism (e.g., 1st-order mechanism “A” or 3rd-order mechanism “ABC”). But among candidates, mechanisms are only those whose cause–effect power fulfills the [postulates](https://www.iit.wiki/glossary#h.irdac769fidh) (save [composition](https://www.iit.wiki/glossary#h.j0xivbr6tr10)). Moreover, a mechanism must specify a cause and an effect that are [congruent](https://www.iit.wiki/glossary#h.cm6by218tf7l) with the system’s [cause–effect state](https://www.iit.wiki/glossary#h.tp4brteczc2p). Operationally, a candidate mechanism is any subset of units in a state. Ontologically, however, what exists is not the mechanism *per se* but rather the causal [distinction](https://www.iit.wiki/glossary#h.ixtdw1emrvga) the mechanism specifies. A mechanism can be understood as an “link” between a potential cause and effect—the three of which together form a distinction. For more, see * [Composition Postulate: Distinctions](https://www.iit.wiki/overview/axioms-and-postulates/composition#h.jndby56e0826) * [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?](https://www.iit.wiki/faqs/postulates#h.j7x0htwr8zwv) * [FAQ: 5\. Do mechanisms emerge from their units?](https://www.iit.wiki/faqs/philosophy#h.90sm4ddawhow) ## **minimum partition** The *minimum partition* (MIP) is used to assess the [irreducibility of a system (*φs*)](https://www.iit.wiki/glossary#h.lv95466kjojq), a [distinction (*φd*)](https://www.iit.wiki/glossary#h.bgvpiaqisd6), or a [relation (*φr*)](https://www.iit.wiki/glossary#h.4won6ixpwruk). It is the [partition](https://www.iit.wiki/glossary#h.tbsgfc5m3fti) that makes the least difference to the [intrinsic information](https://www.iit.wiki/glossary#h.vkva0021by39) specified by a system about itself (*system MIP*), by a [mechanism](https://www.iit.wiki/glossary#h.bdzvjltpbxqw) about its [purviews](https://www.iit.wiki/glossary#h.e5mwd8ynj4am) (*distinction MIP*), or by overlapping distinction purviews (*relation MIP*). Note that in earlier publications, the *minimum partition* was also referred to as the *minimum information partition*. For more, see - [Integration Postulate](https://www.iit.wiki/overview/axioms-and-postulates/integration#h.1019venrnats) - [Principle of minimal existence](https://www.iit.wiki/glossary#h.dtwzpm4kzynp) (for why the minimum partition is used) ## **monad** In IIT, a monad is the smallest [system](https://www.iit.wiki/glossary#h.4bdc61agv7oe) that can exist [intrinsically](https://www.iit.wiki/glossary#h.2w4jmrulzrgg). A monad is constituted of a single [unit](http://www.iit.wiki/glossary#h.y4l991ydyf0n) with a [self-loop](https://www.iit.wiki/glossary#h.1yi7dnebw142); it specifies a single [distinction](https://www.iit.wiki/glossary#h.ixtdw1emrvga), with cause and effect over itself, and a self-[relation](https://www.iit.wiki/glossary#h.yp1dkd8f7s8u). According to IIT, if every connection among the atomic units of the universal [substrate](http://www.iit.wiki/glossary?authuser=0#h.63hvurupgbzf) were severed, we would be left with a collection of monads—each a universe in itself, having the simplest possible experience and isolated from the rest. ## **network** The term *network* refers to the full set of [units](http://www.iit.wiki/glossary#h.y4l991ydyf0n) that are under analysis. Any subset of the network can be considered a candidate [substrate](http://www.iit.wiki/glossary?authuser=0#h.63hvurupgbzf) (or [system](http://www.iit.wiki/glossary#h.4bdc61agv7oe)). ## **neural correlates of consciousness (NCC)** An early definition of the neural correlates of consciousness (NCC) was “the minimal set of neuronal mechanisms jointly sufficient for a specific conscious percept” ([Koch 2004, p. 16](https://books.google.de/books/about/The_Quest_for_Consciousness.html?id=7L9qAAAAMAAJ&redir_esc=y)). More recently, some have subdivided the term ([Koch et al 2016](https://www.nature.com/articles/nrn.2016.22)): * The **full NCC** is “the neural substrate supporting experience in general, irrespective of its specific content.” * A **content-specific NCC**, on the other hand, is “the neural substrate supporting a particular content of experience (for example, faces) whether seen, dreamt or imagined.” These concepts have aimed to offer a theory-neutral framework for empirical studies. The term NCC is rarely used in IIT since the theory explicitly aims to characterize the [substrate of consciousness](https://www.iit.wiki/glossary#h.j5clb514qcec) following the [postulates](https://www.iit.wiki/glossary#h.irdac769fidh); hence IIT rather uses the term [neural substrate of consciousness](https://www.iit.wiki/glossary#h.j16zhlml4tz1) (NSC) when validating the theory empirically. That said, NCC research is helpful to inform IIT’s account—especially to determine where the borders of [complexes](https://www.iit.wiki/glossary#h.b6fxhbe1r3re) are likely to be found in the brain (full NCC) and which parts of the complexes are likely to contribute particular contents (content-specific NCC). ## **neural substrate of consciousness** The *neural substrate of consciousness* (NSC) corresponds to the set of neural [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n) that contribute to an overall maximum of [*φs*](https://www.iit.wiki/glossary#h.lv95466kjojq) in the brain. By IIT, this set of units (with their particular [grains](https://www.iit.wiki/glossary#h.wecg9hts0fae)) form the main [complex](https://www.iit.wiki/glossary#h.b6fxhbe1r3re) in the brain and unfold into a [*Φ*\-structure](https://www.iit.wiki/glossary#h.u3dcbculq7ms) whose properties account in full for all properties of the corresponding [experience](https://www.iit.wiki/glossary#h.97uzewmap754). More generally, the term NSC has some similarities with [full NCC (neural correlates of consciousness)](https://www.iit.wiki/glossary#h.hqe2k9cdzma0), yet two differences are worth noting. First, NCC was devised as a theory-neutral term (hence “correlates”), whereas NSC is based explicitly on the [explanatory identity](https://www.iit.wiki/glossary#h.74qzd0b3gsko) of IIT. Second, “full NCC” more loosely refers to all brain areas that correlate with consciousness, whereas the NSC is always the substrate of a specific experience (a single “moment”). ## **noising** This term was used in earlier IIT publications for what is now referred to as [unconditional causal marginalization](https://www.iit.wiki/glossary?authuser=0#h.ckhrytbflshv). It indicates that some input is made causally inert because every one of its states are equally probable. ## **operational** IIT uses the term *operationalize* in the general sense: to translate an abstract concept into something measurable. Hence *operational* refers to any interventional procedure that involves [manipulation and observation](https://www.iit.wiki/glossary#h.urmduwg8ibdt). In IIT, however, the term *operational* also offers a useful contrast with *ontological*. More precisely, the [IIT method](https://www.iit.wiki/overview#h.ni9r4oe72m9i) recognizes the ontological primacy of [phenomenal existence](https://www.iit.wiki/glossary#h.28lqkhwzfc7x) and first approaches [physical existence](https://www.iit.wiki/glossary#h.dvagt3tcc5y9) in strictly operational terms. For example, IIT works with [candidate](https://www.iit.wiki/glossary#h.8mzotxp600xu) [substrates of consciousness](https://www.iit.wiki/glossary#h.j5clb514qcec), explicitly stipulating the [spatial, state, and update grain](https://www.iit.wiki/glossary#h.wecg9hts0fae) of substrate [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n). These parameters are not presumptions that the [substrate](https://www.iit.wiki/glossary#h.63hvurupgbzf) truly *exists* in this way; they are rather operational assumptions that let us bootstrap our account of experience, and ones that should be updated as our understanding of the system under investigation grows (albeit under the constraints of the [postulates](https://www.iit.wiki/glossary#h.irdac769fidh)). More generally, the [IIT method](https://www.iit.wiki/overview#h.ni9r4oe72m9i) explicitly assumes [physicalism](https://www.iit.wiki/glossary#h.jtbdxiwp9igh) and [atomism](https://www.iit.wiki/glossary#h.rnq3v27h92i6); these too are meant in an operational, not ontological, sense. As such, [*physicalism* does not mean materialism](https://www.iit.wiki/faqs/philosophy#h.4papa5z2cjmq), and [*atomism* does not mean ontological reductionism](https://www.iit.wiki/faqs/philosophy#h.p8d3ayub7a3f). By first approaching the physical in operational terms, IIT aims to start from an agnostic stance about what “truly exists” physically; this way, the theory allows the operational procedures to spur our inferences about a comprehensive ontology. ## **order** *Order* is used to define the number of [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n) constituting a [mechanism](https://www.iit.wiki/glossary#h.bdzvjltpbxqw), [distinction](https://www.iit.wiki/glossary#h.ixtdw1emrvga), or [purview](https://www.iit.wiki/glossary#h.e5mwd8ynj4am). For example, the mechanism ***AB*** is 2nd-order because it is constituted of two units—***A*** and ***B***—and (assuming it is [irreducible](https://www.iit.wiki/glossary#h.sw1ddv976914)) the distinction it specifies is also 2nd-order (the order of a distinction is the order of the mechanism that specifies it). Similarly, cause purview ***Abc*** is 3rd-order because it is constituted of three units. For more, see [Composition Postulate](https://www.iit.wiki/overview/axioms-and-postulates/composition#h.uyfhol2todl). ## **part** A *part* is a subset of [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n) within a [substrate](https://www.iit.wiki/glossary#h.63hvurupgbzf). While the meaning is close to the commonsense notion, in IIT, the term refers specifically to the parts obtained by [partitioning](https://www.iit.wiki/glossary#h.tbsgfc5m3fti) a [system](https://www.iit.wiki/glossary#h.4bdc61agv7oe) to assess its [irreducibility](https://www.iit.wiki/glossary#h.sw1ddv976914). In this context, a part is a subset of units that has been causally separated (through partitioning) from at least one other subset (part) of the system. For more, see: * [Integration Postulate](https://www.iit.wiki/overview/axioms-and-postulates/integration#h.1019venrnats) * [FAQ: How do we calculate *φs* (system integrated information)?](https://www.iit.wiki/faqs/technical#h.itm7yrxtv7qs) * [FAQ: Is "partitioning" the same as severing (eliminating) the connections between units?](https://www.iit.wiki/faqs/technical#h.5xfhtsob8l2d) * Academic papers: * [Barbosa, L. S., Marshall, W., Albantakis, L., & Tononi, G. (2021). Mechanism integrated information. *Entropy*, *23*(3), 362\.](https://www.mdpi.com/1099-4300/23/3/362) * [Marshall, W., Grasso, M., Mayner, W. G., Zaeemzadeh, ... & Tononi, G. (2023). System Integrated Information. *Entropy*, *25*(2), 334\.](https://www.mdpi.com/1099-4300/25/2/334) ## **partition** A *partition* is a mathematical operation used to assess the [irreducibility](https://www.iit.wiki/glossary#h.sw1ddv976914) of a [candidate](https://www.iit.wiki/glossary#h.8mzotxp600xu) [system](https://www.iit.wiki/glossary#h.4bdc61agv7oe) (its [*φs*](https://www.iit.wiki/glossary#h.lv95466kjojq)), of a candidate [distinction](https://www.iit.wiki/glossary#h.ixtdw1emrvga) (its [*φd*](https://www.iit.wiki/glossary#h.bgvpiaqisd6)), or of a relation. A system partition comprises a set of “cuts” that sever all causal connections to or from one or more [parts](https://www.iit.wiki/glossary#h.n1vnhc7wgosr) (for an illustration, see the [Integration Postulate](https://www.iit.wiki/overview/axioms-and-postulates/integration#h.1019venrnats)). For distinctions, valid partitions comprise a set of cuts through the mechanism, separating the mechanism–purview pair into non-interacting and non-overlapping subsets. Finally, we partition a relation by “unbinding” its overlapping distinctions one by one. In all cases, among all possible partitions, we seek the [minimum partition](https://www.iit.wiki/glossary#h.uxjtor35txjh) (MIP) in order to quantify the irreducibility of the system, distinction, or relation in question. For more, see * [FAQ: What is a “legal” or "valid" partition?](https://www.iit.wiki/faqs/technical#h.2xou8qbtjul1) * Computing PHI… ## **perturbational approach** The *perturbational approach* refers to IIT’s method of studying [physical](http://www.iit.wiki/glossary#h.jtbdxiwp9igh) [systems](http://www.iit.wiki/glossary#h.4bdc61agv7oe) in an interventional rather than purely observational way. Using the perturbational approach, we aim to assess causal interactions (as opposed to mere correlations) by actively *manipulating* the system and *observing* the results. This approach is essential in IIT since it characterizes the physical solely in [operational](http://www.iit.wiki/glossary#h.vztp822ktk99) terms of [cause–effect power](http://www.iit.wiki/glossary#h.vlk7u52cim8x) (see [0th Postulate](http://www.iit.wiki/overview/foundations#h.5h9ssjclzgt9)). An exhaustive perturbational approach requires us to repeatedly set the system into all of its available input states and then observe which states the system subsequently transitions into (and with what probabilities). This allows us to build a [transition probability matrix (TPM)](http://www.iit.wiki/glossary#h.rgqyfluj1zit) for the system, which can be used to evaluate whether the system’s cause–effect power fulfills the [postulates](http://www.iit.wiki/glossary#h.irdac769fidh) of the theory and is thus a [substrate of consciousness](http://www.iit.wiki/glossary#h.j5clb514qcec). Needless to say, it is not possible to apply the full perturbational approach in a system as complex as the brain. Yet the [perturbational complexity index](http://www.iit.wiki/glossary#h.wqwrlp5bgkhu) (PCI) aims to do so in a non-exhaustive way, thus providing a proxy of [integrated information](http://www.iit.wiki/glossary#h.o07sudcaz3vq)—the measure proposed by IIT to quantify consciousness. PCI is a causal measure in two senses: First, it relies on direct perturbation of the cortex (through [TMS](https://en.wikipedia.org/wiki/Transcranial_magnetic_stimulation)) followed by observation of the response—as opposed to mere observation. Second, it employs repeated stimulation and observation to extract the deterministic component of the cortical response to the perturbation—thus isolating the neural interactions caused by the perturbation itself from the noise of other brain activity. For more, see * [FAQ; Why is the perturbational approach so important in IIT?](http://www.iit.wiki/faqs/method#h.snkj2nyg1wtd) * [0th Postulate](http://www.iit.wiki/foundations#h.5h9ssjclzgt9) ## **perturbational complexity index (PCI)** The *perturbational complexity index* (PCI) is a proposed measure of [consciousness](http://www.iit.wiki/glossary#h.mnf6qtn02rcp), inspired by IIT and designed as a tool to test and apply the theory. It is a number that quantifies the complexity of the global brain response (typically measured using EEG) to a local direct perturbation (typically applied using [transcranial magnetic stimulation](https://en.wikipedia.org/wiki/Transcranial_magnetic_stimulation)). The measure was published in 2013 by Casali and colleagues, under the supervision of Marcello Massimini, and was the culmination of experimental work in Giulio Tononi’s lab between 2000 and 2010\. Since then, PCI has been refined, tested, and further developed into a measure that can be applied in clinical settings as well as experimental research. PCI involves two operational steps, easily remembered by the phrase “zap and zip.” First, a region of cortex is stimulated (“zapped”) with a [TMS pulse](https://en.wikipedia.org/wiki/Transcranial_magnetic_stimulation) and the response is recorded using EEG. This process is repeated many times to isolate the deterministic component of the cortical response (i.e., the specific pattern caused by the stimulation) from the ongoing activity of the brain and other sources of noise. Second, the cortical response inferred from the EEG pattern is compressed using the same algorithms used to “zip” computer files. If the pattern is highly compressible, we can conclude that there is little causal interaction across cortical areas (low integration) or that the interactions are highly uniform (low differentiation). In contrast, if the pattern cannot be easily compressed, it is indicative of high integration and high differentiation—a reasonable proxy for [integrated information](http://www.iit.wiki/glossary#h.o07sudcaz3vq). As reported in [Tononi et al. 2016](https://www.nature.com/articles/nrn-2016-44), “So far, studies using PCI have confirmed the prediction of IIT that the loss and recovery of consciousness is associated with the breakdown and recovery of the capacity for information integration. This relationship holds true across different states of sleep and anesthesia (using different agents with various mechanisms of action) and in patients with brain damage, at the level of single subjects. Importantly, once PCI is validated in participants that can report on whether they were conscious or not, the index can be used to assess the capacity for information integration in patients who are unresponsive (such as those in a vegetative state) or cannot report (such as newborn infants and non-human species).” PCI is a rough proxy of integrated information in that it only explicitly [operationalizes](http://www.iit.wiki/glossary#h.vztp822ktk99) three of the [postulates](http://www.iit.wiki/glossary#h.irdac769fidh) ([existence](http://www.iit.wiki/glossary#h.hyln43vondn5), [information](http://www.iit.wiki/glossary#h.9xr7m5huna7m), and [integration](http://www.iit.wiki/glossary#h.cpmqk4mzfdb9))—and these only crudely. However, the measure has proven uniquely powerful in objectively characterizing the “level” of consciousness in humans, without the need for explicit reports or collaboration from the subject under investigation. In the coming decades, a main aim is to provide updated measures, applicable in experimental settings, that incorporate the latest improvements of IIT. For more, see - [Casali, A. G., Gosseries, O., Rosanova, M., Boly, M., Sarasso, S., Casali, K. R., ... & Massimini, M. (2013). A theoretically based index of consciousness independent of sensory processing and behavior. *Science translational medicine*, *5*(198), 198ra105-198ra105.](https://www.science.org/doi/abs/10.1126/scitranslmed.3006294) - [Casarotto, S., Comanducci, A., Rosanova, M., Sarasso, S., Fecchio, M., Napolitani, M., ... & Massimini, M. (2016). Stratification of unresponsive patients by an independently validated index of brain complexity. *Annals of neurology*, *80*(5), 718-729.](https://onlinelibrary.wiley.com/doi/full/10.1002/ana.24779) - [Comolatti, R., Pigorini, A., Casarotto, S., Fecchio, M., Faria, G., Sarasso, S., ... & Casali, A. G. (2019). A fast and general method to empirically estimate the complexity of brain responses to transcranial and intracranial stimulations. *Brain stimulation*, *12*(5), 1280-1289.](https://www.sciencedirect.com/science/article/abs/pii/S1935861X19302207) - [Massimini, M., Boly, M., Casali, A., Rosanova, M., & Tononi, G. (2009). A perturbational approach for evaluating the brain's capacity for consciousness. *Progress in brain research*, *177*, 201-214.](https://www.sciencedirect.com/science/article/abs/pii/S0079612309177142) - [Sarasso, S., Casali, A. G., Casarotto, S., Rosanova, M., Sinigaglia, C., & Massimini, M. (2021). Consciousness and complexity: a consilience of evidence. *Neuroscience of Consciousness*, *7*(2), 1-24.](https://academic.oup.com/nc/advance-article/doi/10.1093/nc/niab023/6359982) ## **phenomenology** *Phenomenology* refers to the study of [experience](https://www.iit.wiki/glossary#h.97uzewmap754). In IIT, the term specifically refers to the analysis of experience through [introspection](https://www.iit.wiki/glossary#h.iohmb4ut7uw0) and reasoning to characterize its ([essential](https://www.iit.wiki/glossary#h.qdzuf1i5vio4) or [accidental](https://www.iit.wiki/glossary#h.5ec6914i1gwq)) properties. Phrases such as “starting from phenomenology” and “phenomenology first” refer to the method of starting from characterizing experience itself—[rather than the brain](https://www.iit.wiki/faqs/method#h.mnzdrtiewod)—to develop a [scientific theory of consciousness](https://www.iit.wiki/overview#h.qvp0etiy6a1z). For more, see - [What does it mean to explain consciousness scientifically?](https://www.iit.wiki/overview#h.qvp0etiy6a1z) - [FAQ: What do you mean by consciousness?](https://www.iit.wiki/faqs/method#h.lbk0cbu6w8aw) - [FAQ: Why not build a theory of consciousness starting from empirical neuroscientific research?](https://www.iit.wiki/faqs/method#h.mnzdrtiewod) ## **phenomenal existence** *Phenomenal existence* refers to the existence of [experience](https://www.iit.wiki/glossary#h.97uzewmap754), which is [immediate](https://www.iit.wiki/glossary#h.mtq44ohzelsq) and [irrefutable](https://www.iit.wiki/glossary#h.lfstqcfh9gsn) and the starting point of IIT. See [0th axiom](https://www.iit.wiki/glossary#h.ihc2d4eaahbj). ## **phenomenal structure** In IIT, the term *phenomenal structure* refers to an [experience](https://www.iit.wiki/glossary#h.97uzewmap754) as a structure (or sub-structure) of [phenomenal](https://www.iit.wiki/glossary#h.8j4o0g5ssetv) [distinctions](https://www.iit.wiki/glossary#h.ixtdw1emrvga) and [relations](https://www.iit.wiki/glossary#h.yp1dkd8f7s8u). For instance, when I see a blue book, my experience is composed of various phenomenal distinctions (the color blue, the shape of the book, its location in visual space, etc.), which are all related in a particular way to form a unitary content (“that blue book, right there”). A phenomenal structure captures both the [essential properties](https://www.iit.wiki/glossary#h.qdzuf1i5vio4) of every experience and [accidental properties](https://www.iit.wiki/glossary#h.5ec6914i1gwq) of the specific experience. As such, a phenomenal structure is the *explanandum* of IIT—it is [what we aim to account for scientifically](https://www.iit.wiki/overview#h.ni9r4oe72m9i). For more, see * [Ellia, F., Hendren, J., Grasso, M., ... & Tononi, G. (2021). Consciousness and the fallacy of misplaced objectivity. *Neuroscience of Consciousness*, *2021*(2), niab032](https://academic.oup.com/nc/article/2021/2/niab032/6398202). * [FAQ: What counts as a "component" of experience?](https://www.iit.wiki/faqs/axioms#h.i91i1ri1z1kc) ## ***Φ*** **– “big phi”** See [integrated information](https://www.iit.wiki/glossary#h.o07sudcaz3vq). ## ***φ*** **– “small phi”** See [integrated information](https://www.iit.wiki/glossary#h.o07sudcaz3vq). ## ***Φ*****\-fold** A Φ*\-fold* (“phi fold”) is a substructure within a [*Φ*\-structure](https://www.iit.wiki/glossary#h.u3dcbculq7ms)—a subset of its [distinctions](https://www.iit.wiki/glossary#h.ixtdw1emrvga) and [relations](https://www.iit.wiki/glossary#h.yp1dkd8f7s8u). Types of *Φ*\-folds can be categorized based on different levels of analysis. - A *distinction* Φ-*fold* is a substructure composed of a single distinction and the relations bound to it, which form its *context*. The level of analysis is helpful because it lets us decompose the *Φ*\-structure into non-redundant components—like individual “pieces” of a Lego structure. - A *compound* Φ-*fold* is a substructure composed of the distinction *Φ*\-folds specified by a subset of [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n). For example, for the subset AB within [substrate](https://www.iit.wiki/glossary#h.63hvurupgbzf) ABC, the compound *Φ*\-fold includes every distinction *Φ*\-fold specified by any [mechanism](https://www.iit.wiki/glossary#h.bdzvjltpbxqw) that includes unit A or B. This level of analysis is useful because a compound *Φ*\-fold is the part of the *Φ*\-structure that we “access” by manipulating a particular subset of the substrate. For example, if the gain of units A and B is modulated by attention, all distinctions specified by those units (and probably many of their relations) would be affected by the change—not just the AB distinction *Φ*\-fold. - A *content* Φ-*fold* is composed of a subset of distinctions that are highly interrelated (regardless of the mechanisms and units that specify them). In IIT, a content *Φ*\-fold corresponds to a content of experience (e.g., a “face”). As such, these are a salient aspect of a *Φ*\-structure in that they “hang together well,” as measured by [*ΦR*](https://www.iit.wiki/glossary#h.2491m6kxppvy). ## ***Φ*****\-structure** A Φ*\-structure* (or *cause–effect structure*) is the fully [unfolded](https://www.iit.wiki/glossary#h.frg5mnvcsu7) [cause–effect power](https://www.iit.wiki/glossary#h.vlk7u52cim8x) specified by a [substrate of consciousness](https://www.iit.wiki/glossary#h.j5clb514qcec). In line with IIT’s [explanatory identity](https://www.iit.wiki/glossary#h.u3dcbculq7ms), the properties of a *Φ*\-structure correspond one-to-one to the properties of a [phenomenal structure](https://www.iit.wiki/glossary#h.ci0yggunfaj4) (i.e., of an [experience](https://www.iit.wiki/glossary#h.97uzewmap754)), which allows IIT to account for both the quality and quantity of experience. A *Φ*\-structure is composed of causal [distinctions](https://www.iit.wiki/glossary#h.ixtdw1emrvga) and [relations](https://www.iit.wiki/glossary#h.yp1dkd8f7s8u) among them, and is quantified by [*Φ*](https://www.iit.wiki/glossary#h.vuzkdoevwo06) (‘big phi,’ the sum of [*φ*](https://www.iit.wiki/glossary#h.bgvpiaqisd6) \[‘small phi’\] of all distinctions and relations). For more, see * [Composition Postulate: *Φ*\-structures and *Φ*](https://www.iit.wiki/overview/axioms-and-postulates/composition#h.2verg4nkqj8a) * [Unfolding a *Φ*\-structure](https://www.iit.wiki/unfolding) ## **physicalism** IIT assumes *physicalism* in an operational sense: from within our [experience](https://www.iit.wiki/glossary#h.97uzewmap754), we can [observe and manipulate](https://www.iit.wiki/glossary#h.urmduwg8ibdt) the world outside of us in a way that is *reliable* and *persisting*. Thus we assume that something exists in a physical sense if it can reliably “make a difference” to something or “take a difference” from something—that is, if it has [cause–effect power](https://www.iit.wiki/glossary#h.vlk7u52cim8x). In IIT, operational physicalism is one of [three methodological assumptions](https://www.iit.wiki/overview/foundations#h.8rzkbmyfu80) (together with [realism](https://www.iit.wiki/glossary#h.2v5fky6ntlfw) and [atomism](https://www.iit.wiki/glossary#h.rnq3v27h92i6)), which allow us to translate the [0th axiom](https://www.iit.wiki/glossary#h.ihc2d4eaahbj) into the [0th postulate](https://www.iit.wiki/glossary#h.ny792kcl3wmd). For more, see * [Three Methodological Assumptions](https://www.iit.wiki/overview/foundations#h.8rzkbmyfu80) * [FAQ: If IIT assumes “physicalism,” does this make it a materialist theory of consciousness?](https://www.iit.wiki/faqs/philosophy#h.4papa5z2cjmq) * [FAQ: What is the meaning of cause–effect power in light of other notions of “causal power”?](https://www.iit.wiki/faqs/postulates#h.nh5gykv9jnng) ## **physical existence** *Physical existence* refers to the [0th postulate](https://www.iit.wiki/glossary#h.ny792kcl3wmd) of IIT. ## **physical substrate of consciousness (PSC)** This term *PSC* was used in earlier IIT publications for what is now referred to as a [substrate of consciousness](https://www.iit.wiki/glossary#h.j5clb514qcec) or [complex](https://www.iit.wiki/glossary#h.b6fxhbe1r3re). ## **pinning** This is a casual term for [conditional causal marginalization](https://www.iit.wiki/glossary#h.vq8lj719uzmz). ## **posterior hot zone** The *posterior hot zone* (or the *posterior cortical hot zone*) is an area of the human cortex that—according to ongoing empirical testing—appears to be necessary for normal waking perceptual experiences. It comprises sensory cortical areas in the parietal, temporal, and occipital lobes. The term was coined by Christof Koch and colleagues in a 2016 review article on the [neural correlates of consciousness (NCC)](https://www.iit.wiki/glossary#h.hqe2k9cdzma0), where it was presented as the best current anatomical candidate for where the NCC should be located in the human brain. For more, see: [Koch, C., Massimini, M., Boly, M. and Tononi, G. (2016). Neural correlates of consciousness: progress and problems, *Nature Reviews Neuroscience*, 17(5), 307–321](https://www.nature.com/articles/nrn.2016.44). ## **postulates** The *postulates* of IIT express essential properties of the [substrate of consciousness](https://www.iit.wiki/glossary#h.j5clb514qcec). In the [IIT method](https://www.iit.wiki/overview#h.ni9r4oe72m9i), the postulates are obtained by formulating the essential properties of [experience](https://www.iit.wiki/glossary#h.97uzewmap754) (the [axioms](https://www.iit.wiki/glossary#h.qdzuf1i5vio4)) as [physical](https://www.iit.wiki/glossary#h.jtbdxiwp9igh) properties of the substrate of consciousness—understood solely in terms of [cause–effect power](https://www.iit.wiki/glossary#h.vlk7u52cim8x). Mirroring the axioms, the postulates are [intrinsicality](https://www.iit.wiki/overview/axioms-and-postulates/intrinsicality), [information](https://www.iit.wiki/overview/axioms-and-postulates/information), [integration](https://www.iit.wiki/overview/axioms-and-postulates/integration), [exclusion](https://www.iit.wiki/overview/axioms-and-postulates/exclusion), and [composition](https://www.iit.wiki/overview/axioms-and-postulates/composition). The postulates guide the [computational steps](https://www.iit.wiki/unfolding) required to identify and [unfold](https://www.iit.wiki/glossary#h.frg5mnvcsu7) the substrate of consciousness into a [cause–effect structure](https://www.iit.wiki/glossary#h.hbd8ts8mecq). For more, see: - [Five Postulates: Essential properties of the substrate of consciousness](https://www.iit.wiki/overview/axioms-and-postulates#h.8d1ocowludyo) - [FAQ: Why are the postulates so important in IIT?](https://www.iit.wiki/faqs/postulates#h.v98pk6a5c5qq) ## **powerset** *Powerset* is a standard term from set theory. The powerset of S is defined as the set of all subsets of S, including the empty set and S itself. For example, the powerset of S \= {x, y, z} is Ps={{}, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {x, y, z}}. The notion of *powerset* is used at various points in IIT’s formalism, especially when applying the [postulates](https://www.iit.wiki/glossary#h.irdac769fidh) of [exclusion](https://www.iit.wiki/overview/axioms-and-postulates/exclusion#h.pvmrhffvh06e) and [composition](https://www.iit.wiki/overview/axioms-and-postulates/composition#h.uyfhol2todl). * When applying exclusion, we aim to find the maximum of [system integrated information (*φs*)](https://www.iit.wiki/glossary#h.lv95466kjojq) across all subsets of a [substrate](https://www.iit.wiki/glossary#h.63hvurupgbzf). For instance, if we are evaluating a substrate of 3 [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n) {ABC}, we want to know whether the system with maximal *φs* (“system phi”) is ABC or rather one of its subsets—A, B, C, AB, AC, or BC. Note that the empty set is technically part of the powerset but will never be a [complex](https://www.iit.wiki/glossary#h.b6fxhbe1r3re) as it must be constituted of at least one unit. * When applying composition, we aim to [unfold](https://www.iit.wiki/glossary#h.frg5mnvcsu7) [distinctions](https://www.iit.wiki/glossary#h.ixtdw1emrvga) of every [order](https://www.iit.wiki/glossary#h.tomxnzn3pu4g) and [relations](https://www.iit.wiki/glossary#h.yp1dkd8f7s8u) of every [degree](https://www.iit.wiki/glossary#h.xdmiiu46u8m6). For distinctions, this means we consider any subset from the complex’s powerset as a candidate [mechanism](https://www.iit.wiki/glossary#h.bdzvjltpbxqw) and/or [purview](https://www.iit.wiki/glossary#h.e5mwd8ynj4am). For example, if we assume that system ABC from the previous point is the complex, we would assess subsets A, B, C, AB, AC, BC, and ABC as candidate mechanisms and purviews. For relations, we consider the powerset of distinctions and any overlapping subset as a relation. For more, see [Exclusion Postulate](https://www.iit.wiki/overview/axioms-and-postulates/exclusion#h.pvmrhffvh06e) and [Composition Postulate](https://www.iit.wiki/overview/axioms-and-postulates/composition#h.uyfhol2todl). ## **principle of being** *[This glossary entry is taken from [Albantakis, L., ... & Tononi, G. (2023). Integrated information theory (IIT) 4.0: formulating the properties of phenomenal existence in physical terms. *PLoS Computational Biology*, 19(10), e1011465.](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1011465)]* The *principle of being* states that *to be is to have [cause–effect power](https://www.iit.wiki/glossary#h.vlk7u52cim8x)*. In other words, in [physical](https://www.iit.wiki/glossary#h.jtbdxiwp9igh), [operational](https://www.iit.wiki/glossary#h.vztp822ktk99) terms, to exist requires being able to take and make a difference. The principle is closely related to the so-called Eleatic principle, as found in Plato’s Sophist dialogue \[1\]: “I say that everything possessing any kind of power, either to do anything to something else, or to be affected to the smallest extent by the slightest cause, even on a single occasion, has real existence: for I claim that entities are nothing else but power.” A similar principle can be found in the work of the Buddhist philosopher Dharmakirti: “Whatever has causal powers, that really exists.” \[2\] Note that the Eleatic principle is enunciated as a disjunction (either to do something... *or* to be affected...), whereas IIT’s principle of being is presented as a conjunction (take *and* make a difference). --- \[1\] Cooper J. Plato: Complete Works. Hackett; 1997\. (verse 247d–e) \[2\] Tillemans T. Dharmakirti. In: Zalta EN, editor. The Stanford Encyclopedia of Philosophy. Spring 2021 ed. Metaphysics Research Lab, Stanford University; 2021\. ## **principle of maximal existence** *[This glossary entry is taken from [Albantakis, L., ... & Tononi, G. (2023). Integrated information theory (IIT) 4.0: formulating the properties of phenomenal existence in physical terms. *PLoS Computational Biology*, 19(10), e1011465.](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1011465)]* The principle of maximal existence states that, when it comes to a requirement for [existence](https://www.iit.wiki/glossary#h.hyln43vondn5), what exists is what exists the most. The principle is offered by IIT as a good explanation for why the [system](https://www.iit.wiki/glossary#h.4bdc61agv7oe) [state](https://www.iit.wiki/glossary#h.hnb1zhy1izf8) specified by the [complex](https://www.iit.wiki/glossary#h.b6fxhbe1r3re) and the [cause–effect states](https://www.iit.wiki/glossary#h.tp4brteczc2p) specified by its [mechanisms](https://www.iit.wiki/glossary#h.bdzvjltpbxqw) are what they are. It also provides a criterion for determining the set of [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n) constituting a complex—the one with maximally [irreducible](https://www.iit.wiki/glossary#h.sw1ddv976914) [cause–effect power](https://www.iit.wiki/glossary#h.vlk7u52cim8x), for determining the subsets of units constituting the [distinctions](https://www.iit.wiki/glossary#h.ixtdw1emrvga) and [relations](https://www.iit.wiki/glossary#h.yp1dkd8f7s8u) that compose its [cause–effect structure](https://www.iit.wiki/glossary#h.u3dcbculq7ms), and for determining the units’ [grain](https://www.iit.wiki/glossary#h.wecg9hts0fae). To exemplify, consider a set of [candidate](https://www.iit.wiki/glossary#h.8mzotxp600xu) complexes overlapping over the same substrate. By the [postulates](https://www.iit.wiki/glossary#h.irdac769fidh) of [integration](https://www.iit.wiki/glossary#h.cpmqk4mzfdb9) and [exclusion](https://www.iit.wiki/glossary#h.wk5hvdb57mru), a complex must be both unitary and definite. By the maximal existence principle, the complex should be the one that lays the greatest claim to existence as one [entity](https://www.iit.wiki/glossary#h.dfvlx69kg5m4), as measured by [system integrated information (*φs*)](https://www.iit.wiki/glossary#h.lv95466kjojq). For the same reason, candidate complexes that overlap over the same substrate but have a lower value of *φs* are excluded from existence. In other words, if having maximal *φs* is the reason for assigning existence as a unitary complex to a set of units, it is also the reason to exclude from existence any overlapping set not having maximal *φs*. ## **principle of minimal existence** *[This glossary entry is taken from [Albantakis, L., ... & Tononi, G. (2023). Integrated information theory (IIT) 4.0: formulating the properties of phenomenal existence in physical terms. *PLoS Computational Biology*, 19(10), e1011465.](https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1011465)]* The principle states that, when it comes to a requirement for [existence](https://www.iit.wiki/glossary#h.hyln43vondn5), nothing exists more than the least it exists. The principle is offered by IIT as a good explanation for why, given that a [system](https://www.iit.wiki/glossary#h.4bdc61agv7oe) can only exist as one system if it is [irreducible](https://www.iit.wiki/glossary#h.sw1ddv976914), its degree of irreducibility should be assessed over the [partition](https://www.iit.wiki/glossary#h.tbsgfc5m3fti) across which it is least irreducible (the [minimum partition](https://www.iit.wiki/glossary#h.uxjtor35txjh)). Similarly, a [distinction](https://www.iit.wiki/glossary#h.ixtdw1emrvga) within a system can only exist as one distinction to the extent that it is irreducible, and its degree of irreducibility should be assessed over the partition across which it is least irreducible. Moreover, a set of [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n) can only exist as a system, or as a distinction within the system, if it specifies both an irreducible cause and an irreducible effect, so its degree of irreducibility should be the minimum between the irreducibility on the cause side and on the effect side. ## **purview** In the context of [distinctions](https://www.iit.wiki/glossary#h.ixtdw1emrvga), a *purview* is a generic term for a subset of [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n) over which a [mechanism](https://www.iit.wiki/glossary#h.bdzvjltpbxqw) may specify its cause or effect. In the context of [relations](https://www.iit.wiki/glossary#h.yp1dkd8f7s8u), the term refers to the subset of units that make up the maximally [irreducible](https://www.iit.wiki/glossary#h.sw1ddv976914) overlap of a relation. For more, see: - [Composition: Distinctions](https://www.iit.wiki/overview/axioms-and-postulates/composition#h.jndby56e0826) - [Composition: Relations](https://www.iit.wiki/overview/axioms-and-postulates/composition#h.u591dz8u0iby) ## **realism** In IIT, *realism* is the assumption that something exists (and persists) independently of our own [experience](https://www.iit.wiki/glossary#h.97uzewmap754). This is a much better hypothesis than solipsism, which explains and predicts nothing. Although IIT starts from our own [phenomenology](https://www.iit.wiki/glossary#h.8j4o0g5ssetv), it aims at accounting for the many regularities of experience in a way that is fully consistent with realism. In IIT, realism is one of [three methodological assumptions](https://www.iit.wiki/overview/foundations#h.8rzkbmyfu80) (together with [physicalism](https://www.iit.wiki/glossary#h.jtbdxiwp9igh) and [atomism](https://www.iit.wiki/glossary#h.rnq3v27h92i6)), which allow us to translate the [0th axiom](https://www.iit.wiki/glossary#h.ihc2d4eaahbj) into the [0th postulate](https://www.iit.wiki/glossary#h.ny792kcl3wmd). For more, see [Three Methodological Assumptions](https://www.iit.wiki/overview/foundations#h.8rzkbmyfu80). ## **relation** *Relations* provide structure to (otherwise unordered sets of) [distinctions](https://www.iit.wiki/glossary#h.ixtdw1emrvga), which are aspects of an [experience](https://www.iit.wiki/glossary#h.97uzewmap754) that we can “pick out” through [introspection](https://www.iit.wiki/glossary#h.97uzewmap754). [Phenomenally](https://www.iit.wiki/glossary#h.8j4o0g5ssetv), *relations* refer to how distinctions feel bound together as an [irreducible](https://www.iit.wiki/glossary#h.sw1ddv976914) content of experience. For example, we might pick out a particular shape and a particular color, which are bound together in the content “blue square.” [Physically](https://www.iit.wiki/glossary#h.jtbdxiwp9igh), a relation is the [irreducible](https://www.iit.wiki/glossary#h.sw1ddv976914) overlap of distinctions specified by [mechanisms](https://www.iit.wiki/glossary#h.bdzvjltpbxqw) within the [complex](https://www.iit.wiki/glossary#h.b6fxhbe1r3re). They can bind any number of distinctions (relation degree) based on the overlap between their purviews (relation faces). Like distinctions, relations must adhere to the [postulates](https://www.iit.wiki/glossary#h.irdac769fidh) (save [composition](https://www.iit.wiki/glossary#h.j0xivbr6tr10))—that is, they are intrinsic, specific, unitary, and definite. For more, see [Composition: Relations](https://www.iit.wiki/overview/axioms-and-postulates/composition#h.u591dz8u0iby). ## **relation face** A relation face is the irreducible overlap of a set of purviews, and it is a component of a [relation](https://www.iit.wiki/glossary?authuser=0#h.yp1dkd8f7s8u). The degree of a relation face is the number of purviews it binds, the relation face purview is the elements over which the various purviews overlap, and the relation face *φ*f is the same as the *φ*r of the relation it is a component of. ## **repertoire** A repertoire typically refers to a probability distribution specified by a set of [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n) (e.g. a [mechanism](https://www.iit.wiki/glossary#h.bdzvjltpbxqw) or a [system](https://www.iit.wiki/glossary#h.4bdc61agv7oe)) over its inputs (cause repertoire) or outputs (effect repertoire). It can also be used to refer to the set of states alone without reference to the probability distribution over those states (i.e. the repertoire of effect states). ## **selectivity** A factor in the formula for *intrinsic information.* See [intrinsic information](https://www.iit.wiki/glossary#h.vkva0021by39). ## **self-loop** A self-loop is a self-connection—a connection between a [unit](https://www.iit.wiki/glossary#h.y4l991ydyf0n) and itself—which means that the unit receives an input from itself and provides an output to itself. ## **spot** Coming soon ## **state** Regardless of [grain](http://www.iit.wiki/glossary#h.wecg9hts0fae), the *state* of a [unit](http://www.iit.wiki/glossary#h.y4l991ydyf0n) in IIT is binary, indicated by italicized upper-/lowercase letters, respectively (e.g., ***aB***). When referring to neural units, the convention of ON/OFF may be used at times, but it is best to think of unit states in more abstract terms, where one state is simply the complement of the other—“this way” and “not this way.” The *system state* refers to the state of all its constituent units (e.g., ***abCd***). For the mapping of *micro states* into binary *macro states*, and the justification for why states are binary, see [Marshall et al. (2024)](https://www.biorxiv.org/content/10.1101/2024.04.12.589163v1.full.pdf). For more, see * [Marshall, W., Findlay, G., Albantakis, L., & Tononi, G. (2024). From micro to macro units: a mathematical framework for identifying the causal grain of a system from its intrinsic perspective. *bioRxiv*, 2024-04.](https://www.biorxiv.org/content/10.1101/2024.04.12.589163v1.full.pdf) * [Glossary: grain](http://www.iit.wiki/glossary#h.wecg9hts0fae) * [Information Postulate](https://www.iit.wiki/overview/axioms-and-postulates/information) ## **substrate** A *substrate* is any set of [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n) that we can [observe and manipulate](https://www.iit.wiki/glossary#h.urmduwg8ibdt). The term *substrate* is generally synonymous with [*system*](https://www.iit.wiki/glossary#h.4bdc61agv7oe). Note that we do not presume a substrate to exist *per se*, nor to be a “material” basis from which consciousness “emerges.” We rather treat the substrate as an [*operational*](https://www.iit.wiki/glossary#h.vztp822ktk99) basis from which to assess [cause–effect power](https://www.iit.wiki/glossary#h.vlk7u52cim8x) following the [postulates](https://www.iit.wiki/glossary#h.irdac769fidh). Any set of units can be considered a candidate, but only one that satisfies all postulates is called a *substrate of consciousness* (also called a [complex](https://www.iit.wiki/glossary#h.b6fxhbe1r3re) or [intrinsic entity](https://www.iit.wiki/glossary#h.dfvlx69kg5m4)). For more, see * [0th Postulate](https://www.iit.wiki/overview/foundations#h.5h9ssjclzgt9) * [FAQ: Is IIT an emergentist theory of consciousness?](https://www.iit.wiki/faqs/philosophy#h.2pdoh6tca2nx) ## **substrate graph** A *substrate graph* is a way to visually represent the [substrate](https://www.iit.wiki/glossary?authuser=0#h.63hvurupgbzf) under investigation as a network. It typically consists of the (labeled) [units](https://www.iit.wiki/glossary?authuser=0#h.y4l991ydyf0n) and their causal connections, as nodes and edges of a network respectively. An example is given in the figure below, which represents a substrate constituted of 3 units—A, B, and C—connected in a nearest-neighbor grid with self loops. ![](/corpus/figures/iit-wiki-glossary/glossary-image3.png) ## **substrate of consciousness** A *substrate of consciousness* (also called a [complex](https://www.iit.wiki/glossary#h.b6fxhbe1r3re)) is a set of [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n) in a [state](https://www.iit.wiki/glossary#h.hnb1zhy1izf8) that satisfies all [postulates](https://www.iit.wiki/glossary#h.irdac769fidh) of IIT. In empirical IIT work, the substrate of consciousness may also be referred to as the [neural substrate of consciousness](https://www.iit.wiki/glossary#h.j16zhlml4tz1). Note that we do not presume a substrate of consciousness to exist *per se*, nor to be a material basis from which consciousness “emerges.” Rather, in the ontology of IIT, what exists is the substrate of consciousness [unfolded](https://www.iit.wiki/glossary#h.frg5mnvcsu7) as a [*Φ*\-structure](https://www.iit.wiki/glossary#h.u3dcbculq7ms). This is called an [intrinsic entity](https://www.iit.wiki/glossary#h.dfvlx69kg5m4)—one that exists for itself. In contrast, a generic [substrate](https://www.iit.wiki/glossary#h.63hvurupgbzf) is simply a set of units we can [manipulate and observe](https://www.iit.wiki/glossary#h.urmduwg8ibdt). For more, see * [0th Postulate](https://www.iit.wiki/overview/foundations#h.5h9ssjclzgt9) * [FAQ: Is IIT an emergentist theory of consciousness?](https://www.iit.wiki/faqs/philosophy#h.2pdoh6tca2nx) ## **system** A *system* is any subset of [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n) that can be considered as a [candidate](https://www.iit.wiki/glossary#h.8mzotxp600xu) [substrate of consciousness](https://www.iit.wiki/glossary#h.j5clb514qcec). The term is meant in the generic sense used in physics—as a set of interacting elements considered as a single entity. In IIT, the term is usually interchangeable with [substrate](https://www.iit.wiki/glossary#h.63hvurupgbzf). For more, see * [Intrinsicality postulate](https://www.iit.wiki/overview/axioms-and-postulates/intrinsicality) * [Marshall, W., Grasso, M., Mayner, W. G., Zaeemzadeh, ... & Tononi, G. (2023). System Integrated Information. *Entropy*, *25*(2), 334\.](https://www.mdpi.com/1099-4300/25/2/334) ## **transition probability matrix (TPM)** A *transition probability matrix* (TPM, or state transition matrix) is a mathematical object that completely describes the dynamics of a [substrate](https://www.iit.wiki/glossary#h.63hvurupgbzf) of [units](https://www.iit.wiki/glossary#h.y4l991ydyf0n). More precisely, it is a matrix of numbers that can be used to find the probability that a substrate [state](https://www.iit.wiki/glossary#h.hnb1zhy1izf8) will transition from one to another. For example, the inset shows the TPM for system AB, and we can see that *ab* (OFF, OFF) has a probability of 0.81 to transition to *ab* (OFF, OFF), of 0.09 to transition to *Ab* (ON, OFF), and so forth. In IIT, the TPM is the basis for all mathematical steps required to identify a [complex](https://www.iit.wiki/glossary#h.b6fxhbe1r3re) and [unfold](https://www.iit.wiki/glossary#h.frg5mnvcsu7) its [*Φ*-structure](https://www.iit.wiki/glossary#h.u3dcbculq7ms) following the five [postulates](https://www.iit.wiki/glossary#h.irdac769fidh). For more, see * [FAQ: How do we get a TPM?](https://www.iit.wiki/faqs/technical#h.2l6pbfrrrl37) * [0th Postulate](https://www.iit.wiki/foundations#h.5h9ssjclzgt9) * [Computing *Φ*: Identifying a Complex & Unfolding Its *Φ*-structure](https://www.iit.wiki/unfolding) ### **state-by-node TPM** A state-by-node (SBN) TPM (right) is an alternative way to represent any state-by-state (SBS) TPM (left). It simply shows the probability that a specific output unit (top) will turn ON given a specific input state (left). For many of the computations done in IIT, it is easier to follow the operations when working with the SBN representation. The [PyPhi software](https://centerforsleepandconsciousness.psychiatry.wisc.edu/pyphi-software-2/) also works largely with SBN TPMs. Assuming [conditional independence](https://en.wikipedia.org/wiki/Conditional_independence), we obtain the SBN TPM by simply adding the relevant values from the SBS TPM. For example, to obtain the value that unit ***A*** will turn ON given input ***ab***, we add the two values in the SBS TPM in which ***A*** is ON. ### **cause TPM** Coming soon. For now, see [Computing *Φ*: Step 2—Intrinsicality](http://www.iit.wiki/unfolding#h.5qi5tc64lye6). ### **effect TPM** Coming soon. For now, see [Computing *Φ*: Step 2—Intrinsicality](http://www.iit.wiki/unfolding#h.5qi5tc64lye6). ## **unbinding** *Unbinding* refers to the operation of removing overlapping distinctions one by one to compute relation phi (*φr*). See [relation (*φr*)](https://www.iit.wiki/glossary#h.4won6ixpwruk). ## **unfolding** *Unfolding* is the series of computational steps that allow us to characterize the [*Φ*\-structure](https://www.iit.wiki/glossary#h.u3dcbculq7ms) specified by a [substrate of consciousness](https://www.iit.wiki/glossary#h.j5clb514qcec) (or [complex](https://www.iit.wiki/glossary#h.b6fxhbe1r3re)). The unfolding procedure can be thought of as implementing the [composition postulate](https://www.iit.wiki/overview/axioms-and-postulates/composition) for the [system](https://www.iit.wiki/glossary#h.4bdc61agv7oe) as a whole; this means we apply the [postulates](https://www.iit.wiki/glossary#h.irdac769fidh) of IIT (save composition) to the system’s [mechanisms](https://www.iit.wiki/glossary#h.bdzvjltpbxqw) in order to characterize the [distinctions](https://www.iit.wiki/glossary#h.ixtdw1emrvga) they specify and the [relations](https://www.iit.wiki/glossary#h.yp1dkd8f7s8u) among them, which together compose the *Φ*\-structure. (Note that *unfolding* is sometimes used more casually to describe the full IIT analysis of a system. But most precisely, it is the operationalization of the composition postulate.) For more, see: * [Composition postulate](https://www.iit.wiki/overview/axioms-and-postulates/composition) * [Computing *Φ*: Identifying a Complex & Unfolding Its *Φ*\-structure](https://www.iit.wiki/unfolding) ## **unit** A *unit* is a constituent of a [substrate](http://www.iit.wiki/glossary#h.63hvurupgbzf), [operationally](http://www.iit.wiki/glossary#h.vztp822ktk99) defined by the [grain](http://www.iit.wiki/glossary#h.wecg9hts0fae) at which it is [observed and manipulated](http://www.iit.wiki/glossary#h.urmduwg8ibdt) to evaluate its [cause–effect power](http://www.iit.wiki/glossary#h.vlk7u52cim8x). For example, neurons might be treated as units, but so might the molecules that constitute a single neuron, or even a set of cortical areas within the brain. Following the [exclusion postulate](http://www.iit.wiki/axioms-and-postulates/exclusion#h.pvmrhffvh06e) and the [principle of maximal existence](http://www.iit.wiki/glossary#h.qof4052teerl), a [complex](http://www.iit.wiki/glossary#h.b6fxhbe1r3re) is constituted of units at the grain that maximizes [system integrated information (*φs*)](http://www.iit.wiki/glossary#h.lv95466kjojq). The units at this grain are referred to as *intrinsic units*, but to discover them requires us to assess candidate units at micro, meso, and macro grains: * A *micro unit* is conceived of as an “atom” of [cause–effect power](http://www.iit.wiki/glossary#h.vlk7u52cim8x): it cannot be [partitioned](http://www.iit.wiki/glossary#h.tbsgfc5m3fti) into finer constituents, its updates cannot be partitioned into finer updates, and it cannot have more than two states—the minimum necessary to bear a cause and produce an effect. * *Macro units* are constructed either out of micro units or lower levels of macro units (called *meso units*). Macro units, like micro units, have a repertoire of exactly two states and are considered an “atom” cause–effect power at their respective, macro level of analysis. All units, regardless of grain, are “maximally [irreducible](http://www.iit.wiki/glossary#h.sw1ddv976914) within”: * They must be *irreducible* (*φu* > 0); otherwise, the substrate would be constituted of units that don’t exist—we cannot get something out of nothing. * Likewise, they must be *maximally* irreducible; otherwise, there would be another choice of grain that lays a stronger claim to existence. * They only need to be maximally irreducible *within*—more irreducible than any other unit that could be built from the same constituents. This is in contrast to a complex, which is “maximally irreducible within and without”—more irreducible than any subset, superset, or paraset of its units (see [Exclusion](http://www.iit.wiki/axioms-and-postulates/exclusion)). For more, see * [Marshall, W., Findlay, G., Albantakis, L., & Tononi, G. (2024). From micro to macro units: a mathematical framework for identifying the causal grain of a system from its intrinsic perspective. bioRxiv, 2024-04.](https://www.biorxiv.org/content/10.1101/2024.04.12.589163v1.full.pdf) * [FAQ: How do we determine the causal grain at which integrated information (*φs*) is maximal?](http://www.iit.wiki/faqs/technical#h.hecf38ytd9et) * [0th Postulate](http://www.iit.wiki/foundations#h.5h9ssjclzgt9) * [Atomism: cause–effect power all the way down](http://www.iit.wiki/foundations#h.gc7e9zm8e1ma) * [FAQ: Do macro-units "emerge" from micro-units?](http://www.iit.wiki/faqs/philosophy#h.8awdskknvgn1)