Assessing the commensurability of theories of consciousness: On the usefulness of common denominators in differentiating, integrating and testing hypotheses

How deep is the current diversity in the panoply of theories to define consciousness, and to what extent do these theories share common denominators? Here we first examine to what extent different theories are commensurable (or comparable) along particular dimensions. We posit logical (and, when applicable, empirical) commensurability as a necessary condition for identifying common denominators among different theories. By consequence, dimensions for inclusion in a set of logically and empirically commensurable theories of consciousness can be proposed. Next, we compare a limited subset of neuroscience-based theories in terms of commensurability. This analysis does not yield a denominator that might serve to define a minimally unifying model of consciousness. Theories that seem to be akin by one denominator can be remote by another. We suggest a methodology of comparing different theories via multiple probing questions, allowing to discern overall (dis)similarities between theories. Despite very different background definitions of consciousness, we conclude that, if attention is paid to the search for a common methological approach to brain-consciousness relationships, it should be possible in principle to overcome the current Babylonian confusion of tongues and eventually integrate and merge different theories.


Introduction
In the sciences of mind, a wide variety of proposals to account for consciousness in neurobiological terms has been proposed.As listed by Seth and Bayne (2022) this variety includes Global workspace theories (GWTs), Integrated information theory (IIT), Neural Darwinism, Recurrent Processing theory, Predictive processing, Neurorepresentationalism, Active inference Theory (AIT), Attention Schema theory, Higher-Order theories (HOTs), Dentritic Integration theory, Sensorimotor theory, Information Closure theory, among many others.
On the one hand, significant improvements in the empirical investigation of relevant brain structures and functions have been made possible by advancements in technology, particularly in neuroimaging, electrophysiological measurements, and computing technology.On the other hand, the additional and new kinds of data deriving from empirical investigations have inspired a variety of theoretical interpretations on the neural basis of consciousness, which are not always compatible with each other, at least at a first glance.
As Merker et al. (2021) point out, "schools" advocating disparate theoretical bids for paradigmatic status contend with one another without the benefit of any shared means of adjudicating the relative merits of their conflicting proposals (Merker, Williford, & Rudrauf, 2021).Indeed we agree that the search for such shared means has been an underexposed but important element in the field of consciousness research.In Kuhnian terms, these are the cardinal characteristics of the "prehistory" stage of a nascent science (Kuhn, 1962) (sect.2).On this "route to normal science," the proponents of rival theories, formulated in scientific terms and supported by empirical evidence, often find themselves talking past one another for the lack of shared assumptions or explananda.While the early scientific phase is characterized by the coexistence of many competing models in parallel, the more mature stage will see a more substantial cross-talk among those models (Signorelli, Szczotka, & Prentner, 2021).Whether and how such cross-talk will lead to a unified theory or model of consciousness, however, remains to be seen.Importantly, this more substantial cross-talk does not imply a monistic (in the sense of unified or homogeneous) outcome, especially in the case of particularly challenging and new questions, for which a pluralist scientific approach is ideal (Chang, 2012).
The question has been raised "to what extent this diversity is real, or whether many theories share the same basic ideas with a potential for convergence towards a more unified theory" (Northoff & Lamme, 2020).In fact, there have been calls for developing a "minimal unifying theory of consciousness" that would specify "at least one necessary feature of consciousness … entailed by (many) existing theories of consciousness" (Wiese, 2020).
However, to attempt to "unify" a set of theories, we must first ascertain that the theories in question are commensurable, meaning that they can be compared along one or more dimensions: (a) logical (relating to principles and structures of reasoning and validity, and to how key concepts are understood and defined) and/or (b) empirical (relating to observation, experience, and experimentation rather than to pure logic).If we are not able to compare them, we have no way of knowing if they speak of different things, in which case unification becomes conceptually irrelevant and de facto impossible.Importantly, both the concept and the actuality of (deep) incommensurability are still matter of debate; what it means and whether deep incommensurability does in fact exist (Sankey, 2016).The main issue is whether admitting the possibility that different scientific theories may be incommensurable undermines a realistic and progressive view of science development, as well as the applicability of the same standards of scientific assessment to all the theories.
In what follows we will focus on the possible logical and empirical commensurability of different theories of consciousness, positing some kind of commensurability as a precondition for investigating the possibility of a convergence among theories of consciousness.After reflection on the logical conditions for comparing different theories, some dimensions for inclusion of a theory in a logically and empirically consistent set of commensurable theories of consciousness will be proposed.Our aim is to introduce a methodology for how to proceed on comparisons and attempts at integration and separation of different theories of consciousness.This methodology entails the identification of (dis)similarities amongst theories by way of probing questions and comparisons based on several common denominators rather than a single one.Based on these predictions it can be derived where theories critically differ in terms of experimental outcomes or model performances.We believe that this focus on how to develop a common methodological approach to brainconsciousness relationships may eventually be effective in advancing the comparison and possibly also the integration of different theories.Finally, (dis)similarities based on common denominators can be used to integrate or even merge theories, especially those using different background definitions or assumptions about consciousness.

Commensurability
Commensurability can be understood in the basic sense of 'being comparable'.The opposite term incommensurability literally means 'to have no common measure'.In philosophy of science, the term was made famous by the historian of science Thomas Kuhn in his description of "scientific revolutions" (Kuhn, 1962).The development of science, he argued, is sometimes revolutionary in the sense that one world view replaces another, a dramatic change that is not logically analysable but rather resembles a Gestaltswitch, where you can see one image or another but not both at the same time.When theories are incommensurable in this deep way, they cannot be compared because they share no unit of measure that could serve the purpose of comparison.An illustration of deeply incommensurable worldviews could be theism in the form of a belief in the existence of a god that has created and intervenes in the universe versus the form of agnosticism that conceives this belief as either impossible to verify or meaningless.
As clarified by Kuhn, incommensurable theories may replace one another in different historical stages, where one theory assumes explanatory dominance over others and thus takes over the role of the paradigmatic one.In addition to this diachronic sense of incommensurability, incommensurability can be also synchronic (i.e., incommensurable theories co-exist at the same historical stage).Consistent with the falsifiability criteria defined by Popper, there is no principled way to decide which theory is really valid and which can be assumed as paradigmatic: different, competing theories can co-exist until they are falsified by empirical observation (Josephson & Josephson, 1996;Strevens, 2020).However, as we shall see with specific reference to consciousness theories, incommensurable theories might co-exist without being falsified because they refer to different aspects and/or dimensions of the same object of study.In this case incommensurability would be empirical rather than logical (see below).
De facto, if theories are logically incommensurable, there is arguably no way of knowing that they are even speaking about the same phenomenon (Evers, 1991).The concept "incommensurable" is to that extent paradoxical, for if there is no way of determining a shared topic, there is ipso facto no way of determining incommensurability.This paradox results from the meaning of commensurability described above, which we can refer to as a "strong" sense of commensurability.Another, "weak" sense is possible, according to which some aspects of the theories in question (e.g., formal rules of reasoning and validation) are commensurable enough to allow comparison (see below).
Illustrations and discussions of paradigm shifts often come from physics where the theoretical advances over the centuries have been quite outstanding.To illustrate, in 1687 the natural philosopher Isaac Newton established classical mechanics in his book Mathematical Principles of Natural Philosophy.In 1905, Albert Einstein superseded Newtonian mechanics when he introduced the two interrelated theories of special and general relativity, reinterpreted the inner workings of nature, the very essence of light, time, energy and gravity, and thus fundamentally revolutionised the way we look at the physical universe, including space and time.The philosopher and physicist Niels Bohr (with whom Einstein had vivid scientific debates) made new revolutionary and foundational contributions to understanding atomic and molecular structures developing what is now known as the old quantum theory.In 1927, Werner Heisenberg developed the uncertainty principle and founded quantum mechanics.The commensurability of these deeply different theoretical frameworks has been subject to vivid debates in both physics and philosophy, not least concerning the probabilistic laws governing the world of elementary particles.
Quite such dramatic philosophical and scientific advances in understanding have not yet occurred in the brain sciences and the sciences of mind that are still in what Kuhn would have called a nascent stage, which is not to deny that there have been important shifts already; e.g., from ontological dualism to monism, or from the concept of an immaterial soul to a naturalistic understanding of consciousness.The variety of contemporary empirical investigations and theoretical interpretations of consciousness is scientifically and philosophically enriching, productive of new ideas and knowledge, yet so far without fundamentally revolutionising the way we look at the mental realm, notably consciousness, which remains an elusive concept.Assessing the commensurability of distinct theoretical proposals to account for consciousness is, we propose, a useful contribution towards a further elucidation.

Logical commensurability
The fundamental measure necessary for making theories comparable is logical: if theories adhere to fundamentally different standards of rationality, logical consistency, inferences, or background conceptual definitions, they are logically incommensurable.
It is not self-evident that simply because the same term is used in distinct theories, such as "consciousness", the same phenomenon is being addressed.If not, we would not even be able to ascertain that these theories are 'theories of consciousness' at all, unless we assume a preliminary operational or stipulative definition of consciousness.
Strictly speaking, it would not be legitimate to claim that the above logically imposes a necessary condition for a theory of consciousness, T, to qualify as such, since proponents of T could maintain that T is the only (valid) theory, and reject commensurability altogether.In contrast, we can use the above logical measure as an inclusion criterion in a set of commensurable theories of consciousness.Analytically, there must be something that is common to all commensurable theories of consciousness, at least one smallest common denominator that they share: that is what commensurability means (Kuhn, 1962).In the absence of such a denominator, it would be impossible to know that the distinct theories are theories of the same phenomenon, hence they could not rationally be grouped into that set.In other words, theories within a specific set cannot be strictly logically incommensurable.
This sets the stage for the first question that has logical priority, identifying the issue on common denominator(s): Is there a smallest common denominator that all logically commensurable theories must share and by virtue of which we are justified to assume that these theories have a shared explanandum (object to be explained)?
In a putative set of theories of consciousness, this could be, for example, a preliminary operational or stipulative definition of consciousness that allows the identification of a shared explanandum.In addition, one could formulate very general, "weak" denominators, e.g. that (i) consciousness does exist as a distinct phenomenon; (ii) it can be researched, i.e., is accessible for study (from a first-person or third-person perspective).

Empirically commensurable theories
Empirically similar theories Fig. 1.Relationships between different types of commensurability and similarity.All theories must be logically commensurable, but that does not mean that they are empirically commensurable or either conceptually or empirically similar.For example, philosophical theories can be a priori (and not empirical) and diverge conceptually.Empirically similar theories must be conceptually similar but not vice versa.
K. Evers et al.

Empirical commensurability
If this logical denominator can be formulated, a less dramatic (i.e., more intelligible) form of incommensurability can be addressed.Theories that logically belong to one and the same set may speak about different aspects of the same (broad) reality (e.g., focus on phenomenal consciousness versus access consciousness; see later), or approach the same reality with different methods (e.g., quantitative or qualitative), or rely on different standards of validation (e.g., phenomenological or statistical/mathematical). It may be the case that, although theories are logically commensurable, the aspects of the reality they speak about, or the methods used, may be so different that the theories can be described as empirically incommensurable (Fig. 1; Table 1).De facto, theories that are empirically incommensurable with regards to methodology can speak about the same phenomenon.
Once logical commensurability has been established, this sets the stage for the second question of priority that takes us beyond the realm of pure logic and into empirical reality: Is there a smallest common denominator that all empirically commensurable theories must share and by virtue of which we are justified to assume that these theories can address a shared explanandum empirically?
This denominator would go beyond the logical identification of a shared explanandum and focus on empirical aspects, for example in terms of how consciousness can be measured or otherwise assessed.Below, we suggest that, whilst it appears unlikely that there would be a single denominator by which theories can be unequivocally grouped together, common denominators may nonetheless be useful in the overall taxonomy of consciousness theories.Accordingly, we will identify partial overlaps (Table 3) but no single shared denominator.
As summarised in Table 1, both empirical and logical commensurability are multidimensional and can be framed and quantified in relation to different dimensions.Distinct theories may share one or more empirical and/or logical postulates: the kind and number of shared postulates provide the level or depth of commensurability between the theories.Thus, logical and empirical commensurability result from the combination of several dimensions, which express the overall level of commensurability.For instance, two theories can focus on the same kind of data (e.g., neurophysiological data to assess the presence of or the capacity for consciousness), but they can select and validate them with different criteria: in this case, the theories in question are only partly empirically commensurable.
Furthermore, as represented in Fig. 1, to be empirically commensurable, different theories of consciousness must be logically commensurable, while it is possible that two logically commensurable theories are empirically incommensurable.For instance, they may share the same standards of rationality whilst referring to different kinds of data (e.g., neurophysiological vs. behavioural).
In the assessment of level and depth of commensurability (a question that can be framed with reference to either foundations, contents or methods), we need in particular to assess if proposed dimensions of commensurability (considered by themselves or in conjunction) are (a) relevant (and how relevant); (b) necessary/sufficient for commensurability.As we shall propose further below, a useful method here that may also serve to assess the testability of theories, is to challenge them with key probing questions that bring their (in)commensurability and (dis)similarities to light.

Conceptual versus empirical similarity of theories
In this context, the concept of similarity is relevant to consider.Commensurability is distinct from similarity, but the two concepts

Table 1
Examples of relevant dimensions to assess commensurability of theories of consciousness.Note that this list is not meant to be exhaustive.are logically connected.Similarity denotes the resemblance of the feature(s) of theories by virtue of which these theories are commensurable (given that the theories are commensurable).The terms are distinct but co-extensive in that it is only through comparison that similarity can be established.There are different types of similarity, e.g., conceptual and empirical.Commensurability of theories logically entails a minimal level of conceptual similarity, lest a comparison of them be meaningless.("Logical" and "conceptual" do not mean the same.Principles of logic are a priori and comparable to principles of mathematics, whereas conceptual refers to natural languages and the use of words.)Moreover, it is important to bear in mind that the empirical level (e.g. an empirical hypothesis, interpretation or theory) is never conceptually neutral: it relies on background assumptions and on a theoretical framework.Accordingly, empirical similarity entails (at least partial) conceptual similarity, such as shared definitions of key terms.For example, empirically similar lines of research in affective neuroscience on non-human sentience agree, at least roughly, on how to define sentience, which allows them to strive for consensus on the criteria for its recognition.
In contrast, conceptual similarity need not entail empirical similarity.First, this is because theories (e.g.philosophical theories) need not be empirical at all.Saying that a theory is not empirical means that it may use purely a priori reasoning.It can refer to and describe empirical data, but the reasoning in a non-empirical theory need not rely on or refer to empirical theories, nor be empirically testable.For example, Spinoza's theory of mind (1677) speaks about empirical reality but is purely a priori in each instance of its argumentation.In this case the question of empirical similarity would not even arise.Secondly, this is because conceptually similar empirical theories need not share an empirical focus (they may focus on different parts of empirical reality).For example, distinct theories may agree that sentience by definition requires felt experience, but raise different questions, e.g. one focuses on, say, the molecular biology of sensory receptors and the other on human child psychology.

Methodology for identifying a set of logically and empirically commensurable theories of consciousness
As described above and in Table 1, logical commensurability can be framed with reference to, for example, the following five dimensions: -Logical architecture -Conceptual foundations -Interpretative approach -Standards of rationality -Standards of validity These dimensions can be taken to frame logical commensurability with reference to theoretical structure, conceptual form, and research methodology, regardless of the object's definition.In fact, none of these dimensions requires a shared fine-grained definition of the object of the theory (e.g., consciousness), which would arguably be a too stringent condition for logical commensurability.On the other hand, a generic or macro-level (e.g., behavioural) shared background definition can be considered sufficient for logical commensurability, provided that the dimensions listed above are not incompatible or inconsistent among different theories.
To illustrate, different but logically commensurable theories of consciousness might define consciousness as a special kind of information processing, while at the same time differing substantially about the details and modalities of such processing (e.g., how it is generated, what are the critical thresholds for information to be consciously processed, what is the level of abstraction and granularity with reference to relevant brain structures, etc.).
Analogously, empirical commensurability can also be framed with reference to the dimensions listed in Table 1, each of which is arguably insufficient if taken independently yet necessary as part of a set for assessing how the theories are empirically commensurable.
To illustrate, a relevant dimension is the kind of data the theory relies on: this data should be at least part of the same general class (e.g., observational data vs simulation data), with the empirical commensurability increasing if data are also of the same specific class (e.g., neurophysiological vs. behavioural, functional vs. structural, and so on).Importantly, to be empirically commensurable, it is not necessary for different theories to share all their empirical dimensions in detail lest their difference would be nullified.For instance, as illustrated by Michel (2020), theories of consciousness historically differ in relying on different detection (of consciousness) rules for testing relevant hypotheses.According to our framework, this would be one dimension of empirical commensurablity (i.e., criteria for data selection), which does neither exclude nor imply that the theories are commensurable with reference to other dimensions as well.Analogously, taxonomic (i.e., the concepts in one theory cannot be translated into the concepts in the other theory) and methodological (i.e., no objective criteria to evaluate theories) incommensurability, as usually referred to in philosophy of science, are two particular dimensions of the broader spectrum we here propose.Taxonomy may be identified with Conceptual foundations.Therefore, it is one dimension among them, and taxonomic and logical incommensurability as we describe it are only partly overlapping.
The same may be said about methodological commensurability, which is one among the eight dimensions of empirical commensurability the we identify (see Table 1).Therefore, the dimensions of logical and empirical commensurability that we propose are more fine-grained and encompassing than that sole taxonomic and methodological commensurability.

Assessing commensurability between theories of consciousness and searching for a common denominator
In this section we will analyse illustrative contemporary theories of consciousness against the theoretical background outlined above, leading us to identify theories that share a sufficient basis to consider them commensurable, although not necessarily similar.
The first part of section 5 is conceived to provide an overview of conceptual backgrounds of theories of consciousness in general, and to illustrate cases of incommensurability, while section 5.2 discusses information as a common denominator proposed in the literature.

Examples of logical and empirical commensurability and the search for common denominators
A primary criterion for logical commensurability arises from background definitions of consciousness: what do we understand the concept of consciousness to mean?Intimately linked to this is the epistemological question whether and how we may get to know conscious phenomena.This question relates to, for example, first-versus third-person knowledge about subjective experience, or psychological/behavioural and/or neural manifestations of consciousness.(Here we will not address the sceptical view that the relationship between consciousness and the brain cannot be known by us and must thus remain fundamentally mysterious (e.g., (McGinn, 1989)) -a view that can be considered not or only partially logically commensurable with opposite, non-sceptical views due to different standards of validity (cf.Table 1).).

Idealism versus materialism
One set of theories is grouped around the idealist position that physical matter is only known to exist via our conscious experience, which therefore offers more solid ontological ground than the idea of a physical world existing on its own (e.g.(Kastrup, 2018;Marshall, 2001)).This group contrasts with another set of theories positing that consciousness is contingent upon a physical substrate (the brain) that continues to exist also in the absence of conscious awareness (e.g., under anaesthesia) and is, at least in principle, amenable to empirical investigation, allowing behavioural and neuroscientific data (in addition to first-person observations) as evidence arguing in favour of or against a particular theory of consciousness.The contingency of consciousness on a physical substrate can be regarded as a common denominator placing these theories in the realm of materialism, albeit this comprises wide varieties including both reductionistic and non-reductionistic variants of materialism (a fully reductionistic account implies that consciousness can be fully explained from, and is nothing else than, the relevant constituent neural elements forming the physical substrate of consciousness similar to H 2 O molecules equating to 'water' in its various macrosopic manifestations such as liquid, ice or vapour (E.g., (Block & Stalnaker, 1999;Churchland, 1995;Kim, 2005;Van Gulick, 2001a)).
As compared to materialism in sensu latu, modern idealism is methodologically incompatible with empiricism to the extent that idealism relies on a priori reasoning, whereas the empirical method is a posteriori, although this does not necessarily exclude regarding their respective ideas as complementary.Idealism also differs from the materialist group of theories in that it does not primarily focus on brain-consciousness relationships.For example, one branch of idealism pursues different variants of panpsychism that have to deal with the problem how different persons can have individuated, dissociable minds (e.g.(Kastrup, 2018)).Therefore, even though materialism and idealism are logically commensurable in relation to some dimensions (e.g., they rely on a similar logical structure and refer to comparable standards of rationality and validity), their respective conceptual foundations are deeply dissimilar and they can be considered empirically incommensurable.Below, we will focus the discussion further on the empirical-materialist framework, taken in a broad sense.

Dualism versus monism
Another question of major interest is whether dualism is fundamentally commensurable with monist frameworks, including Spinoza's (supremely idealistic) dual-aspect monism, but also materialism in its various incarnations (e.g., eliminative or reductionistic materialism, non-reductionistic materialism, functionalism; (Velmans, 2009;Block & Stalnaker, 1999;Churchland, 1995;Dennett, 1991;Kim, 2005;McCauley & Bechtel, 2001;Pennartz, 2015;Van Gulick, 2001).With Descartes as famous protagonist in the 17th century, the dualistic framework has witnessed a few revivals in our time (Chalmers, 1996;Eccles, 1990;Popper & Eccles, 1977).At first sight, dualist and monist theories may appear to be logically commensurable if they deploy comparable or even similar conceptual architectures (e.g., definitions and core properties of consciousness, and sometimes also a recognition that a brain-mind relationship exists and can be addressed).The more radical differences between the two approaches emerge on the level of ontology (where dualism asserts the mind's reality independently of matter), which, however, makes them conceptually dissimilar, but not completely logically incommensurable.
An important question arising here is how, in a dualist framework, communication between a material entity (the body) and a nonmaterial entity (the mind or consciousness) may be envisaged.If the law of energy conservation and the closure of the physical domain are to be respected, it becomes problematic how immaterial-to-material influences (or vice versa) can be explained, which raises the issue of which standards of rationality are obeyed (Table 1): does one consider the laws of physics valid, or is one considering exceptions or alternatives to these principles?Even when granting logical commensurability, it can be doubted whether dualism and monism are empirically commensurable.When, for instance, (Popper & Eccles, 1977) pointed to the Supplementary Motor Area as a site for mind-brain interactions in the context of their dualistic framework, it remained unclear what kind of data or methods could be deployed to support or reject the case, or how mind-brain interactions could be measured (other than by physical measurement of behaviour and neural activity).This kind of critique is not limited exclusively to dualist theories, because there are also monist or pan (proto-)psychist frameworks that are unclear or indefinite on the point of empirical tractability ( (Nagel, 1979;Van Gulick, 2001b).Vice versa, some contemporary versions of dualism are non-interactionist (e.g.Chalmers, 1996), which arguably makes them more empirically commensurable with monism.
Despite these significant aspects of empirical incommensurability, it may be interesting to consider whether a common denominator between dualistic and monist theories may nonetheless be found.To illustrate, both theories may employ the same principles and structures of reasoning and validity, as well as the same standards of rationality and validity.Yet dualistic and monistic theories fundamentally differ in their conceptual foundations and interpretative approach.Thus, a common denominator between the two theories might be found at the formal (i.e., logical) level, while they are conceptually dissimilar in both background assumptions and in their interpretative approach.

Information as a common denominator?
Information, or information processing, has been suggested as one possible logical common denominator for dualism and monism.For example, in a defence of dualism, (Chalmers, 1996) proposed that information (or information processing) may be used as a concept shared, or "common currency" between the conscious mind and the brain in both dualistic and monistic frameworks; and, indeed information also constitutes a key concept in several neuroscience-based theories of consciousness (e.g.(Dehaene & Changeux, 2011;Dennett., 1991;Dennett, 2018;King et al., 2013;Tononi, 2004;Tononi, Boly, Massimini, & Koch, 2016)).
However, a problem with using "information" as a common denominator is that it is such a generic concept and so widely applied throughout the natural sciences and computer science, that it can be argued not to add any specific explanatory power on the problem under study.
By default, 'information' is interpreted as Shannon information, which defines information as reduction of uncertainty and is thus set in the mathematical domain of statistics (Shannon, 1948); it deals with the statistical relationships between system elements and as such with the 'syntax' of informational systems, not the 'contents' of what the information is about (Eggermont, 1998).The same applies to different, albeit related concepts of information, such as algorithmic information theory (Kolmogorov complexity) and data compression (Grunwald & Vitanyi, 2003;Lempel & Ziv, 1986): the semantics, phenomenal character and 'aboutness' of conscious experience are not addressed, while many theories consider this to constitute a core property of consciousness (Brentano, 2012;Kim, 2005;Pennartz, 2015;Searle, 2004).Similarly, the concept of information is unitary as it does not recognize that there may be different kinds of information (visual, auditory, olfactory sensations etc.): as such information theory cannot account for qualitative differences between experiences originating from different sensory modalities nor for the complexity of the multimodal nature of subjective experience (Pennartz, 2009).
That the application of information as a potential common denominator for theories of consciousness is fraught with difficulties, is further illustrated by the widespread use of the concept throughout the natural sciences: it is used to describe inorganic matter and systems in the domains of e.g., cosmology, particle physics, quantum mechanicsall domains without a need to invoke conscious phenomena.Information has become such a generic concept thateven if it were to figure as a conceptual 'bridge' between the physical and mental domainit would not work to explain anything about the specific relationships between neural processes and conscious experience.In other words, information would fail as an explanans for the explanandum because it neither speaks in any specific way to the neural mechanisms underlying consciousness, nor about the qualitative richness, integration and phenomenal character characterizing experience.Having said this, information remains very useful as a generic 'common currency' term; we merely wish to caution against attributing explanatory powers to it that it does not possess.
Recently, (Wiese, 2020) proposed to adopt 'information generation' as a common denominator of consciousness, or to use his phrasing more exactly, as a minimal unifying model of consciousness.His argument was derived from the work of (Kanai et al., 2019), who posited that information generation entails the decompression (or decoding) component of generative models, as illustrated by variational autoencoders (VAEs; (Kingma & Welling, 2014)) or predictive processing models (see below).Whereas Kanai et al. considered information generation to constitute a sufficient functional basis for consciousness, Wiese argued that it specifies a necessary (but not sufficient) feature of consciousness, and can thereby be useful in unifying existing theories of consciousness.While the search for common denominators along these and similar lines is to be encouraged, several cautionary remarks need to be made.When 'information generation' is understood as entailing generative models with decompression of information, it will be fairly easy for information-processing systems in general to meet this requirement.In addition to VAEs used in AI systems, it is straightforward to design image or number generators whose outputs are subject to decompression, without having to appeal to consciousness.In short, current artificial information-generating systems can be said to be purely number-crunching devices, lacking any obvious connection to the qualitative richness characterizing conscious experience at its essence (cf.(Jackson, 1982;Shoemaker, 1990;Nagel, 1974;Pennartz, 2015)).While this argument does not preclude that information generation may be a necessary feature of consciousness (Wiese, 2020), it may be criticized, first, for being too loose and too underconstrained to act as a common denominator.It does, in our view, not yet come close enough to capture what a conscious system is and how it functions (Pennartz, 2015(Pennartz, , 2022b)).Wiese argues that a minimal unifying model of consciousness is likely to be an adequate (albeit general) model of consciousness, but precisely this lack of constraints makes this position vulnerable to the critique that too many systems throughout naturewhether organic or inorganiccould easily qualify for being conscious.Moreover, in Wiese's proposal it remains unclear whether the condition of generating information is related to consciousness at all.It may serve to constrain other phenomena such as intelligent behavior, but we have no reason to think it would be necessary or specific to consciousness.Whilst it is considered a truism that conscious experience harbours information, it is not a given that any conscious system should always generate (new) information, as it may primarily engage in representing, or attempting to reproduce, existing environmental and bodily information as in perception.In other words, even though conscious experience is always informative, it can be so by generating new information or recalling stored information.Having said this, Wiese's proposal does point the way to more specific directions in which to search for common denominators and necessary conditions for consciousness (see below).

Examples of commensurable, neuroscience-based theories: How useful are common denominators for a possible unification?
We will next compare several contemporary neuroscientific theories of consciousness that search to define neural substrates and mechanisms of consciousness in the brain, and thus share the common denominator of assuming there are identifiable correlates of conscious processing within the central nervous system, not in a separate 'mental' domain (as in dualism) or exclusively in the interaction between brain, body and environment (e.g.Sensorimotor theory; (O'Regan & Noë, 2001)).Four empirical, brain-based theories will here be considered: (i) Global neuronal workspace theory (GNWT), (ii) Integrated Information Theory (IIT), (iii) Neurorepresentationalism (NREP), (iv) the Active Inference framework as applied to consciousness (Active Inference Theory, AIT; see Table 2 for a brief overview of the main tenets of these theories).In order to advance the analyses, a small selection of empirical, brainbased theories has been made here, noting that this does not imply an evaluation of other theories (that could also serve in such a comparative analysis).We chose to compare these theories here because they can serve to illustrate the issues of commensurability, similarity and (possibly common) denominators at hand, and because their neuroscientific aspects have been elaborated to some extent; they are in line with at least some neuroscientific arguments and findings and are under active investigation (for a recent review, see (Seth & Bayne, 2022)).

Commonalities and differences in denominators of neuroscience-based theories
In addition to sharing a common goal (i.e., to identify neural substrates of consciousness in the brain), these theories share the related denominator that their methodologies allow to consider empirical data as evidence in favour of or against them (i.e., they are empirically commensurable in relation to types of data, criteria for data selection and significance, and tools for selecting and analysing data; Table 1).In addition to verbal or other behavioural reports, examples of such data are fMRI and intracranial EEG data (recorded from humans), single-unit and ensemble recordings (mostly in animals, sometimes in epileptic patients) and results from causally disruptive experiments (e.g., TMS in humans, optogenetics in animals).With this empirical approach and common orientation towards neural substrates and mechanisms in mind, it is not surprising that at least some of these theories have proposed that (neural mechanisms underlying) consciousness can be measured even if they might differ in the type(s) of data considered relevant for measuring consciousness.For instance, IIT proposes integrated information (Φ) as a measure, quantifying the extent to which the cause-effect structure made up by system elements changes if that system is subdivided along the partitions that make the least difference (i.e., the minimum partition).In doing so, IIT postulates that consciousness involves the encoding of potential states of a conscious system (Albantakis et al., 2023b), whereas most other theories (e.g., GNWT, NREP, AIT) explain specific conscious experience as corresponding to an actual state of the system, without taking into account all possible states.
Another quantitative approach comes from GNWT, having proposed a global measure of information sharing across brain areas (the 'weighted symbolic mutual information' (King et al., 2013)) to index consciousness.This index is in line with GNWT's postulate that conscious states are marked by an ignition process by which information gains access to a neuronal workspace of highly interconnected corticothalamic networks, and is thereby 'broadcasted' throughout this system, providing access of the information to executive systems (e.g.working memory, evaluation, motor systems; (Baars, 2002 Tononi, 2016;Tononi, 2015) Phenomenal consciousness (essential aspects or axioms: intrinsic existence, composition, information, integration and exclusion) A high level of consciousness is defined by a high ϕ max value, specified as the irreducibility of a cause-effect structure, which may be implemented in different physical substrates (e. g. neural).This quantifies to what extent the cause-effect structure changes if the system is cut along its minimum partition.
Action not strictly required.
Visual cortical system and lateral interactions with cortices for other sensory modalities Active Inference Theory (AIT) (Friston, 2018;Friston et  Changeux, & Dehaene, 2020).Access to conscious content is key here, otherwise it does not count as consciousness.
Although higher-order theories (HOTs) of consciousness are not listed in Table 2, it is relevant to compare them at least briefly to GNWT and other accounts.They form a fairly hetereogeneous group of ideas which vary, for instance, in their interpretation of what a 'higher-order' representation is, and whether consciousness has a function or not (Brown, Lau, & LeDoux, 2019;Lau & Rosenthal, 2011).HOTs assume that a first-order representation (e.g., a visual image or other sensory pattern) is not sufficient for conscious processing, but that some higher-order mechanism is required, such that the subject becomes aware of the first-order representation.While first-order representations are about the world, higher-order representations are about the subject's own mental states.Different HOT variants make diverging assumptions about what the higher-order mechanism entails and how it makes lower-order contents conscious.For instance, higher-order representations would be needed to guarantee a certain degree of inner awareness of the subject's cognitive functioning in relation to the first-order state (Brown et al., 2019).Rosenthal (2005) posited that self-awareness needs to be coupled to a first-order state in order to render contents of that state phenomenally conscious.Another variant, higher-order thought theory (HOTT), posits that higher-order representations take the shape of thoughts, which links this theory more strongly to languagebased accounts of consciousness (e.g.(Carruthers, 1989;Rosenthal, 2004;Rosenthal & Weisberg, 2008)).In neuroscientific terms, firstorder information would be represented in early sensory regions such as visual cortex, whereas most HOT variants assume that higherorder representations, such as meta-cognitive judgments, are sustained by parietal-prefrontal networks (Dehaene, Lau, & Kouider, 2017;Lau, 2008;Rosenthal & Weisberg, 2008).HOT has in common with GNWT that both theories consider early sensory representations insufficient for consciousness; but whereas HOT appeal to meta-representations to generate a kind of inner awareness, GNWT postulates that higher-order mechanisms boost, stabilize and broadcast sensory representations to enable wide access to cognitive and motor systems.Thus, GNWT is not a higher-order theory, because the representations that are globally broadcast are first-order representations.
Both NREP and AIT deploy principles from predictive processing (Friston, Wiese, & Hobson, 2020;Hohwy & Seth, 2020;Pennartz, 2015Pennartz, , 2022b;;Pennartz, Dora, Muckli, & Lorteije, 2019) to provide an explanatory basis for conscious experience, and work under the (Bayesian) assumption that anatomical structures taking part in thalamocortical hierarchies generate predictions or hypotheses of what causes sensory inputs.Learning and inference in these hierarchical structures take place by way of error computation, based on the comparison of actual sensory input against predictions derived from high-level representations (cf.(Dora, Bohte, & Pennartz, 2021;Rao & Ballard, 1999)).The two theories differ, for instance, on AIT's assumption that action is essential for consciousness, and predictions and error signals are driven by inference on action policies (Friston et al., 2020;Hohwy, 2013;Parr, Corcoran, Friston, & Hohwy, 2019).
In contrast, NREP does not assume an essential requirement for action, but emphasizes that conscious experience results from the interplay between high-level and low-level sensory inference, and the inferential interactions between different sensory modalities, which are necessary to underpin inference on qualitative differences between them (Pennartz, 2009;Pennartz, 2015Pennartz, , 2022b)).Lowlevel sensory inference refers to the generative process of constructing representations (or hypotheses) about simple sensory features (e.g.line orientation in a small part of the visual field), whereas high-level inference is about complex, multimodal objects and their spatial relationships.In this process of sensory inference, motor information also needs to be taken into account.For instance, in our conscious experience we localise an object stably in space while one's eyes may be moving, but nonetheless conscious experience remains ongoing in the absence of motor action.Consciousness thereby subserves a clear function: to enable complex decision-making and deliberative action processes, which are, however, taken to be different from conscious experience itself (Pennartz, 2015;Pennartz, 2018;Pennartz, 2022b).A key point in NREP, further distinguishing it from AIT, is that high versus low levels of representation are not equivalent to the higher and lower cortical areas distinguished by connectional anatomy (see e.g.(Felleman & Van Essen, 1991;Markov et al., 2013;Rockland & Van Hoesen, 1994)), but are understood as different functional-representational levels.At a low representational level, the system uses single-cell and ensemble structures as building blocks, which are subsequently integrated at uniand metamodal representational levels to give rise to phenomenal experience (Pennartz, 2015).
In this sense, both a commonality and a difference between NREP and HOT variants can be indicated.Both theories agree that lowlevel sensory representations are insufficient to render them conscious.They differ, however, in that HOTs consider higher-order representations to pertain to the subject's own mental states and to operate at a subsequent stage of processing (often situated at a prefrontal level) relative to first-order representations.In contrast, NREP works with a distinction between low-level and high-level representations, as defined by the contrast between simpler, cell-based organizations versus complex, network-based organizations (but in HOT terms, these representations remain 'first-order' and would require self-awareness to qualify as 'conscious').Thus, NREP places high-level representations at a higher, more complex level of brain function, which is taken to correspond to a higher aggregate level of organization.In mammals, a high aggregate level comprises e.g. the entire visual corticothalamic system interacting with systems upholding other sensory modalities (with prefrontal cortex playing no or a minor role in phenomenal consciousness itself).
The AIT and NREP positions do not readily result in a single quantitative measure of consciousness, but do point to the neural processes involved (predictive representations laid out across anatomical hierarchies, corrected by error processing).Moreover, it has been argued that the representational capacity of hierarchical generative modelling systems may reflect the degree of consciousness, comprising the dimensions of multimodal richness, spatial extendedness and resolution, as well as (attention-dependent) intensity (Pennartz, 2015(Pennartz, , 2022b)).Thus, the degree of consciousnesss can be estimated in principle from computational models, and their capacity to represent situational information along these three dimensions.A final point on quantitative measures of consciousness is that NREP acknowledges that conscious experience is marked by qualitative properties (linked to the dimension of multimodal richness), which are not quantifiable by definition.Importantly, this acknowledgement does not preclude any definition of a measure of consciousness, because such a measure could still reflect qualitative properties, alone or taken together, in an abstract sense, whilst not capturing or equating with concrete, qualitative aspects of experience.IIT also explicitly acknowledges the relevance of the

Table 3
Possible common denominators for comparing neural theories of consciousness.When two or more theories share a denominator, this is indicated by a horizontal grey bar, marked by a grey circle whenever the theory under the respective column satisfies this commonality.For some denominators, there appears to be no clear commonality amongst any of the four theories; for some others, all theories share a denominator.Under "explanatory target", 'Sentience' is understood as responsiveness to sensory impressions (Friston et al., 2020).Under "Explainability in terms of other, known abilities", it should be noted that GWNT and AIT both refer to such abilities, but explain consciousness in different ways (GNWT: from cognitive control, etc.; AIT: from action-based self evidencing).
(continued on next page) K. Evers et al.Table 3 (continued ) (continued on next page) K. Evers et al. qualitative aspects of consciousness.In fact, the theory starts from the need to explain phenomenology, and IIT makes an attempt to even quantify these aspects (Albantakis et al., 2023b;Balduzzi & Tononi, 2009).

Logical and empirical commensurability of neuroscience-based theories
Thus, at first sight, there appears to be a certain level of logical and empirical commensurability amongst these four brain-based theories, as well as HOT variants, as expressed by common denominators.For instance, at the logical level, they use the same interpretative approach, standards of rationality and standards of validity.At the empirical level, they refer to similar criteria for data selection and significance, they use similar tools for selecting and analysing data, similar methodologies and standards of validation.Digging deeper, however, one stumbles across various obstacles in comparing the theories directly.These can be localized in the domain of logical architecture and conceptual foundations (Table 1).A primary difference, for instance, lies in the background definitions of consciousness used.Even if not all agree about this (Dehaene, Changeux, Naccache, Sackur, & Sergent, 2006;Naccache, 2018), 1 a distinction has been made between access versus phenomenal consciousness, where 'phenomenal' refers to primary conscious subjective sensations such as smell, vision or hearing, whereas 'access consciousness' refers to how experiential content is accessed and subsequently used in decision-making, cognitive problem-solving, evaluation, etc. -being strongly associated with the workspace-related functions referred in Table 2. Along this apparent dividing line, IIT and NREP are best placed on the 'phenomenal' side, whereas GNWT by way of deliberate choice is placed on the 'access' side (in the sense that information processing without access should be qualified as preconscious processing, not as phenomenal consciousness (Dehaene et al., 2006)).The position of AIT also leans towards the 'phenomenal' side, to the extent that proponents speak of 'sentience' or having 'qualia' (Friston et al., 2020).Also, GNWT seems to equate consciousness with cognition, information-pooling and executive control, while some empirical findings suggest that this equation is not absolute: it is arguably possible to have cognitive phenomena without corresponding conscious perception, as it has been argued that consciousness can be dissociated from at least some forms of attention (Koch & Tsuchiya, 2012) (but see: (Marchetti, 2012;Noah & Mangun, 2020)).According to (Panagiotaropoulos, Wang, & Dehaene, 2020) GNWT leaves no room for the 'qualia' of experience, in line with Dehaene & Naccache, 2001) statement that "this global availability of information ( …) is what we subjectively experience as a conscious state".This position is consistent with Dennett's, who posited that consciousness concerns the spreading and pooling of information in a distributed processing architecture ( Dennett, 2001) and that phenomenal, qualitative aspects do not constitute a real problem in consciousness science (i.e., he does not regard the 'hard problem' of consciousness as a genuine problem; (Dennett, 1991;Dennett, 2018).
The objective of GNWT thus starkly contrasts with both IIT and NREP, which take phenomenal consciousness to be the core problem, acknowledging the existence of qualitative properties of conscious experience as explanandum, and offering diverging proposals to address it (Olcese, Oude Lohuis, & Pennartz, 2018;Pennartz, 2015;C. Pennartz et al., 2019;Tononi, 2004;Tononi et al., 2016) (cf.(Clark, Friston, & Wilkinson, 2019)).Following this line, NREP has argued that 'access' to experiential content is not required for (phenomenal) consciousness, but rather addresses the question of how phenomenal content (assumed as a given) can be deployed to direct executive functioning, such as deliberation, future planning and behavioural reporting (Pennartz, 2015;Pennartz, 2018).This amounts to saying that GNWT uses a different background definition of consciousness than IIT or NREP, and focuses on a different set of cognitive-perceptual functions than phenomenal experience per se, even though these theories can still be considered logically commensurable.This conceptual divergence is not necessarily harmful to achieve progress on both theoretical fronts, as long as one is aware of this conceptual divide and the fact that the 'phenomenal' and 'access' approaches study very different -although interlinked -explananda, coupled to different functional processes and neuronal substrates.Moreover, this conceptual divergence is compatible with the commensurability of the theories with reference to different logical dimensions (e.g, standards of rationality and validity).The different background definitions of consciousness may help explain why GNWT has arrived at identifying parietal- 1 While these authors seem to deny both the conceptual and the ontological distinction between access and phenomenal consciousness (i.e., reducing the latter eventually to the former), another possible interpretation is that they are conceptually distinct while de facto not dissociable (i.e., access consciousness and phenomenal consciousness are co-extensive).

Limitations in commensurability and similarity
Other major rifts between seemingly commensurable and compatible theories appear when inspecting further aspects of theoretical foundations.Given the emphasis that IIT bestows upon the complexity of cause-effect structures, this theory gives rise to partial panpsychism, implying that many, but not all, inorganic structures throughout nature and society possess a certain degree of consciousness (e.g., weather systems like cyclones, (Pennartz, 2009); electric power grids, (Merker et al., 2021), photodiodes (Tononi & Koch, 2015) and Vandermonde matrices (Aaronson, 2014)).Even elementary particles engaging in differential interactions will exhibit a certain amount of ϕ and should thereby possess some consciousness (Pennartz, 2022a).This consequence of IIT's measure has been criticized as being too permissive and underconstrained, because there is no behavioural or other evidence indicating consciousness in systems with a presumably high Phi, such as DVD players, glacial lakes or sandy beaches.Overall, the panpsychist implication of IIT seems to arise from a confusion between integration as a sufficient rather than necessary condition for consciousness.Previously the case was indeed made that integrated information is necessary for consciousness, but is not sufficient (Mudrik, Faivre, & Koch, 2014).
In contrast, NREP takes the hierarchical bottom-up/top-down structure for inference and learning as a basal and necessary requirementbut not a sufficient condition -for conscious processing, and while this structure can be emulated in principle in artificial systems, it is too specific and constrained to be found widely throughout inorganic nature.Other major differences between NREP and IIT have been noted, such as IIT's postulate that neurons do not need to be active (i.e., firing) in order to contribute to conscious contents.NREP (and AIT, as well as many other theories) do take neural activity to be necessary because inactive neurons do not influence other cells in the network they are part of, and may thus as well be temporarily disconnected from it.
The critique on IIT's panpsychic permissiveness may be countered by the defence that, so far, theories of consciousness have been too conservative; we may just have to accept a basal level of consciousness in complex systems (although unrecognizable, nonmanifest) as a matter of fact.Arguing against this inclusive position, however, it is brought forward that consciousness becomes a meaningless, void term if it applies to almost every object in nature, and that it does not rationally relate anymore to distinctions humans make in daily life and in the clinic, when telling apart which patient is conscious, anesthetized or comatose; whether a boxer is knocked-out or still awake, or whether a person (consciously) suffers pain or not.Finally, whereas fundamental properties of matter such as electromagnetic interactions can be tested in, e.g., Rutherford cloud chambers, testing consciousness in inorganic systems lacking speech or behaviour, such as subatomic particles, is not feasible, because no criteria are at hand to decide whether a system is conscious or not, other than the criterion postulated by the theory itself (Pennartz, 2022a).Thus, given an inorganic object with a certain complex cause-effect structure, IIT claims that this object must have some consciousness, without taking into account any indicators of it.By consequence, IIT uses a different standard of validation than, for instance, GNWT, NREP or PP, which do recognize the value of other markers for consciousness, such as behavioral or computational criteria.
In addition, in the case of IIT, the logical link between axioms (i.e., features of conscious experience) and postulates (i.e., features of corresponding physical structures) is controversial (Bayne, 2018;Merker et al., 2021).The latter do not always derive deductively from the former, as claimed by IIT proponents.The same holds with the identity claim, i.e. the identification of consciousness with the conceptual structure of the physical system which has the features described by the postulates.All in all, while IIT's identity claim postulates a strong mapping from phenomenology onto physical structure, the road back from physics to phenomenology thus remains free from checks or constraints.This major difference can be summed up with other major contrasts, such as that IIT seeks the basis of consciousness in structure (taking into account its potential states) whereas GNWT, NREP and AIT rely on messaging, information processing and (computational) function, wherein the actual state of the system determines conscious experience.We may conclude that IIT is overall more conceptually dissimilar, and less empirically commensurable, than the other three theories relative to each other.
Thus, although some theories may seem logically commensurable at first glance, sharing some conceptual and even empirical similarities, vast gaps nevertheless exist in other domains, for instance in the further specification of consciousness and the approach to testing and verifiability.In other words, logical commensurability does not imply or guarantee conceptual similarity, and does not exclude vast empirical differences.Thus, we conclude that 'neural' theories such as IIT, GNWT, AIT and NREP are, at least in part, empirically incommensurable as they use different definitions as well as different standards of empirical validation (cf.Table 1).What might seem to lie nearby in terms of conceptual similarity according to a given dimension (cf.(Signorelli et al., 2021)) may turn out to be quite remote by other criteria.
To conclude this section, we have seen several theories which operate within the same range of logical commensurability, but nonetheless show vast empirical and conceptual dissimilarities.An example of a pair of relatively similar theories would be the GNWT and HOT, which both focus on higher-order functions centered on prefrontal cortex.Their similarity is relative indeed, considering that GNWT emphasizes a function of broadcasting (first-order) information in access consciousness and enabling executive functions, whereas HOT requires high-order processes to instantiate a kind of inner awareness, or alternatively, thoughts or meta-judgments (Brown et al., 2019;Lau & Rosenthal, 2011).Another example is presented by the combination of NREP and AIT, which both rely on predictive processing as a principle to build internal generative models of the world, but differ on the essential requirement of action for conscious experience, and have a different approach to tackle the hard problem of consciousness.The dependence of consciousness on action can be empirically addressed by experiments attempting to dissociate action (overt, or internal: via endogenous attention) from consciousness,2 whereas the hard problem is addressed by different theoretical, logical arguments.Although it remains necessary to compare NREP and AIT (or other pairs of similar theories) to other, less commensurable theories, an advantage of working with conceptually similar theories is that it becomes less difficult to agree on experimental approaches that can meaningfully distinguish between the predictions made by those theories, thus moving the field forward to favour one or the other theory, whilst also speaking about the validity of other theories.For instance, testing for action contingencies in (conscious) perception is also highly relevant for assessing sensorimotor or externalist accounts of consciousness (O'Regan & Noë, 2001;Pennartz, 2018).

Quo Vadis? from common denominators to similarities and testable predictions from consciousness theories
The title of this paper raises the question whether common denominators are useful.Thus far, we found it possible to designate particular assumptions that are shared between neuroscientific theories as common denominators (such as the generation of information; or the brain as biological substrate underlying consciousness).Yet, this designation comes with several caveats and limitations.First, denominators such as 'information' or 'information generation' may well be too generic to tell anything specific about the theories commonly using them as core concepts, and to push the science of consciousness forward in a specific direction.(In parenthesis we may note that, theories sharing a specific denominator may still be incorrect; therefore such sharing does not offer an argument in favour of those theoriesthe point is, however, that a denominator can be useful for comparing and grouping theories).Second, we have witnessed that a denominator shared between two theories does not necessarily imply that they are also conceptually similar.As we suggested above, it appears unlikely that there would be a single denominator by which theories can be unequivocally grouped together.Yet, in the overall taxonomy of consciousness theories, common denominators may nonetheless be useful.Our answer to the original title question is thus twofold: yes, common denominators are possible and useful as 'markers' to indicate crossconnections and prima facie similarities between theories.The clarification of possible common denominators may provide a conceptual clarification on the (dis)similarity of theories, and thereby conceptually advance the field.On the other hand, they are not ipso facto useful or helpful in empirically advancing the field, for instance by suggesting novel experiments that test differential predictions from various theories.They may help to characterize relationships between theories and group them (cf.(Signorelli et al., 2021)), but the landscape of current theories resembles an irregular web of cross-connections more than an orderly taxonomic tree.Consequently, the sum of denominators shared between theories may suggest how commensurable or similar theories are, but this does not imply that theories can be unified or integrated into a larger, overarching frameworkthe discrepancies between theories may simply be too vast to allow this.What, then, would be another fruitful way forward in the field?
We argue it may be more productive to take a step back from common denominators and attempts to unify models, and focus on how to develop a common methodological approach to brain-consciousness relationships (noting that this step is part of the wider research program outlined in Table 1).As far as neuroscientific advances can be expected, they should come from theoretical and empirical approaches combining satisfactory degrees of conceptual sophistication, reproducibility and evidence accumulation by empirical testing.As noted, the empirical approach to consciousness is already a common denominator of neuroscientific theories in itself, but it is also a very general one, shared by many if not all of them.More can be said, however, than recommending the empirical approach per se: it should be sharpened to test extant or new theories more productively.
A foremost way of assessing the testability of theories whilst simultaneously assessing proposed dimensions of commensurability (considered by themselves or in conjunction) in terms of relevance and modality (necessity/sufficiency) is to challenge them with both general and more concrete, probing questions, such as: (1) What exactly does the theory purport to explain, and what is the kind of explanation being sought (e.g., in terms of neural mechanisms, causative mechanisms)?What is understood by the term 'consciousness' and what does it not include?
(2) Does the theory follow an empirical approach?Which experimental outcome(s) will 'kill' (refute) the theory under scrutiny under its own account?3 ( Popper, 1935).
(3) Does the theory conform to multiple realizability such that its model can be realized in hardware, other than by living neurons?What does this hardware look like?Can the theory be translated into a model that allows at least a minimal artificial implementation of consciousness (cf.Doerig, Schurger, & Herzog, 2021)?
(4) Does the theory permit first-person and/or third-person measures of consciousness?What are these measures and what is the method or protocol to report or quantify consciousness?
(5) If the theory is forced to indicate which animal species or inorganic systems (e.g.robots, AI computers) are conscious, how does it decide to do so?By which criteria, and of what type, e.g., behavioural, physiological?(similar questions can be posed for consciousness in unresponsive patients); (6) If the theory suggests that an organic or inorganic system is conscious, how does it propose to test this in a realistic manner that does not make the proposition true (or false) by definition?
(7) How does the theory seek to identify neural substrates and/or causal mechanisms of consciousness and what kinds of experiment and evidence are accepted to associate or dissociate consciousness from related phenomena such as motor activity, memory, sensory processing and attention?(8) Does the theory account for the empirical evidence supporting that some brain structures (e.g., corticothalamic systems) are more clearly involved in conscious processing than others (e.g., cerebellum)?If not, does the theory entail some form of (partial or complete) panpsychism?If it does, how does the theory account for differences in conscious states in humans (e.g., deep sleep, wakefulness)?Should a theory fail to provide clarity on too many of these questions (which do not constitute an exhaustive list), it would be more appropriate to develop it first up to the point where it can be more unambiguously compared to contenders in the field.
Next to this first barrage of probing questions, the issue of commensurability of theories does remain significant in the search for unification versus differentiation of theories.In Table 3 we list possible common denominators to aid this search.For example, it was noted above that GNW and predictive processing-based (AIT and NREP) accounts use different background definitions of consciousness and consequently focus on different processes, but this does not imply that these theories have nothing to say to each other (they are, in fact, commensurable in relation to other dimensions, such as the acceptance of an empirical approach and of certain brain measurements yielding relevant evidence).Because predictive processing addresses phenomenal consciousness by way of generative modelling and GNWT focuses on 'access consciousness' understood as having access to experiential content for its deployment in executive functions, these approaches may be less incommensurable and more complementary than anticipated.For instance, (Naccache, 2018) conceives subjective reporting not as a result of passive broadcasting of information into a global workspace, but as a product from an active chain of dynamic processing that includes interpretation and belief attribution.(Whyte & Smith, 2021) proposed a formal model that integrates the concept of a global neuronal workspace with the framework of active, Bayesian inference, resulting in a 'predictive global neuronal workspace'.In line with this, we may thus see the emergence of more computational models that combine inferential, generative modelling with a subsequent stage of broadcasting of predictive representations.In the methodology outlined here, comparison by way of commensurability-similarity assessments may thus lead to integrative efforts, combining elements from different theories.
A second example of a potentially fruitful integration may arise from the realization that also IIT and predictive processing-based theoriesalthough very different in their implications for panpsychism and the significance of neural activitymay be less incompatible or incommensurable in other aspects than one might expect.The case in point here is that the amount of integrated information, quantified by ϕ, may increase with the amount of information coded in predictive representations arising from the kind of feedforwardfeedback architectures playing a key role in predictive processing theories.In other words, while IIT does not postulate a particular neural architecture (e.g., hierarchical) as conducive to reaching high ϕ values, it may be conjectured that the sort of sensory processing hierarchies one finds in cortex is precisely the type of architecture suited to yield such high values (not excluding the option that other structures generating high ϕ may also exist, perhaps in cephalopods or other vertebrate nervous systems).An indication that a joint IITpredictive processing approach may become productive comes from animat simulations suggesting that feedback architectures may generate more integrated and complex information than feedforward systems (Albantakis, Hintze, Koch, Adami, & Tononi, 2014).Further integrative attempts are conceivable, but will not be reviewed here.
While efforts to unify theories into larger aggregate frameworks are undoubtedly important to advance the field in the future, we do wish to end on a cautionary note in the sense that 'the proof of the pudding is in the eating': it is the empirical testing of theories that must point out their validity.Referring to Table 1, while not neglecting considerations of logical consistency, theoreticians should agree on proper testing methods and standards of validity in the first place: what constitutes, for instance, a sufficiently unambigous result?In addition to the eight probing questions posed above, a guideline for future research can be to seek those empirically testable points where two or more theories differ most tangibly, and focus on concrete experiments that will maximally discriminate theories on those very points.This approach is pursued by the adversarial collaborations sponsored by the Accelerating Research on Consciousness (ARC) program of the Templeton World Charity Foundation.Indeed, within this program experimental experts and theoreticians must first agree on methods, standards of validity, protocols, etc., before embarking on actual experiments (e.g., (CogitateConsortium, 2023;Melloni et al., 2023;Yaron, Melloni, Pitts, & Mudrik, 2022); see also https://www.templetonworldcharity.org/projects-database/0646).
Based on considerations set forth in the current paper, however, we also wish to signal some caveats and caution against claiming rapid successes.First, experiments may zoom in on differences in aspects of theories which are highly commensurable, but are only capable of revealing tangential insights rather than addressing core tenets of the theories under scrutiny.Second, a consequence of the Duhem-Quine thesis is that, if a particular result speaks against a theory, this theory can be 'patched up' by including an auxiliary hypothesis or background assumption, thus making outright rejection of a theory (next to) impossible.In relation to this, binary reject/ accept verdicts on theories are unlikely to occur, and 'easy wins' based on single predictions and experiments are not to be expected.Instead, the evaluation of theories is more likely to follow a gradual path, with evidence incrementally building up based on abductive inference ("inference to the best explanation", (Josephson & Josephson, 1996;Pennartz, Farisco, & Evers, 2019), e.g. by accumulating Bayesian evidence, cf.(Corcoran, Hohwy, & Friston, 2023)) rather than on a binary type of falsificationism.