Consciousness and Category Theory

In the comments on the previous post I was alerted, by Matthias Michel, to a couple of papers that I had not yet read. The first was a paper in Neuroscience Research which came out in 2016:

And the second was a paper in Philosophy Compass that came out in March 2017:

After reading these I realized that I had heard an early version of this stuff when I was part of a plenary session with Tsuchiya in Tucson back in April of 2016. The title of his talk is the same as the title of the Philosophy Compass paper and some of the ideas are floated. I had intended writing something about this after my talk but I apparently didn’t get to it (yet?). I am in the midst of battling a potty-training toddler so it may not be anytime soon but I did want to get out a few (inchoate) reactions to these papers now that I have read them.

Both of these papers were very interesting. The first was interesting because it is the first time I have seen proponents of IIT acknowledge that they need to examine their ‘axioms’ more carefully. Are these axioms self-evident? Not to many people! Might there be alternate formulations? Yes! At the very least there should be some discussion of higher-order awareness (or awareness at all). There ideally should be an axiom like:

Awareness: Consciousness is for one. If one is in no way aware of oneself as being in a mental state then one is not consciously in that mental state

Of course they don’t want to add anything like this because as it stands the theory clearly assumes (without argument) that higher-order theories of consciousness are false. This is a problem that will not go away for IIT. But I’ll come back to that (by the way, the first ‘axiom’ of IIT sometimes seems to me to suggest a higher-order interpretation so one might assimilate this to an unpacking of the first axiom).

The central, and very interesting, idea of these papers that they are presenting is that category theory can help IIT address the hard problem (and some of the issues I raised in the previous post). There are a lot of mathematical details that are not relevant (yet) but the basic idea is that category theory lets us look at the structures that mathematical objects have and compare it to the structure of other mathematical structures. They want to exploit this by making a category out of the integrated information cause-effect space and one for quaila and then use category theory to examine how similar these two categories are.

First, can qualia form a category? They address this issue in the first paper but (to use a low hanging pun) this looks like a category mistake. Qualia are not mathematical objects. I suppose you could form the set of qualia and that would be a mathematical (i.e. abstract) object. But if you show that this structure overlaps with IIT have you shown anything about qualia themselves? Only if the structure captured in this category exhausts  the nature of qualia, but that is highly controversial! My guess is that there will be many categories that we could construct that would have some functors to both the category of qualia and the category of IIT structures. So, take the category of the set of Munsel color chips (not the experience of them, the actual chips). Won’t they stand in relations to each other that can be mapped onto the IIT domain in pretty much exactly the same way as the set of qualia!? If so, then IIT is Naive Realism? That is a joke but the point is that one would not want to claim that this shows that IIT is a theory of color chips. All we have shown is that there is a similar structure that runs in common in these two mathematical structures that at first seemed unrelated. That is interesting, but I don’t see how it can help us.

To their credit they recognize that this is a bit controversial and here is what they say about the issue:

In the narrow sense, a quale refers to a particular content of consciousness, which can be compared or characterized as a particular aspect of one moment of experience or a quale in the broad sense (Balduzzi and Tononi, 2009; Kanai and Tsuchiya, 2012). Can category theory consider any qualia we experience as objects or arrows? Some qualia in the narrow sense are straightforward to consider as objects: a quale for a particular object or its particular aspect, such as color. There are, however, some aspects of experience that are apparently difficult to consider as objects. For example, we can experience a distance between the two cups, which is a relationship between the objects but itself has no physical object form. Such abstract conscious perception can be naturally regarded as a relationship between objects: an arrow. Further, there are some types of qualia that seem to emerge out of many parts, such as a face. A whole face is perceived as something more than a collection of its constituent parts; there is something special about a whole face. Psychological and neuroscientific studies of faces point to configural processing, that is, a web of spatial relationship among the constituent parts of a face is critical in perception of a whole face (Maurer et al., 2002). In category theory, a complicated object, like a quale for a face, can be considered as an object that contains many arrows. Considered this way, any quale in the narrow sense can be considered as either an object, an arrow, or an object or arrow that contains any combinations of them.

But even if this is ok with you (and you set aside questions about whether ‘to the right of’ can be an arrow in category theory (will it obey the axiom of composition?)) what goes into the qualia category? They seem to assume that (at least some of) it is non-controversial but that isn’t so clear to me. Even so, what about Nagel’s bat? In order to use this procedure we would have to already know what kinds of qualities, conscious experiences, the bat had in order to form the category. But we have no idea what kinds of ‘objects’ and ‘arrows’ to populate that category with! That was kinda Nagel’s point!

To hammer this point home recall the logic gates that serve as simple illustrations of IIT. How are we to use this approach on it? We know what IIT says and so we can form that category without any problems. But what goes into the category of ‘qualia’ for the logic gate system’? We have no idea. In response to a question about Scott Aaronson’s objection Tsuchiya says that the expander grid may have a huge conscious field but would not have any visual experience. But what justifies this assertion?

They conclude their paper with the following remarks:

We proposed the three steps to apply the category theory approach in consciousness studies. First, we need to characterize our own phenomenological experience with detailed and structured descriptions to the extent to accept the domain of qualia as a category.

This may prove to be a difficult task and not just for the reasons having to do with higher-order awareness. Phenomenology is tricky stuff and it is notoriously hard to get people to agree on it (N.B. this is an understatement!) and since that is the case this general strategy seems doomed.


Another frustrating assertion with minimal evidence comes in the second paper linked to above and it has to do with the No-Report paradigm.

Noreport paradigms have implied that certain parts of the brain areas, such as the prefrontal areas, may not be related to consciousness, but more to do with the act of the reports (Koch, Massimini, Boly, & Tononi, 2016).

IF one buys this then one will see the IIT irreducible ‘concepts’ as corresponding to phenomenally conscious states but if instead one thinks that these results are overrated then one will see these irreducible IIT ‘concepts’ as picking out mental representations that may or may not be conscious. Thus we cannot extrapolate from the results of IIT until the debate with higher-order theories is resolved.

And that cannot happen until the proponents of IIT actually address the empirical case for higher-order theories. This is something that they have been very reluctant to do and when they discuss other theories of consciousness they studiously avoid any mention or discussion of higher-order theories. Higher-order theories need to be taken as seriously as Global Workspace, local re-entry, and other theories one finds in neuroscience and for the same reasons; because there is a significant (not decisive) evidence in favor of the theory.

But ok, what about the limited claim that we could in principle know whether the bat’s phenomenology was more like our seeing or our hearing? If we could generate the relevant category for the human conscious visual experience versus auditory experience and then if we could generate the IIT category for the bat’s echolocation we could compare them and see if it resembles our visual or auditory categories. According to Tsuchiya if we found that it resembled the IIT category for our auditory experiences (instead of our visual) or vice versa then we would have some evidence that they experienced the world in the same way we did.

But this seems to me to be a fundamental misunderstanding of Nagel’s point. His point was that there is no reason to expect that the bat’s experience would be anything like our seeing or our hearing. To know what it is like for the bat requires that we take up the bat’s point of view (according to Nagel). It is not clear that this addresses this issue at all! Even if we found that the bat’s brain integrated information in the way our brain integrates auditory information, and which results in the conscious experience of hearing for us, even if (stress on the IF) we discovered that why should we think that the bat’s experience was just like our experience of hearing? The point that Nagel wanted to make was that conscious experience seems somehow essentially bound up with the idea of subjectivity, of being accessible only from one’s own point of view. This is entirely missed in the proposal by Tsuchiya et al.

Integrated Information Theory doesn’t Address the Hard Problem

Just in case you are not aware Hakwan Lau has started a blog, In Consciousness we Trust, where he is blogging his work on his upcoming book on consciousness. He has lately been taking fire at the Integrated Information Theory of Consciousness and has a nice (I think updated) version of his talk (mentioned previously here) in his post How to make IIT (and other Theories of Consciousness) Respectable. I have some small quibbles with some of what he says but overall we agree on a lot (surprised? 😉 At any rate I was led to this paper by Sasai, Boly, Menson, and Tononi arguing that they have achieved a “functional split brain” in an intact subject. This is very interesting, and I enjoyed the paper a lot but right at the beginning it has this troublesome set of sentences:

A remarkable finding in neuroscience is that after the two cerebral hemispheres are disconnected to reduce epileptic seizures through the surgical sectioning of around 200 million connections, patients continue to behave in a largely normal manner (1). Just as remarkably, subsequent experiments have shown that after the split-brain operation, two separate streams of consciousness coexist within a single brain, one per hemisphere (2, 3). For example, in many such studies, each hemisphere can successfully perform various cognitive tasks, including binary decisions (4) or visual attentional search (5), independent of the other, as well as report on what it experiences. Intriguingly, anatomical split brains can even perform better than controls in some dual-task conditions (6, 7).

Really?!?! Experiments have shown this? I was surprised to read such a bold statement of a rather questionable assumption. In the first place I think it is important to note that these patients do not verbally report on what it ‘experiences’. I have argued that these kinds of (anatomical) spit brains may have just one stream of consciousness (associated with the one capable of verbally reporting) and that the other ‘mute’ hemisphere is processing information non-consciousnesly.

This is one of the problems that I personally have with the approach that IIT takes. They start with ‘axioms’ which are really (question begging) assumptions about the way that consciousness is, and they tout his as a major advance in consciousness research because it takes the Hard Problem seriously. But does it? As they put it,

The reason why some neural mechanisms, but not others, should be associated with consciousness has been called ‘the hard problem’ because it seems to defy the possibility of a scientific explanation. In this Opinion article, we provide an overview of the integrated information theory (IIT) of consciousness, which has been developed over the past few years. IIT addresses the hard problem in a new way. It does not start from the brain and ask how it could give rise to experience; instead, it starts from the essential phenomenal properties of experience, or axioms, and infers postulates about the characteristics that are required of its physical substrate.

But this inversion doesn’t serve to address the Hard Problem, (by the way, I agree with the way the formulate it for the most part). I agree that the Hard Problem is one of trying to explain why a given neural activation is associated with a certain conscious experience rather than another one, or none at all. And I even agree that in order to address this problem we need a theory of what consciousness is but IIT isn’t that kind of theory.  And this is because of the ‘fundamental identity claim’ of IIT that an experience is identical to a conceptual structure, where ‘experience’ means phenomenally conscious experience and ‘conceptual structure’ is a technical term of Integrated Information Theory.

This is a postulated identity, and they do want to try to test it, but even if it was successfully confirmed would it really offer us an explanation of why the experiences are associated with a particular brain activity? To see that the answer is no consider their own example from Figure 1 of their paper and what they say about it. nrn.2016.44_IIT - From Consciousness to Physical Substrate

They begin,

The true physical substrate of the depicted experience (seeing one’s hands on the piano) and the associated conceptual structure are highly complex. To allow a complete analysis of conceptual structures, the physical substrate illustrated here was chosen to be extremely simple1,2: four logic gates (labelled A, B, C and D, where A is a Majority (MAJ) gate, B is an OR gate, and C and D are AND gates; the straight arrows indicate connections among the logic gates, the curved arrows indicate self-connections) are shown in a particular state (ON or OFF).

So far so good. We have a simplified cause-effect structure in order to make the claim clear.

The analysis of this system, performed according to the postulates of IIT, identifies a conceptual structure supported by a complex constituted of the elements A, B and C in their current ON states. The borders of the complex, which include elements A, B, and C but exclude element D, are indicated by the green circle. According to IIT, such a complex would be a physical substrate of consciousness

So, when A=B=C=1 (i.e. on) in this system it is having a conscious experience (!), as they say,

The fundamental identity postulated by IIT claims that the set of concepts and their relations that compose the conceptual structure are identical to the quality of the experience. This is how the experience feels — what it is like to be the complex ABC in its current state 111. The intrinsic irreducibility of the entire conceptual structure (Φmax, a non-negative number) reflects how much consciousness there is (the quantity of the experience). The irreducibility of each concept (φmax) reflects how much each phenomenal distinction exists within the experience. Different experiences correspond to different conceptual structures.

Ok then. Here we have a simple system that is having a conscious experience, ex hypothesi, and we know everything about this system. We know that it has these  concepts specified by IIT, but what is it’s conscious experience like? What it is like to be this simple system of 4 logic gates when its elements A, B, and C are on? We aren’t told and there doesn’t seem to be any way to figure it out based on IIT. It seems to me that there should be no conscious experience associated with this activity, so it is easy to ‘conceive of a physical duplicate of this system with no conscious experience’…is this a zombie system? That is tongue in cheek but I guess that IIT proponents will need to say that since the identity is necessary I can’t really conceive of it (or that I can but it is not really possible). Can’t we conceive of two of these systems with inverted conscious experiences (same conceptual structures)? Why or why not? I can’t see anything in IIT that would help to answer these questions.

If IIT is attempting to provide a solution to the Hard Problem of Consciousness then should allow us to know what the conscious experience of this system is like, but it seems like it could be having any, or none (how difficult would it then be to extend this to Nagel’s bat!?!?). There are some who might object that this is asking too much. Isn’t this more like Ned Block’s “Harder Problem” than Chalmers’ Hard Problem? Here I suppose that I disagree with the overly narrow way of putting the Hard Problem. It isn’t merely about how this brain state is associated with a particular phenomenal quality rather than none at all, it is how it is associated with any physical, functional state at all that os the Hard Problem. Sure brain states are one kind of physical state and so the problem arises there but more generally the Hard Problem is answering the question of why any physical state is associated with any qualitative state at all instead of another or none at all.

IIT, and Tononi in particular, seem committed to giving us an answer. For instance, in his Scholarpedia article on IIT Tononi says,

IIT employs the postulates to derive, for any particular system of elements in a state, whether it has consciousness, how much, and of which kind.

But how do we do this for the 4 logic gates?

How do we do it in our own case?


Integrated Information Theory is not a Theory of Consciousness

The Integrated Information Theory of Consciousness has been garnering some attention lately. There was even a very high profile piece in Nature. Having just listened to Hakwan Lau’s talk on this (available at this conference website) I thought I would write down a couple of reactions.

Like everyone else who is interested in consciousness, I have been interested in the integrated Information Theory. I attended a talk by Tononi back in 2012 (and wrote about it here) but I also attended a workshop at NYU on it back in 2015. I had always meant to write something about it (John Horgan did here) and thought I would do so now. I wish I had written about this sooner, but to be completely honest I found out about the Paris attacks as I was leaving the workshop and it shook me up enough to distract me from blogging.

I had a couple of take-away’s from that workshop and these have really influenced how I have thought about IIT. I suppose I would sum it up by saying that IIT doesn’t look like a theory of consciousness. In the first place it purports to be a theory of phenomenal consciousness, what it is like for one to have a conscious experience, but it starts from the phenomenon of fading into a dreamless sleep. This makes it look like the main phenomenon is creature consciousness. Is IIT trying to give an account of the transition(s) from sleeping to wakefulness (and vice versa)? This is where ‘levels of consciousness’ talk seems most at home. Is being in hypnogogic reverie ‘in between’ sleeping and wakefulness? Probably yes, but does that translate to phenomenal consciousness being graded? There it seems less clear. You either have phenomenal consciousness or you do not (pace Dennett). It is the contents of consciousness that can be graded, distorted, etc. So right from the beginning it seems to me to be off on the wrong foot: the comparison is not that between waking and dreamless sleep, it is the comparison between conscious (i.e. reported) and unconscious (denied) states that one should begin with if one is looking to explain consciousness.

Another of the main ideas that came out of the workshop (again, for me) was that the ‘axioms’ of IIT seem to encode assumptions about conscious experience that are controversial. For example, is some kind of higher-order awareness necessary (and/or sufficient) for conscious experience? The axioms are silent on this, seeming to suggest that the answer is no, but a lot of people seem to think that there is a kind of higher-order awareness that is manifest in our phenomenology (old examples like Aristotle, and newer ones like Brentono, and even newer ones like Uriah Kriegel). So could we have another version of IIT that adds an axiom about consciousness requiring higher-order awareness? Can this axiom be mathematized? Or could we interpret the first axiom (i.e. consciousness exists from *my* perspective) as implying higher-order awareness?

The current defenders of IIT clearly have a first-order theory of consciousness in mind when they discuss Sperling. They say in their Nature Neuroscience Reviews paper,

In short, the information that specifies an experience is much larger
than the purported limited capacity of consciousness

But there is no argument for this other than that IIT predicts it! Doesn’t it seem the least bit fishy that a theory that starts off with axioms that encode first-order assumptions about consciousness ends up ‘predicting’ first-order readings of controversial experiments? There is nothing in IIT that seems to indicate that we should not instead say that the Sperling distinctions encoded in the integrated information are unconscious and what is conscious is just what the subjects report.

Thus it seems to me that IIT is best interpreted as giving an account of mental content. This mental content may be conscious but it may also be unconscious. To resolve this debate we need to go back to the usual debate between first-order and higher-order theories of consciousness. IIT seems to have added nothing to this debate and we would need to resolve it in the usual way (by argument, appeal to phenomenology, and experimental evidence).

Finally another of the main ideas to come out of the workshop, for me, was that IIT, can be interpreted differently from the metaphysical point of view as well. Is IIT physicalist or dualist? Well, it seems you could have a version of it that went ether way. You could, like David Chalmers seems to incline towards, view IIT as giving you a handle on what the physical correlates of consciousness might be, and then one would posit, in addition, a fundamental law of nature connecting states of physically integrated information with conscious states. This is clearly not the way that Tononi wants the theory to be developed but it is a consistent way to develop the theory. On the other hand one might end up with a physicalist version of IIT, identifying consciousness with the physical implementation of the integrated information. Or you could, like Tononi, claim that consciousness is identical to the ‘conceptual structure’ which exists over and above the parts which make it up (conceptual structures are irreducible to their physical parts for Tononi). So which one of these is the real IIT? Well, there is Tononi’s IIT and then there might be Chalmers’ IIT, etc.

This is not even to mention the problems others have pointed out, that it is hard to know what to make of a grid being ‘more conscious’ than a typical Human, or which of the many (many) different ways of formulating phi are correct, or whether it is even possible to measure phi in humans at all. Even if one wasn’t worried by any of that it still seems that IIT leaves open all of the most important questions about the ultimate nature of consciousness.