Modelling Consciousness

Prof. C.J.S. Clarke
E-mail: cjsc@maths.soton.ac.uk
(copyright: all rights reserved)

Thinking over the last 3 years in the Network and elsewhere has greatly clarified what we are about. I will be taking Chalmers' characterisation of "The Hard Problem" as defining my direction in consciousness research. Until we have solved (or circumvented) the Hard Problem of unifying the subjective/internal and objective/external areas of experience, there are three separate activities to be considered:

  1. modelling consciousness (which by definition is on the subjective side)
  2. modelling brain functions
  3. relating the two

To make a parenthetical remark, the term 'mind' is used in different ways so as sometimes to fall under (a) and sometimes under (b). The term is also used to point to a unifying concept that might unite (a) and (b), and hence is in (c). This last usage can serve as a guiding idea but does not remove the actual work needed to articulate the unification in detail.

Modelling the brain

Item (b) covers most of the work that tends to be cited in relation to consciousness, even though it is in itself not necessarily relevant. It includes such things as

  1. quantum models in which the quantised systems might be any or all of
    • phonons for the vibrational modes of cell membranes (Frohlich)
    • ditto for microtubules (Hammeroff)
    • free conduction electrons in the intercellular fluid
    • the electromagnetic field
  2. phenomenological approximations to any of the above, for instance those using an order parameter to describe the spatial distribution of a Bose condensation of phonons (Marshall)
  3. functional models concentrating on what the brain does rather than what it's made of, which includes
    • analogies with neural networks (paradoxically, since the neural nets were originally supposed to be analogous to neurones, rather than vice versa)
    • hierarchical models in which small-scale operations are integrated by larger-scale organising functions (Sommerhof)
    • models which attribute non-algorithmic decision making to some aspects of brain function (Penrose)
  4. physiological models in which particular anatomical systems are associated with particular functional roles.

Any of the above can be judged in the light of the Hard Problem by considering which seem to offer the best hope of being united with (a) at some stage. I must stress that there a lot of areas of imaginative non-standard brain-research, involving non-locality, healing, etc etc which may very properly be of interest to the SMN but which are not concerned with consciousness and which I presume are not the subject of this meeting. Much of the material listed above falls, in my opinion, into this category.

Modelling Consciousness

By definition, in this section I am not talking about brains, neurones, electrical signals etc etc but about consciousness.

The immediate issue encountered is a lack of definition as to what it is that I am conscious of at any given time. The standard psychological methodology (Marcel, Yeates etc) is to ask the subject to report on what he/she was conscious of at a time coincident with some marker (e.g. "when the buzzer sounded, what colour was showing on the screen?"), but the problem with this is that it appears not to distinguish between being non-conscious of something, and being conscious of it and then forgetting it. This is a key factor in Dennett's formulation, in which these are no longer two separate options; his approach, however, denies the experience of consciousness altogether. The more conventional alternative is to regard consciousness as a kind of movable spotlight, with ill-defined edges, that ranges over a field of mental activity that is either conscious or potentially conscious. It seems inevitable that the study of consciousness must take into account this whole field, and not just those things of which we are conscious at a given time. The same is all the more true of Lockwood´s model, in which all parts of this field are, as it were, conscious to themselves, but only the part that is momentarily in functional connection with the linguistic areas receives the label of "my" consciousness. I will call this field, within which consciousness operates, the preconscious field.

Previous correspondence with Peter Marcer raised the question of whether the basic structure of consciousness should be regarded as geometrical or logical. I would argue that geometrical relations alone are insufficient, because (i) they are applicable only to visually and bodily perceived sensations (and to some extent with sounds) and (ii) even visually perceived sensations have other attributes as well as geometrical ones (eg colours). I conceive of the preconscious field as a collection of entities having a rich structure of relationships which include geometrical ones. Linguistic items are also part of this field, and some linguistic items stand in the relation of designation to some perceptual items.

For the sake of making a definite model, it would seem appropriate to handle these entities and their relationships in a way that is, in general terms, of a logical nature - largely because of the lack of any adequate alternative. Though there are arguments for adopting some sort of fuzzy logic rather than a classical logic, my own view is that one should try two-valued logic in the first place, and adopt many valued logic as and when the evidence guides one in this direction. I do, however, think that it is profitable to adopt a logic that is a little more general than classical logic. I have argued in my Cambridge conference talk modelling participatory consciousness that the distributive law

(a & b) or (a & c) = a & (b or c)

should be suspended. The weaker law

(a & b) or (a & c) -> a & (b or c)

will hold as a result of the other axioms of classical logic. I will refer to this equation as (*). The reason for using only this weaker law is that the resulting system (which is quantum logic) will then allow for the possibility of there being different schemes of relations which are complementary in the quantum mechanical sense. This in turn allows a participatory element into consciousness: there is a need to choose one scheme rather than another, and it is only this sort of choice that (i) makes a place for free will that is neither random nor determinate; and (ii) allows consciousness to participate in the world in a way that is alongside the ordinary dynamics of physical causation, rather than interfering with ordinary physical processes.

In order to understand the meaning of the above logic, let me repeat an illustration that I gave in my Cambridge talk.

I will illustrate (*) in the case where

a = "Devas are blessing my garden"

b = "My garden has a nitrogen-rich soil"

c = "My garden does not have a nitrogen-rich soil". To simplify the example I will also assume the special case where there is a full negation expressed by `not' in the example.

Suppose, for the sake of argument, that we are applying the logic so that explanations in terms of immaterial beings of healing energy, on the one hand, and explanations in terms of biochemistry, on the other, belong to different reference frames. (This is not, of course, necessarily the case.) The rules of this game use the convention that if p and q belong to different reference frames then the conjunction p & q is the identically false proposition, f (because there are no circumstances under which both propositions could be entertained at once, and hence no circumstances under which they could both be true at once). We can then evaluate the two sides of (*) as follows:
(a & b) or (a & c) a & (b or c)
= f or f = a & t
= f = a

We can see that, while the left hand side implies (->) the right hand side (recall the definition of ->), the two are not the same, as they would have to be in classical logic.

Relating brain and consciousness

The underlying problem here is that at a strictly physical level the brain has no logical structure: it is, as Crick would say, "nothing but" a collection of atoms. At that level, there is no possibility of making any correspondence between the brain and the mind because of their structural difference. We, as intelligent humans looking at the brain, name structures at various hierarchical levels: molecules, organelles, cells, neural tracts, brain substructures and so on, as well as dynamic structures such as resonant circuits and dynamically encoded memories; and there is some hope in the future of making a correspondence between these and some of the logical structures described above. There is, however, a danger in this that the logical structures used to explain consciousness are derived from the conscious investigator in the first place. There is thus a need to adopt a physical description which already contains logical aspects. In other words, to enlarge the scope of physics so as to include elements of "meaning", "pattern" and so on. I would argue that this can be done if quantum logic is used for the description of physics (which, of course, includes classical mechanics as a special case).

I am therefore arguing for descriptions both of consciousness and of the brain that use quantum logic as their basic foundation. At the weak level of establishing correspondences between the brain and consciousness, this gives at least the hope of setting up some structural similarity. I woul in fact go further than this, to suggest that, by persuing the suggestions in the above Cambridge paper, that we can go beyond correspondence, to an actual explanatory relation between the brain and consciousness. This relation would, however, be an explanation of the world in terms of consciousness, not vice versa.

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