Center for Theoretical Study, Charles University, Prague
Abstract. The paper presents selected topics from Artificial Intelligence (AI) and Connectionism (Neural Network Modelling) and assesses the contribution of both disciplines to our understanding of the human mind and brain. Firstly three different ways of approaching the mind are discussed, that is, through inner experience (introspection), by means of objective scientific method, and by using artificial models. Two philosophical issues related to AI are treated, the logical limitation of formalized thought and the phenomenological limitation of external modelling. Connectionism is presented as a science of collective phenomena similar to those in physical systems. Its relationship to AI is exemplified by a theory of knowledge representation. The paper concludes with a description of Dennet's theory of consciousness.
1 Introduction
Mind, thought, intelligence, knowledge, cognition - these are words that all of us use quite commonly in our everyday language without worrying about their vagueness, ambiguity, and context-dependence. We easily understand each other when we use them - as long as it is not in a scientific context. Then we start to hesitate, especially those among us who adhere to the imperative of scientific exactness and objectivity. What do these words actually mean? What is the nature of the entities they refer to?
We can hardly expect a satisfactory answer to this and there is little hope that the disciplines that are able to say something about the mental sphere would ever agree upon common definitions. Does this suggest that mental phenomena, though familiar to us, are entirely beyond the reach of scientific method? Or is it only due to the temporary lack of a proper scientific language?
The mere absence of a definition should not distract us. Indeed, in order to acquire knowledge of something, we actually do not need, and often cannot have, a precise, a priori definition of the subject of our study. This is unlike the analytical approach, exemplified by mathematics, which is engaged in uncovering facts that are already contained, albeit implicitly, in definitions. The cognitive sciences (including the psychologically motivated school in AI) are at the opposite end of the spectrum: the central topic of their questioning is not exactly specified and the goal of their endeavor is not well-known. Yet there are quite a few great achievements and - what is noteworthy - they tend to converge.
2 Three roads to understanding the human mind
Our main concern here will be the soundness of "artificial intelligence" (the concept) and its relevance to both Artificial Intelligence (the discipline, AI) and Connectionism (a paradigm). However, intelligence is only one of many aspects of human mental life and thus, to provide this topic with more general understanding, let us start with a review of three different roads to the knowledge of the mind.
The first road chooses the individual inner experience and introspection, as accented by the phenomenological school in philosophy. The second is the road of objective natural sciences, based on observation, measurement, and experimentation. The third is the constructive road: building artificial models, whether mathematical, computational, physical, or technical. AI and Connectionism typically belongs to this third road. But let us start with the first one.
2.1 The road of inner experience
We have pointed out the disparity in easily understanding mentalistic terms in everyday language on the one hand, with the difficulty of dealing with them by objective science on the other. What is the root of this disparity?
The majority of notions in ordinary language have their origin in natural experience. In the case of notions related to the mind, like thinking, knowing, perceiving, dreaming, meaning, intention, will, consciousness etc., the experience is, moreover, entirely internal, intimate, and intuitive. As such, these notions cause no problem in understanding: both speaker and hearer (or writer and reader) can always rely on each one's inner experience, with no need to verify whether they mean exactly the same thing. On the other hand, the scientist's maxim of objectivity in this instance fails completely: no statement about these so very familiar concepts can be proved or verified - their intimate character spreads over the whole sentence and thus one can at most agree, that is, to claim their accordance with one's own experience.
In the history of official psychology there were periods when introspection was not admitted as a legitimate scientific method. Consequently all mentalistic terms were either completely avoided or they were considered as something that could be defined in a purely behavioral way. No meaning was ascribed to the origin, essence and inner relationships of phenomena. Explicit behaviorism was gradually replaced (under the influence of the physical sciences) by reductionist and later functionalist materialism (cf. [20]). These psychological schools still regard introspection and inner experience as problematic, due to their subjectivity and difficult communicability. It is scarcely noticed, however, that they serve as the only source of heuristics and terminology.
In any event, it is certain that the inner view offers one of the alternative ways of approaching the mind. Anyone who is able to stop and concentrate on his own mental life is on this road. Among philosophers, the phenomenologists and their followers take it seriously: "[The] pure phenomenology of the experiences of thinking and knowing [...], like the more inclusive pure phenomenology of experiences in general, has, as its inclusive concern, experiences intuitively seizable and analyzable in the pure generality of their essence, not experiences empirically perceived and treated as real facts, as experiences of human or animal experients in the phenomenal world that we posit as an empirical fact." ([13], p.249).
The term introspection is often used ambiguously, without the differentiation of two possible orientations: the inward orientation and the outward orientation. To explain the difference, we have to mention the concept of the self. (This was vividly brought to the attention of the wider AI community some time ago by D.R.Hofstadter [12].)
The self is the entity which says "I" and means itself. I have my self (note that I am talking only for myself) always with myself and thus I know it more intimately that anything else. It is tacitly present in my every sentence, independently of what I am talking about. It is present in the world that surrounds me and I cannot think it away from that world. It is therefore inappropriate to talk about two separately existing entities, the self and the world, but we can clearly distinguish two orientations: the inward and the outward. My ordinary perception is oriented outward, hence I do not see my self directly, I only see the world distorted by it. Nobody else can see my self as well: it is not accessible from the outside.
What orientation do we assume in self-reflection, when we strive to know ourselves? Both orientations are meaningful. When we consciously observe ourselves, or introspect (in the proper sense), we behave as if we had stepped out of ourselves, in order to look back into our inside. On the other hand, during an emotional experience we fully live by ourselves, albeit internally, without observing ourselves and without even being aware of this. When I introspect (inwards) I can talk about myself, i.e. my self is my topic, while in the outward view my self is the talker.
2.2 The road of natural science
The sciences have the objects of their study present before them, they may observe them, touch them, measure them, they may theorize and speculate about them. Indeed, they have to have them first at their disposal, individually, they have to know how to identify and name them. Since inner mental phenomena are not accessible in this way, the sciences prefer to investigate the brain rather than the mind.
One cannot say that the brain is devoid of mystery. There are four principal conundrums:
- How is it possible that each individual brain works at all and that it can perform so many difficult tasks
- How is it possible that each brain develops practically from nothing - from a single cell - into such a sophisticated form within only a few years
- How is it possible that this phenomenon has evolved on Earth, and
- How is it possible that the above questions remain unanswered in spite of the enormous amount of data that the brain sciences have gathered.
Indeed, since the middle of the last century brain scientists have acquired much knowledge about the structure of brain tissue and regarding the processes that take place at different sites under different circumstances. We know what happens at the molecular level, where ion pumps and channels control electrostatic potentials and chemical concentrations. We know what happens at the level of cells and neurons, how signals are fired, transmitted and summed up. We know about behavior of neuronal collectives, columns, and modules. We know about the a number of functionally specific areas in brain, about their interconnections and purposes and failures. However, in spite of all that, we know nothing about how the brain is related to the mind and whether a thought is the accompanying phenomenon of a biological process or conversely.
Neuroscience is an example of a discipline which proceeds by the "bottom-up" method in investigating the substrate supporting mental phenomena. On the other hand, psychology proceeds "top-down" in studying primarily those features of the mind which are within reach of objective, third-person view. The differentiation between the bottom-up and top-down strategies is doubly metaphorical and has little to do with real spatial scales. Of course, neurons are small, but can we say the mind is large? (Let us not contemplate here whether "up" and "down" have some ontological justification, i.e. whether there exists some linear scale in respect to which "up" and "down" would be two complementary orientations, or if there is a point where they could conceivably meet.)
In the last twenty years the term "neuropsychology" came to be used for the discipline that combines both mentioned approaches (cf., e.g., [15]). This discipline, however, still uses the methodology of objective science, carefully avoiding any reference to inner experience.
Some philosophers of AI discuss the so called "folk psychology" - or a commonsense framework for understanding mental states and processes, and used in daily life for explaining human behavior as the outcome of beliefs, desires, perceptions, expectations, goals, sensations, and so forth (cf. [3], p.299). The conceptual framework of folk psychology is closely related to the use of mentalistic terms in natural language, which themselves are rooted more or less in intuitive inner experience. Most cognitive scientists tend to suppress the latter fact and try to eliminate folk-psychological concepts by some reductive strategy (e.g. [25]) or by replacing them with a formal model (e.g. the logic of beliefs, of intentions, etc.)
2.3 The road of artificial modelling
With few exceptions the third, constructive road is based on computer related models. The computer may serve as a device for simulation and implementation of a suitable abstract model, but it may also serve as a metaphor. Metaphorical models, in general, are constructs that help us to clarify, explain or visualize some entity that we do not entirely understand, by revealing its similarity with something we know better. When perceiving the similarity we should not, however, forget the difference: it is the very tension between similarity and difference which enhances our knowledge. This is independent of the nature of such constructs - whether they are physical devices, computer simulations, or abstract theoretical models.
The so called "computer metaphor of the mind" became the prevailing paradigm of AI from its earliest beginnings in the early fifties. People were fascinated by the abilities of the first computing machines and by their truly automatic nature: the user not only had been freed from deciding about every subsequent step of the computation, he was even cut off from detailed information about these steps. No wonder that people started to contemplate the possible parallels between computer functioning and human thinking, as well as between the computer and the brain. These parallels were observed at various levels, from the lowest level of all-or-none signals and threshold operators up to the surface level of serial processing. An illustrative example of this is the history of words like "memory" or "computation". Originally denoting human capacities, these words have been used, first as metaphors and later as common technical terms, in computer science - now to be often used again as metaphors, but in an opposite direction which emphasizes the mechanistic interpretation of brain functioning.
The serial discrete computational process, i.e. the sequence of precisely defined primitive operations chosen by a given control program from a limited repertoire of operation types, is the main feature of the well-known von Neumann computer architecture. The operations have access to a working memory as well as to a long term memory where data and programs are stored. Only at a lower level is this serial process supported by a parallel activity of a certain number of binary logical units.
Two different levels, one serial computational and one of the logical circuitry working in parallel, hint at two modelling strategies, one top-down and the other bottom-up. This resembles the two approaches of the natural sciences as outlined in the previous paragraph, but without the large gap between the two levels, since both are part of the same design project. With the development of software systems in subsequent years, these two levels have parted and now it is rather difficult to deal with both of them (and with other intermediate levels) at the same time. However, the uppermost computational level retains its essentially serial and symbolical character. In the contemporary AI, the uppermost level is referred to as the logical-symbolical level and its functional independence of its hardware implementation is one of the postulates of functionalism in AI. A dedicated functionalist would claim that the upper level is not a mere model but already a realization of the mind.
In this respect it is worth noting that von Neumann's architecture was in fact motivated by Turing's abstract model of the universal computational device. It would also not be surprising to find that Turing, when conceiving of his model, was deliberately using his own intuition: he would introspectively try to observe how he, a mathematician, went about solving mathematical problems or performing computations, and how he broke down the sequence of mental acts into their primitive components (cf. Dennet, [4], p.212). He would naturally consider only that part of his mental activity which is within the reach of consciousness; there it appears as a basically serial process. This does not say anything about the nature of real events in the brain, which demonstratively are of a highly parallel nature. Thus the computer metaphor appears not to be as great a revelation as it seemed to some, and its extension to lower functional levels is debatable, at the least.
The history of the bottom-up approach in modelling the mind (or rather, the brain) took different paths and it is beyond the scope of this paper to survey it in detail. In this respect it is worth noting that the visionary paper of McCulloch and Pitts [21] on the one hand influenced both von Neumann in his design of the digital computer and the early AI researchers in their attempts to find formal models of thought, and on the other hand it contained ideas that gave birth to the bottom-up connectionist approach. The current boom of connectionism originated, however, approximately only some ten years ago, when it was suddenly easy to run extremely large and time-demanding simulations even on table-top computers and as new inspirations were being drawn from nonlinear physics and dynamical systems theory.
2.4 On transdisciplinary ideas
In this century we have witnessed the emergence of quite a few scientific disciplines that called themselves interdisciplinary. Cybernetics is a classical example, neuropsychology and cognitive science are more recent ones. Interdisciplinarity is often understood as an attempt to combine the knowledge, methods, and subject fields of two or more established scientific disciplines, resulting in a new independent discipline.
Above, I have outlined three essentially different ways of approaching one common theme: the mind. Each way may be further subdivided into various disciplines, schools, methods, or strategies (as e.g. the top-down versus bottom-up strategy). Moreover, each of them may have a different language and vocabulary, each may start from different assumptions and their findings may be interpreted differently. Yet we feel, as we do in the case of human mind, that there is a common theme, that all those disciplines, schools, etc. actually move around one single topic, even if evasive. (And if a reductionist or an eliminativist would claim that there is no mind, that all that really exists is nothing but physical phenomena occuring in the brain, we may still say, "OK, let's tentatively identify the mind with precisely those physical phenomena that are associated with what we call the mind.)
I believe that once we feel there is a common theme, it is always worth trying to make a joint effort to study it as a multidisciplinary subject. (In ordewr to avoid misunderstanding I should remark that this is entirely compatible with pluralism in science.)
There is a third term in this family which is worth mentioning. In recent years there were more and more cases when a relatively concrete idea, concept, relationship, or phenomenon has turned out to be relevant or common to many areas of scientific research. Some prominent examples include: chaotic behavior, catastrophes, various other nonlinear phenomena, cooperative behavior, evolution by selection, phase transitions and phase coexistence, emergent phenomena, self-reference, self-similarity, self-organization, complementarity, symmetry as well as many others. These concepts or ideas pervade through many fields in which they may, of course, have different guises and different names. I believe the term transdisciplinary is appropriate for such themes.
In fact, cybernetics has been the first large-scale program aimed at identifying and studying transdisciplinary phenomena (feedback, information, adaptation, homeostasis, stability and many others) and thus, instead of interdisciplinary, cybernetics would be better termed transdisciplinary.
There are reasons to believe that various transdisciplinary ideas play a crucial role in the sciences of the mind (or brain). A representative example are collective phenomena in large assemblies of interacting elements - neurons, processors, abstract units. I shall say more about it when discussing the connectionist paradigm for modelling the mind.
Another, less salient but more ubiquitous case of a transdisciplinary idea, also relevant to the study of the mind, is the concept of scale dimension. The ordered continuum of scales of magnitude may be treated as a new geometrical dimension (orthogonal to the three spatial ones). Shifting along its axis represents zooming up or down over some scene. Our natural experience as well as that of most sciences treats the objects of study as more or less "flat" in this respect, i.e. inhabiting only a relatively short segment in the scale dimension. One may distinguish entities and processes which are widely spread over many scales, while preserving, in a certain sense, their identity. The same holds for the scale dimension of time and, indirectly, for any hierarchy of levels of description.
The brain obviously belongs to the category of such entities that can function on a continuum of spatial and temporal scales as well as on many levels of description concurrently. One specific case of temporal scale difference is associated with the concept of coupled heterochronous dynamical systems. In many natural systems (including the brain) we can easily distinguish two prominent dynamics, one much slower in comparison to the other. The slow one represents development, evolution, or learning of the system, the fast one its actual "runtime" behavior. The slow dynamics sets parameters for the fast and, in a cumulative way, the fast influences the slow.
3 Artificial Intelligence: a view from without
In this chapter we will be concerned with the traditional logical-symbolical-computational AI (recently nicknamed GOFAI for Good Old-Fashioned AI ([10], 1985) as opposed, e.g., to Connectionist AI). In the several decades of its existence there has been a continuing debate on the validity of the thesis that AI, besides its successful practical applications, is also on the right track towards the ultimate project of constructing a truly intelligent machine. There were voices of optimism and pessimism in this debate, mostly dependent on concrete successes or failures of AI in its attempts to model particular humanlike abilities. It would be rather difficult even to sort out the key contributions in this debate (cf. e.g. ([1, 6, 8, 10, 17, 26]); here I will comment on just two selected issues.
3.1 Artificial logic
This term "artificial logic" may sound odd. Thus the opposite to "natural logic" remains "unnatural logic". Yet logic, as an expressive as well as a deductive tool, is among all human intellectual activities the most suitable for mechanization. The reason is obvious: when man uses logic he actually simulates a machine. One should not be surprised at the fact that the theoretically soundest parts of AI are based on logic or logical methods: theorem proving, problem solving, planning, knowledge representation, logic programming.
Successes of AI in these areas has been often wrongly interpreted as successes in constructing the artificial mind. Logic resides only on the mind surface and the claim that a logical machine is sufficient for simulating the mind is as superficial as the claim that a scooter simulates the horse. The trot is more than associated speed and to understand a theorem is more than to know that it has a proof.
Emphasis on the logical aspects of AI induced the first extensive debate on the validity of AI some thirty years ago. In 1961 J.R.Lucas [17] proposed to use Gödel's incompleteness theorem for refuting the mechanistic thesis, viz. that the human mind can be simulated by a machine. Gödel's theorem can be rephrased in this way:
(1) For every (computer) program answering questions (about Peano arithmetic) there exists an answerable question which the program cannot answer.
Here "answerable" means that people will able to find the correct answer, regardless of the effort he would have to make. It is not difficult to refute the following, stronger version of the mechanistic thesis:
(2) There exists a program that can answer all answerable questions.
It is just the negation of (1). It does not follow, however, that the following mentalistic thesis hold:
(3) There exists an answerable question which no program can answer.
A technical aspect of the problem is that we have to deal with two infinitely growing hierarchies, one consisting of increasingly sophisticated programs, and the other of increasingly difficult questions. For each program one can find a question beyond its answering power, while for each question one can write a program able to answer it (in addition to all the previous questions).
One type of argumentation could now point to the fact that people also have questions beyond their answering power (try to answer this question: "Will your answer to this question be wrong?"). Another possibility would be to ponder over the human capacity to perceive a whole infinite hierarchy at once, without the need to resort to stepwise extensions. Let us mention a third type of argument (in favor of AI) put forth by Hofstadter ([12], p.577), namely that even if general programs, including those of AI, are subject to Gödelian limitation, this concerns only their lowest hardware level. But since there may be higher levels (as is certainly the case for AI programs), this is not the last word on the subject.
An interesting point may be made here. The hierarchy of levels is not conceived in the traditional algorithmic sense (upper level instructions equal lower level programs) but in the intuitive sense of increased flexibility, informality, and even inconsistence in the upward direction. According to Hofstadter intelligence resides on the top, "informal" level where "there may be manipulation of images, formulation of analogies, forgetting of ideas, confusing of concepts, blurring of distinctions, and so forth" (ibid, p.578). Even if there are logical thought processes, such as propositional reasoning, at this top level (as happens in humans), this does not mean they have to be preprogrammed. They rather "emerge as consequences of the general intelligence of AI program" (ibid).
3.2 Can artificial things think?
This brings us to the idea of emergent intelligence. The concept of emergence, especially in the context of mental phenomena would deserve a separate study. There are actually three meanings of this word, not always easy to distinguish. The traditional meaning in evolutionary theory (G. H. Lewes in mid-19th century, C. Lloyd Morgan in early 20th century) emphasizes the temporal aspect: the rise of a system that cannot be predicted or explained from antecedent conditions, e.g. the emergence of life, of man, etc.
In its second meaning, the word emergence has recently been increasingly used for phenomena that appear to be natural on a certain level of description, but somewhat resist (though not completely exclude) their reduction to an appropriate lower level (cf., e.g. [11]). Typical examples of this are collective or mass properties: the liquidity of water (a molecule of H2O is not liquid) or democracy in society (one person cannot form a democratic regime). Often this type of emergence is only apparent when caused by the intractable complexity of the lower-level structure.
The third meaning is inspired by the second and is used often as an argument against reductionism. A property (specified by a certain theory T1) is said to be (properly) emergent if it has real instances, if it is co-occurent with some property recognized in a reducing theory T2, but which cannot be reduced to any property definable in T2 (cf. [3], p.324). Property dualism is characterized by the conviction that "even if the mind is the brain, the qualities of subjective experience are nevertheless emergent with respect to the brain and its properties" (ibid, p.323).
Let us consider the thesis that thought occurs as an emergent phenomenon on some higher level of a hierarchical system, with low levels being purely mechanistic. This thesis would help materialistic monism avoid the concept of the soul as an unknown ghostly substance, which is regarded as flowing or flying in another world. However, if the motivation for this avoidance is the mere resistance of accepting an unknown or unknowable entity, then not even the concept of (proper) emergence would help, at least until something more is known about the matter. For instance there is little or no understanding of communication or interaction between different levels, as well as of interlevel causation.
On the other hand the emergentist thesis cannot be easily refuted and we can tentatively accept it for the sake of discussion of the chances of AI. And we immediately observe that what is wrong with the AI thesis (that intelligence can be constructed artificially) is not the concept of intelligence but rather the idea of something artificial.
What does it mean for an entity E to be artificial (or manmade, fabricated, synthetic, imitated)? It presumes, firstly, that there is some natural (genuine, authentic, true etc.) object which is in some interesting (to us) sense equivalent to E. Secondly, E has to be made (manmade) with the intention to achieve this specific equivalence, and thirdly, there has to be a coherent and methodical design activity leading from this intention to a realization of E. This I shall shortly call the project.
If I play randomly with pieces of cloth and wire and suddenly - lo and behold! - a flower appears in my hands, we should not, I believe, claim it is an artificial flower. At least we would not say this, if instead of me it had been, let us say, a wind which was playing with the cloth and the wire. But the intention is not sufficient: even if my random playing with the cloth and wire, or my waiting for the wind to do it for me, were accompanied by the conscious hope that the flower would sooner or later appear, I would still hesitate to call the flower artificial. What would be missing is the project.
The project presumes an explicit design specification,i.e. an a priori external and objective description of all the relevant properties of the intended product. External because the construction is an external activity, and objective because anyone else should be able, in principle, to use it with same outcome. Now, can we ever have an external and objective description of the mind? The so called strong AI thesis says yes. Its opponents say no.
My argument against the strong thesis is based on the belief that the human mind as well as all its particular aspects or qualities like thought, perception, intelligence, understanding, and most of all consciousness, are intimately and inseparably connected to the human self. And the self is not accessible from the outside, it can be experienced only internally, and in principle it cannot be described and presented in the form of a design specification. Hence artificial intelligence in the proper sense is an ill-defined task. (I hope there is no need to stress that this is only an opinion that cannot be proved or disproved.)
4 The connectionist alternative
Whatever our opinion concerning the strong AI thesis, there is another alternative using the bottom-up strategy. One can try to construct a complex dynamical system in the form of a large collective of communicating units, and then patiently wait whether some rich hierarchy of emergent phenomena will arise, the top level of which would support processes of "thought", though of some alien and incomprehensible nature.
Connectionism, neural network modelling or parallel distributed processing (PDP) are several names for new approaches that can be assigned to such a challenging task. A great deal of research has been devoted to particular connectionist models and there are impressive applications including object recognition, learning of skills, optimization etc. The AI debate has obtained new impetus in the form of the question of validity of objections against the AI thesis also with respect to the connectionist paradigm. However, as follows from what I have said in the previous section, we should be careful with qualifying anything as "artificial" that transcends the level of our design project.
4.1 Connectionist models and neural networks
Connectionist models are reminiscent of and/or inspired by the neural networks in the brain. They are parallel-processing systems, involving cooperative "computations" grounded in local interactions between connected units.
Many variants of connectionist models with different network topologies, unit activity functions, learning rules, and teaching strategies have been introduced; some models are deterministic, some involve noise or "temperature", some are discrete, some continuous. Surprisingly enough, these variants do not yield radically different potential global properties, at least not those which have a role in discussion about the validity of the bottom-up approach in modelling the human mind. (An exception seems to be the degree of noise or autonomy in behavior of individual elements - I shall comment on this later.) For our purposes it will be useful to introduce a simplified "canonical" model of a connectionist system.
Let U = {1,...,N} be a set of units (formal counterparts of neurons) where N is assumed to be very large. At every time each unit i is in a certain state xi, which typically belongs either to a two-element set {0,1} or to a continuum of values. There are connections (formal synapses) between some units; each connection (i,j) is associated with a positive or negative real number, its connection weight wij. Local dynamics (neuronal excitation) in the network is specified by the uniform activation rule, typically of the form
N
j=1
where S is a sigmoidal operator (or its special case, a threshold operator), and where discrete time is assumed. As for the connection weights we assume the more general (and more interesting) case when their value slowly changes depending on the averaged activity of the corresponding pair of connected units by the learning rule:
wij(t+1) := F(wij(t), xi(t), xj(t)) (2)
The most widely used is the Hebbian learning rule
wij(t+1) := wij(t) + e xi(t)xj(t) (3)
where e is a small constant. In the latter case the positive or negative weight represents synaptic plasticity - long term memory of the frequency of the cases of agreement or disagreement respectively, between the activities of both units in their past values.
The current total activation state of the network is represented by a point x = (xi)i in N-dimensional activation state space, and the current total learning state of the same network is represented by a point W = [wij]ij in N x N-dimensional learning state space associated with the network. The local activation and learning rules determine for any initial state the unique trajectory in the respective space. (I leave to the reader a simple extension of this definition for the case of external time-variable input.)
Thus we can view a connectionist network as a pair of coupled heterochronous dynamical systems (mentioned in Sec. 2.4), one representing its fast active behavior, the other its slow learning process.
4.2 Collective phenomena and the autonomy of units
The global behavior of a connectionist system can be viewed as a specific case of a much more general, transdisciplinary concept (in the sense of Sec. 2.4) of a collective behavior. Collective phenomena typically occur in large collections of elements, the behavior of each being at least partly dependent on the behavior of some other elements in its "neighborhood". The independent, autonomous part of its behavior may be based on a random and/or rational individual decision. (In the previous section we introduced the connectionist system in its deterministic form; there is no technical problem to extend it by assuming the activity as well as the learning rules to be probabilistic.)
The connectionist model is an example of a single-level system (all units at the same level of description). In contrast, the concept of a hierarchical collective system incorporates the idea of iterated division of larger tasks to smaller subtasks. This idea is natural for the top-down AI strategy ([22]), but at the same time it may support emergent collective phenomena.
According to the degree of the autonomy of units we can distinguish two opposite modes of global behavior (in single-level as well as hierarchical systems) or, using the language of statistical physics, two phases:
(1) the rigid, bureaucratic system of primitive obedient agents (low autonomy), and
(2) the chaotic, anarchic system where everybody does whatever they like.
(Cf. [4,5].) Various disciplines, from physics to the social sciences, offer many examples of mixed or intermediate cases. For instance we may have a system of initiative agents, competing for recognition, each with their own idea, while at the same time all are attentive to the ideas of their colleagues. In a rigid system a good new idea can occur with great difficulty, in the chaotic system it is always lost, but in the intermediate system it may propagate easily through large areas of the network. In physical systems we encounter similar situations near phase transitions.
Collective systems with highly parallel activity are interesting alternatives to classical serial computational models. Dennet [4] uses the idea of multiplicity of competing agents (he calls them homunculi) in his theory of consciousness. Collective systems have extremely large combinatorial complexity (the number of global states grows exponentially with the number N of units). Such a complexity is not, however, a disadvantage. It yields redundancy and redundancy supports self-organization and self-improvement.
4.3 The biodynamics of the mind
There are possible extensions of the connectionist idea which promise some novel views and transdisciplinary bonds. The connectionist approach hints that such a bond may be particularly strong between what is offered by dynamical systems theory and mathematical physics on the one side and dynamical aspects of mental processes (and other biological phenomena) on the other (cf. also Dvořák 1991, Little 1990)).. Let us coin the term biodynamics for this new attractive direction of research.
Our first thought concerns the question of the nature of the modelled entity, to be studied as a dynamical system. An obvious avenue would be to start with real neuronal tissue, as studied by neurophysiologists. This would call for an abstract model in the form of a network of elementary units, formal neurons, wherein the individual dynamics of each formal neuron should be as identical as possible to the individual dynamics of the real neuron. The main obstacle against this approach is the difficulty to completely formalize the functioning of something as complex as the biological neuron.
There are methodological reasons to proceed in a different way. Let us assume we want to use the formal modelling method with the aim to achieve a deeper understanding of a certain particular phenomenon. It is then advantageous to construct a variety of alternative models and for each of them to ask which of its specific features are essential for our phenomenon and which are not. This is especially helpful in case the chosen phenomenon is very involved. In our case of mental phenomena to be studied as dynamical processes evolving in time (measured in different time scales) we should not restrict ourselves to one preferred formal model that imitates, at the lowest level, the behavior of real neurons. The functionalistic ideology has certain epistemological justification here.
Further, we should not expect to be able to directly model the higher-level phenomenon we are interested in (e.g., a particular mental state), since we would face the design specification problem discussed in Section 3.2. Rather, we use the bottom-up strategy of indirect modelling by choosing, firstly, a specific type of substrate (a system with specified structure and behavior at the lowest level, e.g. a network of functional units of a given type) and then posing a question of the kinds of behavior emergent on upper level(s). We may seek the answer either with the help of computer simulations or by looking for analogies in existing physical systems, such as molecular gases, magnetic materials, or spin glasses, but also in collectives of people, ant colonies ([12]), or in other collections of communicating agents. After accumulating extensive knowledge of various emergent phenomena in different kinds of systems, we may look for at least superficial analogies with mental phenomena.
The connectionist models described in Section 4.2 are just a special case of a substrate fertile for collective phenomena (characterized by local dynamics of the type (1) and by modifiable connection weights (2)). Another, considerably different example is Kauffman's idea of a random Boolean network ([14]). With its help one may study, in particular, various emergent phenomena on the edge of chaos.
A random Boolean network consists of N binary variables, each dependent on an average number K of randomly chosen variables of the network, its inputs. The individual dynamics of each variable, whether it will be "on" or "off" at the next moment, is governed by a randomly chosen Boolean function of its inputs. Over a succession of moments the system passes through a sequence of total states - a trajectory in the state space of the network. Due to the finiteness of N, all trajectories sooner or later end up in cyclic attractors.
We can study the typical behavior of such complex Boolean systems for different values of preselected parameters (e.g. number K, or certain quantifiable characteristics of chosen Boolean functions). For certain values of parameters the systems exhibit "chaotic" behavior (the cycle lengths of their attractors grow exponentially with increasing N), for other values the behavior is "ordered" (there are only small isolated islands of changeable elements inside a large web of elements frozen in either an "on" or "off" state). The two types of behavior resemble various physical phases of matter. Interesting dynamic behaviors emerge in networks close to the phase transition area in parameter space, e.g. both small and large unfrozen islands coexist. A small perturbation (a random change of the state of some element) may cause a large avalanche of changes of states propagating through the network. In this way distant sites in the network can "communicate". Moreover, these special modes of behavior have homeostatic quality: structural mutations of the system do not considerably affect its dynamical behavior.
We thus have an example of a rather different system from the neuron-like connectionist network, yet with interesting emergent properties that for instance resemble various collective phase phenomena mentioned in the previous section. Their relevance to actual functioning of neural tissue in the brain is an interesting topic for further study.
4.4 AI versus Connectionism
In view of the obvious relevance of connectionist research to brain theory on the one hand and to advanced computer architectures on the other, one would expect its intensive cooperation with AI. Instead, there is a lasting debate between two opposing camps, the connectionist (in the extreme: symbolic thought is an illusion, an epiphenomenon arising from the dynamic flow of subsymbolic information through a neural network) and the logicist (in the extreme: symbolic thought is all that is needed for a genuine robot agent). Of course, there are "ecumenical" schools too (cognition can in principle be studied profitably and accurately at any level of description). (Cf. [2], p. 324.)
The emergentist thesis formulated in Sec. 3.2 presupposes the existence of at least two fundamental levels, the lower level of activity of individual units and their small collectives and the upper level of cognitive processes. Following Smolensky [28] we shall call the lower level subconceptual and the upper level conceptual. The latter is the preferred level of symbolic AI. A methodological clash occurs whenever representatives of each camp claim they are using the only correct level, the other level being a superfluous construct.
This is, of course, a rather short-sighted view. Firstly, there may in fact be a whole hierarchy of levels, perhaps with a certain weak reduction being possible, but only between relatively nearby levels. Secondly, the ontological status of the conceptual level may be somewhere between physical reality and imaginary fiction. Thus, for instance, certain fuzzy and overlapping patterns of activity over large collections of units (neurons) may represent concepts and propositions, while these patterns may - but need not - be accessible to external observation.
As an illustrative example, let me outline an approach of the knowledge representation theory which implants some AI ideas into the connectionist framework ([9]).
The development of a connectionist theory of knowledge representation involves establishing suitable interlevel relationships. In the current view this consists in finding a correspondence between upper-level objects, like concepts, propositions, frames, schemata etc., on the one side and certain dynamic phenomena at the subconceptual level, such as distributed activity patterns in the network, on the other. If we say that a connectionist system represents structured knowledge, we actually refer to its emergent conceptual level. On the subconceptual level there are no prepared data structures, no identifiable locations of knowledge items, and no individual "decisions" about where and how information should be stored.
In spite of this we can develop a formalism that introduces a hierarchy of abstract representational objects, called schemata: where with the lowest level consisting of knowledge atoms (elements of meaning, associated with specific patterns of activity) and the higher-level objects are each composed of a cluster of lower-level objects with various strengths (a long-term parameter) and various activations (a short-term variable). The strength is a generalization of connection weight in the connectionist network and represents the long-term memory, and the activation is a generalization of the activation of units and represents currently active knowledge. Schemata become active at the moment they are relevant and those which are active often become stronger.
Schemata may be compared to the frames used in traditional AI representational systems. Here, however, probabilities of activation of some schemata are influenced by the external context. An active schema then activates other schemata in its own cluster; they could play the role of slot fillers for the original schema - default fillers as well as those set by external information.
Basic assumptions of the symbolic AI (originally based on our logical and linguistic intuitions) are not, however, completely endorsed by the bottom-up connectionist framework. Firstly, there is the already mentioned absence of a priori information structures, only later to be filled with data. Secondly, the basic representational objects (knowledge atoms, schemata) could hardly possess explicit semantics besides statistical properties of their combined activation histories. Thirdly, the ordinary sharp logical distinction between representing objects (individuals) and facts (propositions) is blurred. Fourthly, there are no logical types and there is only one kind of a "link" based on dynamically correlated activities. Fifthly, the distinction between universals (types) and particulars (tokens) appears rather hazy and again can be captured only dynamically.
No wonder that subscribers to the Good Old-Fashioned AI are somewhat reluctant to accept the shift of paradigm caused by the connectionist approach.
5 Is consciousness a topic for science?
Indeed, there are intellectual acts with a relatively unsubstantial inner component, for instance numerical computation, formal deduction, and perhaps even chess playing. But there are also inherently internal phenomena, consciousness among the first. If the sciences are based on the third-person point of view, can consciousness become a topic for science at all?
There is a noteworthy recent shift of interest, both in the cognitive sciences and in analytical philosophy, towards the issue of consciousness. While a monograph on neuropsychology ([15]) still may not have the word "consciousness" in the index, there is a growing number of philosophical books concerned with this topic (e.g. [4, 19, 27]). Even among physicists there are those who raise this issue (e.g. Penrose [23]).
Particularly interesting is the new book Consciousness Explained by D.C.Dennet [4]. He argues in favor of an objective science of consciousness and formulates a methodological principle, called heterophenomenology, which by-passes the objection of external inaccessibility. Dennet proposes that we should investigate the other persons' inner worlds by interpreting their own verbal accounts - and deliberately not asking them how they know what they assert - in the same way as we interpret fictional narratives or mythologies without questioning their actual truth. He believes that this "method of phenomenological description ... can (in principle) do justice to the most private and ineffable subjective experiences, while never abandoning the methodological scruples of science" (ibid, p.72).
Dennet's approach to the issue of consciousness begins by refuting the traditional metaphor that he calls the Cartesian Theater, i.e. the idea of a centered locus in the brain where there is an imaginary observer who monitors everything and does all the decision-making. In its place he proposes his own Multiple Drafts Model of consciousness: "Instead of ... a single stream [of consciousness], there are multiple channels in which specialist circuits try, in parallel pandemoniums, to do their various things ... [They produce] fragmentary drafts of "narrative" [most of which] play short-lived roles ... but some get promoted to further functional roles ... The seriality of this machine (its von Neumannesque character) is not a "hard-wired" design feature, but rather the upshot of a succession of coalitions of these specialists." (ibid, pp.253-4).
According to Dennet consciousness is an evolutionarily recent phenomenon that occurs in the brain, which was not at all designed for such seemingly serial processes. Our inner experience of the stream of consciousness is, he claims, the outcome of a (very inefficient) simulation of a serial logical-linguistic machine in highly parallel hardware.
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