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To the guy in Canada who e-mailed me all those questions about T. S. Eliot: read the comments made by Jimi St Pierre after the posts of Nov 27, Feb 04 and Feb. 05.

OBJECTIVITY AND SUBJECTIVITY

Reason is and ought always be the slave of the passions. (David Hume)

 

We have a long road to travel before we can be said to understand, on even the most elementary of levels, the intricate relations between human reason and human emotions. The object-besotted, thing-obsessed nature of the assumptions that underlie much of modern Western culture is nowhere more evident than in the concepts of ‘objectivity’ and ‘subjectivity’. As far as the acquisition of factual knowledge is concerned, and we are obsessed by this as well, objectivity is a virtue and subjectivity is a vice. One hears all the time, in a tone of criticism, “don’t be so subjective!” or “you really should be more objective about this.” Good practice in the gaining of knowledge is the scrupulous observance of the criterion of objectivity, and subjectivity is something to be avoided, even shunned and reviled. So what do we mean by these two terms? Why this polarisation of our minds into virtuous saintly part and vicious sinful part? It is true that emotions fog the mind and distort the perceptions; but to announce that all emotion has to be proscribed from the life of the intellect is simply barmy, if only because there are both destructive and constructive emotions and rather than banning them all, we need to sort out the latter from the former.

Objectivity is, as the term itself suggests, a determination of the mind by objects. It is the attitude of mind that, at its best, is a resolve to stick to the facts of experience, whatever they are, whether the investigator likes them or not, to respect the facts and to give the facts pride of place as opposed to any interpretation. This is very laudable; but it has naturally a downside. At its worst, objectivity is the belief that objects, in the sense of three-dimensional objects, are all that there is in the universe and that these objects should be imagined to speak for themselves, without the imposition of any interpretations. This species of objectivity becomes difficult to sustain when one reflects that knowledge is precisely the business of human beings and their talking about the objects of their experience. This means that the objects are by definition not speaking for themselves, but are rather being spoken for in a language loaded with presuppositions that arise in the subjectivity of those who talk and who may not be aware of them. The whole notion of ‘letting the objects speak for themselves’ means no more than the expression of a belief in absolute precision of representation such that the difference between the object and the representation disappears. It is unnecessary to point out that such a belief must be misguided.

In the acquisition of knowledge, experience is all we have; but we cannot say in all honesty that our experience is only of objects, at least not of objects conceived in the manner of things we can grasp in our hands. When we start to think of our experience of objects, moreover, it becomes very difficult to sort out what in our experience belongs entirely to the object and what belongs only to our minds, so to the subject. Let’s not bother with the debate over primary and secondary characteristics which speculated that the secondary characteristics – smells, colours, tastes, textures etc. – were provided by the subject, whereas geometrical properties and solidity were real features of the object. The profoundest influence upon perception is emotion. We don’t think of any thing without at the same time having feelings about it. The experience of the feelings we have about objects is as much experience as anything else. If then our experience is of more than just objects, why do we sometimes get so hot under the collar when people start to talk about objects in language that attributes to them more than just their 3D space-occupying properties? Why do we get so worked up when we think people are simply expressing their own feelings and inner states, when they think they are talking about matters outside of themselves? Well, we don’t necessarily get worked up, if we share their feelings, but if we do get worked up, the main reason seems to be that we don’t all have the same feelings about objects that we all nevertheless identify as being the same. The objects are thought of as being entirely public, the feelings, on the other hand as entirely private. So it is regarded as a vice to confuse private feelings with public properties when talking about objects. And indeed, that can be the case. Nevertheless, since all thought arises in feeling, historically and on the individual level, we have to ask ourselves, whether we are not losing something by this policy of trying to eliminate all feeling, whether there is not a some understanding of the vital cognitive role for feelings that we do well to consider and appreciate .

Passions can, it is true, get out of control. We can hugely overvalue or undervalue objects on account of our emotions, where a ‘dispassionate’ assessment of them would come to a different view. Thus we are afraid of our passions because of their potentially distorting effect. But are we well served by the practice of simply suppressing them in all situations where the acquisition of knowledge is supposedly the goal. Can one be objective about inner states of the subject? Can one be objective about subjectivity? We all recognise when a poet or a musician or a dramatist or a novelist has accurately portrayed a feeling that we have had with regard to something. Sometimes the artist in question portrays the feeling so exactly that we seem to be experiencing it ourselves and with great intensity. We recognise it as a feeling we have had. Even stand-up comedians can get to the essence of very intimate feelings of a troubling or embarrassing nature and their humour often has to do with this revelation of ourselves to ourselves through the portrayal of feelings. Often the more accurate the portrayal, the funnier the act. So perhaps one can be objective about subjective states, about subjectivity. But then, if this is so, objectivity cannot be simply about letting objects, tangible, solid objects speak for themselves. It must have to do with more complex facts than the space-occupying properties of perceptible things. Moreover, one has to at least suspect that such a limitation of the concept of ‘knowledge’ is itself driven by an emotion: the fear of emotion – that of others at least. A far more rational attitude would seem to be to recognise the place of emotion in knowledge and strive to understand it. The notion of the emotionless subject, passionlessly contemplating a universe of senseless objects is incoherent.

The notion of that subject’s being ‘merely’ an object is also incoherent. Nevertheless, there is a dogma that claims that subjective states are ultimately identical with perceptible objects since thought is just brain-function. There are people who find it reassuring to be able to assert that all mental events are brain-states. But if one believes this, one has to concede that objective knowledge in a mind is also ultimately a perceptible object. This means that one particular set of perceptible objects is somehow ‘knowledge’ of yet another set of perceptible objects, and the perception of this state of affairs yet another. Since the same incomprehensible principle goes for feelings about objects, it is impossible to see how knowledge and feelings differ. If, furthermore, knowledge and feelings are ultimately in themselves objects, this fact could presumably not be fully known without perceiving the objects in question. Thus this knowledge in turn would be yet another set of perceptible objects. We start to get dizzy at such reflections, but at least they make us aware that the whole business of objectivity and subjectivity is far more complex than we seem to imagine. Moreover, the understanding of objectivity seems to have far more to do with a desire to ignore the conscious subject and cut it out of the equation than anything else, principally because it is too unruly an entity.

 

*****

 

People are liable to talk about some statement’s being ‘objective’ if they mean that they find it accurate and so they may mean no more than that they agree with it. Moreover, they do not limit the term ‘objective’ to the description in dispassionate terms of items of foreworld. They can talk about the objective assessment of someone’s capacities, qualities, character and so on. Thus, the term ‘objective’ seems to mean nothing more now than a sort of lowest common denominator of experience – ‘what we can all agree on’ – and that is a function of communities of discourse and their conventions, not a matter of ‘letting the world speak for itself’. Communities of discourse are riddled with feelings (‘consensus’ means ‘feeling together’), but they can ignore them because everyone in the community has the same feelings. So, if all communities of discourse – including those of scientific discourse – work with feelings and if these feelings are only factored out because everyone shares them, why do we not recognise that feelings are an integral part of the knowledge-gathering process? The desire to know is a passion and without it there is no accumulation of knowledge. Thus we should have the clear-headedness to pay closer attention to the sorts of feelings that influence thought in order to be in a much better position to understand which feelings tend to aid cognitive accumulation and which feelings hinder it.

The difficulties involved in making a distinction between feelings that are cognitively helpful and those that are the contrary of this are major. There is clearly a lot wrong with simply claiming that all and any feelings should be allowed to influence the gathering of knowledge. Take members of a jury, for example, who all happen to be passionate racists and are found sitting in judgement on a member of a group they despise? Here, if the feelings interfere with the question of the facts suggesting the guilt or innocence of the person concerned, then they are clearly inappropriate. When someone says of something, “this is beautiful,” or “this is interesting,”  “this is cruel,” “this is wrong,” “this is good” and another says (perhaps with increasing annoyance) of the same things the opposite of these adjectives, then there is clearly something more than mere disagreement going on. The parties concerned, here, are likely to continue asserting their individual position despite the assertions of the other. That is to say that a concern for the facts seems not to be up to resolving the situation and bringing about harmonious agreement. So while feelings can cement a community of discourse, they can clearly be a source of discord and disharmony, of conflict and disagreement between communities. And as we all know only too well, such discord and conflict can often flare up into unpleasant things such as violence, intolerance, hatred, discrimination and the like. Such discord does not however prove that feeling as such is out of place in the gathering of knowledge, only that certain feelings are. We all know that certain methods are unsuitable to the accumulation of valuable insight; but we do not on that account proscribe all method. Why then can we not admit that certain feelings are appropriate to it?

Do the negative results of the intrusion of feelings upon the observation and description of facts necessarily mean that we have to exclude all feeling from our experience of the world if we are to come up with what we call ‘knowledge’? This hardly seems likely, if only because certain feelings play such a vital role in the attitudes and activities that result in our finding out things about the world. Take the feelings of being interested, of being intrigued, of being curious. Surely these are essential to any attempt to learn anything. In their absence we learn nothing. Yet they are feelings and they remain feelings throughout the processes that they may set in train. We feel perpetually curious or intrigued about almost everything in the world. If we didn’t, we would stagnate as a race and neither learn nor create anything new. The feelings of being curious and being interested drive what is intrinsic to what it means to be human, namely the search for understanding. These feelings may be temporarily satisfied when a discovery is made, but they soon flare up again when the discoveries concerned or at least the terms in which they are expressed – no longer seem to deal adequately with the facts or simply lead to dissatisfaction, i.e. another feeling. This has always been so with the human race. Often it is a new generation that feels differently, less satisfied, about the ‘facts’ that satisfied the older generation. But this is not necessarily so. Sometimes an individual will remain throughout life intrigued, interested, curious, dissatisfied about his or her understanding of the world around.

But these feelings are not the only ones that drive us to learn things. We also have feelings of meaningfulness, of beauty, of awe, of wonder, and their opposite, feelings of ugliness, chaos, contempt and boredom, that drive us to try and understand our experience. The most desiccated mind, intent on screening all emotion out of any comment upon experience is not immune to feeling but merely pretending to be so. The interesting question is why this pretence should be maintained. The answer to this is found in an ideology, the ideology of the thing-world, foreworld as the only world, the world as a soulless collection of mindless, feelingless three-dimensional objects, knowledge of which can only be some incomprehensible, feelingless configuration of another set of objects. The ideology that states that only solid things in three-dimensional space exist and nothing else, and that knowledge of these is essentially equivalent to quantifying them, clearly has no use for feelings. The ideology also states that the human perceptual apparatus is equipped to give a completely accurate assessment of these things. The ideology then states that with the piling up of detailed descriptive information of these things (which is equivalent to the measurement of various quantitative values), the interpretations will simply come along, simply be read off from the large number of details. The careful, unemotional work of cataloguing, measuring and describing the things of the world goes ahead according to the logic of resemblance, contiguity or cause and effect or according to the deductive logic of drawing inferences from known facts. Everything is clinical and dry. Well, this is such a travesty of the process of the increase of our knowledge that it beggars belief that anyone ever believed it. It is even more astonishing that this pretence of passionlessness is still part of the official self-image of the scientific enterprise. The search for knowledge is a passion. And yet the ideology fosters belief in this passionless view of things? Why?

The reason, may be detectable in the origins of the word ‘passion’. The word means something passive, something one ‘suffers’, something that happens to one, something involuntary; whereas the human ego wants to be solely responsible for knowledge and to take all credit for it. Another reason, however, is possibly the simplifying desire to screen out of our consideration of the world the destructive passions that distort and diminish people’s view of things and interpretations of facts. But we also in the process exclude anything like the passions that are found in the poetic, lyrical, mythical or religious views of the world, where emotions are consciously included into the theories about the universe and positively drive them forward. Consequent upon the insight that emotions can be destructive, we gave in to the knee-jerk condemnation of all emotion indiscriminately. But the most fundamental reason for the exclusion of emotion was itself again an emotion: the self-aggrandizing desire to confer upon the observing mind, the observing ego a kind of infallibility, a potential omniscience.

With the increasing success of the mechanical conception of the universe, the all-conquering Newtonian mechanics, the subject became both an embarrassment and the source of a seductive dream of gigantic proportions. It became an embarrassment not only because the destructive nature of certain emotions is well understood by all, but also because of the excesses of the Middle Ages with its religious ecstasies and because of the Romantic Movement with its deep mystification about the hidden depths of the soul. But it became the source of a seductive dream when the possibility opened up of the ego’s acquiring and possessing an absolute viewpoint on the universe, a God’s-eye view of things. The observing ego was shut out of the scientific picture of the nineteenth and twentieth centuries as far as its emotional depths were concerned, but it was inflated to divine proportions in its supposed ability to acquire truth. The emotional baggage that was dragged along with the Medieval and Romantic conceptions of the world gave it both terrifying and deeply satisfying features: it had mysterious unknown and therefore threatening depths to it, but it was also suffused with sense, meaning and direction. The theories of the universe redolent with meaning that result from the Medieval or Romantic ways of viewing the world were ditched by the scientific spirit. They were replaced by an ideology of strict meaninglessness for no other reason than that the feeling that the world had a deep objective significance that often suffuses poetry, myth and the like had to be stripped away from any consideration of the world and replaced with the subjective sense of significance of the ego. With the loss of objective meaningfulness went the feeling of purposefulness that is closely related to it and with purpose went value: the objective world became meaningless and valueless. The reason for this is simple: without the ability to follow those emotional responses to reality, that suggested to us that it was in itself meaningful, it loses its value. Now when reality loses its value, we lose our reason, our purpose for living. It is after all our emotions, our sense of meaning and purpose that make us get up in the morning.

But the doctrine of meaninglessness was actually a huge subterfuge. The scientific ego was in fact only apparently wedded to it. In actual fact it was secretly attached to an emotionally given meaning to the universe that up to this point had not been fully tried out: this emotionally given meaning was the delicious thought that the scientific ego was itself the meaning and purpose of the universe.  Of course this nonsensical idea was never articulated by any scientific community, but it was there nevertheless, and all the more powerful for not being articulated. Its presence became clear in the outworking of some philosophical tendencies within the idealism of the Enlightenment, from Kant through Fichte to Hegel. The scientific version of the same tendency was evident in the pronouncements of the Count Pierre Simon de Laplace, the eminent physicist of the nineteenth century who taught Napoleon at the Ecole Militaire in Paris. Laplace was a true scientific son of the Enlightenment. He produced the classical formulation of the theory of probability which attempted to prove that probabilities arise from ignorance and that in actual fact the world is entirely determined, just like a piece of clockwork. He imagined that if a mind (a ‘daemon’) sufficiently capacious to hold all the information knew the location and the trajectories of all the particles in the universe, then knowledge of any sort about the universe would simply be a matter of calculation, not of the probabilities of any future states but the certainties of all future states. Thus, for example, moral questions would be resolved in exactly the same manner as mechanical questions. This vision was nonsensical because it involved an ambiguity or a confusion over the notion of the ‘mind’ that was doing these calculations. Laplace pretended to be talking about a superhuman mind, but in fact he was talking about his own mind endowed with superhuman qualities. That he was talking at one and the same time about a human and a non-human mind is obvious, because he imagined the information that the daemon’s mind would hold and manipulate as being organised and used according to human plans, wishes designs and intentions. Therefore what he envisaged in his completely deterministic universe was a universe completely under the intellectual – and presumably as a result, the physical – control of the ego – his own, no doubt. This vision of pseudo godhood was the driving force behind most of the science of the nineteenth and twentieth centuries. It was the vision that underpinned the ideologies of mechanism, deterministic materialism, and it still drives the ideology of objectivity today.

It was this ideology that mightily influenced Friedrich Nietzsche and led him to come up with his spine-chilling myth of the Eternal Return of the Same. Nietzsche drew the consequences of Laplace’s vision of the complete material determinism of an atomistic conception of reality and reasoned thus: if the universe is composed of a finite number of definable particles and if those particles are moving according to definite mechanical laws, such that their trajectories can be predicted, then such a universe must go through all the permutations available to the particles moving thus, in a finite amount of time. However, since time is infinite (as it was in Newtonian physics) it must go through all the permutations an infinite number of times. The upshot of this view of things for the human individual is that each human life has already happened an infinite number of times and will happen an infinite number of times in the future. We are doomed mechanically to perform the same gestures that we have performed, are performing, or will perform in our lives an infinite number of times. Thus nothing actually happens in such a universe, since it repeats itself identically ad infnitum.

The state of modern physics no longer permits such chilling visions to be true. Determinism has gone. Atomism has gone. Infinite linear time has gone.  Complete predictability has gone. And, most significantly, the absolute separation of the observer and the observed has gone. Thus the old basis for the distinction between objectivity and subjectivity, at least in the manner understood by the thing-ideology has also gone. What have we left? Well what we have is what we always had before the separation of object and subject came on the scene. We have an intimate connection between object and subject.

 

*****

 

It is in fact impossible to define in any rigorous way any boundary between object and subject. The consciousness of the subject is constituted not only by its emotional interest, but also by perceptions of objects that are constructions of its 3D space-processor: hindworld and foreworld are so entangled as to be inseparable. The objects themselves are only present to us by virtue of our conscious perceptions and not in any other way. It is impossible to separate consciousness and objects. Therefore in a very real sense, without going as far as George Berkeley, the objects themselves are dependent upon our conscious perceptions and have no existence without them. This can be admitted without the mind that admits it being obliged to give in to an ideology that states either that “the world is one big thought” or that “the world is nothing but objects”. The simple fact is that subject and object are locked together in mutual dependence: there is no foreworld without a hindworld. How then do we tease the two apart? Do we need to? The partial answer is this: language, i.e. midworld, mediates between subject and object. Language is the precipitate that is deposited at the interface between what we call experiencing subject and what we call experienced world. But it is in language that the difference between the two becomes evident. It is also in language that the indivisibility of the two becomes evident. Foreworld is mirrored in some way in hindworld and this mirroring is reproduced in midworld. The self reflects the world and further reflections of this reflection are given in language. But we do not have a simple set of transformation-rules by means of which the ‘objective’ outer world itself, the inner ‘subjective’ conception of the world, and the linguistic representation of the world can be related unproblematically. The problem is the high dimensionality of the situation. The relation subject-language-object is not representable in the three or even four dimensions that we are accustomed to. In short, there is no easy connection between ‘external’ reality, our ‘internal’ consciousness and the supposed ‘laws of nature’ that we talk about in language. The three are in constant dynamic interaction and always have been.

Our conception of the world apart from ourselves is constantly evolving and it evolves as the three partners in the dynamic system interact with each other like three gravitating bodies. Language broadens horizons and permits wider experience; but it is itself broadened by widening experience; the mind is enlarged, the world and language become more complex and there seems to be no end to this process of expansion. It is for this reason that we require a fourth aspect to the world – hyperworld – which is the ultimate indeterminate source of this series of infinitely deep reflections, the reflection of world in mind, the reflection of this reflection in language, the reflection of language in mind and the reflection of mind in language. In discovering the object, the subject discovers itself. The role of the subject, thus the role of subjectivity, is clearly no less important in this than the role of the object and the job of language is ultimately to allow the subject and the object to flow together. Let us try and get a handle on the possible role of the subject in discovering the object.

Could there be such things as cognitive emotions or cognitive feelings? Well, it would seem that the increase in human knowledge is inseparable from feelings of one sort or another. Feelings are the guilty secret of the scientific enterprise because, like creativity, they are not under the ego’s control. But a radical distinction must be made between those feelings that lead to discovery and those that turn knowledge into dogma and lead to conflict. The famous physicist Paul Dirac stressed that an important element in his equations and an important indicator of their appropriateness in describing the processes they were intended to model was their beauty. The feeling of aesthetic pleasure related to mathematical elegance and economy was vital to Dirac as an indicator of the truth of his discoveries. The beauty of an equation is assessed by a feeling and Dirac and others clearly attributed cognitive worth to this feeling. Similarly, the hunches and heuristic passions (the term in Michael Polanyi’s) that have always driven the researches and investigations of the best and most ground-breaking minds have always had an intensely emotional character to them without which the genius concerned would not have maintained the intensity of effort nor the intensity of zeal required to perform the gargantuan task of perhaps re-casting an entire field of knowledge.

No groundbreaking genius has ever subscribed to the notion of a passionless, disinterested, purely mechanical attitude to discovery. Discovery has always been a passionate business and the passion is for the satisfaction of a desire. The desire is to bring into parallax world, mind and language, to harmonise foreworld, hindworld and midworld; and this happens in an ever-renewed act of human creativity. But there is a difficulty at least as far as scientific discourse is concerned. This difficulty is that there is no common denominator of the three spheres. There is no simple mechanism whereby the subjective states of the thinker, the rules of the language and the laws of nature can be shown to have a common structure. By contemplating the world and by attempting to reflect the world thus experienced in language, the three spheres are each enlarged. There is a process of cross-fertilisation going on between the three. Now since the process is not mechanical, since there is no mechanical method of having new ideas, since there is no method of generating novelty, the confluence of the three worlds appears to be constantly troubled, constantly revitalised, constantly upset, constantly re-created, constantly reconfigured by feelings that encourage the creation of new formal techniques in which to clothe themselves with rigour. This revitalisation, it seems clear, cannot arise in any determined system and must arise in the undetermined itself: what we call ‘hyperworld’ in which distinctions between subject and object are of no significance.

So where does all this leave us with regard to the question of the relative merits of objectivity and subjectivity? Well clearly, we can no longer sustain a conception of knowledge that does not take seriously the dynamism of the subject, since all increase of knowledge is a work of subjects. The creativity of the subject is entirely responsible for the major increases in knowledge. All major new ideas arise passionately in the minds of the creative innovators. The religious visions of the past arose in the minds of creative individuals. The philosophical and scientific visions that grew out of them and that replaced them were the work of different creative individuals.  The ideology of objectivity was also the work of creative minds. The subject, the ideology states, does not exist but is itself an object. And this ideology proved very fruitful in the nineteenth and twentieth centuries. But this ideology has now been shown by the apparently most ‘objective’ of sciences to have serious weaknesses and has succumbed to further work on the part of further creative minds. It is time that we relieved it of its uniquely and exclusively authoritative position in our culture.

The passions of the investigating thinker cannot be neglected, nor can they be reduced to any mechanism, even the most sophisticated. Subject and object and language are locked together in an apparently eternal dance in which each revivifies the other, passionately. The entire accumulation of knowledge from its prehistoric roots through religion to science has been driven by passions. Language is the locus of human creative discovery of the depths of the world – depths that are still unknown. Subject, object and language are, however, parts of a world which itself appears to be in a process of perpetual evolution, perpetual generation of new form. We do not know how this evolution arises, where, if anywhere, it is tending, nor what drives it. All we know is that we find it infinitely fascinating and wonderful and wish to capture that sense of wonder in convincing and perhaps even useful terms. There is no reason to believe that there in any end-station in this process. Our knowledge is eternally being re-created and with it our world, ourselves and also our language. Why should there be any end to this? Why should we have to believe that some definitive ‘objective’, weights and measures account of all that is brute object, and from which the subject has been eliminated, will soon be worked out? We can concede that no end is in view and yet nevertheless, passionately embrace the challenge of our incomprehension, embrace the creation of new forms of expression that strive to elucidate the mystery. We are fundamentally convinced that the relation between mind, world and language is essentially meaningful. Why can we not simply revel in the creative effervescence that arises from the interaction of foreworld and midworld and see the entire interaction as generated and maintained by that which engages us most, namely hyperworld, the uncracked riddle?

We have to acknowledge the role of feeling in the increase of human knowledge. It is vital. We have to develop the vocabulary for being intelligently objective about subjectivity. The old conception of objectivity as ‘letting the world speak for itself’ must be supplemented by a preparedness to ‘let the psyche speak for itself’ as it contemplates its world. The thing-world we have foisted upon ourselves is a sterile fiction. It exists only in language and has been dissolved in language. The real world includes the feeling world and the perception-world. Together they feed our creativity. The real world as such is the unknown; but our consciousness of it widens perpetually as world, self and language interact. The increase of knowledge does not depend upon the clinical, dispassionate ‘letting objects speak for themselves’ for this has no sense at all. The objects of the 3D world do not speak for themselves, we speak for them and we speak for them in language loaded with emotion, because loaded with human designs and purposes. We as subjects speak of objects because ultimately they are us. It may well be, though, that through us and through our constructive passions it is after all the real world that speaks for itself through us.

We don’t know what objects are in the world and we don’t know the nature of the objects that we encounter. Our feelings about the objects of our experience are an inalienable part of experience. There is no feelingless experience, or if there is, it doesn’t interest us. Our interest is a measure of the strength of the feelings we invest in our experiences.  We will have done ourselves a great service when we come to a mature understanding of the role of the emotions in cognition, and to an understanding of which emotions are appropriate and which are not.  We could start by recognising that many of the emotions of the rational ego are definitely inappropriate: its vanity, its self-love, its territoriality, its arrogance, its intolerance and so on. We could then counteract them by recognising how emotions such as curiosity, a sense of wonder, a sense of beauty, a love of the natural world, a desire for total honesty and so on are working in the opposite direction and thus may be appropriate. We could characterise the former set of feelings as cognitively damaging since they lead to partisanship, orthodoxy, dogma, conflict, repression and so on; and we could characterise the latter set of passions as cognitively constructive since they have always driven the expansion of our consciousness. Our knowledge depends to a very great extent and essentially upon these constructive emotions. It therefore depends upon factors within us that we do not control, that must be considered to be pure world. Understanding this is clearly vital to any understanding of our knowledge, our world and ourselves; and as to the question of the relative merits of subjectivity and objectivity – the apparent opposition is spurious and the avowed abandonment of the former in favour of the latter, incoherent.

 

THE TROUBLE WITH TRUTH

I met an old acquaintance the other day and I was surprised at how grey and defeated he appeared. He was shrunken, pale and demoralised. It turned out, astonishingly, that his suffering arose from his preoccupation with an abstract concept: the truth. He admitted to me that he was overcome by the discovery that either the truth was unobtainable or if it was obtainable, it was so ghastly as to be best ignored. This individual had been a professor for most of his life and was now discovering that according to new criteria of professional excellence, his work was judged as not up to scratch. He had acquired a string of prestigious degrees from a no less prestigious string of universities. He was a highly cultured man, a linguist and philosopher who had an impressive list of publications to his name. He had devoted his life to improving the cultural awareness of the young, convinced that this awareness would do something positive for mankind as a whole; a worthy and a wordy person. Now, as we sat in the pub drinking water, these ideals – which were derived from his humanist background – appeared to have withered away, to be replaced by a kind of nihilistic moroseness. The reason was fairly simple to see: his truth, which was a matter of words, had begun to wither, too; and since devotion to THE TRUTH, as a collection of statements, is devotion to the ego – i.e. self-love – when the sense of the absolute finality of one’s truth is shaken, the self-love suffers also. I tried to tell him that this was potentially a wholly positive state of affairs; but he was not in a mood to accept such a view.

We talked for awhile and it became apparent that he was much occupied with the fanaticism of religious, suicide-bombing extremists. He saw these people as having discredited, or even destroyed in some fundamental way the whole concept of truth; and his own truth appeared to him to be cast in a similar sickly light. That these people could believe so uncritically such destructive and primitive nonsense and call it ‘the truth’ he found discredited humanity as a whole, for whom truth is a very precious notion. But as we talked it became obvious that this individual, intelligent and cultured though he was, still believed in some ultimate set of sentences in which THE TRUTH about life, the universe and everything would be encapsulated. And this, it seems to me is precisely the problem with our notion of truth. His choice of religious extremists, as those believers in truth who most slandered the very idea of truth, was revealing. The religion concerned still works with the view that there is an absolute truth about the world expressible and expressed in a specific human language and accessible to speakers and readers of that language. Now that degree of literalism in the approach to truth illustrates precisely what is wrong with the whole concept. That a few words in the very fallible sentences of one human language should be invested with such potency says much about the delusions to which humans are prey.

This human obsession with some perfect formula, some magic code, some incantation, some spell or whatever form of words that will open up the entire inner mystery of the universe is as old as language-using primates. For the whole of recorded history and probably for the whole of the unrecorded history of our talking ancestors, human beings have been in search of some right form of words that would give them, firstly, access to knowledge of the inner processes of the world and then, as a consequence of this knowledge, access to control. The inner structure of most science and most religion is just this: the articulation in some language, natural or symbolic, of the supposedly essential principles of reality with a view to controlling it, by technology or by ritual. Some religious believers happen to believe that words in some language, uttered by some prophet, do this job. Some physicists believe that scientific papers written in a mixture of natural language and mathematical formalism will do it. Pagans believed that an incantation or a spell would perform the task. Christians believe that the Bible does it; Moslems believe that the Koran does it. But this needs saying: such belief in the absolute power of language is simple idolatry. How a few sentences in natural language or a few algebraic equations could be expected to sum up the whole of reality is a mystery. An even greater mystery, however, is the resilient human belief that such a thing is possible. The religious throughout the world cling to forms of words and kill each other over them; the scientific imagine that the inner processes of reality will one day be encapsulated in a very big binary number. Both have this conviction: that a number of marks on paper, a number of sounds issuing from the larynx, a number of calculations constituting a mathematical model, a long string of 1s and 0s, will constitute the definitive and final accomplishment of what humanity has been striving to achieve for millennia: namely, to utter the ‘open sesame’ that will admit humanity (or at least the egos that believe such stuff) into the inner sanctum of reality and to the levers of universal power. Such a conception of truth has danced before the human mind for as long as we have been able to speak. It is an illusion. It is a delusion. It is a dangerous obsession that turns us into idiots. And it is time we unmasked it for what it is, as a first step in abandoning it forever. The notion of truth that has obsessed us throughout history is a will o’ the wisp that, if followed, will lead only to discord and disappointment at best, universal conflagration and the termination of the species at the worst. This fusion of truth and power-lust is a work of the devil; and the devil’s name is Ego.

Those who believe in this outdated, linguistic notion of truth will at some point in their lives do one of two things: they will either admit defeat, like my friend, as they see the cacophony of voices, religious, scientific, political, philosophical, that all claim with equal certainty to speak THE TRUTH; or else they will decide that just this form of words, just this theory, just this ‘holy’ book, just this sentence or whatever, is THE TRUTH and they will defend it by all means possible. They will denounce those who do not believe it as liars, cheats, delusional imbeciles, or by the use of any other term in the truth-believer’s arsenal of insults; and the sad tale of human conflict will continue as insults turn into murders.

Bu there is another way and it is this: it is the development of an understanding of the inability of any language, natural, mathematical or whatever, to come to any final truth on any matter. Language is just a bunch of sounds or a bunch of symbols in which we humans couch the traces of certain experiences for their communication to our fellows. We have done this for as long as we have been language-using animals; and for most of that time, as long as the communication was for practical purposes – the hunt, the making of tools, the organisation of groups etc. – language has served us well. Unfortunately, it served us so well, that some of us began to develop immoderate ambitions for it: we developed the notion of THE TRUTH. As long as truth was simply the opposite of the lie, i.e. as long as truth remained in the purely practical sphere of description of concrete facts and its opposite the misrepresentation of those facts, truth was an inoffensive notion. Unfortunately, certain ambitious dreamers and hotheads extended the notion of truth thus established to pronouncements concerning matters of which no-one had any experience at all and claimed to speak of the inner essence of reality. When this happened, the whole idea of truth became a quagmire of potential and actual conflict.

What is the legitimate use of the concept of truth? It is in the descriptions of our experience that allow us to make things, to make tools, to make art, to make machines, to make institutions, to make business deals, or whatever. Truth exists and this is its definition: IT IS WHAT WE MAKE. It is provisional and subject to development and improvement, just like our technology. Of course, misrepresentation is possible in these spheres, too. Lies can serve practical ends, too. But the disputes that arise in this way are amenable to resolution: if the theory works, it can be regarded as true until a better model is developed. This is a pragmatic conception of truth and the criterion of its truthfulness is the extent to which a form of words or symbols representing experience functions in a practically successful manner: technology is developed, institutions are established and improved, law is written and modified, trade is conducted and the economy regulated and so on. Truth has exclusively practical value, unless – and this is the big proviso – unless it be subjective truth about which nothing will be said here.

What is the illegitimate use of truth? It is in the pronouncement of so-called ‘absolute’ verities about the universe and reality as a whole. The phrase ‘absolute truth’ is an oxymoron and can be used with reference to knowledge of the world only by a moron. When anyone claims to be articulating ‘absolute truth’ about the inner essence of any reality that we can in any way grasp, such a person is both a fool and a liar. He or she is a liar simply because the wholly legitimate pragmatic notion of truth as a provisional, modifiable form of words possessing practical usefulness has been turned into its opposite: an immutable encapsulation of the absolutely veracious and definitive account of the heart of reality. There is no such thing as this sort of illusory ‘truth’ accessible to human language of any sort; and for that reason, it is a lie.

Why then, if such a conception of truth is equivalent to its opposite do we as a species continue to be obsessed by it and continue to kill each other in its name? The answer to this question is found in the powerfully delusional nature of the human ego. The ego’s sense of its own existence is bound up with what it believes about the world. Since the ego’s inner nature is the wish to live for ever and exercise absolute control over the world, it will elevate any belief that gives it a sense of identity into an absolute theory concerning the universe that seems – even by symbolic means – to do this job. Since the ego, moreover, is closely connected with the flight and fight mechanisms of the mammalian brain, its pet theories will lead it either to retreat into mental reservation and untrustworthiness or else to open warfare with those defenders of an alternative truth whom it considers to be its mortal enemies. The ego is a self-adoring mechanism; its principal emotion where its truth is concerned, therefore, is a sense of rhapsodic camaraderie with those who share its truth, on the one hand, and a sense of enraged offense at the existence of those who defend another truth. The ego that believes in definitive truth will therefore strive to create ever greater groups of co-believers in order to be able to take flight into the protection of the herd; or else it will express violent hatred for and opposition to those who do not believe and strive by all means to destroy them.

How can we wean people from their devotion to such ruinous notions of truth?

The answer to this is ‘by critical education’. Criticism of the very concept of ‘truth’ should be at the heart of the educational process. Truth exists; but it is not what many people think it is. Knowledge likewise. There is no such thing as sacred, inviolable, immutable, truth; nor is there ultimate knowledge. Most believers in such truth suffer from some sort of possession, possession by words. They also suffer from purblindness. This might be the purblindness of the Moslem or Christian fanatic; or it might be the purblindness of the autistic defender of a scientific orthodoxy. ‘Purblindness’ here means the inability to break out of the charmed circle of a certain form of words, a certain string of mathematical reasoning. But let us be quite clear: any formula, any sentence, any theory, any doctrine is never what it claims to represent. This should be obvious; but it is not. Those who believe doctrines expressed in words as if they were absolute truth suffer from the delusion that the theory can replace the reality. Thus the first stage in ridding humanity of the scourge of that kind of metaphysical belief that becomes an instrument of oppression is to educate people in the artificiality of theory and the weakness of its powers of representation. The holiest religion, the most exact scientific hypothesis – both of these can never be more than mere metaphor, mere metaphysical stammering. To invest them with the aura of absolute truth is an indication of a very primitive state of ego-consciousness. The next stage, therefore, in weaning people from their devotion to such truth is the abolition of the ego.

It is one of the greatest and most persistent delusions of the ego to believe that humans posses ‘absolute truth’. The ego is a deluded mental structure that worships itself and that is convinced of its own absolute value, that wishes more than any other thing for its own immortality and divine power. To come to the state of mind in which the ego is seen for what it is – the unwarranted projection into the representative sophistication of the cerebral cortex of primitive fight and flight emotions that belong in the limbic system – is the first stage on the road to a new conception of the human self. Humans need to become aware of the gigantic distortions that take place when the projection of such phantoms into the realm of symbols occurs. One merely has to observe the ego’s phantoms in order for them to evaporate. The egoless structure of the human self involves the awareness, on the part of the individual, that he or she is not some split-off atomic unit of humanity, but an aspect of the whole biological process that is humanity, an aspect of the whole process that is life on this earth, an aspect of the universal process of evolution and change that is the universe. We are no more separate from the universe than an eddy is separate from the river. We are intimately connected to the entire movement of life on earth and, in the wider context, to the process of universal seamless change. There is no definitive truth expressible in human language; and there is no ego that needs to defend it. Once the ego is seen for what it is – a delusion – then its pet notion of truth goes along with it. Truth is a matter of immediately useful belief that allows us to achieve practical goals; and any attempt to characterise it as something ‘higher’, something ‘absolute’ is a device of the ego to achieve its delusory goals of world domination and control. Merely being aware of the delusions of the ego and the dependence of the ego on ‘truth’ for its delusions leads to a withering of the ego and to a consequent shrivelling up of its crackpot notion of truth.

So what would we be left with if we abandoned the ego and its darling, THE TRUTH? We would be left with the language machines that we have always used to enable us to manipulate our world, for such a use of language is an integral part of the success of the species. But all other uses of language – for example to express our emotions at the nature of life and of existence in the world as a whole – would be left to poetry. Poetry would continue to satisfy our metaphysical urges; but we would not dream of killing those who use a different poetry. When one considers the inter-communal violence that still sullies our history, one is struck by the fact that precisely this is happening: people are killing each other because of poetic notions. This was very clear in the use made of poetry in the Balkan wars of the nineties. Of course there are economic factors involved to enflame the situation. But these are practical matters that can be sorted out by discussion. The essential problem is the attachment of the ego to certain words.

The ego with its addiction to its precious ‘truth’ is the bugbear of history and responsible for the entire dismal phenomenon of man’s inhumanity to man. Abolish this villain of history and humanity would be well on the road to solving its most intractable problems. Human life that is unclouded by rigid, ego-bolstered belief can be creative and harmonious. Of course creative living in the timeless present is a state that is achieved by passing through all the delusions of truth in language. That’s what has happened in our history. So language, and its various formulations of the notion of truth, is vital to the process of increasing consciousness by which the human species passes from mere consciousness to self-consciousness; and ego-consciousness seems to be an inevitable, if regrettable, part of the process. Once the ego is put in its place, however, and seen for the delusion it is, all truth becomes the provisional structure it is in essence, its value being that of its usefulness. Truth is a ladder to understanding; it is not the understanding itself. Any understanding that is based upon the holiness or the orthodoxy of a formula or a form of words is understanding that is on the way to disaster. Essential understanding is wordless. The essence of human understanding is a wordless awareness, derived from perpetual discovery, that the individual self is an integral part of the entire movement of the cosmos; and this awareness is not a function of language though it may grow out of language-use. It is as extra-linguistic as the irreducible sense of self and as incommunicable as this. But this awareness is the heart of an activity that is as creative as the rest of reality, for it is an integral part of reality and not a split-off strident, deluded, time-bound, truth-obsessed ego.

The self, because it is not tied to a form of words that needs defending, can live its creativity, can indeed be created in exactly the same manner in which the world as a whole is continuously and uninterruptedly being created. The ego is uncreative because it is rigid and sclerous. Until the self achieves dominance in human life and affairs and as long as the ego continues to rule, the problems of the human race, its entirely soluble problems, will continue to haunt us.

Destroy the ego, establish the creative self: there’s a plan for a less pain-filled consciousness and a less conflict-filled future. I tried to explain all this to my friend; but I failed to convince him.

DARWINISM AND THE TWO-FINGERED SALUTE

 

The two-hundredth anniversary of the birth of Charles Darwin provoked a large number of programmes both on the radio and on the television, and press articles devoted to the work of the great man, his life, times, family life, bereavement, tragedy, illness, scientific work and general outlook. As one of the towering figures of nineteenth century science, such devotion is entirely justified. By all reports Darwin was not only a great scientist but also a very admirable human being; and since these two things do not necessarily or even frequently correspond, we have to be grateful that one of the landmark thinkers of the nineteenth century, whose influence has continued strongly through the twentieth and now into the twenty-first, was a man of humanity and wisdom. But it should not be forgotten that Darwin was a man of his time; and this fact shaped his theory. What strikes one in all of the tributes and indeed in almost everything that is written on him is the hagiographic veneration of the figure and the pious reverence with which the unassailable veracity of his findings is referred to. Darwin has become a secular saint and his status is protected by that aura of sanctity that protects religious figures from criticism in the minds of the believer. It cannot be stressed too strongly that Darwin for all the seminal power of his work was a theoretician whose mind was imbued with Victorian sentimentality.

What do I mean by this? What I mean is that Victorian sentimentality, the lachrymose emphasis on the tragedy of suffering and loss is based upon the growing awareness in the nineteenth among the general public that the God of the European Middle Ages, the anthropomorphic, paternally providential God perhaps did not, and could not, exist. Victorian sentimentality arises from this loss of the Father in Heaven figure. It is the first reaction to our sense of orphanhood; and Darwin was thoroughly suffused by it. The disappearance of the father figure behind the universe is dramatised in a uniquely powerful manner by the success of the theory of natural selection and by the zeal with which people cling to it as if to revealed truth. Why is this important? It is important because it is not what many of those who are now most vociferous in their lionisation of Darwin think it is. The loss of the Father God is a sign of the end of the childhood of the Western European psyche. But far from being the victory for some sort of humanistic atheism, it is simply a stage in the evolution of our understanding of the divine. Those atheists who see some kind of definitive victory, some sort of definitive negative truth in Darwin’s theory behave as they do – as triumphalist ideologues – only because they are deeply imbued with the same Victorian sentimentality as their mentor. So what do I understand by Victorian sentimentality?

As already pointed out, the origin of the Victorian obsession with death and loss and with the human experience of the contrast between human warmth and the brutality of nature, arises from a sense of disappointment at the insight that the Father God cannot exist. Why can he not exist? He can not exist for essentially moral – not scientific – reasons: if He were to exist, He would be an evil, malicious, sadistic Father and that would be worse than no Father at all. The Victorian society was the first society that, as a whole, began to realise that the universe had changed for good and that many of the old comforting certainties that had sustained humanity for centuries had suddenly and brutally been found wanting. They began to realise that the circumstances of life on earth, both in the animal kingdom and in human society, could never be expressive of the concern of a fatherly deity. Karl Marx did for human society what Darwin did for nature: the father was found to be a figure of human families and not an essential principle behind the phenomena that we observed upon the planet that was our home. But is this such a staggering insight? The answer is ‘yes’, because the Heavenly Father was believed in so implicitly for so long, the perception that he could not be there was profoundly unsettling. But was the belief in the Father God ever reasonable? The answer is ‘no’; but that does not means that the belief was meaningless. It served a very valuable purpose. The Heavenly Father disappeared because humanity grew out of Him. So it is all the more surprising that the modern day atheists are still grappling in their atheism with the same Father God as the Victorians. If one studies the writings of Richard Dawkins, the entire thrust of his arguments depend on two theses: 1) Darwinism is a theory that accurately interprets the facts and require no divine intervention to explain the origin of species; and 2) that since Darwinism is in this sense ‘true’, then God cannot exist (or it is highly probably that God does not exist). Now the logic of this argument is of course very shaky and depends upon two unconnected elements: firstly there is a scientific case not only for the well-foundedness, but also for the definitiveness of the theory of Darwinism; and secondly there is a metaphysical thesis based on the science concerning the nature of reality as a whole that strives to establish the negative thesis of God’s non-existence. Let us say right away, that the logic proves nothing, simply because 1) though the theory of Darwinism is very credible, it does not and in principle can not rule out the possibility of other factors’ being involved in the evolution of species apart from random mutations and selective pressure (such empirical theories are never proven but merely corroborated and improved as the evidence mounts); and 2) it is impossible on the basis of this theory to demonstrate an absolute negative concerning the nature of the universe (God’s alleged non-existence). One has to ask, then, why the argument, if it is so shaky, convinces so many people. The answer to this is again to be found in the power of Victorian sentimentality. Let us take a closer look at this.

Nietzsche was the first great Victorian (even though he was German) to announce to the world, ‘God is dead’. Now he meant something very precise by this. He meant that the anthropomorphic deity who guaranteed the eternal justice of the universe and the providential care of human beings as allowed for in the mixture of Platonism and Christianity, that had governed the West for two millennia almost, could no longer be believed in. He could no longer be believed in precisely because an anthropomorphic deity operates according to human conceptions of justice, beauty, kindness, beneficence etc. etc. and the natural world seemed not to incarnate those human values. Nature ‘red in tooth and claw’ showed none of the features of the ‘lovingkindness’ of the anthropomorphic deity because it was cruel, wasteful, brutal and appeared not to care a fig for human sensibilities and values. So the slogan ‘God is dead’ meant, ‘there is no human set of values and sensibilities governing the course of nature’. What Nietzsche put in the place of the old benign anthropomorphic God was a blind ‘Will to Power’ that ruthlessly, but with volcanic creativity, produced creatures locked in perpetual struggle to maximise their power over the environment and over their competitors.

The late nineteenth century was imbued with the conclusions of Enlightenment thinkers who had demonstrated to their own satisfaction that the Father God of the dominant religions of the West (monotheism of the Christian and Jewish kind) could no longer be retained. In the wake of this discovery there arose an entire culture of dramatic pathos that fostered a kind of adolescent bravado on the part of some of those who believed it. The pathos pointed out that since the Father God no longer existed, we were now on our own; and the bravado asserted that since we were on our own we didn’t need God anyway, we could cheerfully insult Him and enjoy relying only on ourselves. The great political, scientific and philosophical  thinkers of the nineteenth century  and even the religious thinkers were preoccupied with the non-existence of the providential God of monotheism. They were almost one in giving voice in some form or another to either, or both of the pathos and the bravado; but the emotional component varied: some were delighted and greeted the discomfiture of the Church with glee, others were elegiac and almost regretful that man no longer had a benign parent in the sky. Darwin was probably one of the latter and his theory arose in this environment. What is really surprising is that today’s Darwin-enthusiasts, who are mostly in to the bravado, still warm to the basic issues of that nineteenth century debate as if there were somehow fundamental principles of thought involved and not just a powerful cultural prejudice.

Dawkins was responsible for the recent advertising campaign on London buses with its catchy slogan GOD PROBABLY DOES NOT EXIST. His books are full of the victorious gleeful reaction to the discoveries of the nineteenth century, but they remain intrinsically nineteenth century nevertheless. The God in whom Dawkins champions unbelief is the anthropomorphic God of nineteenth century monotheists. All of his arguments derived from the science of biology adduce the purely biological evidence and then in essence assert, ‘if this evidence is true, then the universe and specifically the natural world here on earth cannot be governed by principles such as justice, kindness, beneficence and so on that characterise an anthropomorphic God. At no point does Dawkins pause to ask himself this question: ‘why should the universe and the biosphere of this planet be governed by human values?’ He seems to think that to have demonstrated that the biosphere and specifically the process of evolution are not governed by conceptions of human value and comfort means that he has demonstrated the non-existence of God. That so intelligent a man should fall for such a bad argument is surprising; but it is of a piece with the bad arguments of the Victorians and its force derives again, not from the logic or the evidence of the case, but from the powerful sentimental appeal in the thesis that the Father God does not govern the universe. Let us be quite clear, the arguments are metaphysical and not scientific, even though they dress themselves up as scientific prose. Dawkins may to his own satisfaction have demonstrated the non-existence of the monotheistic anthropomorphic God; but he has demonstrated the non-existence of a phantom who does not in fact deserve to exist, or who ceased to exist at least a century ago as man began to grow up. The slogan on the London buses should read FATHER CHRISTMAS PROBABLY DOES NOT EXIST. Is that such a staggering discovery?

The essential point in all this is the manner in which the notion of ‘intelligence’ is understood. The sentimentality of the Victorians was rooted in the discovery that cosy, cuddly human values did not govern the universe and that the human intelligence did not guide its processes. That we should have ever believed that human values did govern the processes of nature is surprising to say the least, but then perhaps not so surprising after all. Why should human values and human rationality govern anything except human affairs? The answer to this lies in the deep-rooted anthropomorphism of all human thought. We understand by projection. We have for millennia been extricating ourselves from an obvious anthropomorphism – the very human deities of religion being only the most obvious of the kind – that continues to haunt us in all sorts of disguises. The fact that we expect human language to be able to grasp the fundamental nature of reality and express this in propositions is a more subtle sort of anthropomorphism. Even the fact that we believe in the ability of mathematics – a creation of the human mind – to express the fundamental verities of the universe is a species of anthropomorphism. When it comes down to it, even the touching expectation that the human mind is equipped to understand the whole of reality is a sort of anthropomorphism. Once the anthropomorphic projections are understood, they can be forgiven, except by adolescent minds that still take them seriously. Dawkins is such a one and his crass slogan on the London buses is no more than an immature two-fingered salute to the vicar.

 But what does the demonstration of the non-existence of the monotheistic God prove? To believe that the demonstration of the non-existence of the anthropomorphic God in nature demonstrates the non-existence in principle of every possible deity is simply bone-headed. Human intelligence certainly does not govern the universe. Anyone with half an eye and very little intelligence can see that. But equally, that there are all kinds of intelligence in nature is also obvious. That there could be a non-human intelligence guiding the processes of nature and the course of evolution is a possibility that seems never to have occurred to Dawkins and his ilk, mainly because they assume that ‘intelligent’ means ‘humanly intelligent’. They all profess to a sense of wonder before the marvellous productions of the natural world, a sense of the almost miraculous adaptedness of organisms not only to their environment but also to other organisms; and this sense of wonder is not only akin to religious awe, but also expressive of the sense that the mind so awed does not completely understand what it is contemplating, but assents to its intelligence its cleverness, its subtlety and so on. What is completely understood ceases to interest us. What is part understood we grasp by metaphysics. Of course scientists such as Dawkins, wedded as they are to the metaphysics of eliminative materialism and the negative demonstrations associated with it, always fall back on the principle of chance to explain those things they do not fully understand. But an appeal to chance is not in any sense a means of understanding a situation, even though the chances of a given concrete situation maybe  mathematically computable. An appeal to chance on the universal scale, is simply an expression of metaphysical pseudo-understanding, i.e. no understanding at all but simply the replacement of intelligence by what is explicitly not intelligence – intelligence understood in all these cases, it must be stressed, only as human intelligence. To our perception, there is perhaps no difference between chance and non-human intelligence. But the appeal to purely random factors in situations where our wonder is excited is probably less rational than an appeal to a non-human intelligence. It is purely negative, a negative reaction to the sentimentality of belief in the Father God.

So once one has ditched Victorian sentimentality in the wake of the demise of the monotheistic God, one does not have to lurch to the opposite extreme of triumphantly announcing that no deity of any sort can have any presence in any possible universe. One can rationally concede that the course of nature in general and the process of evolution in particular could well be guided by a non-human intelligence, that can be understood by analogy with human intelligence after its productions have been examined and found to be unaccountably marvellous. Once one has ditched the infantile notion of a Father Christmas God presiding benignly in accordance with his essentially human attributes over the course of nature, it is quite possible to recognise that intelligence superior to ours, but of which ours is a reflection, may well govern the natural order. It was only infantilism in the first place that encouraged the belief that human intelligence and human values govern the universe; and the abandonment of these infantile fantasies enables us to grow up as humans without sinking into the pathos and bravado of the atheists who are no more than disbelievers in an outmoded and now unconvincing figment.

MATHEMATICS

... the map is not the territory...(Alfred Korzybski)

 

One day, Alfred Korzybski the inventor of the theory of general semantics was giving a lecture to a group of students, and he suddenly interrupted the lesson in order to retrieve a packet of biscuits, wrapped in white paper, from his briefcase. He muttered that he just had to eat something, and he asked the students on the seats in the front row, if they would also like a biscuit. A few students took a biscuit. “Nice biscuit, don't you think”, said Korzybski, while he took a second one. The students were chewing vigorously. Then he tore the white paper from the biscuits, in order to reveal the original packaging. On it was a big picture of a dog's head and the words “Dog Cookies”. The students looked at the package, and were shocked. Two of them wanted to throw up, put their hands in front of their mouths, and ran out of the lecture hall to the toilet. “You see, ladies and gentlemen”, Korzybski remarked, “I have just demonstrated that people don't just eat food, but also words, and that the taste of the former is often outdone by the taste of the latter.” Apparently his prank aimed to illustrate how some human suffering originates from the confusion or conflation of linguistic representations of reality and reality itself.

For Bohm this confusion was not limited to words but extended also to mathematical models.  He referred to Korzybski’s thesis that maths is a limited linguistic scheme and that necessarily what we say about a thing in this language is always less, than the thing itself, the thing is always different from what we say, always more than what we say. If reality stopped exhibiting features that are not in our thought, then the distinction between reality and our thought would cease, but the notion of objective reality, which proposes that reality has an existence apart from us precludes that possibility. Despite the declarations of some physicists, mathematics is an abstract system that cannot cover the whole of reality. Different kinds of thought and different kinds of abstraction may give us a better understanding of reality than the exclusively mathematical type. To borrow David Peat’s image, what Bohm was talking about is reminiscent of René Magritte’s painting Ceci n’est pas une Pipe (a painting designed to question our tendency to confuse reality and representation) insofar as he believed that every theory of the universe should have the caption ceci n’est pas un univers. It is not a universe because it is just a model. There is no possibility that a model of the universe could equal or replace the universe: model and reality are eternally distinct. And this disjunction, moreover, goes for every use of a mathematical model whether in science, economics or whatever. It almost seems fatuous to make these points, but they are made because the confusion of model and reality is an ever-present danger in our ‘scientific’ approach to our affairs.

These words are being written as one of the worst recessions in modern history begins to bite and begins to look like a 1930s-style Depression. It is a sobering fact that this economic crash was caused, in major part, by the rash confidence of investment bankers who were using exotic mathematical models derived from rocket-science. These so-called ‘masters of the universe’ were using their models to construct exotic financial instruments for the creation of wealth out of its opposites, debt and poverty. The mathematical models proved to be all too fallible precisely because they aroused the confidence of investors in wholly illusory possibilities of risk-free speculation. As these mathematical models were applied more and more and on a large scale by computers without the intervention of human beings, their inadequacies – the things they left out – compounded  their damaging effects and the result was a near total collapse of the world’s financial system. This is just one example of the possible disasters lurking behind the seductions of bewitching  mathematical models. There are many others, but the point is this: in the urge to mathematise reality as far as possible and in a culture for which mathematics is almost the only intellectual authority, the dangers are evident: they are dangers of a wholly misleading precision fostering decisions made on the basis of imperfect information. The problems of the planet are in large part caused by this kind of decision. More of the same kinds of decision can hardly be expected to help. I what follows a modest attempt will be made to put our passion for mathematical reasoning in its place.

Those with a mathematical bent should not expect to find any interesting mathematics here, for there will be none; and those who are allergic to mathematical squiggles need not worry, for the same reason. The point here is simply to show firstly, that everyone is a mathematician, just as everyone is a philosopher (all things being equal), it’s simply a matter of following the natural bent of the mind; and secondly that our dependence upon mathematics indicates in many ways that it is almost an essential image of fallible human understanding as such. The philosophically interesting issue here is why this should be the case. Why should we owe so much to mathematics?

 

Models and Pictures: Our Urge to ‘Represent’

 

Whenever we say of something that it is ‘round’ or ‘square’, or whenever we say of a group of some things that there are ‘a couple’ or ‘one or two’ of them, we are showing our everyday dependence upon mathematical modes of thought. We do it from our very earliest age. Little children, when they first start to draw trees or people, do so in a very stylised manner which is substantially mathematical, involving the simple ‘things’ of mathematics, points and lines. They represent a face as a circle with three or four points in it. They represent a tree as two vertical parallel lines with a circle on top – a kind of lollipop. They represent a human being as an inverted ‘V’ with a straight line rising from its apex to a circle and a horizontal line drawn across the vertical one – the ubiquitous ‘stick’-person. The resemblance between these drawings and what they are supposed to represent is not very great, but they are instantly recognisable, nevertheless; and no-one hesitates to use the word ‘is’ in statements such as that is a man’ whereas it is no more than a few lines. We are clearly simplifying the resemblance between the things we see before us to a very great extent, reducing things that are very complex shapes to the simplest of geometrical patterns. We have been doing this sort of thing for a long time as the abstract patterns of ancient rock art show, but why we do it is in itself a very deep and interesting question. Answering it would give us insight into the origins of mathematics.

We might ask, ‘where does mathematics come from?’ One ‘obvious’ answer is, ‘from our minds.’ That doesn’t get us very far. But it’s a start. Another possible answer is ‘from the world’; but no-one has ever found an equation lying under a hedge. If mathematics does come from our minds, then we are naturally disposed to count similar things, things that appear to us to exist in numbers greater than one. The repetition of similar appendages of our own bodies could well have been among the first similar things we spotted in early childhood. The realisation that we possess the same number of fingers on our hands as we do toes on our feet must have been an illuminating discovery to our early ancestors. The fact that the word ‘digit’ means both ‘number’ and ‘finger’ is revealing and there is obviously a connection between our fingers and our use of a number system to the base ten. We must have developed the practical need for simple geometrical and numerical ideas as soon as we began to cultivate land, keep animals, make tools and construct shelter; but the most obvious origin of the use we make of more complex geometrical forms is probably our fascination with the sky and the objects we find in it both during the day and at night.

The sun and the moon are discs that move in apparently repetitive, curved paths across the sky with great regularity, with a periodicity that invites us to count. The ‘stars’ do the same, though some of them are not stars but planets and do more complicated things than simply describe arcs. The sun and the moon themselves are the most prominent natural circles in our world. At all events, one of the first insights of the earliest major civilisations was mathematical abstraction from the regular movements of heavenly bodies and the imposition of the idea of circles on their movement, in a directly analogous way to that in which children represent faces as disks and trees as lollipops. The earliest astronomers, simply by observation, decided that the heavens are organised on the basis of circles: when one completes the visible arc of the sun, one must conclude that wherever it goes when it disappears, the simplest explanation is that it moves in a circle. Ditto for the moon, and the same then goes for the stars, or at least most of them.

Thus it became ‘obvious’ to these early observers that the entire universe was organised on the basis of things moving in circles, except the earth which obviously did not move. It’s not surprising therefore, that the first comprehensive model of the universe was that of a spherical set-up with concentric spheres containing all the various bodies we espy in the sky above our heads. For the Ancient Greeks, the fact that the heavenly bodies moved in circles, in a perfectly orderly manner, and didn’t just tumble to the ground like earthly objects, proved that they were made of more noble stuff than the things on earth. Now we know that these early astronomers were ‘wrong’, that the heavenly bodies do not move in perfect circles, and that some of the circular movements are only apparent. Moreover, we know that the ‘falling’ of earthly bodies is directly similar to the ‘falling’ of heavenly bodies. But were the ancients so wrong? Their insight, that the world could be modelled by means of geometrical shapes and arithmetical concepts was the important thing and successive models of the universe have largely become more ‘right’ because they have refined the original insights of those pioneers, replacing circles with ellipses, for example, expressing geometrical notions algebraically, showing which bodies appear to move, relative to a particular frame, and which do not, and so on.

The essential character of the process of understanding in this way, however, has always remained the same. It has to do with comparison. We not only compare natural objects and events to each other and to mathematical abstractions thought to capture their similarities, we also compare them to things that we invent and that are not real in the sense that objects are real, but to which we attribute a higher sort of reality; and then we compare natural events and processes to these things – as in myths, for example, and in mathematical models. What precisely is going on in all this? Why do we tend to attribute more reality to the repetitions of our abstractions than to what we actually experience as, for example, when we consider the abstract, mathematical ‘laws of nature’ as having more reality than the changing events they govern? This is a complex question, but it certainly has to do with the ‘reliability’ of mathematical objects: they are predictable and one knows that two mathematical abstractions that are identical are truly identical without any possibility of hidden differences. This dual problem of apparent similarity and hidden difference is the great bugbear of our cognitive approach to the world. At least what is on either side of the ‘=’ sign in an equation is really the same and not just similar.

What is going on in the eternal tendency of our imagination to try and compare different things and to say that this is ‘like’ that? In our comparisons, we get the impression that we have latched on to some invariant feature of different processes, some unchanging feature of the world. Most frequently we even drop the ‘like’ and just say, “this is that,” – just as a child, pointing to its lollipop may say, “this is a tree.” Our fundamental desire to understand is closely related to our desire to find natural correspondences to find occasions for detecting essential similarities between quite disparate items of our experience. In mythology, we likened the thunder of the storm to the bellowing of a bull, we likened the wind to the chords of a harp, we likened the curling rollers that crash on the beach to the charging chariots of war, we likened the constellations of the night sky to the protagonists of our legends and so on. But we became dissatisfied by these likenesses: though there was perhaps a satisfying moral truth in many mythologems, there was always something deeply unsatisfying in the clear differences involved in the specific comparison. The profound similarities in the comparisons were insufficient to keep us happy. We were always able to see where our comparisons succeeded and where they failed. In our geometrical and arithmetical analogies, however, we seemed to be able to see directly where the comparison succeeded; and the failure (e.g. the lack of a moral dimension to the comparison) was less important. In conceiving of the movement of the heavenly bodies as circles, we could see directly that we were on to something deep.

The most satisfying feature of these comparisons more geometrico, however, was the precision, rigour and sense of control that we were able to bring to our analogies. Once we got the habit of inventing abstractions, we began to get interested in the internal properties of these abstractions themselves in the patterns that our imagination espied within them. We were able to ‘prove’ certain things by demonstrating that the mathematics gave rise to constant relations, ‘necessary truths’, as some optimists called them, that were true simply by virtue of our thinking about them. We didn’t have to do the legwork and go scouting around for the evidence; we simply extracted it by thought. The necessary truths were obviously true in an irrefutable sense. They just ‘had to’ be true; and if people denied this they contradicted themselves and demonstrated their ignorance. The properties of a circle were demonstrable simply by pure reflection on what was obvious and we did not have to adduce examples to make the case. The fact that many different items could be seen as moving in circles, for example, and the fact that circles could be demonstrated mathematically to have the same properties in all possible circumstances gave us a powerful tool for seeing regularities in the processes of the world around us.

By comparing natural phenomena with mathematical models, we invented a most productive method of talking about the ‘likenesses’ between various phenomena and their common ‘likeness’ to our mathematical conceptions. The reason why this kind of comparison was so much more satisfying than the mythological comparisons was that we could demonstrate with convincing rigour the exactitude of our conception without any fuzzy bits hanging out. The fuzzy bits were just chopped off. And moreover, we could remain in complete control of the images. The mathematics worked out with complete irrefutability and anyone could see the force of the analogy between the observed phenomenon and the mathematical model. The mathematical model could therefore be put in place of the observed phenomenon and more mathematical deductions could be made from the model in order to come to conclusions about the universe as a whole. We could begin to make predictions about devices that we made – such as the antikythera mechanism and the later mechanical timepieces that in many senses were miniature universes working on the principle of circular movement – and once we had mastered that trick, not only was our technological Pandora’s Box open, the delicious dream of controlling our environment by means of abstract models seemed close to realisation.

Once we had developed the skill of modelling reality in mathematics, we were off on the passionate quest that we call ‘precise science’ and the modern world of amazing technology had begun. But the method that has permitted this modern world certainly goes back at least to the ancient civilisations of Babylon and Greece and probably further back to a long gone civilisation of the Indian sub-continent. The essence of the method is closely similar to the child’s modelling of complicated items of its experience, faces as disks, trees as lollipops, mountains as triangles, houses as cubes and so on, with simple geometrical shapes. The method proved fantastically successful in classical physics and is still operating, though with far more exotic geometries, in the world of quantum physics, where the mathematics involved is vastly more complicated than the simple plane and solid geometry of Euclid.

The really interesting questions concerning our use of mathematical models are questions such as these: 1) why do we have this urge to compare different things and to say ‘x is like y’ or even ‘x is y’?  2) why do we instantly reach for mathematical concepts and models in our urge to compare? 3) since the mathematics by means of which we refine our conceptions of reality is thought up, in many cases, for its own sake and long before the observations to which we find we can apply it, where does it originate?

There is a deep issue here that concerns the very nature of our intellect and our irresistible urge to apply our minds to our environment in more than routine ways. The animals around us do incredibly clever things and show staggering abilities. But they are to a large extent both limited in and to a definite range of behaviour and cannot adapt outside of the environment in which their skills have sense. We, by contrast, have fewer such pre-programmed patterns of behaviour and apply our eternal tendency to find correspondences and similarities to every aspect of our experience. In this we discover the regularities of our natural environment, become able to predict its behaviour and thereby acquire the ability to manipulate it. By means of our comparisons we become masters of our environment in a broader sense than is available to any of the other animals with which we share the planet. Yet this ability seems capable both of setting us apart from nature and also of establishing deeper links between us and it than could ever have been provided by a purely instinctive life.

But where does this ability come from that we possess not only to compare the regularities of the environment with mathematical models, but also to create entirely new mathematics and new models that both follow and drive the expanding range of our experience?

Why mathematical models? We can simply throw up our hands and say, ‘well, our minds just work like that!’ and give up the urge to understand. Philosophy, however, wishes to understand everything, even our methods of understanding. The puzzle gets even deeper when you realise that mathematics is almost miraculously successful at modelling the processes of the universe that we can experience and also in uncovering some we cannot – at least in physics which describes the behaviour of matter. There is a deep truth in our discovery of mathematical regularities in the universe that we have not yet got to the bottom of. The physicist Dirac believed that by following the principle of what he called ‘beauty’ in our equations, we could be confident that we were moving towards deeper understanding of the world. Mathematics is by far the best method of describing the physical processes of the world, since these processes seem in themselves, at least to the extent that we can observe them, to work in many ways on deep mathematical principles. We ought to be cautious of such a perfect fit between the world and our minds, however, and at least entertain the idea that we might only be seeing what we are programmed to see. Our tendency to interpret our experience in accordance to what we wish to find in it is notorious. The chief disadvantage with our mathematical way of understanding is that often we confuse the precision and rigour of the maths, that we happen to be using, with the processes that we are observing. We have, as observed, a deep tendency to confuse the model with the reality, description with thing described, midworld with foreworld. Once we realise that we have this tendency, however, we are liberated anew to generate yet more mathematical models. The way in which we do this is profoundly wonderful and clear demonstration that our minds are in some sense always above and beyond any formal language that we may use to express our thoughts. Our minds are in some almost miraculous way superior to all the forms in which we think. Herein lies a conundrum of the most fascinating kind.

The origin of mathematics would seem to be both in the enumeration of similar items and in the exploration of shapes and solids by the infant, in the discovery of the relationships and differences between open, closed disjoint and intersecting figures, between squares, triangles and circles. It would seem to lie in the detection of patterns of resemblance between 3D objects. This is not an abstract intellectual process, but a process of active sensory experience and physical, muscular discovery. The manipulation of objects, internal visualisations, the ability to distinguish between various types of sizes, areas, volumes etc. involves not abstract reasoning, at the outset, but much more simple physical sensation. The perception of an object is almost one with the intention to grasp and manipulate it. Imagine the mathematical principles encoded in the motor skills of the gibbon that flings itself with such astonishing athletic ability and precision through the trees, swinging at enormous speed through the branches and rarely making mistakes in its estimation of trajectory and force of launch or distance of landing sites. There is no point in saying that maths has no role to play in a gibbon’s gymnastic skill because that forces one to say something like, ‘that’s just what gibbons do, it’s instinct’ or some such lame nonsense. That fact is, if we wanted to construct a gibbon or even to reverse-engineer a real one, we would have a very complicated mathematical task on our hands. Imagine then the gibbon’s discovering intellectually through the invention of an abstract mathematical formalism these depths of mathematical potential in its own brain.

Something analogous to such a discovery must have gone on in the development of mathematics from the simple activities of our prehistoric forefathers: the counting of animals and measuring areas of fields, of quantities of grain and the best dimensions of tools. The discovery of mathematics extends conscious thought down through the musculature of the body and beyond into the very structure of matter itself. This may be the origin of the celebrated mathematical ‘intuition’ that is at the heart of all truly creative mathematical thinking. The algorithmic, formalised part of mathematical thought is only its public, consensual part. The body of knowledge known as ‘mathematics’ is no more than the frozen traces of countless spasms of creative frenzy that still continue alongside the discipline unabated. The real work of generating mathematical insight goes on in the conscious and unconscious uncovering of principles that are encoded in our bodies, in the memory-traces of the interaction of these bodies with the material world and in the structure of the stuff out of which both we and the world are made. Perhaps situating the origin of maths vaguely in our minds is totally misguided: perhaps maths is inherent in the structure of the physical world of which our bodies and our brains are a part. Here again, the spurious distinction between subject and object is abolished.

The self-similarity of the universe from top to bottom guarantees that mathematical principles of fundamental similarity and applicability will be found at all levels. Small wonder then that the mathematical principles that we invent are applicable to all parts of the world of our experience. Like the self-similarity (with rich, subtle differences) of all levels of a piece of fractal geometry, the universe must give evidence of its fundamental unity in the reappearance of similar mathematical regularities in systems of great diversity, from sub-atomic particles to the behaviour of large numbers of people.  The science of chaos-theory has taken mathematics beyond the world of three dimensions as boldly as it has taken the discovery of mathematics beyond the deductions of formal reasoning into realms of empirical investigation. It may be that now, with the strange non-Euclidean and fractal geometries, mathematics has finally been cut loose from our experience of the 3D world and our weddedness to it. It may be that now mathematics, thus cut loose will open up vistas of possibility unimagined in the past. If this is so, then our mathematical ability would seem to be an ability that takes us in principle beyond the limitations of the body, not only by prosthetically extending the body, but also by transforming the mind and enabling us to overcome the mental habits of millennia of our forefathers. This suggests that there is some agency in the mind that from a vantage beyond the physical is constantly transforming and extending us and taking us beyond the evidence of our senses. What then could be going on?

 

The Limits of Our Mathematical Thinking

 

There is a very deep connection between 1) the human tendency to go beyond the evidence in any theory of the world, 2) the so-called mind-body problem, and 3) the famous Incompleteness Theorems of Kurt Gödel.

Obviously, as one convinced of the imperfections of language and of its inability to provide a structure corresponding to our conception of what truth should be, I’m not about to elaborate a neat and tidy theory with all the ends tied up about how these three things fit together. Language is only good at the description of three-dimensional objects and their everyday disposition or movement in space. We apply concepts derived from the objects of sense-experience to entities of which we could never have had experience, and we could never have had experience of them simply because such entities have no presence in the world of three-dimensional objects. Thus language is strained and begins to crack up. Yet we do it nevertheless, and do it with much greater enthusiasm and persistence than ever we applied to the description of objects in front of our noses. The whole world of abstractions, the world of universals, the world of so-called a priori concepts is manipulated by us according to logical concepts and rules that are derived from the world of three-dimensional objects. In mathematics, we have the freedom to vary the rules and can use that very logic and those very rules to go beyond the world from which it and they are derived. We can think up geometries which are not-three-dimensional simply by dropping this or that assumption which seems intuitively to belong to logic because logic too is derived from the three-dimensional world. We drop the fifth axiom of Euclidian geometry (the one about parallel lines meeting at infinity, which is the weakest of the five) and hey presto! we can dream up abstract worlds in which parallel lines meet in all sorts of circumstances, where space is curved, where triangles have internal angles adding up to more or less than two right-angles and so on. On the basis of such uncommon-sense geometries, we can then construct models of the physical universe which stack up mathematically and which fit the observational evidence, but which correspond not at all to our pre-programmed way of imagining reality that still handicap our logic. Once one masters the significance of imaginary numbers, and other exotic mathematical notions, the maths gets ever further from thelogic of everyday sense-experience. This is why the most modern theories of physics seem unacceptable or unsettling to some: they appear illogical.

The state of modern physics is such that its best theory of everything seems immune from experimental validation. Critics of String- or M-Theory say that this lack of experimental corroboration means that the theory is not physics at all but philosophy. But it was ever thus. Theory has very often led the way in science. Remember Dirac! The theory is dreamt up to account for the facts as they are known, sure, but every theory validated by experiment always throws up new and inconvenient facts which destroy the integrity of the theory. For this reason, theory will always be speculative and go beyond the evidence of the senses. The question is: how do we perform the trick of imagining and then discovering depths to reality that our sensory experience could never have opened up to us? From what position in the world do we dream up these things, if not in some sense from outside of it? We certainly do not dream them up from within any closed system of deductions: not from within a closed system of physically limited experience and not from within a closed system of mathematical possibility. How can that be?

One can imagine the whole of mathematics as a system which validates itself and which is then both internally self-consistent and complete, i.e. safe from new discovery. The basic axioms would be demonstrated from the fundamental logic of the system and all its theorems would then be derived from the basic axioms. Such a beautifully tidy and definitive system is still the Holy Grail of some pure mathematicians. When such a system is presented to certain physicists – who are completely dependent upon mathematicians – they are likely to be encouraged in their ambition to write the fundamental algorithm of the universe. The alliance between mathematician and theoretical physicist would then seem to hold out the possibility of definitive and absolute truth being attained, truth which would be self-validating, since the language in which it is written is a self-validating system.  Unfortunately, the great mathematician Kurt Gödel demonstrated by his famous theorems that such a dream is a pipe-dream. He pointed out that in any system of mathematical formulations more complex than arithmetic, there are bound to be some axioms which are used and understood, but which can not be proven from within the system. The upshot of this is the truth that for any mathematical language more complex than arithmetic, the user is always in some sense beyond or above the system, because he is using knowledge which is not derived from within the system. He is always going beyond the evidence within the system; and he is thus superior to the system in the sense that he is beyond it. And there is no purpose served in saying that he is simply in a super-ordinate and higher system, which is complete and internally self-consistent. The reason for this is that in order to manipulate such a higher system, one has to be beyond it in exactly the same fashion. So we are always beyond and above our logic and our maths. If we describe our experience in the language of mathematics, we are always beyond and above the resultant system of ‘truth’. This probably means that we are inevitably beyond and above all our truth.

What does this ‘beyond’ and this ‘above’ mean?

Well this brings me back to the statement used earlier: there is a deep connection between the mind-body problem, Gödel’s theorems and the human tendency to go beyond the evidence in any picture of the world. In Descartes’ view, the mind, since it had properties different from and opposite to those of the body, was a different substance from the body. Being a different substance, it did different things. One of the different things it did was to think of the experience of the body in terms of the eternal and necessary truths of God. In a sense, then, the mind was always above and beyond the body in that it had access, in a way that the limited body could never have, to a vantage-point from which it could contemplate reality without the constraints of special and temporal finitude. I see no reason at all why the mind should not be conceived of as logically utterly different from the body as 3D object, in the manner suggested by Descartes, despite the notorious difficulties concerning the interaction of the two, which the grand man simply ignored. (The contemptuous speculation about weird transactions in the pineal gland is no more than a provocation.) If the mind is always above and beyond any system of description of physical objects, there is a real sense in which the mind is in different dimensions from the body, if the body is conceived of as a 3D object.

One has only to think of the fact that human beings are judged when all is said and done not by their physique, nor by their possessions, nor by their power, nor by their accomplishments, but by their moral qualities. To take a homely example, “the spirit is willing but the flesh is weak” we say; and we thereby state the schism between mind and body. But if the spirit is after all only body, how can a thing be both weak and strong in the same sense? If the body is strong and the sprit weak there is patently a distinction to be made between the two. We can describe the human mind in terms of 3D objects located in the three dimensional space inside our skulls until the cows some home and we will never eradicate this distinction. We simply cannot shake off this unshakeable intuition that the mind is different from the body in the face of the best arguments that it is not. Gödel’s theorem and our innate (and justified) tendency to go beyond the evidence of our body-mediated experience seem to suggest that there is something in our belief. What then is the point of sticking dogmatically to the belief of the eliminative materialists that ‘essentially’ the mind is just an object?

But let us return to the flipside of this freedom for a moment, to our dogmatising tendency to confuse our models with what is modelled. Take the concept of ‘necessity’, i.e. the idea that some truths just ‘have to’ be true and cannot not be true. This is a feature of mathematics, not of the world. If you disagree with a mathematical equation that is done correctly, then for a mathematician that is because you are stupid or ignorant or both. The correct calculation cannot be wrong. Now when we apply that calculation to a natural process, we have the impression that the rigour and necessity of the calculation is the same as the necessity of the process that we observe. At that point we say of this or that natural process “it just has to be that way!” and we think that we have found an example of natural necessity, something in nature that just has to come about in the way that we think it comes about. We confuse the necessity of the calculation with the properties of the phenomenon observed. This can make us dogmatic and certain where we have no right to be certain. The certainty of the mathematics misleads us into thinking that we are certain about the natural phenomenon. This sometimes makes us arrogant and likely to embark on ill-advised courses of action, like the ‘masters of the universe’ mentioned earlier. But this unfortunate tendency arises precisely because maths is so staggeringly successful at modelling the world and because we can come up with ‘right’ answers to our questions rather than with hit-and-miss analogies. So there are huge advantages and real disadvantages in our method. But all of this simply evokes anew the question “where do we get the mathematics from?” Now we are not going to answer that question in these few pages. But we can continue to ask the question and raise some of the interesting issues that surround it.

It almost seems as if our tendency to use mathematics as models for reality and the tendency of the world to conform, at least apparently, to our mathematical models, indicates a kind of pre-existent harmony between the world and our minds. We don’t simply find the mathematics in the world, as we simply find rocks and trees, even though some things such as crystals, orbiting moons, traces in the bubble-chamber and so on, look pretty mathematical in themselves. We have more frequently invented the mathematics first and then found that we could apply it to the world. The most complicated mathematics arises often from the purely mental operations of gifted and creative mathematicians who dream these things up, spin them out of their minds like weirdly creative spiders, simply because they follow the implications of a particular line of thought. The biography of the philosopher Blaise Pascal is very instructive in this respect. His father thought it wise to keep him away from mathematics until he was older, so the little boy just went ahead and invented a lot of it for himself. We could also cite the case of the weirdly talented Indian mathematical genius, Ramanujan who had little education but who amazed the Cambridge establishment with his staggering mathematical creativity.

We have a passion for mathematical invention and we often discover, after the mathematics has been invented, that we can use it to model ever more complicated and subtle processes of nature. This process seems endless. The more complicated the mathematics we invent (or is it ‘discover’?), the more the reality we apply it to seems to us to be subtle and complicated. There seems to be a feedback loop involved: as the maths gets more complex, so does the world. We are now at a frontier in our understanding of the complicated world of ‘string-theory’ because we lack a sufficiently powerful mathematics to deal with the problems it poses. But that mathematics will doubtless be discovered (or ‘we’ will invent it) and the process of understanding by means of mathematical models will take off again and lead us into an understanding of new, unsuspected depths to the natural world – as long, that is as we can make our hypotheses conform to experiment. There seems no possible end to this process of discovery.

Why do we do this? Where does the mathematics come from? If it comes from our minds, then how can we be sure that it really does apply to the world? How can we be sure that we are not deluding ourselves? If it comes from the world, how do we discover it? We do not simply ‘read it off’ from nature, because nature does not appear mathematical to our eyes, it’s too messy. We have to impose simple mathematical models that distort reality before we discover more complicated and ‘truer’ models by a process of refinement. This is certainly not ‘reading off’ mathematics from what we see around us. Take pi for example. Everywhere in physics where rotations, i.e. circles, are of importance in the modelling of physical process, pi is a vital number to our understanding. And yet we do not understand it. Perhaps if we were creatures with eight fingers and eight toes we might see some pattern in its extension. But for our base ten numbers system, pi is irrational and we can’t get a handle on it. Since we can’t get a handle on it, we work at the problem in purely theoretical ways and that theoretical work illuminates our exploration of nature. The point here is that it doesn’t work the other way around: we don’t discover pi in natural circles, we discover circles, we discover pi as an important number to understand them and then we extend our understanding by mere calculation, not by observation (the discoveries made by observing a computer that is working through the complex implications of a calculation too long for us to do is a different matter). This nicely illustrates the manner in which we apply maths to reality without understanding how the two relate, but feeling that in some wonderful way they do. We just ‘know’ that there is an intimate connection between our delight in doing maths and our delight in finding that the world responds to mathematical description. The origin of maths would then seem not to be in the world, nor in our minds, nor in our bodies but in the confluence of all three.

So if we want an answer to the question where does maths come from? We can only say that it comes from the creative imagination of the mathematicians who over the ages have dreamt up the ‘formalisms’, as they are called, in which mathematical ideas are expressed. It is useless to say that maths is a property of either mind or matter: it demonstrates that the two are one. These creative individuals dreamt up counting, maybe starting from the invention of the tally-stick. Then they dreamt up measurement, giving quantity to shapes. Then came plane geometry. Then solid geometry. Once these things were formalised, the stage was set for the explosion of mathematical creativity that characterised first ancient civilisations of the Indian sub-continent, then Greek civilisation, then the Islamic world and then the European civilisation after the Renaissance, when Indian, Greek and Arabic inventions in mathematics came together and cross-fertilized each other. Mathematical invention is always a matter, in the end, of rigorous ‘proof’. But mathematical creativity is not primarily to do with proof. It has more to do with the spontaneous working of the creative fantasy, of imagination, that espies, perhaps without understanding all the details, that further patterns, further mathematical depths can be opened up by altering the assumptions that govern existing knowledge. This suggests again that the creative mathematical imagination is always outside of any system of axioms and theorems that it might be using, always ‘above’ and ‘beyond’ such a system in some indefinable region of thought where entirely new insights are sparked off from the contemplation of old problems.

Gödel’s theorems show that the mind using such a system will always ‘know’ certain things that cannot be demonstrated from within the system. The mind, itself is always creatively beyond its mathematical inventions and able to survey its mathematical systems from a vantage-point outside them. The really weird thing is that the world itself seems to possess this property, too: it too is somehow always ‘beyond’ any mathematical models that we impose upon it, in the sense of being more complex than the model. Nature is almost but not quite mathematical. We can capture it to a certain extent in our net of conceptual thought, but something will always slip through. That’s why Plato, the great admirer of maths, though that dialectical reasoning was above mathematical reasoning. That’s why our mathematical models get progressively more complicated. Mathematical creativity is a matter firstly of conceiving in imaginative terms an abstract possibility and then of generating ever more powerful formalisms and ever more powerful models to deal with the world’s slipperiness. It may well be that this new mathematics arises from the same indeterminate essence of the world as is at the heart of what we call ‘matter’. It may be that at the heart of foreworld, at the heart of hindworld and at the heart of midworld, there lies the same indeterminate fund of creative and meaningful novelty. After all, the world is a co-ordinated totality and not a bag of marbles. So it is entirely possible that its indeterminate core is everywhere the same, whether it is in the world we observe (foreworld) in the subjective reactions consequent upon that observation (hindworld) or in the publicly accessible thoughts we generate in consensus-building language (midworld). It is for reasons such as this that the fourth term ‘hyperworld’ is here considered necessary. This is only a speculation, but beware of simply rejecting it out of hand, for that way lies dogmatism.

Maths as established formalism is a world in itself. It is pure midworld. It has properties that can be discovered. But it is not the world of sense. This demonstrates once more that the concept ‘world’ has more to it than we generally think. So the problem remains; and a very deep problem it is. The power of mathematics is in its ‘obviousness’, in our conviction that the truths of maths are obvious and that they obviously apply to the world. That we invent (or discover) them and that they do apply to the world are two almost miraculous facts in themselves. The comprehensibility of the world in terms of mathematics is a very suggestive link between mind and world, a link that seems to suggest that the observer is not just a featureless subject facing a monolithic and alien object, but that there is a much more intimate connection between the self and the world that it encounters. Self and world and language seem to flow together in mathematics and seem all three to be harmonised by some mysterious fourth term. There seems to be an intimate connection between our mathematical ability and the world itself. We seem to be more deeply enmeshed in the world than we ever suspected. This ‘enmeshedness’ seems to speak to us of an intelligence in nature that our own intelligence constantly pursues but never catches. But there is a connection between our intelligence and the intelligence we devine and that some call ‘divine’. We are at home in the universe. We are part of the universe and our mathematical ability is an indication of how as parts we reflect the whole.