There seem to be three stages in the emergence of the 'law of contradiction'. The first is training the child to respond to the commands 'Yes' and 'No' and their equivalents; the second is the child's use of these symbols as levers to control the actions of others; the third is the use of 'Yes' and 'No' with reference to verbal activities. Stein's daughter used the word 'Nein' at eighteen months in answer to the question, 'Shall we take Hilde away?'. But when she was asked 'Is this a doggie?' while the wrong animal was shown her, she remained silent, then echoed 'doggie'. Four months later, however, she began to contradict a wrong name by substituting the right one; and another two months later -- at two years -- she firmly said 'No' in denial of blatantly false verbal statements.
Thus we see that the principle of contradiction is applied to symbolic activities precisely at the stage where symbolic relations as such become relevant to the child and call out discriminatory reactions. Once this stage has been reached the child uses 'No' not only to prevent undesirable action, but to reject incorrect symbolic propositions. This new verbal device is for the child a source of satisfaction comparable to the discovery of the naming game. It is expressed by the frequent use of antithetic statements which are characteristic for this age; three-year-olds delight in phrases which sound as if they had been borrowed from the Proverbs of Solomon: 'I am fast runner, not slow runner', 'I not old boy, new boy', etc. The use of such paired antithetic statements marks the beginning of the process of abstracting the relation of mutual exclusion as such, followed by the other, now familiar, stages: the gradual downing of the generalized relation; the implicit grasp of the principle; and finally its explicit naming -- though this last stage may never be reached. But regardless of whether or not the subject is able to give a verbal definition of it, the principle of the mutual exclusion of opposites previously discriminated as such, will enter as an important rule of the game into all matrices of rational thought.
Thus the so-called 'laws of thought' in traditional logic are, from the point of view of developmental psychology, merely the explicit formulations of implicit relations, abstracted by the usual procedures characteristic for all forms of learning. We may say that the principle of contradiction exists a priori in the organization of the nervous system, because the power to discriminate is built into that organization, and contradiction is merely an epi-phenomenon of discrimination. But we may also say that our judgements of what is a contradiction and what is not are empirically derived, because the gradients of relevance along which abstraction and discrimination proceed, are subjective and differ according to individual and culture.
But this subjectivity does not detract from the great power which the principle of contradiction exercises over the mind. And not only over the human mind; the experimental neuroses which Pavlov induced in his dogs testifies to it. The dog is trained to discriminate circles, or nearly circular ellipses, from flat ellipses, the former signalling food, the latter 'no food'. So long as the two types of signals are comfortably distinguishable from each other, the dog shows no sign of strain. But when intermediary forms are shown which could be interpreted as belonging to one class or its opposite, experimental neurosis sets in: the dog goes wild, then becomes apathetic, and seems to lose altogether its power of discrimination; it goes emotionally and intellectually to pieces. One might say that the dog has lost confidence in a world in which the law of the excluded middle has ceased to operate, and A is no longer not not-A.
It appears that dogs are not only emotionally more stable and loyal, but also more orthodox logicians than their masters. For the powers of discriminatory judgement are more diluted on the level of symbolic thought than in perception; and when thought is dominated by emotion and faith, the Red Queen always scores against reasonable Alice, who asserts that 'One can't believe impossible things'; whereas the Queen, after a little practice, managed to believe 'as many as six impossible things before breakfast'.
Which is, all things considered, quite a modest estimate.
NOTE
To p. 613. Once upon a time Lashley and Wade (1946) tried to make a distinction 'between the "so-called generalization" which means only a failure to observe differences and the generalization which involves perception of both similarities and differences. The amorphous figure, lacking in identity, is generalized in the first sense only.' The quotation is from Hebb (1949, p. 27), who seemed to share Lashley's view, although Lashley himself later dropped the distinction. The 'amorphous figure' in the quotation refers to 'an irregular mass of colour or a pattern of intersecting lines drawn at random'. Being amorphous it does per definitionem lack identity, i.e., the prerequisites for the formation of an object-concept; but it is nevertheless seen as some kind of figure on a background that is discriminated. In fact, abstraction without discrimination is a contradiction in terms. The abstracted quality -- whether 'nose', 'doily', or 'sound of the tuning fork' is always differentiated from non-nose and non-doily and no-sound. (If the sound of the tuning fork is very weak, it will approach the limen of no-sound; about the effect of simple gradients of intensity, see Hebb (1958), p. 189; about pitch and octave gradients, see Osgood, op. cit., p. 361. Since perception of intensity, pitch, etc. is part of the animal's perceptual organization, they must influence the functioning of the analyser-codes.)
XVI
SOME ASPECTS OF THINKING
Multi-Dimensionality
In the preceding chapter we have discussed the processes by which the rules of the game of symbolic thought are acquired; let us now turn to adult thinking and problem-solving.
Thinking is a multi-dimensional affair. The Sterns recorded all the questions asked by their little daughter in the course of four days; but the record gives us only the scantiest pointers to what went on in the child's head. Perhaps one day a super-EEG will be constructed, which will record all the thoughts -- or at least all verbalized thoughts -- which the stream of consciousness carries through the subject's wired skull; yet even such a record, far more complete than anything James Joyce could dream of, would be but a poor pointer to the multi-dimensional patterns underlying the linear stream. The oscillating curve on the gramophone record needs a human auditory system to yield all the information it contains. The super-EEG would record larger units of information -- entire words; but it would still need a psychoanalyst or a Joyce-interpreter to divine the meaning behind the meaning: the connotations of individual words, their unconscious echoes, the motivation behind it all, the rules of the patient's game, hidden to himself, and the memories which crop up as landmarks in his internal, mental environment.
We must nevertheless try to sort out some of the dimensional variables in this immensely complex, multi-dimensional activity; these variables will then yield gradients of different kinds; for instance:
(1) Degrees of consciousness; (2) Degrees of verbalization; (3) Degrees of abstraction; (4) Degrees of flexibility; (5) Type and intensity of motivation; (6) Realistic versus autistic thought; (7) Dominance of outer or inner environment; (8) Learning and performing; (9) Routine and originality.
Each of these headings has been repeatedly discussed in various contexts in various chapters. Most of them cut across the conventional classifications of thought such as 'associative' versus 'directional'. All variables are inter-dependent.
Now if variables depend on each other, there must be a function which defines their inter-dependence -- a rule of the game. The question: 'If y=f(x) and x is 7, how much is y?' is meaningless unless I define f. Similarly, if in the experimental laboratory the subject is given the stimulus word: S='big' and is asked for the 'response', the question is meaningless unless f is defined as 'synonyms' or 'opposites' or 'rhymes', or whatever game is to be played.
One of the main contentions of this book is that organic life, in all its manifestations, from morphogenesis to symbolic thought, is governed by 'rules of the game' which lend it coherence, order, and unity-in-variety; and that these rules (or functions in the mathematical sense), whether innate or ac
quired, are represented in coded form on various levels, from the chromosomes to the structures in the nervous system responsible for symbolic thought. The codes are assumed to function on the trigger-release principle, so that a relatively simple signal-pattern releases complex, pre-set action-patterns, as the referee's whistle initiates or stops the activities of the football players. The rules are fixed, but there are endless variations to each game, their variability increasing in ascending order; this lends elasticity to habit, and gives rise to the subjective experience of freedom of choice between alternate possibilities of action. There is also an overall-rule of the game, which says that no rule is absolutely final; that under certain circumstances they may be altered and combined into a more sophisticated game, which provides a higher form of unity and yet increased variety; this is called the subject's creative potential.
Faced with the imaginary EEG record of the patient's stream of thoughts, the only way of interpreting it would be to find out what game the patient is playing at any moment, and why. This actually is the procedure of the free-association method in psychotherapy: the patient's words provide the record, and his dreams, it is hoped, will provide the interpretation of the underlying patterns of his individual matrices of thought. We follow, as we saw earlier on, similar methods in perceptual analysis: the sequence of pressure-variations reaching the ear-drum must be dismantled, analysed, and reassembled if we want to get at the underlying patterns of timbre, melody, and speech. The stream of sounds, like the stream of thoughts, yields its meaning only if the percipient knows the rules of the game.
The Experience of Free Choice
Let us consider some of the dimensions of thinking listed on pp. 630-1. Regarding consciousness I proposed to make a distinction between the 'linear scale' of awareness on the one hand, and hierarchic levels of consciousness on the other (Book One, VII, VIII). The former was to be regarded as a continuous gradient extending from completely self-regulatory physiological processes, through more or less automatized skills, to peripheral, and lastly, focal, awareness of events; the latter to be represented by quasi-parallel layers of mental organization -- comparable to geological strata -- which are discontinuous and governed by codes formed at different stages of phylogenetic and ontogenetic development. All this has been discussed at length in the previous volume, and need not be recapitulated; but I must append two additional points.
The first concerns 'linear' awareness. I have described, somewhat perversely, awareness as that dimension of experience which diminishes and shrinks away with the progressive automatization of a skill. For 'awareness' is an irreducible term, a black box like that other which contains the power of organic life to extract energy and information from its environment -- and, in fact, continuous with the latter. On the other hand, the progressive automatization of motor skills, perceptual skills, verbal and mathematical skills, is an observable and to some extent even measurable factor of behaviour -- epitomized on its lowest level by sensory habituation. Thus by expressing awareness by the inverse ratio of the automatization of the ongoing process, a certain strategic advantage is gained. Other things being equal (i.e. under stablized environmental conditions), automatization manifests itself in predictable, stereotyped performance, where the matrix has no degrees of freedom left for strategic decisions, because these are made by pre-set feedback controls, and do not require the attention of higher centres. Conversely, the less automatized the skill, the greater the freedom of choice between alternatives, to be decided on higher levels according to more complex feedbacks -- 'loops within loops' -- from the outer and inner environment. Thus the logic of the argument led first to a negative criterion of awareness as the reciprocal of habit-formation, and now to the positive criterion of awareness as being directly proportional to the degrees of freedom of the centre controlling the activity to make alternative choices, based on its estimate of the lie of the land. We must assume that the higher in the hierarchy the centre is placed, the more vivid will be the subject's experience of his 'freedom of choice'. Freedom of the will is a metaphysical question outside the scope of this book; but considered as a subjective datum of experience, 'free will' is the awareness of alternative choices.
Degrees of Self-Awareness
The above was related to degrees of awareness on the continuous, 'linear' gradient. The second addendum relates to the hierarchic levels of consciousness. At any moment of our existence, we carry on activities on various levels, simultaneously and more or less independently from each: we breathe, metabolize, drive the car, and talk to the passengers all at the same time, 'in parallel' as it were.
But there are moments when a person perceives what he is doing from a bird's eye view as it were; from a 'parallel' level of consciousness which is not at all involved in the activity in hand. Take a simple example: you are absorbed in a game of chess; you concentrate on a stratagem to defeat your opponent. You look up for a moment to light a cigarette, and at that moment your awareness jumps to another plane, as it were; you say to yourself 'what fun I am having playing chess with old Henry on a Sunday afternoon'. Then you go back to your game. It was a brief break-through from the activity in hand to the contemplation of that activity from an upstairs balcony -- a vertical shift of awareness which enabled you to look down at the top of your own head. To put it in a different way, attention has been displaced from the object of the ongoing activity to the subject engaged in carrying it out -- that elusive entity, the self.
It is a paradox as old as Achilles and the Tortoise, that the subject who is aware can never become the object of his awareness; at best he can, if so inclined, achieve successive approximations which form a convergent series. One may call this the paradox of the dog at dinner. The dog is eating his dinner; the wagging of his tail indicates that he is enjoying himself; but does he know that he is enjoying himself? . . . A little boy is watching a Western on the TV screen. He is enjoying himself. He knows perhaps that he is enjoying himself. Does he know that he knows? . . . The philosopher is thinking of a problem. He is aware that he is thinking of this problem. Is he aware that he is aware, etc. . . .? The known is always one step ahead of the knower, and they chase each other up a spiral staircase, as it were. In Craik's terminology one might say that the model can never make a complete model of itself.* Regarding verbal models in particular, we have seen (pp. 592 ff.) that verbal statements are initiated by unverbalized intentions on higher levels, so that we again arrive at a receding series. This seems to indicate that the mind-body problem is not amenable to any solution in explicit, verbal terms.
On the other hand, the fact that the subject who is aware can nevertheless become, to some extent, the object of his own awareness, is of course of outstanding importance in mental life. Animals, apparently from planaria onwards, display attention and expectancy which indicate varying degrees of 'linear' awareness; primates, as well as domestic pets, may also have some rudiments of self-awareness. But the many-layered hierarchies of man, and particularly his symbolic hierarchies, place him on a lonely peak, and impose on him the impossible command to 'know thyself'. Awareness of awareness is a tantalizing gift; and 'I think therefore I exist' is a hopeful beginning. But the end, the identification of the knower and the known, which alone would constitute complete conscionsness of existence, though always in sight, is never achieved. The successive forms of self-identification, starting from the child's fluid world of experience which knows as yet no firm boundary between self and not-self, can be likened to a mathematical series converging towards unity, or to a spiral curve converging towards a centre which it will only reach after an infinite number of involutions.
The aim of certain mystic practices -- such as Hatha Yoga -- is to permeate the self with awareness of itself by gaining voluntary control over visceral processes and isolated muscles. It would seem that this focussing of consciousness on the self, the inward core of the contracting spiral, is the direct opposite of the self-transcending aspirations of other schools of mysticism -- the ex
pansion of consciousness in an unfolding spiral, and its final dissolution in the 'oceanic, feeling'. In fact, however, the Yogi's effort to gain conscious mastery of the body is considered as merely a detour towards attaining 'pure consciousness' -- that is, 'consciousness without object or content other than consciousness itself'. Thus turned upon itself, pure consciousness is supposed to penetrate the Real Self -- which, unlike the transient self, is part and parcel of the Atman, the universal spirit. [1] Both methods, therefore, each with a long historical ancestry, share the same ultimate aim -- situated at the point where opposites meet; after all, as the bright little boy said, 'the infinite is where things happen which don't'.
'Self-awareness', in the sense of the preceding paragraphs, has of course nothing to do with 'self-consciousness' in the sense of gauchery, stage-fright. The latter is our old friend, the paradox of the centipede -- the disorganization of behaviour which results when higher centres interfere with the autonomous functioning of parts on lower levels. 'Self-consciousness', used in this sense, is a typically English coinage; it provides an amusing and rather revealing contrast to the equally malapropos German coinage Selbstbewusstsein -- meaning self-confident, conscious of one's own value. As for the French, faithful to the Cartesian spirit, they use conscience to designate both consciousness and moral conscience.