Bion, W.R., Cogitations. London: Karnac Books (1992), pp. 84-7
4 October 1959
In spite of the advances of science in recent years, the methods employed in scientific work are under critical scrutiny. The moral questioning amongst scientists themselves of the use to which scientific knowledge is being put is scarcely relevant to discussion of the methods themselves, yet it has contributed to that discussion.
In philosophy the question is not new though it is unnecessary to go back earlier than Hume to find the origins of the present controversies. The problem as it appears to the philosopher has been stated by Prichard (Knowledge and Perception, p. 69). He says,
Though we are aware that any knowledge at which we arrive is the result of a process on our part, we do not reflect on the nature of the process – at any rate in any systematic way – and make it the object of a special study. But sooner or later knowledge of our mistakes and the desire to be sure that we are getting the genuine article, i.e. something which is really knowledge, lead us to reflect on the process … in the end we find ourselves having to ask whether we are capable of knowing at all and are not merely under the illusion of thinking that we can know.
In the natural sciences the quantum mechanical theories have disturbed the classical concept of an objective world of facts which is studied objectively. And the work of Freud has at the same time excited criticism that it is unscientific because it does not conform to the standards associated with classical physics and chemistry; it constitutes an attack on the pretensions of the human being to possess a capacity for objective observation and judgement by showing how often the manifestations of human beliefs and attitudes are remarkable for their efficacy as a disguise for unconscious impulses rather than for their contribution to knowledge of the subjects they purport to discuss.
But, it may be argued, do not the facts discovered as a result of the application of scientific methods constitute a proof that the methods employed – for example mathematical formulas in the prediction of astronomical phenomena – have a validity independent of the observer who elaborates and employs them, that the methods belong to ontology, not epistemology, and are ‘objective’, not ‘subjective’? Unfortunately not, for as Heisenberg has shown through the interpretation of quantum mechanical theory made by himself, Nils Bohr, and others of the Copenhagen School, no single fact is unrelated to and uninfluenced by the totality of facts, and that totality must remain unknown. Even the concept of space may have only a very limited application because there need be no reality corresponding to the concept. As Poincaré has pointed out, our methods of mensuration, which have played and still play a considerable part in the concept of space, are clearly related to man’s awareness of his own body (Science and Method, p. 100), and can in fact be ignored as they are ignored in the positional geometry of Riemann. No psycho-analyst would be surprised at the attribution of the origins of mensuration to the experiences of infancy and childhood.
Since the philosophy of modern physics – the most successful and most rigorous of scientific disciplines – can be seen here to be quite compatible with a philosophical view of uncoordinated and incoherent elements similar to the mental domain of isolated elements from which Poincaré describes the mathematician as attempting to escape by his discovery of the selected ‘fact’, and since moreover the mental state described by Poincaré is quite compatible or even identical with that described by Melanie Klein in her discussion of the paranoid-schizoid and depressive positions, it is reasonable to suppose that the investigation and explanation of these unco-ordinated elements will be dictated by the impulse described by Poincaré and investigated in detail psycho-analytically by Melanie Klein and her co-workers, and limited by the mental capacity which in the final analysis is the tool by which the investigation is carried out. This in turn means that of the totality of facts, only those will be investigated which are illuminated and rendered comprehensible by existing mathematical calculi. If they lie beyond the scope of such methods, they will not be discovered; if they are discovered, then obviously they will be such facts as conform to, and so appear to confirm, the mathematical calculi that have been employed. There is no reason to suppose that the totality of facts, or even any considerable proportion of them, support the view that there is a realization (Semple and Kneebone, Algebraic Projective Geometry, p. 4) which corresponds to the mathematical calculi and the scientific deductive systems they represent. For the psycho-analyst there is every reason to regard mathematical phenomena as belonging to the domain of epistemology, and therefore as a matter for psycho-analytical investigation, and in particular that mathematics should be regarded as having, as Heisenberg says of ‘every word or concept’, ‘only a limited range of applicability’ (Physics and Philosophy, p. 111). As he says,
When we represent a group of connections by a closed and coherent set of concepts, axioms, definitions and laws which in turn is represented by a mathematical scheme, we have in fact isolated and idealized this group of connections with the purpose of clarification. But even if complete clarity has been achieved in this way, it is not known how accurately the set of concepts describes reality. [p. 96]
In short, mathematics must be regarded by the psycho-analyst as one of the limiting classes that belong to psycho-analysis in so far as it attempts to be a coherent system of concepts, and in particular as one of the methods by which the paranoid-schizoid and depressive systems are brought into a dynamic relationship with each other, and therefore as an aspect of those mental phenomena that are concerned in the achievement of mental development by facilitating that dynamic relationship. It will therefore be seen that from a psycho-analytical point of view mathematics does not belong to the realm of ontology nor yet even of epistemology, but rather to that class of mental functioning which, since transition from paranoid-schizoid to depressive positions and back is essential to mental development, is essential to sanity itself.
This is not to belittle mathematics but to show how fallacious is the view that pre-eminent importance in any one sphere, however important, confers some universally equal significance in all – a fallacy that has tended to make some observers suppose that failure to produce calculi representing the deductive system of biology, and in particular of psycho-analysis, is necessarily a condemnation of the subject for which no calculi exist. Mathematics may have a very important role as an object of study psycho-analytically, and at the same time and for the same reason be an important element in the mental processes of the individual which makes it possible for him to be a psycho-analyst.