Abstraction, reductionism and dialectics

First, Jon. It is undeniably true that some Marxists see the invocation of dialectics as a substitute for thinking about the world. Nobody but a blind, dogmatic idiot - and there are some around on the left - could deny that advances in knowledge take place as a result of non-dialectical forms of thinking. What advocates of dialectical method do claim is that it gives a richer, more systematic view of the world, or as Trotsky puts it in the 'shockingly bad' ABC of Materialist Dialectics: 'Dialectical thinking gives to concepts, by means of closer approximations, corrections, concretisation, a richness of content and flexibility; I would even say 'a succulence' which to a certain extent brings them closer to living phenomena.'

This occurs primarily through the recognition of the pervasiveness and extent of change, interconnection and contradiction in reality. Dialectical thought (if done well...) avoids one-sidedness, static descriptions of constantly changing phenomena and the confusion of partial explanation with the whole story. However it is not a mysterious key to perfect knowledge - human knowledge will always remain limited and develop in a specific historical and social context.

To deal with Jon's and Les' arguments it is necessary first to talk about abstraction. Abstraction is the process that arises because we cannot deal with the world as a whole, but rather begin to break it down into pieces that are meaningful for us in our activity and appear to encapsulate true distinctions in the world. The concepts we create to describe the pieces do not capture their object in every respect: we are always selective in forming concepts.

Abstraction is a human activity, which may be carried out consciously or unconsciously. Its content shifts in relation to our purpose. Yet it has also got to have an objective content - in the words of the Marxist psychologist Vygotsky: 'To every ultimate concept, even to the most abstract, corresponds some aspect of reality which the concept represents in an abstract, isolated form.' Some abstractions serve better than others may for particular purposes and some may simply give a misleading view of the world.

Abstraction is therefore central to the relationship of human subjects to the world. When we grasp or appropriate the world in thought, we establish the boundaries that distinguish one thing from another by selecting and focussing on some properties and relationships and ignoring or rejecting others. This clearly affects how we see and what we see. The drawing of boundaries serves to define what we see as integral to the behaviour of the part of reality we have bounded and what appears as chance or contingent.

Richard Levins points out that in science 'the objects of study are themselves intellectual constructs. The investigator chooses the system and specifies its boundaries. Thus 'inside' and 'outside' are not properties of nature but of science'. He mentions the absence of social causes such as poverty from models of disease in epidemiology, putting this down to the established division of labour between academic disciplines rather than any natural division of the world.

This process of selection and the consequent creation of abstractions originates in a number of different types of process, both conscious and unconscious. It is built into our perceptual mechanisms, such as sight and hearing; learnt in the process of socialisation, in particular through our mastery of language; unconsciously undertaken through participation in certain social activities that involve reducing things to a limited subset of their properties (e.g., monetary exchange); and, as in experimental science, consciously undertaken in order to achieve certain goals.

We can now return to Trotsky's assertion that 'A is never equal to A' and Jon Pike's assertion that 'A does equal A if I stipulate that in order to abstract common properties from individual entities'. Trotsky does not deny that it is possible to create abstractions that correspond to one another - but asserts that they can only do so as abstractions, that is as partial and imprecise descriptions of the world.

He writes: 'The axiom 'A' is equal to 'A' appears on one hand to be the point of departure for all our knowledge, on the other hand the point of departure for all the errors in our knowledge. To make use of the axiom of 'A' is equal to 'A' with impunity is possible only within certain limits.' In other words, the dialectician will always be able to go beyond abstractions by adding back elements that have been excluded so as to find that at the same time as identity there is always difference. (Whether this proves Russia was a workers' state in 1939 is of course a different matter!)

Jon both misses the point of what Trotsky is actually saying and falls into the idealist view that to 'stipulate' that two things are equal in the realm of thought makes them so in reality. The biologists Lewontin and Levins deal with this: 'We can hardly have a serious discussion of a science without abstraction. What makes science materialist is that the process of abstraction is explicit and recognised as historically contingent with the science. Abstraction becomes destructive when the abstract is reified and when the historical process of abstraction is forgotten, so that the abstract descriptions are taken for descriptions of the actual objects.'

There is then a real contradiction here between our abstractions - including both common sense and formalised systems like logic and mathematics - and, on the other, the way the world really is. In the field with which I am most familiar (computer science and information systems), this explains a number of common problems, particularly those relating to the translation from real world situation to a formalised model and from the model to the computer system.

For example, however accurate the translation from the formalised model to software is, it can never overcome the limited nature of the formal model as an abstraction. Despite the efforts of many computer scientists, it is therefore impossible to create a computer system that can be proven to work correctly in its real world environment, given that what has been left out of the model may then wreak revenge on the limitations of the system.

Dialectical method helps us to become aware of this gap, explain it and minimise its effects by providing us with tools to cut away some of the problems this causes. Particularly important here is the insistence on looking at 'wholes' (or in dialectical jargon, 'totalities'), which enable us to grasp the essence of objects. Having cut the world up through abstraction, we can, if not completely, put it back together into units where the essential relationships between the pieces become something inherent to what we are studying rather than accidental.

One aspect of these 'wholes' is that they exist at a number of levels simultaneously. For example, it is possible to describe a computer system in terms of the basic physical principles governing its operation; the workings of its components; the instructions it executes (at several different levels); its embeddedness in forms of human activity; and its role in a system of social relations. Each of these descriptions taken alone would be partial; each would be true, though taken in isolation contradict the others; each would serve certain purposes. They cannot all necessarily be mapped onto one another in a meaningful way as each more complex level cannot be reduced to a less complex one.

To describe the role of, say, a computer system in a bank's activities in terms of the principles of physics is a mismatch of levels between what is being explained and what doing the explaining. It is only possible to understand the interaction and scope of the levels adequately within the context of the system taken as a whole.

Against this background, it becomes apparent how it is possible for orthodox scientific method to be both useful and limited and why reductionism is both a necessity (something that Steven Rose does not deny) and a danger.

The scientific method of the last 300 years is in large part a form of conscious abstraction designed to provide a systematic way of looking at nature. Vygotsky comments: 'Even the most immediate, empirical, raw singular natural scientific fact already contains a first abstraction. The real and the scientific fact are distinct in that the scientific fact is is a real fact included into a certain system of knowledge, i.e., an abstraction from the inexhaustible sum of features of the natural fact. The material of science is not raw but logically elaborated, natural material which has been selected according to a certain feature. Physical body, movement, matter - these are all abstractions.'

Experimental science seeks to create the conditions whereby an hypothesis can be demonstrated or disproved. In order to do this, it is usually necessary to manipulate nature into a form in which the relationships being considered become apparent and testable. There is often a gap between the experimental abstraction and the typical environment in which the process occurs. Scientists spend much time trying to minimise or account for it.

Following from this, Levins draws the distinction between 'reduction as a research tactic' where 'the detailed examination of parts in isolation has a legitimate role within a broader research strategy' and 'reductionism as a philosophy, the belief that a detailed study of the smallest parts in isolation will lead to a sufficient understanding of the whole and that the behaviour of complex systems are epiphenomenal to the properties of parts'. Rose makes a similar distinction. Reductionism as philosophy results in the mismatch of levels discussed earlier.

In this context, Les' insistence that the best theories are those 'which explain the facts most economically' is at best ambiguous. Does 'economy' itself necessarily make for a theory of greater explanatory adequacy? Only if one accepts the principle that the parts tell us all we need to know of the whole. Levins argues that the most economical explanation may not be the best one, rather an adequate explanation may require us to 'examine a larger system than is generally thought relevant'.

Secondly, Les seems to assess whether theories hold or not by whether they can or cannot conform to formalisation according to the rules of mathematics. The mathematics works for Selfish Gene theory and for socio-biology's explanation of altruism (see his review of Susan Blackmore's book), therefore they must be true.

While I don't know how the maths relates to these cases, the same problem arises here as with proving computer programs correct - it is possible to make the maths fit the model or hypothesis and show it is mathematically consistent without showing that it necessarily corresponds to reality. Mathematical precision can be a substitute for either asking the right question or being able to demonstrate a causal relationship. It may also be a mystification of science to prove an ideological point.

Both Rose and Lewontin and Levins point out that the use of statistical correlation (e.g, to link IQ to race and class) allows the smuggling in of all sorts of hidden assumptions which are obscured by the demonstration of a statistical relationship. Lewontin and Levins comment that 'correlations may be the consequence of causal processes, but they cannot reliably be used to infer those processes... any statement about the real world must come from the content imported into the analysis'. The invocation of mathematics cannot necessarily be the end of the argument.

Les is right that we should not choose to believe particular scientific theories just because they correspond to our political views. We should also not accept scientific findings purely because they conform to orthodox scientific method or see that method itself as something beyond criticism.

Dialectical method provides us with some tools for that critique and for the development of an alternative without requiring us to throw out the undoubted gains that mainstream science has made.

Bruce Robinson

References

Richard Levins, 'The Internal and External in Explanatory Theories,' Science as Culture, Vol. 7, p. 557, 1998.

Bertell Ollman (1993), Dialectical Investigations.

Steven Rose. (1997). Lifelines: Biology, Freedom, Determinism.

Richard Lewontin and Richard Levins (1985). The Dialectical Biologist.