The ability of men and women to think logically is the product of a lengthy process of social evolution. It antedates the invention of formal logic, not by thousands, but by millions of years. Locke already expressed this thought in the 17th century, when he wrote: “God has not been so sparing to men as to make them barely two-legged creatures, and left it to Aristotle to make them rational.” Behind Logic, according to Locke, stands “a naïve faculty to perceive the coherence or incoherence of its ideas.”[44]

The categories of logic did not drop from the clouds. These forms have taken shape in the course of the socio-historical development of humankind. They are elementary generalisations of reality, reflected in the minds of men and women. They are drawn from the fact that every object has certain qualities which distinguish it from other objects; that everything exists in certain relations to other things; that objects form larger classes, with which they share specific properties; that certain phenomena cause other phenomena, and so on.

To some extent, as Trotsky remarked, even animals possess the ability to reason and draw certain conclusions from a given situation. In higher mammals, and in particular the apes, this capacity is quite advanced, as the most recent research into bonobo chimpanzees strikingly reveal. However, while the capacity to reason may not be a monopoly of the human species, there is no doubt that, at least in our small corner of the universe, the ability to think rationally has reached its highest point so far in the development of the human intellect.

Abstraction is absolutely necessary. Without it, thought in general would be impossible. The question is: what sort of abstraction? When I abstract from reality, I concentrate on some aspects of a given phenomenon, and leave the others out of account. A good mapmaker, for instance, is not someone who reproduces every detail of every house and paving stone, and every parked car. Such an amount of detail would destroy the very purpose of the map, which is to make available a convenient scheme of a town or other geographical area. Similarly, the brain early on learns to ignore certain sounds and concentrate on others. If we were not able to do this, the amount of information reaching our ears from all sides would overwhelm the mind completely. Language itself presupposes a high level of abstraction.

The ability to make correct abstractions, which adequately reflect the reality we wish to understand and describe, is the essential prerequisite for scientific thought. The abstractions of formal logic are adequate to express the real world only within quite narrow limits. But they are one-sided and static, and are hopelessly inadequate to deal with complex processes, particularly movement, change and contradictions. The concreteness of an object consists of the sum total of its aspects and interrelationships, determined by its underlying laws. It is the task of science to uncover these laws, and to get as close as possible to this concrete reality. The whole purpose of cognition is to reflect the objective world and its underlying lawfulness and necessary relationships as faithfully as possible. As Hegel pointed out, “the truth is always concrete.”

But here we have a contradiction. It is not possible to arrive at an understanding of the concrete world of nature without first resorting to abstraction. The word abstract comes from the Latin “to take from”. By a process of abstraction, we take from the object under consideration certain aspects that we consider important, leaving others to one side. Abstract knowledge is necessarily one-sided because it expresses only one particular side of the phenomenon under consideration, isolated from that which determines the specific nature of the whole. Thus, mathematics deals exclusively with quantitative relations. Since quantity is an extremely important aspect of nature, the abstractions of mathematics have provided us with a powerful instrument for probing her secrets. For this reason, it is tempting to forget their real nature and limitations. Yet they remain one-sided, like all abstractions. We forget this at our peril.

Nature knows quality as well as quantity. To determine the precise relation between the two, and to show how, at a critical point, one turns into the other is absolutely necessary if we wish to understand one of the most fundamental processes in nature. This is one of the most basic concepts of dialectical as opposed to merely formal thought, and one of its most important contributions to science. The deep insights provided by this method, which was long decried as “mysticism”, are only now beginning to be understood and appreciated. One-sided abstract thought, as manifested in formal logic, did a colossal disservice to science by excommunicating dialectics. But the actual results of science show that, in the last analysis, dialectical thinking is far closer to the real processes of nature than the linear abstractions of formal logic.

It is necessary to acquire a concrete understanding of the object as an integral system, not as isolated fragments; with all its necessary interconnections, not torn out of context, like a butterfly pinned to a collector’s board; in its life and movement, not as something lifeless and static. Such an approach is in open conflict with the so-called laws of formal logic, the most absolute expression of dogmatic thought ever conceived, representing a kind of mental rigor mortis. But nature lives and breathes, and stubbornly resists the embraces of formalistic thinking. “A” is not equal to “A”. Subatomic particles are and are not. Linear processes end in chaos. The whole is greater than the sum of its parts. Quantity changes into quality. Evolution itself is not a gradual process, but interrupted by sudden leaps and catastrophes. What can we do about it? Facts are stubborn things.

Without abstraction it is impossible to penetrate the object in “depth”, to understand its essential nature and laws of motion. Through the mental work of abstraction, we are able to get beyond the immediate information provided by our senses (sense-perception), and probe deeper. We can break the object down into its constituent parts, isolate them, and study them in detail. We can arrive at an idealised, general conception of the object as a “pure” form, stripped of all secondary features. This is the work of abstraction, an absolutely necessary stage of the process of cognition, described by Lenin as:

Thought proceeding from the concrete to the abstract, provided it is correct (and Kant, like all philosophers, speaks of correct thought) – does not get away from the truth but comes closer to it. The abstraction of matter, of a law of nature, the abstraction of value, etc., in short all scientific (correct, serious, not absurd) abstractions reflect nature more deeply, truly and completely. From living perception to abstract thought, and from this to practice – such is the dialectical path of the cognition of truth, of the cognition of objective reality.[45]

One of the main features of human thought is that it is not limited to what is, but also deals with what must be. We are constantly making all kinds of logical assumptions about the world we live in. This logic is not learned from books, but is the product of a long period of evolution. Detailed experiments have shown that the rudiments of this logic are acquired by a baby at a very young age, from experience. We reason that if something is true, then something else, for which we have no immediate evidence, must also be true. Such logical thought-processes take place millions of times all our waking hours, without us even being aware of them. They acquire the force of habit, and even the simplest actions in life would not be possible without them.

The elementary rules of thought are taken for granted by most people. They are a familiar part of life, and are reflected in many proverbs, such as “you can’t have your cake and eat it” – a most important lesson for any child to learn! At a certain point, these rules were written down and systematised. This is the origin of formal logic, for which Aristotle must take the credit, along with so many other things. This was most valuable, since without a knowledge of the elementary rules of logic, thought runs the risk of becoming incoherent. It is necessary to distinguish black from white, and know the difference between a true statement and one that is false. The value of formal logic is, therefore, not in question. The problem is that the categories of formal logic, drawn from quite a limited range of experience and observation, are really valid only within these limits. They do, in fact, cover a great deal of everyday phenomena, but are quite inadequate to deal with more complex processes, involving movement, turbulence, contradiction, and the change from quantity to quality.

In an interesting article entitled The Origins of Inference, which appeared in the anthology Making Sense, on the child’s construction of the world, Margaret Donaldson draws attention to one of the problems of ordinary logic – its static character:

Verbal reasoning commonly appears to be about ‘states of affairs’ – the world seen as static, in a cross-section of time. And considered in this way the universe appears to contain no incompatibility: things just are as they are. That object over there is a tree; that cup is blue; that man is taller than that man. Of course these states of affairs preclude infinitely many others, but how do we come to be aware of this? How does the idea of incompatibility arise in our minds? Certainly not directly from our impressions of things-as-they-are.

The same book makes the valid point that the process of knowing is not passive, but active:

We do not sit around passively waiting for the world to impress its ‘reality’ on us. Instead, as is now widely recognised, we get much of our most basic knowledge through taking action.[46]

Human thought is essentially concrete. The mind does not readily assimilate abstract concepts. We feel most at home with what is immediately before our eyes, or at least with things that can be represented in a concrete way. It is as if the mind requires a crutch in the shape of images. On this, Margaret Donaldson remarks:

“even preschool children can frequently reason well about the events in the stories they hear. However, when we move beyond the bounds of human sense there is a dramatic difference. Thinking which does move beyond these bounds, so that it no longer operates within the supportive context of meaningful events, is often called ‘formal’ or ‘abstract’.”[47]

The initial process thus goes from the concrete to the abstract. The object is dismembered, analysed, in order to obtain a detailed knowledge of its parts. But there are dangers in this. The parts cannot be correctly understood apart from their relationship with the whole. It is necessary to return to the object as an integral system, and to grasp the underlying dynamics that condition it as a whole. In this way, the process of cognition moves from the abstract back to the concrete. This is the essence of the dialectical method, which combines analysis with synthesis, induction and deduction.

The whole swindle of idealism is derived from an incorrect understanding of the nature of abstraction. Lenin pointed out that the possibility of idealism is inherent in any abstraction. The abstract concept of a thing is counterpoised artificially to the thing itself. It is supposed not only to have an existence of its own, but is said to be superior to crude material reality. The concrete is portrayed as somehow defective, imperfect and impure, as opposed to the Idea, which is perfect, absolute and pure. Thus reality is stood on its head.

The ability to think in abstractions marks a colossal conquest of the human intellect. Not only “pure” science, but also engineering would be impossible without abstract thought, which lifts us above the immediate, finite reality of the concrete example, and gives thought a universal character. The unthinking rejection of abstract thought and theory indicates the kind of narrow, Philistine mentality, which imagines itself to be “practical”, but, in reality, is impotent. Ultimately, great advances in theory lead to great advances in practice. Nevertheless, all ideas are derived one way or another from the physical world, and, ultimately, must be applied back to it. The validity of any theory must be demonstrated, sooner or later, in practice.

In recent years there has been a healthy reaction against the mechanical reductionism, counterpoising the need for a holistic approach to science. The term holistic is unfortunate, because of its mystical associations. Nevertheless, in attempting to see things in their movement and interconnections, chaos theory undoubtedly comes close to dialectics. The real relationship between formal logic and dialectics is that between the type of thinking that takes things apart, and looks at them separately, and that which is also able to put them together again and make them work. If thought is to correspond to reality, it must be capable of grasping it as a living whole, with all its contradictions.

  1. Quoted in A.A. Luce, Logic, p. 8.

  2. LCW, Vol. 38, p. 171.

  3. Donaldson, M. Making Sense, pp. 98-9.

  4. Donaldson, M. Children’s Minds, p. 76.