George Walford: The Ideology of Logic

It is seldom easy for the two parties to any serious discussion to speak directly to each other’s arguments, and when they are adherents of different major ideologies the difficulty is increased. They often find they are talking past each other; each feels the other is failing to meet his points and is in some indefinable way cheating. It is a difficulty which causes bad feeling, and when the subject under discussion is the way a society ought to be run, and the two sides not individual people but social movements, the consequences are sometimes serious.

Such discussion often turns to recrimination. This can range from restrained questioning of the motives of the honourable Member to a blunt ‘Nonsense’ and beyond, but the theme is always the same, and it can be formulated as a charge that the opponent is not thinking logically. The general assumption is that when two people, or two groups, are faced with the same circumstances, then if both are thinking logically they must come up with the same response. It is assumed, that is to say, that there is only one logical way of thinking, only one valid logic.

Some who readily accuse their opponents of lack of logic would be hard put to say what they mean by the term, but when a definition is given it usually turns out that ‘logic’ is understood to mean the system of rules for thinking derived from the laws first formulated by Aristotle. It may be recognised that there are other logics, but these are thought to be valid (if at all) only in some rarefied atmosphere of advanced mathematics or high-flying modern philosophy. When it comes down to specifying the system of thinking to be used in daily matters and the social questions that affect us all, then ‘logic’ usually means Aristotelian logic.

There is, however, one notable exception: dialectical logic stands in explicit opposition to Aristotelian, and although it cannot be said to be generally accepted yet it does have a good claim to recognition as a social influence: the communist movement, at least in its more thoughtful expressions, claims to use dialectical logic. Communists see themselves as distinguished from their opponents of the right by the use of a different logic, and this is at least one of the things that make it so hard for the two sides to reach, even on the most abstruse questions, solutions enduringly acceptable to both. In the communist view it is not only the political and social beliefs of their opponents that are to be repudiated but also their physics, philosophy, religion, literature and art; these also are ‘bourgeois’ and therefore to be rejected, and ‘bourgeois’ thinking, in whatever field, may be recognised by its adherence to non-dialectical logic.

In its modern developments Aristotelian logic is extensive and complex, but as an explicit system it derives from the three laws formulated by its eponymous founder:

1. The law of identity; X = X.
2. The law of contradiction; nothing can be both X and non-X.
3. The law of the excluded middle; everything is either X or non-X. Of these the law of contradiction has priority.

The nature of dialectical thinking means it is not susceptible of being reduced in this way to a set of rigid rules, but its central principle is the unity (or identity) of opposites, and when this is expressed in terms of X and non-X it becomes:

Every X is also non-X.

Those engaged in politics rarely stop to analyse their behaviour in the terms of abstract logic but these two contradictory propositions, that every X is also non-X, and that nothing can be both X and non-X, are the logical presuppositions governing the thinking (and the actions governed by thinking) respectively of the communists and their opponents of the right. If nothing can be both X and non-X then society, being a unity (as it evidently is, otherwise we could not sensibly speak of it in the singular) cannot also be an opposition; any appearance of opposition in the structure of a society must be illusory, and those proclaiming it must be evil people promoting false ideas; hence the accusations from the right that communists are agitators and traitors. If, on the other hand, every X is also non-X, then just because society is a unity it must also be an opposition; to the communists, society is an opposition between classes and it is this that produces social progress; to deny the reality of class struggle is to repudiate progress. Hence the accusations from the communists that their opponents of the right are reactionaries.

Whatever else may or may not be involved, these respective logical presuppositions, the one that X is a simple identity, the other that it is an identity of opposition, are themselves sufficient to account for opposition between communists and the right. When an Aristotelian and a dialectician attempt discussion there is no common ground on which they can meet. To the Aristotelian everything spoken of, every X, is a simple identity, to the dialectician it is an identity of opposition. The two parties, even when they use the same words, are talking about different things.

I have been speaking of communists and their opponents of the right. Having shown some ground for accepting that these two bodies operate by different logics, and that this is related to their respective modes of behaviour in social affairs, we may enter upon some finer distinctions, both in politics and in other forms of social activity.

The major ideologies have not all existed as significant social influences since the beginning of society, and the same is true of the various logics with which they are respectively associated. Harold Walsby has shown that dialectical logic can be traced much farther back than one might think, back even to the “Chinese Classics” dating from the twenty-fifth century B.C., but he also shows that these early expressions of dialectic were suppressed, relegated to fields of thought regarded as the preserve of freaks and eccentrics. Only with Hegel’s work and the subsequent emergence of the revolutionary movement as a recognised (though still widely resented) component of the established social structure did dialectic come out of the shadows, and it is still very much a subsidiary influence. Even in the states ruled by groups flying the communist banner it is Aristotelian thinking that predominates.

Aristotelian logic as a formulated system was also a late emergence. We tend to think of Ancient Greece as standing near the beginnings, but there were some eight thousand years of agriculture and herding (and thus of the possibility of civilisation) preceding it, and humanity goes a long way farther back still. It is about a quarter-million years since homo sapiens emerged; set against that background the society that produced Aristotle and the logic known by his name barely preceded our own.

The society which produced the Aristotelian system was preceded by other civilisations. In these the most sophisticated mental activity exercising substantial influence was religion, and religious thought does not move in accordance with Aristotelian laws – it is, of course, largely because of this that religion comes to be condemned, by those who do accept this system, as illogical. Religion has its own method of thinking, its own logic, and even this is not primordial; religion also had a predecessor. There are societies known today in which the endeavour to establish a distinction between the sacred and the secular, definitive of religion, plays no part, and anthropology gives reason for believing that at one stage in the development of human society – the hunter-gatherer stage, which lasted without being superseded for something over nine-tenths of the time mankind has been on this planet and still survives on the periphery today – religion had not yet developed, the place which it later came to occupy being held by magic. Magic seems to be co-eval with humanity; there is no society known to history without it, and the burials and cave-paintings left by prehistoric societies also indicate its presence.

To modern ears the word ‘magic’ carries an aura of the forbidden, but this has been imposed by religion. The paradigm of magical wickedness is the Black Mass and this, being an inversion of the Christian ceremony and needing an unfrocked priest for its effective performance, presupposes that religion. Since it is religion that condemns -magic this condemnation cannot have preceded religion, and in fact magic in societies without religion – what F. M. Cornford calls “primary magic” – has nothing wicked, occult or mystical about it; it is simply a technique, ineffective doubtless but, in intention, eminently practical. And magic has its own distinctive logic.

There are many accounts and interpretations of magic, but among those who study the subject there is general agreement that two features play a large part, namely those termed by Sir J. G. Frazer ‘sympathetic’ and ‘contagious.’ These together amount to a tendency to ignore what a scientist or logician would regard as substantial distinctions, a tendency to regard two objects, which to the rational mind are clearly distinct, as substantially identical, so that an action performed on one affects the other. A wound is treated by anointing the weapon that caused it and to injure a doll containing hair or nail-parings of a person is to injure that person.

One major form of magical belief that has been much studied is totemism, and a distinctive feature of totemism (as compared with, say, religion or science) is the absence of firm distinction between people and totemic objects:

In a pure system of totemism, the human and non-human members… are not distinguished, but considered as identical… when we speak of the dances as mimetic we must beware of interpreting that term from our own civilised conceptions. ‘Imitation’ suggests to us the act of deliberately copying or mimicking the external appearance of something unlike oneself, with the object of creating an illusion in the spectator. The mimetic magical dance is not imitative in this sense; the focus of attention is not centred on an unlikeness which has to be overcome, or on any impression to be imposed on the onlooker. The disguise is rather an incidental means of helping out the emotions and desires of the actors themselves. If they want to feel with religious intensity what they at all times believe – that they are emus or kangaroos, it is obviously helpful to paint themselves so as to resemble the animal… The circumstances of the performance exalt the identity of nature by producing identity of behaviour. (F. M. Cornford: From Religion to Philosophy, a Study in the Origins of Western Speculation. Edward Arnold, London 1912, p.57)

When thinking of this type is considered in the terms of abstract logic it is clear that it does not operate in accordance with the law that nothing is both X and non-X. The totemist does not show himself to be thinking that a human member of his tribe cannot also be an emu. Neither, on the other hand, does he show himself to be using the dialectical concept of a unity of opposites. He is not thinking either that opposites are always rigidly separate (nothing is both X and non-X) or that they are united or identical (every X is also non-X). He is not thinking in terms of opposites at all. The concept of opposition, simple as it may seem to students of logic, is in fact highly sophisticated. It arose late in the development of humanity and has a long history of thinking behind it. It presupposes, in particular, systematic differentiation, and this is not found in magical or totemic thinking.

A totemist is less ready to kill a fellow-tribesman than an emu and thereby shows himself not to be thinking of them as simply identical. But neither does he think of them as clearly distinct. He treats them as different, or identical, as may be convenient at the time. His behaviour, even his considered behaviour, is governed not by principle but by expediency.

The central law of the logic by which magic operates may be formulated thus: X and non-X are not in principle differentiated.

In the historical development of society magic was superseded by religion as the outstanding mental influence, and a distinctive feature of religion, as Durkheim has shown in Elementary Forms of the Religious Life, is the effort to establish a principled distinction between the sacred and the secular. The central law of the religious logic may be formulated thus:

X and non-X are in principle distinct.

The gods (unlike the spirits of magic) are located away from their worshippers, usually in the sky, and the distinctions between good and bad, orthodox and heterodox are stressed. But the distinctions sought are in principle only, they are not remorselessly carried through. Although apart from the world God is not detached; worldly activities affect him, provoking his wrath or arousing his pleasure and he on occasion interferes with them. Also, there is often some direct connection between God and earth, God coming to earth either in person as the Greek Gods did or by proxy as in the Christian conception, or originating as a human who later achieves deification, as the Caesars were held to have done. All men are sinners but those who repent, showing themselves to have the right principles, will none the less get to heaven.

The primordial logic is one without principled differentiation, one governed by practical requirements. The next, the religious, is one in which the principle of differentiation has been accepted. In the next again, the Aristotelian, the emphasis is upon not the principle (that has already been accepted) but the details of differentiation. Each phenomenon is now to be precisely defined, to have its limits specified and to be allocated either to this class or to that, and to act in this way is to demonstrate acceptance of the logical principle that nothing can be both X and non-X, acceptance of Aristotle’s law of contradiction and the system of thinking that goes with it; it is at this point, in the scientific mode of thinking, that Aristotelian logic becomes dominant. In order to be accepted as good magic a procedure has only to work; in order to be good religion behaviour has to be right in principle. But if a proposition, a theory or a procedure is to be recognised as fully scientific it must be in accordance with Aristotelian logic, it must accept that the phenomenon with which it is concerned is, not only in principle but precisely and in detail, this and not that, that X is X and not non-X.

One aspect of the search for precision accompanying identification with, Aristotelian logic is a tendency to value definition. It is for this reason that when a definition of logic is offered it is usually Aristotelian logic that is defined.

I have been speaking of ‘science,’ but this should have been, more strictly, ‘hard’ or ‘exact’ science, for the studies dealing with the organic world (and sometimes described as sciences only with reservations) do not function by Aristotelian logic. In biology an organic being is not, in the sense that a rock or a bucket of water may be, an independent object, an X that is nothing else. It is a member of a species which itself is one component of the evolutionary system, and these connections are themselves part of the object; without them it would not be what it is and would in fact soon cease to be an organic object. Also, of course, it is not internally homogeneous in the way that a rock or a quantity of water may be; it is constituted of organs and cells distinct from and internally related to one another. This is the view that biological studies present of their subject-matter, and it shows that those studies function by a logic other than the Aristotelian, by a logic of which the central principle is:

Every X is internally related to non-X.

X and non-X were separated at the (inorganic) science stage, and the effort made to establish precisely their respective identities; now, no longer as mere undifferentiated homogeneities but as differentiated, concrete and specific heterogeneities, they are brought into a relationship of interdependence. It is a view which appears in social practice as the belief that for a society to be what it ought to be all its parts must enjoy full freedom of development, none being excluded or suppressed. That is to say, it is the view, and the logic, finding expression in all those movements – feminism, labour-socialism and anti-racism prominent among them – that strive to install, as fully accepted members of society, groups thought to have been excluded. Every constituent of society, every X, is seen as internally related to every other, every non-X. This is the logic finding expression as the emphasis upon the value of totality against separation of parts, the ‘holism’ found particularly in the conservationist and ecological movements.

I have already spoken of dialectical logic; the feature to be emphasised here is that, unlike the previous logic, it emphasises not that X and non-X are related but the specific form of that relationship, namely that they are opposed to one another. It is this that constitutes their unity.

Communism sees modern capitalist society as primarily divided into bourgeoisie and workers. It is the workers who do the useful work but the bourgeoisie also perform a function necessary for the operation of capitalism: they exploit the workers. Both groups, X and non-X, are functional and therefore real, and the opposition between them therefore appears as real conflict, as the class struggle.

The successive logics we have looked at can be seen as forming a series along which X and non-X, at first undifferentiated, become increasingly specific until in dialectical logic they are seen as united in opposition. The next step is the resolution of this opposition by the elimination of one pole.

In anarchist thinking, and most explicitly in the fully-developed version of it promoted by the tiny group calling themselves the Socialist Party of Great Britain, all function, that is to say all social reality, resides with the social group with which they identify themselves, the working class. They define the working class as those who, because they do not own the means of production, are obliged to sell their labour-power for a living and (unlike the communist, movement, which is flexible on this issue, speaking of intellectuals, the middle class, and other groups held to be neither capitalist nor working-class) they go a long way toward accepting the consequences of this definition. According to them the working class does not only the production and distribution but also the research, management, education and administration. It is, the Socialist Party say, the working class that handles the financing; the working class runs capitalism “from top to bottom.” In fact, although they themselves do not directly say so, if their argument be consistently followed through it is the working class that exploits the working class, handing the proceeds to the capitalists.

On the Socialist Party’s definitions of the two classes the bourgeoisie are functionless parasites depending for their survival entirely on the willingness of the working class to be deceived. The party have explicitly stated (in their pamphlet Questions of the Day) that the armed forces are not only manned but also mainly officered by the working class and on their definition of the working class the same is evidently true of the police. It follows that if only the working class were to realise its position and pursue its own interests instead of supporting capitalism the bourgeoisie, being a small minority, would be reduced to impotence. The violent class struggle envisaged by the communists is unnecessary; if the workers want to end capitalism they need only stop supporting it and establish socialism in its place.

When the arguments put forward by the Socialist Party of Great Britain (and, though less clearly, also by the anarchists) are followed through they lead to the conclusion that the power apparently enjoyed by the capitalist class is an illusion. The capitalists are parasites, producing nothing for themselves and depending upon the workers for the means of life. They hold their position on sufferance and can be evicted from it whenever the workers decide to do so. And the apparent oppression of the working class by the capitalist class is also an illusion. If anybody oppresses the workers it is the working class itself, for (according to the Socialist Party) this is the only functional class, this is the class which exercises actual control over society. The working class is, if it would only realise its true position, the master class.

When these concrete social conceptions are reduced to the abstract symbols which reveal the bare logic involved they appear as the assumption that X is an illusion, it is non-X that is real. Or:

X is not X but non-X.

I began by noting the widespread assumption that there is only one logic, so that if people or groups facing the same circumstances are thinking logically they must all come up with the same response. Now, having looked more closely at logic, we see that assumption to be unfounded; far from leading to agreement, logical thinking, at least when people or groups identified with different major ideologies are concerned, is a source of dissension. Each major ideology has its own logic. It is because human behaviour is not governed exclusively by logic that general agreement and concerted action are possible.

from Ideological Commentary 12, August 1984.

See also George Walford: Editorial Notes (14) and Ideologic.