Logic and Society:
Contradictions and Possible Worlds

Jon Elster

INTRODUCTION: LOGIC AND SOCIETY

Relations, numbers, probabilities, conflict, choice: this is the stuff societies are made of, this is what the social sciences are all about. In this book I try to bring out the abstract structure of these concepts by translating them into the more austere and more transparent language of formal logic. A brief outline of logical theory will be given in Chapter 1. In this introduction I shall not use this formal language, but rather try to give an intuitive motivation for what will be felt by some, perhaps, to be a rather strange endeavour. I do, indeed, stake out rather stronger claims for logical theory than what is usually done. Everyone will agree, I think, that logical analysis is a useful tool in constructing axiomatic theories, be it in the formal, the natural, or the social sciences. I want to take a further step, from the formal to the substantive level of theorizing. [1] I want to argue that logical theory can be applied not only in the formalization of knowledge already obtained by other means, but that logic can enter in the creative and constructive phase of scientific work. To take but one example which is explored in Chapters 4 and 5 below: most philosophers of science would argue that the notion of a contradiction has its place at the meta-level, that is, in the analysis of the logical form of scientific theories. I think it is possible to talk unambiguously about real contradictions, i.e. mental or social phenomena that—in a sense to be specified later—can be linked to the logical notion of a contradiction.

My general argument for regarding the language of logical theory as a vehicle for scientific research is the following. Science, in general, proceeds by way of abstraction, by throwing away information in order to focus upon some general feature of the object under study. In order to explain economic man and his behaviour in the market, we do not need to know (or so we assume) the colour of his hair or his place of birth. Probabilistic models of social mobility

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abstract from most features of the concrete man, except present and perhaps past class membership. The logical models used in this book carry this process of abstraction to what I think must be the ultimate limit. Instead of letting the number of individuals vary over the whole set of natural numbers, logic knows three degrees only: none, some, and all. Rather than quantifying probabilities along the continuum from 0 to 1, logic deals only with possibilities, impossibilities, and necessities. These two abstractions are at the root of quantified logic and modal logic, respectively. When performed simultaneously, they give us the full-blown structure of quantified modal logic which is the basic framework of this book. Just as important as the formal structure of quantified modal logic, is the interpretation of the concept of possibility. The crucial feature of the recent interpretations is that possible states are seen not as possible tout court, but as possible relatively to a given (actual) state. The affinity at this point with the social sciences hardly needs stressing.

I hope, of course, that this process of abstraction can be reversed; that insight into the abstract logic of social situations can lead the social scientist to ask new questions at a more concrete level. A typical example to show that logical theory can at least suggest new concepts is the following. In the study of social mobility an individual from a given class is sometimes described as having various transition probabilities to each of the several classes, including his own. In logical terms all the classes to which he has a non-zero probability of acceding are possible relatively to the initial class. The features, if any, that are common to all the possible classes, could then be called necessary features of the individual in his initial situation. It might—or it might not—turn out that these necessary features could serve as explanatory variables where the merely factual features of the individual did not. A more well-known example is the fact that abstract properties of relations—such as symmetry, transitivity, and reflexivity— are often useful in characterizing social relationships, e.g. power.

This book is primarily addressed to social scientists, and only secondarily to logicians. With the possible exception of some of the ideas in Chapter 6, the professional logician will not find much here of theoretical interest, even though I hope that parts of the material will prove useful for illustrative and pedagogical purposes. One sometimes gets the impression that logicians seek actively for examples either trivial or fanciful; I, for one, believe that the teaching of logic would benefit from more complex and realistic applications, much as physical examples are of great help in teaching mathematics. Perhaps this comparison could also be used to buttress a somewhat stronger claim. It was John von Neumann (I think) who said that mathematics out of touch with physical problems tends to become baroque, this term being used as a contrast to the classical style of thinking that is constantly revitalized by contact with the empirical sciences. As far as I can judge (but then I am no specialist in modal logic, so this may not be very far), there is a certain slant of the baroque—the somewhat futile embellishment of past glories—in some of the work done today by modal logicians. It is not to be excluded that a more extensive contact with the empirical sciences, and perhaps especially with the social sciences,

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could infuse a new life in the discipline. This has already been the case with temporal logic, which has drawn (even if not very extensively) upon problems in the philosophy of history. [2]

I would like to convey a feeling for some of the problems that made me write this book. The most important source of inspiration has been the long-standing controversy over Hegelian or dialectical versus formal logic. Proponents of the former have accused the latter of dealing with trivialities only; they have referred to a distinction between the lowly understanding that is at work in everyday life and in the sciences, and the elevated reason that is capable of metaphysical argument and dialectical insights. Analytical logicians have retorted by saying that dialectics overcomes triviality only at the cost of incomprehensibility. In Chapters 3, 4, and 5 below I try to work out an intermediate position. I believe that dialectical thinkers have had a unique gift for singling out interesting and sometimes crucial problems, even if their attempts at a new method must be deemed a failure. As I see it, there is nothing of real importance in Hegel or Marx that cannot be formulated in ordinary language and formal logic. [3] If this statement is not to be a tautology, we clearly need some independent criterion for what is really important. My criterion is simply to take the analyses that are held up by the dialectical philosophers themselves as paradigmatic examples of dialectical reasoning, and show that they can be rendered into a straightforward logical argument.

Actually, as the reader will see for himself, the promises of the preceding paragraph are kept only for some of the dialectical notions. Towards the end of Chapter 3 I briefly indicate how the notion of the negation of the negation may be interpreted in terms of modal logic. The most important category which is subjected to translation from dialectical to formal logic is, however, the concept of a contradiction. We know what a logical contradiction is, but is it not a category mistake and an abuse of language to talk about ‘real contradictions’? A priori I think one would like to impose the following conditions upon a workable concept of ‘real contradiction’ in the social sciences:

—It should be firmly linked to the concept of a logical contradiction,

—it should be linked to a theory of (individual or social) change,

—it should be fairly precise and operational,

—it should fit in with (at least some of) the writings of Hegel and Marx on the subject.

The first requirement is imposed for reasons of clarity of expression. The term ‘contradiction’ is basically a logical one, and should not be extended in a way that is totally divorced from the primary meaning. If by ‘contradiction’ we mean only opposition, conflict or struggle, then we should say opposition, conflict or struggle. We should firmly resist the temptation to play upon the logical connotation in order to make our opinions seem interesting, and then fall back upon the non-logical connotations in order to make them look plausible. The second requirement is reasonable in light of the link that from Heraclit onwards has been drawn between contradictions and change: ‘Without

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Contraríes is no Progression’ (William Blake). The third remark should not need any justification, but a brief remark may be useful in order to bring out the polemical intention behind this condition. A useful concept must be substantially less than all-embracing, which means that it is not very helpful to say with Mao Tse-Tung that there are contradictions in all things. Upon my definition of a real contradiction, there is a contradiction within the working class, but no contradiction between the capitalist and the working class. This restriction, far from being a disadvantage, is in my opinion a distinct asset of the notion proposed below. In the later Marxist tradition, from Engels onwards, there has been a tendency to use the term ‘contradiction’ in a manner so elastic as to rob the notion of all analytical cutting edge; it would seem worth while, therefore, if one could ‘donner un sens plus pur aux mots de la tribu’. The last requirement is the least important; its fulfilment should be seen more as an extra bonus than as a desideratum in itself.

It is by no means obvious that these requirements can be simultaneously fulfilled, and one might ask whether the intention to do so does not itself constitute a contradiction in the sense of Chapter 4 below. I do think, however, that they can be fulfilled, and in a manner that is not vulnerable to the standard criticism by positivist or analytical philosophers of science. The general notion of a ‘real contradiction’ is subdivided in two species: the individual contradictions and the social contradictions that form the subject of Chapters 4 and 5, respectively. The notion of an individual or mental contradiction really is very simple, as it is based only upon the idea that a person can very well entertain self-contradictory opinions or desires, even if it is impossible that they could be or become true. The notion of a social contradiction is slightly more complex. It is tied up with the well-known fallacy of composition, which I interpret (somewhat differently from the usual treatment in logic textbooks) in terms of quantified modal logic. This fallacy can be used as a key to the understanding of the two classes of social phenomena that I call suboptimality and counterfinality: the gap between the intention and the result, the gap between the possible and the actual.

For both varieties of contradictions—individual as well as social—I also try to show that they are indeed conducive to change. The link is only briefly sketched for the individual contradictions, but rather more elaborated in the case of social contradictions. In Chapter 5 the reader will indeed observe that the substantive sociological discussion tends to assume equal importance with the logical analysis. I do not apologize for this, even if it may throw some readers off the track. It is important, I think, to see the concepts at work if one is to be convinced of their fertility. Mere assertion will not make the reader agree that the notion of a real contradiction can and should be the core of a theory of social change. On the other hand it has not been possible, because of lack of space, to present the theory in full detail, a task that I hope to undertake elsewhere.

[pp. 4-9: counterfactuals and possible worlds]

Notes

1. I do not claim to be the first to do this. For other attempts in the same direction, see Kanger and Kanger (1966), Pörn (1970), or Körner (1976). These authors, however, write mostly for philosophers and suffer (in my view) from a poverty of good examples and concrete material that could persuade the social scientist that their work makes a difference.

2. Cf. for example Rescher and Urquhart (1971).

3. This implies a rejection of all attempts to formalize the Hegelian dialectics in a language that is different from standard logical theory, such as Günther (1959) or Dubarle (1970).

References

Dubarle, D. (1970). Logique f'ormalisante et logique Hégélienne, in J.d’Hondt (ed.), Hegel et la Pensée Moderne, Paris: Presses Universitaires de France.

Günther, G. (1959). Idee und Grundriss zu einer nicht-Aristoteliscken Logik, Hamburg: Felix Meiner.

Kanger, S. and Kanger, H. (1966). Rights and parliamentarism, Theoria, 32, 85-115.

Kórner, S. (1976). Experience and Conduct, Cambridge: Cambridge University Press.

Pörn, I. (1970). The Logic of Power, Oxford: Blackwell.

Rescher, N. and Urquhard, A. (1971). Temporal Logic, Vienna New York: Springer.

SOURCE: Elster, Jon. Logic and Society: Contradictions and Possible Worlds. Chichester; New York: John Wiley & Sons, 1978. Introduction (pp. 1-9), excerpted here: pp. 1-4, 9, [223, 225, 226, 227, 229, 230].

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Logic and Society: Contradictions and Possible Worlds
by Jon Elster