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Example text

In Chapter III, the axioms of Boolean algebra and the laws for constructing formulae are introduced. In distinction to the usual practice, implication is expressed as an exponent, and this allows us to express long chains of implications compactly. In Chapter IV, formal definitions of an individual and of a situation are introduced. A formula with a special hierarchical structure is called an 'individual'. An individual has an 'inner world', which may consist of images of this individual, of his partner, and of the relationships between them (confrontation or compromise).

Luzhin is aggressive, and Lebeziatnikov tends to compromise. Thus we see that our model is capable of predicting the type of behavior of the main characters. In Chapter XVI, the correlation between ideology, morality, and political organization is analyzed. The main formulations of Soviet 'ethical ideology' are contained in the so-called "Moral Code of a Builder of Communism," which is a part of the Program of the Communist Party. We compare this Moral Code with the main principles of Christianity and find an interesting difference.

A+B will be interpreted as a union or compromise between individuals A and B, and the situation A • B will be interpreted as a conflict or confrontation between individuals A and B. A formula Win the formula aw will be called the inner world of individual A. Sometimes we will say that individual A contains an inner world W, or that individual A sees W, feels W, knows W, sometimes we will say that W is an image of reality which belongs to individual A, or reality from A's point ofview. The symbol a in the formula A = aw will be called the root of individual A; thus, individual A 'consists' of two parts: a root and an inner world.

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