In this book two ethical systems are described in the language of mathematics. Ordinarily mathematics is thought to be a science of quantity. Indeed, manipulation of quantities constitutes much of mathematics. Elementary applied mathematics deals with reckoning and measurement, where concrete quantities are objects of attention, such as counting sheep or weighing corno But the operations on these quantities are performed with the help of symbols, from which concrete referents have been 'abstracted out': 3 + 5 = 8 regardless of whether the symbols stand for numbers of sheep or tons of corno Thus, the first principle that exhibits the power of mathematics is abstraction. It is one ofthe three pillars on which the edifice of mathematics rests. Another pillar is precision. Ordinarily, man communicates by words. W ords serve communication to the extent that they refer to things, events, states of affairs, feelings of the speaker, and so on. These are the meanings attributed to words. Communication is successful to the extent that the meanings coded upon words by the speaker correspond to the meanings decoded by the hearer. As is weH known, the degree ofthis correspondence varies enormously in different contexts of discourse and with the back grounds or attitudes of the speakers and hearers. Mathematics is a language in which the meanings ofthe symbols (the 'words' ofthis language) are absolutely precise. This precision is achieved by abstraction. Abstract terms are defined by their relations to other terms and by nothing else.

Inhalt
I. Moral Cognition.- II. Ethical Systems and Boolean Algebra.- III. Boolean Algebra, Exponent, Logarithm.- IV. Individuals, Reflection, and Interaction.- V. Automata with Semantics and Ethical Status.- VI. A Formal Representation of Doubts and Feelings.- VII. A Formal Comparison of Ethical Systems: Feeling Guilty, Condemnation, Doubt.- VIII. A Formal Comparison of Ethical Systems: Doubts and Ethical Status.- IX. Ethical Analysis of Artistic and Propagandistic Literature.- X. Experimental Analysis of Normative Individuals.- XI. The Principle of Maximization of the Ethical Status of One's Image of Oneself.- XII. Feelings and Sacrifices.- XIII. Formal Connections Between Modules of Inner Structures and Individuals.- XIV. Interaction. Activity and Its Measure.- XV. Ethical Typology in the Novel Crime and Punishment by Dostoevsky.- XVI. Ideology, Morality, and Political Organization.- XVII. Generalization. Proof of Existence of Ethically Nonmeasurable Situations.- Conclusion. The Problem of Substantiating the Initial Axioms.- Epilogue.- Appendix 1. Construction of Judgments about the Correctness of Images and Judgments.- Appendix 2. Ethical Systems and Multivalued Logics.- Appendix 3. Self-generation of Environments.- Appendix 4. A Method of Calculating Mean Ethical Statuses.- Appendix 5. Types of Adequacy of Reflexion.- Appendix 6. Schemes of Empirical Procedures.- Appendix 7 Tables.- Appendix 8. Problems of Substantiating the Initial Axioms in an Arbitrary Environment.- Appendix 9. Another Method of Representing Individuals.- Appendix 10. The Principle of Complementarity and the Phenomenon of Interference in the Algebraic Model of Ethical Cognition.- References.