## Algebra of ConscienceConscience is an essential human attribute. Nevertheless, in the construction of formal models of the subject it is customarily left outside the framework of theoretical analysis. The Algebra of Conscience, whose first edition appeared in 1982, was the first specialized work modeling the phenomenon of conscience. The method used in this book made it possible to connect moral experience with decision-making procedures on the level of mathematical models. The application of such models allows us to propose the hypothesis of two fundamentally different ethical systems determining the normative patterns of human behavior in situations of conflict. Under the first ethical system the subject's self-esteem is raised if the subject seeks to resolve the conflict; in the second it is raised by seeking to dramatize the conflict. The new edition of The Algebra of Conscience is significantly expanded. The second part of the book, devoted to moral choice, is completely new. Based on the theory presented in the first part, it constructs the model of a subject capable of making an intentional choice. A special variable corresponds to the subject's intention. This development allows us to include within the model freedom of will and freedom of choice, and also to generalize classical 2×2 game theory to the case where outcomes, in addition to having utility measures, are either `positive' or `negative.' In its concluding chapters the book constructs a dynamic model of the intentional subject faced with a choice between two alternatives, neither of which is morally acceptable for the subject. It is shown that in this case the probabilities of choice of the alternatives may change chaotically. From this it follows that one cannot predict which alternative will be chosen or even the probabilities with which they will be chosen. Audience: The book is addressed to a broad readership having elementary knowledge of mathematical logic and the theory of probability. It can be used in college courses studying the modelling of moral choice. The book's material can also be used in the design of artificial intelligence systems. |

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### Contents

MORAL COGNITION | 36 |

ETHICAL SYSTEMS AND BOOLEAN ALGEBRA | 43 |

BOOLEAN ALGEBRA EXPONENT LOGARITHM | 46 |

INDIVIDUALS REFLEXION AND INTERACTION | 50 |

AUTOMATA WITH SEMANTICS AND ETHICAL STATUS | 55 |

A FORMAL REPRESENTATION OF DOUBTS AND FEELINGS | 63 |

A FORMAL COMPARISON OF ETHICAL SYSTEMS GUILT CONDEMNATION DOUBT | 68 |

A FORMAL COMPARISON OF ETHICAL SYSTEMS DOUBTS AND ETHICAL STATUS | 74 |

CHAPTER VII A BOOLEANLINEAR MODEL OF THE SUBJECT | 203 |

EXAMPLES OF MODELING THE PROCESS OF CHOICE | 214 |

IMITATION OF THE OTHER | 222 |

THE SUBJECT CONTROLLING HIS RELATIONSHIPS WITH ANOTHER SUBJECT | 228 |

TWO ASPECTS OF CHOICE | 232 |

GENERALIZATION OF CLASSICAL GAME THEORY OF 2x2 ZEROSUM GAME | 235 |

RISK AND CAUTION | 242 |

THE NONLINEAR MODEL OF THE SUBJECT | 245 |

ETHICAL ANALYSIS OF ARTISTIC AND PROPAGANDISTIC LITERATURE | 82 |

EXPERIMENTAL ANALYSIS OF NORMATIVE INDIVIDUALS | 88 |

THE PRINCIPLE OF MAXIMIZATION OF THE ETHICAL STATUS OF ONES IMAGE OF ONESELF | 94 |

FEELINGS AND SACRIFICES | 98 |

FORMAL CONNECTIONS BETWEEN MODULES OF INNER STRUCTURES AND INDIVIDUALS | 109 |

INTERACTION ACTIVITY AND ITS MEASURE | 112 |

ETHICAL TYPOLOGY IN THE NOVEL CRIME AND PUNISHMENT BY FEDOR DOSTOEVSKY | 116 |

IDEOLOGY MORALITY AND POLITICAL ORGANIZATION | 126 |

GENERALIZATION PROOF OF THE EXISTENCE OF ETHICALLY NONMEASURABLE SITUATIONS | 135 |

THE PROBLEM OF SUBSTANTIATING INITIAL AXIOMS | 143 |

EPILOGUE TO PART ONE | 148 |

MORAL CHOICE | 151 |

PROLOGUE TO PART TWO | 153 |

INTRODUCTION TO PART TWO | 155 |

THE THREEFACED JANUS AN INITIAL METAPHOR FOR THE MODEL OF THE SUBJECT | 160 |

A BOOLEAN MODEL OF BIPOLAR CHOICE | 165 |

METACHOICE | 174 |

MODELING OF AWARENESS | 184 |

THE PRISONERS DILEMMA | 192 |

THE MORALITY OF RESULTS AND THE MORALITY OF MEANS | 198 |

SUBJECT WITH A QUADRATIC MODEL OF THE SITUATION | 249 |

STREAMS OF CONSCIOUSNESS AND DIFFERENCE EQUATIONS | 252 |

STREAMS OF CONSCIOUSNESS AND ACTS OF AWARENESS | 256 |

EPILOGUE TO PART TWO | 261 |

APPENDICES | 263 |

CONSTRUCTION OF JUDGMENTS ABOUT THE CORRECTNESS OF IMAGES AND JUDGMENTS | 265 |

ETHICAL SYSTEMS AND MULTIVALUED LOGICS | 269 |

SELFGENERATION OF ENVIRONMENTS | 291 |

A METHOD OF CALCULATING MEAN ETHICAL STATUSES | 298 |

TYPES OF ADEQUACY OF REFLEXION | 307 |

SCHEMAS OF EMPIRICAL PROCEDURES | 311 |

TABLES | 316 |

PROBLEMS OF SUBSTANTIATING THE INITIAL AXIOMS IN AN ARBITRARY ENVIRONMENT | 321 |

ANOTHER METHOD OF REPRESENTING INDIVIDUALS | 327 |

REPRESENTATION OF COMPLETED GRAPHS WITH POLYNOMIALS | 329 |

THE PRINCIPLE OF COMPLEMENTARITY AND THE PHENOMENON OF INTERFERENCE IN THE ALGEBRAIC MODEL OF ETHICAL COG... | 339 |

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### Common terms and phrases

act of awareness adequate image adversary analyze Anatol Rapoport Appendix automaton axioms behavior belongs bipolar choice Boolean algebra Boolean function Boolean-linear model Chapter completed graph compromise condemnation conflict confrontation connected consider construct correct image corresponds described Dostoevsky doubts the correctness enemy environment equal ethical cognition ethical status evaluation evil example expression external observer fixed point formal formula frequency game theory given graph G guilt hero hypocrite impulse incorrect individual individual's inner world interaction interpretation intuition Lebeziatnikov Lefebvre Luzhin matrix metachoice minimal moral cognition negative pole Niels Bohr Nikolai Ostrovsky nodes normative obtain one's image opportunist partner person player point of view positive pole prisoner's dilemma probability Proof Raskolnikov realized reflexive structure relation relationships represented result reverse transformation root sacrificial saddle point saint schema second ethical system situation solution Statement strategy stratified subgraphs substitutions suffering Svidrigailov symbol Table Theorem tier variable