Algebra of Conscience

1. Front Matter

   Pages i-xxvii

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2. Moral Cognition

   • Vladimir A. Lefebvre

   Pages 1-8

3. Ethical Systems and Boolean Algebra

   • Vladimir A. Lefebvre

   Pages 9-11

4. Boolean Algebra, Exponent, Logarithm

   • Vladimir A. Lefebvre

   Pages 12-15

5. Individuals, Reflection, and Interaction

   • Vladimir A. Lefebvre

   Pages 16-19

6. Automata with Semantics and Ethical Status

   • Vladimir A. Lefebvre

   Pages 20-27

7. A Formal Representation of Doubts and Feelings

   • Vladimir A. Lefebvre

   Pages 28-32

8. A Formal Comparison of Ethical Systems: Feeling Guilty, Condemnation, Doubt

   • Vladimir A. Lefebvre

   Pages 33-38

9. A Formal Comparison of Ethical Systems: Doubts and Ethical Status

   • Vladimir A. Lefebvre

   Pages 39-44

10. Ethical Analysis of Artistic and Propagandistic Literature

    • Vladimir A. Lefebvre

    Pages 45-49

11. Experimental Analysis of Normative Individuals

    • Vladimir A. Lefebvre

    Pages 50-54

12. The Principle of Maximization of the Ethical Status of One’s Image of Oneself

    • Vladimir A. Lefebvre

    Pages 55-57

13. Feelings and Sacrifices

    • Vladimir A. Lefebvre

    Pages 58-66

14. Formal Connections between Modules of Inner Structures and Individuals

    • Vladimir A. Lefebvre

    Pages 67-69

15. Interaction. Activity and its Measure

    • Vladimir A. Lefebvre

    Pages 70-73

16. Ethical Typology in the Novel Crime and Punishment by Dostoevsky

    • Vladimir A. Lefebvre

    Pages 74-82

17. Ideology, Morality, and Political Organization

    • Vladimir A. Lefebvre

    Pages 83-91

18. Generalization. Proof of Existence of Ethically Nonmeasurable Situations

    • Vladimir A. Lefebvre

    Pages 92-103

19. Conclusion

    • Vladimir A. Lefebvre

    Pages 104-108

20. Epilogue

    • Vladimir A. Lefebvre

    Pages 109-110

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.

• Dostoevsky
• cognition
• construction
• discourse
• event
• ideology
• individual
• interaction
• mathematics
• morality
• organization
• science
• semantic
• structure
• typology

• School of Social Sciences, University of California, Irvine, USA

  Vladimir A. Lefebvre

Policies and ethics