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MATHEMATICAL METHODS IN ETHICS

Paper views the possibility of application of mathematical methods such as matrix algebra and game theory to analyzing the ethical contexts. Philosophical problems of usage of formal systems in humanities are described in general and analogies with economical mathematics and historical processes modeling are drawn. The moral dimension is proposed to be introduced for some famous scenarios in game theory and the potential of cooperation of this part of mathematics and philosophical ethics is studied. The moral estimation of players and connected hypotheses are then proposed to be introduced. The main new idea of the first chapter of the paper is that it is possible to provide an additional matrix which will estimate the moral events happening in the scenario (at least for some of the scenarios). Every decision of a player will cause not only the changes in strategies of other players and outcomes of the game but also certain precise moral evaluation of the particular action. The famous game theory scenario called prisoner's dilemma is given as a working example of such an approach. Consequently now we can use not only the gradation of players according to their initial strategies but also their "moral type". Paper than centers on exploring of how the moral influences the "material" strategies and decisions and also proposes the basic classification of moral types of players. A separate attention is given to one of such types which should be a mathematical encompassing of the negative sides of human nature in social activites. The paper will be useful for everyone who is interested in ethics, philosophical methodology of ethics, philosophy of mathematics and general relations between formal systems and humanities.