Two Formal Models of the Concept of Temperance

Abstract

Temperance is one of the four cardinal virtues which were first formulated by Plato. Today the notion of temperance has a central position in many ethical systems, especially in ecophilosophy (environmental philosophy). Temperance, involwing balance and moderation, may give resolution to many contemporary human problems. The attempt of analysis of this concept with simple formal means can make clear some hidden assumptions and the structure of the concept of temperance. The analised concept includes both – a decision (a choice) and an action/behaviour as an effect of the decision. First model is based on Aristotle’s theory of golden mean presented in his Nicomachean Ethics. The attempt of reconstruction Aristotle’s idea using mathematical notion of weighted mean shows that the concept of temperance is strongly restricted to the cultural background. Therefore in extremal cases the universal concept of temperance may not exist.

Second model given by Epicurus is based on the notion of consequence. It concerns pleasure and pain only, but temperance is just recommended in using pleasures. The set of temperant decisions is built recurently. A – the set of pleasure – is modified step by step by consequence C_R(A) where R – set of rules – includes modus ponens, law of identity and some simple laws of everyday provenience. U is the set of temperant choices in Epicurean sense iff  ∀p ∈ P, ~(p ∈ C_R (U)) where P – set of pain.