Jerzy Kalinowski’s Logic of Normative Sentences Revisited

Abstract

The paper tackles two problems. The first one is to grasp the real meaning of Jerzy Kalinowski’s theory of normative sentences. His formal system K ₁ is a simple logic formulated in a very limited language (negation is the only operator defined on actions). While presenting it Kalinowski formulated a few interesting philosophical remarks on norms and actions. He did not, however, possess the tools to formalise them fully. We propose a formulation of Kalinowski’s ideas with the use of a set-theoretical frame similar to the one presented by Krister Segerberg in his A Deontic Logic of Action. At the same time we enrich the language used by Kalinowski with more operators on actions (parallel execution and free choice) and present an adequate axiomatisation of the resulting system. That allows us to disclose some unrevealed aspects of Kalinowski’s theory. The most important one is a relation between acts which we call moral indiscernibility. Our second problem is a proper understanding of moral indiscernibility. We show how a repertoire of agent’s actions, defined with the use of simple observable elements of actions, can be filtrated by the relation of moral indiscernibility. That allows us to understand the consequences of Kalinowski’s claim that not doing something good is always bad.