Definitions in Stanisław Leśniewski's System of Ontology. The Problem of Creative Definitions

Abstract

In the first part of the article S. Leśniewski's system of ontology is characterized. It is a name system, one of the broadest systems of this type built in the first half of the 20^th century. Ontology is built on the basis of only one axiom; hence definitions play such an important role in this system.

The second part of the article is devoted to a characteristic of definitions in ontology. Two kinds of definitions are most often mentioned in ontology: protothetic and ontological ones. This division results from the kind of functor that the given definition introduces into the system. Protothetic definitions introduce functors that generate propositions and ontological ones introduce functors that generate names.

In the third part of the article comments are made on creative definitions in ontology. An important feature of definitions in ontology is their creativity. A definition is creative if after it is included in a system it allows proving such a theorem that could not be proved without this definition. The most important motive for selecting creative definitions for building a deduction system is the postulate of formulating a minimum number of the strongest axioms and primary rules. In ontology some of the protothetic and ontological definitions are distinguished by the creative property.