ABSTRACT

This chapter considers what modes of connexion suffice to determine a system. It also considers familiar examples of terms, or elements, arranged in an order. The chapter examines some examples of systems of relations that have the same structure. It defines similarity by means of a one-one relation. The chapter adapts the definition so as to apply to a relation in which the correlating relation is many-one. It argues that Euclidean geometry is only one such system. The chapter determines what is meant by an important interpretation. The system of the actual world, because it is actual, cannot be determined by logical considerations alone. A system is an ordered system only if all its constituent elements are related by relations having certain logical properties. The possibility of different interpretations is due to the fact that deductive systems are completely formal. A system of geometry is a deductive system the nature of which is determined by the initial concepts and propositions.