coordinative definition

A coordinative definition is a postulate which assigns a partial meaning to the theoretical terms of a scientific theory by correlating the mathematical objects of the pure or formal/syntactical aspects of a theory with physical objects in the world. The idea was formulated by the logical positivists and arises out of a formalist vision of mathematics as pure symbol manipulation. Formalism In order to get a grasp on the motivations which inspired the development of the idea of coordinative definitions, it is important to understand the doctrine of formalism as it is conceived in the philosophy of mathematics. For the formalists, mathematics, and particularly geometry, is divided into two parts: the pure and the applied. The first part consists in an uninterpreted axiomatic system, or syntactic calculus, in which terms such as point, straight line and between (the so-called primitive terms) have their meanings assigned to them implicitly by the axioms in which they appear. On the basis of deductive rules eternally specified in advance, pure geometry provides a set of theorems derived in a purely logical manner from the axioms. This part of mathematics is therefore a priori but devoid of any empirical meaning, not synthetic in the sense of Kant. It is only by connecting these primitive terms and theorems with physical objects such as rulers or rays of light that, according to the formalist, pure mathematics becomes applied mathematics and assumes an empirical meaning. The method of correlating the abstract mathematical objects of the pure part of theories with physical objects consists in coordinative definitions. It was characteristic of logical positivism to consider a scientific theory to be nothing more than a set of sentences, subdivided into the class of theoretical sentences, the class of observational sentences, and the class of mixed sentences. The first class contains terms which refer to theoretical entities, that is to entities not directly observable such as electrons, atoms and molecules; the second class contains terms which denote quantities or observable entities, and the third class consists of precisely the coordinative definitions which contain both types of terms because they connect the theoretical terms with empirical procedures of measurement or with observable entities.