Terms

Abstract

Terms are the signs which make up sentences. These signs have certain physical properties which suit them for this role: ease of construction and perception; general availability; unlimited repeatability, etc. We assume all these properties to be given: i.e., we make the following assumption: in every branch of science one knows the properties signs must have in order to be terms. In other words, we assume that relative to a set of objects it is known that they are terms. The task now becomes to study the rules for forming from them new terms and for forming sentences from terms. Terms will be designated by the symbols t, t¹, t², ... . Everything that was said about signs in general applies to terms. Below we will present a series of definitions and theorems relative to terms. But, from them one can obtain theorems and definitions for signs in general by replacing the word “term” with the word “sign”. This means that we regard terms exclusively as signs. The fact that these are signs of a definite physical form plays no role in the exposition undertaken below. We will therefore not introduce a strict definition of “term”. We will limit ourselves to the assumption: terms are the signs which are the elements of the language of science.