The Axiomatic Theory TLTk of Label Tokens

Abstract

Let us imagine the situation of a user of an ethnic language who wants to write a letter or the situation of a mathematician who wants to formulate theorems or to produce proofs in a formalized language. Both of them select ahd write out simple labels of’ a definite shape, combine them into more complex labels that follow one another, and -frequently reproduce them. Linguistic expressions used by a given language user are concrete, physical, sensorily perceivable objects, namely label tokens (in Latin (labels) in concreto, in English also label events; see Ch.S.Peirce [1931–19351; R.Carnap 119427). A precise explanation of the properties of those material objects encounters greater difficulties than those which we face when we establish the properties of ideal, abstract objects. We face such difficulties when we want to formulate an intuitive characteristic of a given language. (1)