## ABSTRACT

In spite of maintaining rigorously the formalistic position, this chapter considers the logical calculus not as a language but as a formal construction (of logicians and mathematicians). We make the following distinction: A calculus is exposed in a language, but we are calculating with something which is denoted by part of a language. An expression is a finite sequence of typographical signs. A language is considered as a set of expressions. Certain sub-sets of a language which only consist of theorems are called "systems." The symbols of the usual logical systems will be classified principally into symbols of variables and symbols of constants. The symbols of variables denote variables, whereas we understand by "variable" that which (in different connections) is identifiable with different fixed formal objects (the constants) that are the values of the variables. We classify now the symbols of variables and constants as propositional symbols, connectives, individual symbols, p-functional (or predicative) symbols, and operators.