136 IV. STRUCTURAL FACTORS IN A LANGUAGES
method is structurally the only one by which we may expect to acquire A oo-valued s.r. In a strict sense, the problems in life and the sciences do not differ structurally from this mathematical problem. In life and science, one deals with many, actual, unique individuals, and all speaking is using abstractions of a very high order (abstractions from abstraction from abstraction,.). So, whenever we speak, the individual is never completely covered, and some characteristics are left out.
In our example, we may call x the independent variable, meaning that it is the one to which we may assign any value at our pleasure, if not limited by the conditions of our problem, and y would then be the dependent variable, which means that its value is no longer dependent on our pleasure, but is determined by the selection of the value of x. The terms dependent and independent variables are not absolute, for the dependence is mutual, and we could select either variable as the independent one, according to our wishes.
The notion of a 'function' has been generalized by Bertrand Russell to the very important notion of a 'prepositional function'.1 For my purpose, a rough definition will be sufficient. By a propositional function, I mean an co-valued statement, containing one or more variables, such that when single values are assigned to these variables the expression becomes, in principle, a one-valued proposition. The oo-valued character of propositional functions seems essential, because we may have a one-valued descriptive function with variables, or a one-valued expression formulating a semantic relational law expressed in variable terms., yet these would be propositions. Thus, the oo-valued statement, 'x is black', would exemplify a propositional function; but the one-valued relation 'if x is more than y, and y is more than z, then x is more than z' exemplifies a proposition. This extended m.o notion of a propositional function becomes of crucial importance in a-system, because most of our speaking is conducted in oo-valued languages to which we mostly