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An Introduction To Non-aristotelian Systems And General Semantics.

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ON FUNCTION
135
quantum character of the variable has serious structural and semantic consequences, which will become clearer further on. It allows us, without stretching our definitions, to apply the new vocabulary to any problem whatsoever. It is in structural accord with the trend of the quantum theory, and, therefore, with the structure of this world, as we know it at present.
The notion of a variable originated in mathematics, and, in the beginning, dealt only with numbers. Now numbers, when given, represent, structurally, a manifold or aggregate which is not supposed to change. So, when we consider a variable, we should 'think' not of a changing entity, but of any element we choose out of our perfectly constant collection (when given). Let me repeat that the notion of change enters in, only in connection with the volition and the s.r of the one who operates these unchanging entities. The notion of a variable is taken always in an extensional sense, to be explained later, as it
always implies structurally a collection of many individuals, out of which collection a selection of one can be made. The notion of a variable is general and, in principle,; a constant is a special one-valued
case of a variable in which the collection contains a single element, making alternative selection impossible.
Variables are usually symbolized by the end letters of the alphabet, x, y, z,. The supply is increased as desired by the use of indices; for instance, This gives a
flexible means of denoting numerous individuals, and so manufacturing them indefinitely, as the extensional method of mathematics requires. Another method, introduced not long ago, has proven useful in dealing with a definite selection of variables in a simplified manner. One letter or one equation can be used instead of many. The variable sign x is modified by another letter which may have different values, in a given range; for instance, Xi, Xk,. The modifying letter i or k can take the serial values; let us say i or k - 1, 2, 3,. Since the one symbol Xk stands for the array of many different variables xx, x2, xs., statements can be greatly simplified, and yet preserve structurally the extensional individuality.
It is important that the non-mathematical reader should become acquainted with the above methods and notations, as they involve a profound and far-reaching structural and psycho-logical attitude, useful to everybody, involving most fundamental s.r.
The extensional method means dealing structurally with many definite individuals; as, for instance, with 1, 2, 3., a series in which each individual has a special and unique name or symbol. This extensional