206 IV. STRUCTURAL FACTORS IN
A LANGUAGESrestrictions are not arbitrary or purely etymological, but they follow the rejection of the 'is' of identity of a-system.
Before we can apply the term 'infinite' to physical processes, we must first theoretically elucidate this term to the utmost, and only then find out by experiment whether or not we can discover physical processes to which such a term can be applied. Fortunately, we have at our disposal a
semantic process of generating numbers which, by common experience, by definition, and by the numerical technique, is such that every number has a successor. Similarly, our semantic processes are capable by common experience, by definition, and by the numerical technique to divide a finite whole indefinitely. Thus, if we do not identify external physical objective processes with internal semantic processes, but differentiate between them and apply correct symbolism, we can see our way clear. If we stop this semantic process of generating numbers at any stage, then we deal with a finite number, no matter how great; yet the process remains, by common experience, by definition, and by the numerical technique, such that it can proceed indefinitely. In the A sense, 'infinite', as applied to processes, means as much as 'indefinite'. We should notice that the semantic process of generating numbers should not be identified with a selection of a definite number, which, by necessity, is finite, no matter how great. The identification of the semantic process of generating numbers with a definite number; the identification of the semantic process of infinite divisibility of finites in the direction of the small with the generating of numbers in the direction of the great; and the identification of semantic internal processes with external physical processes., are found at the foundation of the whole present mathematical scandal, which divides the mathematical world into two hostile camps.The process of infinite divisibility is closely connected with the process of the infinite generation of numbers. Thus we may have an
array of numbers 1, 2, 3, ... n, all of which are finite. The semantic process of passing from n to n +1 is not a number, but constitutes a characteristic of the semantic process. The result of the semantic process; namely, n + 1, again becomes a finite number. If we take a fraction, a/n, the greater an n is selected, the smaller the fraction becomes, but with each selection the fraction again is finite, no matter how small.Although the two processes are closely connected on the formal side, they are very different from the semantic point of view. The process of generating numbers may be carried on indefinitely or 'infinitely' and has no upper limit, and we cannot assign such a limit without becoming tangled up in self-contradiction in terms. Not so with the process of indefinite or infinite divisibility. In this case, we start with a finite. |
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