SCIENCE AND SANITY - online book

An Introduction To Non-aristotelian Systems And General Semantics.

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but it becomes a physical ring in which new characteristics appear not listed in our definition.
From the above observations, very important consequences follow. Mathematizing represents a very simple and easy human activity, because it deals with fictitious entities with all particulars included, and we proceed by remembering. The structure of mathematics, because of this over-simplicity, yet structural similarity with the external world, makes it possible for man to build verbal systems of remarkable validity.
Physical or daily-life abstractions differ considerably from mathematical abstractions. Let us take any actual object; for instance, what we call a pencil. Now, we may describe or 'define' a 'pencil' in as great detail as we please, yet it is impossible to include all the characteristics which we may discover in this actual objective pencil. If the reader will try to give a 'complete' description or a 'perfect' definition of any actual physical object, so as to include 'all' particulars, he will be convinced that this task is humanly impossible. These would have to describe, not only the numerous rough, macroscopic characteristics, but also the microscopic details, the chemical composition and changes, sub-microscopic characteristics and the endlessly changing relationship of this objective something which we have called pencil to the rest of the universe ., an inexhaustible array of characteristics which could never be terminated. In general, physical abstractions, including daily-life abstractions are such that particulars are left out - we proceed by a process of forgetting. In other words, no description or 'definition' will ever include all particulars.