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Uit: Language in Thought and Action, door S.I. Hayakawa. Chapter 10 Why We Must Abstract This process of abstracting, of leaving characteristics out, is an indispensable convenience. To illustrate by still another example, suppose that we live in an isolated village of four families, each owning a house. A's house is referred to as maga, B's house is biyo; C's is kata, and D's is pelel. This is quite satisfactory for ordinary purposes of communication in the village, unless a discussion arises about building a new house-a spare one, let us say. We cannot refer to the projected house by any one of the four words we have for the existing houses, since each of these has too specific a meaning. We must find a general term, at a higher level of abstraction, that means "something that has certain characteristics in common with maga, biyo, kata, and pelel, and yet is not A's, B's, C's, or D's." Since this is much too complicated to say each time, an abbreviation must be invented. So we choose the noise, house. Out of such needs do our words come-they are a form of shorthand. The invention of a new abstraction is a great step forward, since it makes discussion possible - as, in this case, not only the discussion of a fifth house, but of all future houses we may build or see in our travels or dream about. A producer of educational films once remarked to the writer that it is impossible to make a shot of "work." You can shoot Joe hoeing potatoes, Frank greasing a car, Bill spraying paint on a barn, but never just "work." "Work," too, is a shorthand term, standing, at a higher level of abstraction, for a characteristic that a multitude of activities, from dishwashing to navigation to running an advertising agency to governing a nation, have in common. The special meaning that "work" has in physics is also clearly derived from abstracting the common characteristics of many different kinds of work. ("A transference of energy from one body to another, resulting in the motion or displacement of the body acted upon, in the direction of the acting force and against resistance." Funk and Wagnalls' Standard College Dictionary.) The indispensability of this process of abstracting can again be illustrated by what we do when we "calculate." The word "calculate" originates from the Latin word calculus, meaning "pebble," and derives its present meaning from such ancient practices as putting a pebble into a box for each sheep as it left the fold, so that one could tell, by checking the sheep returning at night against the pebbles, whether any had been lost. Primitive as this example of calculation is, it will serve to show why mathematics works. Each pebble is, in this example, an abstraction representing the "oneness" of each sheep - its numerical value. And because we are abstracting from extensional events on clearly understood and uniform principles, the numerical facts about the pebbles are also, barring unforeseen circumstances, numerical facts about the sheep. Our x's and y's and other mathematical symbols are abstractions made from numerical abstractions, and are therefore abstractions of still higher level. And they are useful in predicting occurrences and in getting work done because, since they are abstractions properly and uniformly made from starting points in the extensional world, the relations revealed by the symbols will be, again barring unforeseen circumstances, relations existing in the extensional world. Naar Hayakawa, contents 
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