Structural and Operational Approaches to the Physical World

STRUCTURAL AND OPERATIONAL APPROACHES TO THE PHYSICAL WORLD PYTHAGORAS and his followers placed great emphasis on geometrical structure as a key to understanding the natures and the operations of bodies, and their regard for mathematics as the key with which to unlock nature's secrets was in harmony with this view. They realized that harmonious sounds were produced by strings whose lengths were related according to mathematical proportion and by such things as this were led to regard number and geometrical form as involved in the essence of the physical world. Plato, following the Pythagoreans, continued to associate the properties of 'elements' with basic geometrical forms. The Aristotelian-Thomistic emphasis, on the other hand, must be looked upon as one which regards geometrical forms as being inadequate for explaining the operations of bodies. Aristotle gave a simple illustration of his point by noting that air and water can take any shape determined by their container and yet remain air or water. He also was aware that those who tried to account for the properties of elements in terms of their shapes attempted to account for the same property with entirely different shapes. Thus, some thought that the mobility of fire was accounted for by tiny particles of pyramid shape and others accounted for it in terms of tiny spherically shaped particles. Aristotle rejected all this and affirmed that it is the operations which one must study in order to come to a knowledge of the nature of things. "... it is clear that the difference of the elements does not depend upon their shape. Now their most important differences are those of property, function and power; ... our first business, then, will (A revision of a portion of the author's doctoral dissertation from The Catholic University of America, The Concept of Nature in Philosophy and Physics, 1952.) 889 890 JAMES F. o'BRIEN be to speak of these, and that inquiry win enable us to explain the differences of each from each." 1 In this way he says that the natures of things transcend the realm of geometry. There is an important point to be noted here. For, although Aristotle rejects geometrical forms as the key to operation, he retains the word form and gives it another significance. Form becomes for him the unseen principle of activity and operation. adopting this view Aristotle is affirming a deep faith in the ability of our intellects to understand the natures o£ things in the physical world. Nevertheless, precise elucidation as to what these forms are is only determined by how they manifest themselves , that is, how the bodies of which they are forms operate. Thus, it is of the greatest importance to recognize the power of a famous scholastic axiom in conformity with Aristotle's view-" A thing operates in that manner in which it is." Here is a principle which indicates awareness of the power of the human intellect in its ability to affirm the :reality of a principle operation. the same time the principle (used properly) reflects the inability of the intellect to perceive these sources of operation directly. It will be worthwhile to note in some detail how the scholastic definition of man as a rational animal may be regarded in the light of this functional or operational approach. The definition reduces ultimately to saying that man is a rational, sentient, living, material substance. The observed basis fo:r the more specific elements in the definition is, of course, the observed functions or operations of :reasoning, sensing, growing and reproducing. Use of the principle that, " A thing operates in that manner in which it is," then enables one to infer the unseen powers of the soul, and thus to infer the nature of man. It is in the light of the preceding considerations that one may :regard Aristotle and Aquinas as operationalists in some sense, and one may now attempt to relate this view to modern physics. 1 McKeon, R. Basic Worlcs of Aristotle, (New York: Random House, 1941) De Caelo, 307 b lli. APPROACHES TO THE PHYSICAL WORLD 391 It must be remembered that both the Pythagorian and the Aristotelian-Thomistic views on this point are in opposition to...