Natural Philosophy

by Wilhelm Ostwald

The procedure of science is similar to that of practical life, though freer. Whenever an investigator seeks to test a natural law of the form: if A is so, then B is so, he endeavors to choose or formulate the experiences in such a way that the fewest possible extraneous elements are present, and that those that are unavoidable should exert the least possible influence upon the relation in question. He never succeeds completely. In order, nevertheless, to reach a conclusion as to the form the relation will take without extraneous influences, the following general method is applied.

A series of instances are investigated which are so adjusted that the influence of the extraneous elements grows less and less. Then the relation investigated approaches a limit which is never quite reached, but to which it draws nearer and nearer, the less the influence of the extraneous elements. And the conclusion is drawn that if it were possible to exclude the extraneous elements entirely, the limit of the relation would be reached.

A case in which none of the extraneous elements of experience operate is called an ideal case, and the inference from a series of values leading to the limit-value is an extrapolation. Such extrapolations to the ideal case are a quite natural procedure in science, and a very large part of natural laws, especially all quantitative laws, that is, such as express a relation between measurable values, have precise validity only in ideal cases.

We here confront the fact that many natural laws, and among them the most important, are expressed as, and taken to be, conditions which never occur in reality. This seemingly absurd procedure is, as a matter of fact, the best fitted for scientific purposes, since ideal cases are to be distinguished by this, that with them the natural laws take on the simplest forms. This is the result of the fact that in ideal cases we intentionally and arbitrarily overlook every complication of the determining factors, and in describing ideal cases we describe the simplest conceivable form of the class of experiences in question. The real cases are then constructed from the ideal cases by representing them as the sum of all the elements that have an influence on the experience or the result. Just as we can represent the unlimited multitude of finite numbers by the figures up to ten, so we can represent an unlimited quantity of complicated events by a finite number of natural laws, and so reach a highly serviceable approximation to reality.

Thus geometry deals with absolutely straight lines, absolutely flat surfaces, and perfect spheres, though such have never been observed, and the results of geometry come the closer to truth, the more nearly the real lines, surfaces, and spheres correspond to the ideal demands. Similarly, in physics, there are no ideal gases or mirrors, or in chemistry ideally pure substances, though the expressed simple laws in these sciences are valid for only such bodies. The non-ideal bodies of these sciences, which reality presents in various degrees of approximation, correspond the more closely to these laws, the slighter the deviation of the real from the ideal. And the same method is applied in the so-called mental sciences, psychology and sociology, in which the "normal eye" and a "state with an entirely closed door" are examples of such idealized limit-concepts.

15. The Determinateness of Things.

A very widespread view and a very grave one, because of its erroneous results, is that by the natural laws things are unequivocally and unalterably determined down to the very minutest detail. This is called determinism, and is regarded as an inevitable consequence of every natural scientific generalization. But an accurate investigation of actual relations produces something rather different.

The most general formulation of the natural law: if A is experienced, then we expect B, necessarily refers in the first place only to certain parts of the thing experienced. For perfect similarity in two experiences is excluded by the mere fact that we ourselves change unceasingly and one-sidedly. Consequently, no matter how accurate the repetition of a former experience may be, our very participation in it, an element bound to enter, causes it to be different. Therefore we deal with only a partial repetition of any experience, and the common part is all the smaller a fraction of the entire experience, the more general the concept corresponding to this part. But the most general and most important natural laws apply to such very general ideas, and accordingly they determine only a small part of the whole result. Other parts are determined by other laws, but we can never point out an experience that has been determined completely and unequivocally by natural laws known to us. For example, we know that when we throw a stone, it will describe an approximate parabolic curve in falling to the ground. But if we should attempt to determine its course accurately, we should have to take into consideration the resistance of the air, the rotatory motion of the stone upon being thrown, the movement of the earth, and numerous other circumstances, the exact determination of which is a matter beyond the power of all sciences. Nothing but an approximate determination of the stone's course is possible, and every step forward toward accuracy and absoluteness would require scientific advances which it would probably take centuries to accomplish.

Science, therefore, can by no means determine the exact linear course that the stone will take in its fall. It can merely establish a certain broader path within which the stone's movement will remain. And the path is the wider the smaller the progress science has made in the branch in question. The same conditions prevail in the case of every other prediction based upon natural laws. Natural laws merely provide a certain frame within which the thing will remain. But which of the infinitely numerous possibilities within this frame will become reality can never be absolutely determined by human powers.

The belief that it is possible has been evoked merely by a far-reaching method of abstraction on the part of science. By assuming in place of the stone "a non-extended point of mass" and by disregarding all the other factors which in some way (whether known or unknown) exercise an influence on the stone's movement, we can effect an apparently perfect solution of the problem. But the solution is not valid for real experience, merely for an ideal case, which bears only a more or less profound similarity to the real. It is only such an ideal world, that is, a world arbitrarily removed from its actual complexity, that has the quality of absolute determinateness which we are wont to ascribe to the real world.