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.