method in his Apologia Tychonis. All science is based on hypotheses. But hypotheses are by no means to be regarded as arbitrary notions. They must vindicate their title by the harmony of their logical consequences with the given facts and the consistency of their implications. Science begins with the observation of facts, uses these data for the formulation of hypotheses and finally seeks to discover the causes which account for the uniformity of events.
c. Galileo Galilei (1564-1642) is the real founder of modern science, because he shows the clearest understanding of modern methods—the method of induction and deduction as mutually complementary.
If induction demanded the examination of every possible case, inductive inference would be impossible. But it is possible to examine a number of characteristic cases, and formulate a hypothetical principle by an analysis of these cases, and finally prove that the consequences deduced from this principle are in accord with experience. In order to make this deduction and show its agreement with the facts correctly we must be in position to state our facts in quantitative terms. We are therefore under necessity of measuring phenomena exactly. Galileo raised the watchword; Measure everything which is measurable and reduce the things which will not admit of direct measurement to indirect measurement.
Kepler had previously shown that matter cannot of itself pass from rest to motion. Galileo advances a step farther. According to the principle of simplicity,—which, like Copernicus, Bruno and Kepler, he regarded as a universal law—he maintained that a body tends to remain in its given state so long as it is unaffected by external influences. A body can therefore of itself neither change its