A Brief History of Modern Philosophy. Harald Høffding

not merely to follow nature, but to bring forth a new, higher order of nature, that he may become lord of the earth. In the Degli eroici furori (1585) Bruno describes the heroic man as one who is aware that the highest good can only be realized through strife and suffering, but who never despairs, because pain and danger are evils only from the viewpoint of the world of sense, not from the viewpoint of eternity (ne l’occhio del eternitade). The possibilities ​of pain increase with the height of the aim. But the heroic man finds his joy in the fact that a noble fire has been kindled in his breast—even though the goal should be impossible of realization and his soul should be consumed by its profound yearning. This courageous wisdom typifies Bruno’s character as it appears in his life and in his heroic death at the stake.

      C. The New Science

      Without any disparagement of the tremendous importance of the free investigations in the sphere of mental science, or even the radical change in the general theory of the universe, the fact nevertheless remains that the founding of modern natural science had a far profounder influence upon human life. The contributions of antiquity are likewise in evidence here, particularly the study of the writings of Archimedes. The real cause however must be traced to the increasing interest in the industries, mechanics and engineering operations, especially in the Italian cities. Galileo makes mention of this fact at the opening of his chief work. It was but natural therefore that this should give rise to a desire to understand the laws and principles by which to promote these operations. Then followed a transition from the achievements of man to the majestic products of nature, because man depends, more or less consciously, on the analogy between human mechanics and the efficiency of nature.

      Modern natural science created a new method. It substituted observation and experiment together with analysis and computation for speculation and dogmatic construction on the one hand and the mere collection of facts on the other. The human mind evolved new functions, whose nature and value necessarily suggested new ​problems in the philosophy of knowledge. Owing to the fact that the new method was applied almost exclusively to the realm of matter, the concept of matter naturally came to the foreground. And as a matter of fact it was not until then that the problem of the relation of mind and matter could be sharply and definitely stated. Ethics and the philosophy of religion likewise received their complement of new data. The self-sufficiency of man was magnified. New forms of social life were evolved, especially through the progressive division of labor made possible and necessary through the mechanical inventions. The growing conviction of the prevalence of fixed natural laws required a restatement and a more precise definition of the problem of religion. Man’s general attitude to the universe, both in its theoretical and its practical aspects, underwent a most remarkable change.

      We shall mention three men as the real founders of modern science.

      1. Leonardo da Vinci (1452-1519), the famous artist, whose varied talents made him one of the most remarkable characters of the Renaissance period, is known to us through several fragments in natural science and philosophy which are of great importance. His manuscripts became scattered and none were published until late in the nineteenth century. (H. P. Richter has published a good collection. London, 1883. A German translation of the most important fragments was published by M. Herzfeld, Leipzig, 1904.)

      Experience is the common mother of all knowledge. But we cannot stop on the plane of mere observation. We must find the internal bond of nature (freno e regula interna) which explains the vital relation of things and events. And the only possible method of doing this is ​by the aid of mathematics. Mathematical deduction is the only method of discovering the unknown from the given facts of nature. We thus find even here a clear expression of all the characteristics of modern method, viz. the proper coordination of induction and deduction.—Certain statements of Leonardo’s indicate a sturdy naturalism. The only thing we can know about the soul is the nature of its functions and its activity as an organic principle; whoever cares to know more must inquire of the Monks! Nature consists of a majestic cycle between the inorganic and the organic, and between the animate and the inanimate. Nature always takes the simplest course. There is reason therefore to hope for a great future with respect to the knowledge of nature.—Leonardo suggested a number of interesting anticipations of the principle of inertia and of energy. He stands solitary and alone in his own age. It was not until a century later that any advancements were made along the lines which he indicated.

      b. John Kepler (1571-1630), the famous astronomer, is an interesting example of the evolution of an exact scientific conception of nature from a mystic-contemplative starting-point. His first treatise (Mysterium cosmographicum, 1597) is based on theological and Pythagorean principles. The universe is the manifestation of God. The paths and motions of the heavenly bodies must therefore reveal certain harmonious and simple geometrical relations. The Holy Ghost is revealed in the harmonious ratio of magnitudes of stellar phenomena, and Kepler thinks it possible to construe this magnitudinal ratio. Later on however he simply maintained the general belief that certain quantitative ratios must exist between the motions of the planets and formulated the results deduced from ​Tycho Brahe’s observations in the laws which bear his name. He afterwards demonstrated the quantitative ratios on the basis of the facts of experience. Here his method involved the combination of the experimental with the mathematical method. Just as he had at first established the principle that nature conforms to mathematical laws by the theological method, so he further believes that the planets are guided in their course by separate planetary souls, even as the entire world-system is directed by the world-soul which dwells in the sun. His explanation of nature therefore was thoroughly animistic or mythological. Later on in life he held that science must make no assumptions except such as can be actually deduced from experience. He calls such causes vera causa. He also rejected the idea of planetary souls which as a matter of fact are never actually given in experience. In his Astronomia nova s. physica coelestis (1609) he makes the transition from theology and animism to pure natural science. He defends his belief in the importance and truth of the quantitative method psychologically and empirically as well as theologically. Mathematical knowledge is the clearest and the most certain knowledge which we possess and it becomes us therefore to apply it as widely as possible. The processes of nature are qualitatively modified by our subjective states (pro habitudine subjecti). Perfect certainty and objectivity can only be attained by the quantitative method. And, finally, experience reveals the fact that all material phenomena have quantitative, especially geometrical, attributes; “the method of measurement can be applied wherever there is matter” (ubi materia, ibi geometria). As a matter of fact the universe participates in quantity (mundus participat quantitate).

      Kepler elaborates his general conception of scientific ​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