Natural Philosophy

PART I. General Theory of Knowledge 11

GENERAL THEORY OF KNOWLEDGE 11

1. The Formation of Concepts 11

2. Science 13

3. The Aim of Science 13

4. Concrete and Abstract 16

5. The Subjective Part 17

6. Empirical Concepts 18

7. Simple and Complex Concepts 19

8. The Conclusion 24

9. The Natural Laws 28

10. The Law of Causation 31

11. The Purification of the Causal Relation 34

12. Induction 38

13. Deduction 40

14. Ideal Cases 44

15. The Determinateness of Things 47

16. The Freedom of the Will 50

17. The Classification of the Sciences 53

18. The Applied Sciences 57

PART II. Logic, the Science of the Manifold, and Mathematics 61

LOGIC, THE SCIENCE OF THE MANIFOLD, AND MATHEMATICS 61

19. The Most General Concept 61

20. Association 63

21. The Group 65

22. Negation 68

23. Artificial and Natural Groups 69

24. Arrangement of the Members 75

25. Numbers 78

26. Arithmetic, Algebra, and the Theory of Numbers 79

27. Co-ordination 80

28. Comparison 82

29. Numbers 85

30. Signs and Names 86

31. The Written Language 89

32. Pasigraphy and Sound Writing 92

33. Sound Writing 96

34. The Science of Language 97

35. Continuity 101

36. Measurement 107

37. The Function 109

38. The Application of the Functional Relation 112

39. The Law of Continuity 113

40. Time and Space 118

41. Recapitulation 124

PART III. The Physical Sciences 127

THE PHYSICAL SCIENCES 127

42. General 127

43. Mechanics 128

44. Kinetic Energy 132

45. Mass and Matter 136

46. Energetic Mechanics 138

47. The Mechanistic Theories 140

48. Complementary Branches of Mechanics 144

49. The Theory of Heat 147

50. The Second Fundamental Principle 150

51. Electricity and Magnetism 154

52. Light 156

53. Chemical Energy 159

PART IV. The Biologic Sciences 163

THE BIOLOGIC SCIENCES 163

54. Life 163

55. The Storehouse of Free Energy 168

56. The Soul 171

57. Feeling, Thinking, Acting 174

58. Society 179

59. Language and Intercourse 182

60. Civilization 184

INDEX 187

INTRODUCTION

Natural science and natural philosophy are not two provinces mutually exclusive of each other. They belong together. They are like two roads leading to the same goal. This goal is the domination of nature by man, which the various natural sciences reach by collecting all the individual actual relations between the natural phenomena, placing them in juxtaposition, and seeking to discover their interdependence, upon the basis of which one phenomenon may be foretold from another with more or less certainty. Natural philosophy accompanies these specialized labors and generalizations with similar labors and generalizations, only of a more universal nature. For instance, while the science of electricity, as a branch of physics, deals with the relation of electrical phenomena to one another and to phenomena in other branches of physics, natural philosophy is not only concerned with the question of the mutual connection of all physical relations, but also endeavors to include in the sphere of its study chemical, biological, astronomical, in short, all the known phenomena. In other words, natural philosophy is the most general branch of natural science.

Here two questions are usually asked. First, how can we define the boundary line between natural philosophy and the special sciences, since, obviously, sharp lines of demarcation are out of the question? Secondly, how can we investigate and teach natural philosophy, when it is impossible for any one person to master all the sciences completely, and so obtain a bird's-eye view of the general relations between all the branches of knowledge? To the beginner especially, who must first learn the various sciences, it seems quite hopeless to devote himself to a study that presupposes a command of them.

Since a discussion of the two questions will afford an excellent preliminary survey of the work in hand, it will be well to consider them in detail. In the first place, the lack of complete and precise boundary lines is a general characteristic of all natural things, and science is a natural thing. If, for instance, we try to differentiate sharply between physics and chemistry, we are met with the same difficulty. So also in biology if we try to settle beyond the shadow of a doubt the line of separation between the animal and the vegetable kingdoms.

If, despite this well-known impossibility, we consider the division of natural things into classes and orders as by no means useless and do not discard it, but regard it as an important scientific work, this is practical proof that such classification preserves its essential usefulness, even if it does not attain ideal definiteness. For, this imperfection notwithstanding, classification reaches its end, which is a comprehensive view, and thus a mastery, of the manifoldness of phenomena. For example, with the overwhelming majority of organic beings there is no doubt whether they are animals or plants. Similarly, most phenomena of inorganic nature can readily be designated as physical or chemical. For all such cases, therefore, the existing classification is good and useful. The few cases presenting difficulty may very well be considered by themselves wherever they occur, and we need merely take cognizance of them here. It follows from this, to be sure, that classification will be all the better fitted to its purpose the less frequently such doubtful cases arise, and that we have an interest in repeatedly testing existing classifications with a view to finding out if they cannot be supplanted by more suitable ones.

In these matters it is much the same as when we look upon the waves on the surface of a large body of water. Our first glance tells us that a number of waves are rolling there; and from a point giving us a sufficiently wide outlook, we can count them and gauge their width. But where is the line of division between one wave and the next? We undoubtedly see one wave following another, yet it is impossible for us to indicate precisely the end of one and the beginning of the next. Are we then to deduce that it is superfluous or unfeasible to designate the waves as different? By no means. On the contrary, in strictly scientific work we will endeavor to find some suitable definition of the boundary line between two consecutive waves. It may then be called an arbitrary line, and in a degree arbitrary it will certainly be. But to the investigator this does not matter. What concerns him is, if, with the help of this definition, wave lengths can be unequivocally determined, and if this is possible, he will use the definition as suitable to the purposes of science, without dismissing from his mind the idea that possibly some other definition may provide an even easier or sharper determination. Such an one he would instantly prefer to the old one.

Thus we see that these questions of classification are not questions of the so-called "essence" of the thing, but pertain merely to purely practical arrangements for an easier and more successful mastery of scientific problems. This is an extremely important point of view, much more far-reaching than is apparent here at its first application.

As to the second objection, I will admit its validity. But here, too, we have a phenomenon appearing in all branches and forms of science. Therefore we must familiarize ourselves with it in advance. Science was created by man for man's purposes, and, consequently, like all human achievements, possesses the indestructible quality of imperfection. But the mere fact that a successful working science exists, with the help of which human life has been fundamentally modified, signifies that the quality of incompleteness in human learning is no hindrance to its efficiency. For what science has once worked out always contains a portion of truth, hence a portion of efficiency. The old corpuscular theory of light, which now seems so childishly incomplete to us, was adequate, none the less, for satisfactorily explaining the phenomena of reflection and refraction, and the finest telescopes have been built with its help. This is due to the true elements in it, which taught us correctly to calculate the direction of rays of light in reflection and refraction. The rest was merely an arbitrary accessory which had to fall when new, contradictory facts were discovered. These facts could not have been taken into consideration when the theory was propounded, because they were not yet known. But when the corpuscular theory of light was replaced by the theory of waves of an elastic ether, geometric optics at first remained quite unchanged, because the theory of straight lines of rays could be deduced from the new views also, though not so easily and smoothly. And geometric optics was then concerned with nothing but these straight lines, in no wise with the question of their propagation. It did not become clear until recently that this conception of straight lines of rays is incomplete, though, it is true, it made a first approach toward the presentation of actual phenomena. It fails when it comes to characterize the behavior of a pencil of rays of large aperture. The old idea of a straight line of rays was to be replaced by a more complex concept with more varied characteristics, namely, the wave-surface. The greater variety of this concept renders possible the presentation of the greater variety of the optical phenomena just mentioned. And from it proceed the very considerable advances that have been made, since the new theory was propounded, in optical instruments, especially the microscope and the photographic objective, for the purposes of which pencils of rays of large aperture are required. The astronomic objective with its small angle of aperture has not undergone particularly important improvements.

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