[113]. For the various views here summarised, see as original sources, Geulincx, Metaphysica Vera, Pars Prima, 5-8; Malebranche, Entretiens sur la Metaphysique et sur la Religion, 7th dialogue; Berkeley, New Theory of Vision, pp. 147, 148; Principles of Human Knowledge, §§ 25-33, 51-53, 57, 150; Second Dialogue between Hylas and Philonous.
[114]. Geulincx expresses the principle in the following formula (op. cit., pt. 1, 5): quod nescis quomodo fiat, id non facis.
[115]. Not that existence can intelligibly be treated as a property; on this point Kant’s famous criticism of the “ontological proof” seems conclusive. But from the point of view of Leibnitz it must be imagined as an additional predicate, somehow added by the creative act of God to those already contained in the concept of the world as “possible.”
[116]. For Leibnitz’s doctrine consult further, The Monadology etc., of Leibniz, edit. by R. Latta, Introduction, pts. 2 and 3, and translations of Monadology, New System of the Communication of Substances, with the First and Third Explanations of the New System. Also see the elaborate criticisms of B. Russell, The Philosophy of Leibniz, chap. 4 and following chapters.
BOOK III
COSMOLOGY—THE INTERPRETATION
OF NATURE
CHAPTER I
INTRODUCTORY
[§ 1.] Distinction between the experimental sciences and a Philosophy of Nature and Mind. The former concerned with the description, the latter with the interpretation, of facts. [§ 2.] Cosmology is the critical examination of the special characteristics of the physical order. Its main problems are: (1) the problem of the nature of Material Existence; (2) problem of the justification of the concept of the Mechanical Uniformity of Nature; (3) problems of Space and Time; (4) problem of the Significance of Evolution; (5) problem of the Place of descriptive Physical Science in the System of Human Knowledge.
§ 1. In our two remaining Books we shall have to deal with the more elementary of the problems created by the apparent existence of two orders of Reality, a physical and a psychical, which again at least seem to stand in reciprocal interaction. In the present Book we shall discuss some of the leading characteristics which everyday thought and scientific thought respectively assign to the physical order, and shall ask how these characteristics compare with those we have seen ground to ascribe to Reality, i.e. we shall attempt to form a theory of the place of physical existence in the whole system of Reality. In the Fourth Book we shall discuss in the same way some of the leading characteristics of the psychical order as currently conceived, and the nature of its connection with the physical order. Our treatment of these topics will necessarily be imperfect and elementary for more reasons than one: not only are the facts of which some account must be taken so numerous and complicated that they would require for their mastery something like an encyclopædic acquaintance with the whole range of the experimental sciences, physical and psychological, but their adequate interpretation, especially on the cosmological side, would demand a familiarity with the ultimate foundations of mathematical theory which is rarely possessed either by the experimentalist or by the metaphysician. The utmost we can hope to accomplish in this part of our work is to establish one or two broad results as regards general principles: any suggestions we may make as to the details of interpretation must be avowedly tentative.
We must be careful to distinguish the task of a Philosophy of Nature and a Philosophy of Mind from those of the experimental sciences which deal directly with the fact of the physical and psychical orders. The fundamental business of the latter is, as we have already seen, the discovery of descriptive formulæ by the aid of which the various processes which make up the physical and psychical orders may be depicted and calculated. The fewer and simpler these formulæ, the more they economise the labour of calculation, the more completely do the experimental sciences perform the work for which we look to them. And so long as our formulæ adequately accomplish this work of calculation, it is indifferent for the experimental sciences whether the language in which they are couched represents a “reality” or not. The “atoms,” “forces,” and “ethers” of our physical, the “sensations” of our psychological formulæ, might be as purely symbolic creations of our own imagination as the “imaginary quantities” of mathematics, without their unreality in any way interfering with their scientific usefulness. In the words of an eminent physicist, “the atomic theory plays a part in physics similar to that of certain auxiliary concepts in mathematics, ... although we represent vibrations by the harmonic formula, the phenomena of cooling by exponentials, falls by squares of times, etc., no one will fancy that vibrations in themselves have anything to do with the circular functions, or the motion of falling bodies with squares” (Mach, Science of Mechanics, p. 492). When it is asserted that the usefulness of a scientific hypothesis, such as, e.g., the atomic theory or the hypothesis of the existence of an etherial undulating medium, of itself proves the real existence of things corresponding to the concepts employed by the hypothesis, the same fallacy is committed as when it is contended that if an algebraical calculus is generally capable of geometrical interpretation, every step in its operations must be interpretable.