THE

LONDON UNIVERSITY

MAGAZINE.

ART. I.—THE PHILOSOPHY OF THE INDUCTIVE SCIENCES, Founded upon their History. By the Rev. William Whewell, B.D., Fellow (now Master) of Trinity College, and Professor of Moral Philosophy in the University of Cambridge, Vice President of the Geological Society of London. In Two Volumes. London: John W. Parker, West Strand. Cambridge: J. and J. J. Deighton.

1840.

IN a former Number of this Magazine we inserted a notice of the work upon which the volumes now before us are founded; and as both these works were written in pursuance of the same design, and the principal object of the History was to form an Introduction to the Philosophy of the Inductive Sciences, we now proceed to the completion of our task, by introducing to our readers this second and most important part of Mr. Whewell's labours. This being the case, it will not be necessary for us to repeat any of our preliminary remarks, and we shall therefore proceed at once to the consideration of the subjects of which these volumes treat.

Mr. Whewell has defined the Philosophy of any given Science to be, an exposition and discussion of the Fundamental Ideas of that Science ;" and a consideration of these different Fundamental Ideas furnishes the most natural, and, at the same time, the most philosophical arrangement of which scientific truths are susceptible. Such an arrangement, combined with the discussion of each Fundamental Idea, and an exposition of the process by which the Sciences are evolved from these Ideas, is what we understand by the term Philosophy of the VOL. I.-NO. 3.

T

Sciences. That the truths and discoveries, of which general Science is composed, would themselves admit of a scientific arrangement, constituting something different from the mere aggregate of the several knowledges, was sufficiently evident to the two great champions of the rival systems of Ideas and Facts-Plato and Bacon. Thus the former defines philosophers, “ ὡς μὲν γιγνωσκόντας τίνος ἔστιν ἐπιστήμη ἑκάστη τούτων τῶν ἐπιστήμων, ὁ τυγχάνει ἂν ἄλλο αὐτῆς τῆς ἐπιστήμης;” and the latter, in explaining his division of the Sciences, adopts a striking illustration. "Because the distributions and partitions of knowledge are not like several lines that meet in one angle, and so touch but in a point; but are like branches of a tree, that meet in a stem, which hath a dimension and quantity of entireness and continuance, before it come to discontinue and break itself into arms and boughs; therefore, it is good, before we enter into the former distribution, to erect and constitute one universal Science, by the name of 'Philosophia Prima,' primitive or summary philosophy, as the main and common way, before we come where the ways part and divide themselves ;" and shortly afterwards, he states that he has assigned to this summary or highest Philosophy, "the common principles and axioms which are promiscuous and indifferent to several Sciences." Viewing philosophy then in these two distinct lights;-first, as an analysis and examination of the Ideas and Truths of which the several Sciences, the branches of the tree, are composed; and secondly, as an exposition of the connexion which exists between these various systems, the stem of the tree ;-we see great force in the observations of a modern metaphysician,† who, in attempting to reconcile the apparently incongruous principles of Plato and Bacon, states the difference between them as simply this; "That, philosophy being necessarily bipolar, Plato treats principally of the truth, as it manifests itself at the Ideal pole, as the Science of Intellect, (i. e. de mundo intelligibili); while Bacon confines himself, for the most part, to the same truth, as it is manifest edat the other or material pole, as the Science of Nature, (i. e. de mundo sensibili.) It is as necessary, therefore, that Plato should direct his inquiries chiefly to those objective truths that exist in and for the intellect alone, the images and representatives of which we construct for ourselves by figure, number, and word; as that Lord Bacon should attach his main concern to the truths which have their signatures in nature, and which, (as he himself plainly and often

asserts), may indeed be revealed to us through and with, but never by, the senses or the faculty of sense.-Hence, too, it will not surprise us, that Plato so often calls Ideas, Living Laws, in which the mind has its whole true being and permanence; or that Bacon, vice versa, names the laws of nature, Ideas; and represents what we have called facts of science and central phenomena, as signatures, impressions, and symbols of Ideas." The sense, however, in which Mr. Whewell uses the term Idea, which we propose to adopt in this article, is not identical with the meaning which we attach to the phrase, Laws of nature or living Laws; yet these axiomatic Laws are, as we shall afterwards see, involved in the Ideas, and flow directly from them; or rather, to speak more strictly, not directly, but through the medium of the Ideal Conceptions, which are peculiar modifications of the original Fundamental Idea. "The combination of Ideas and experience is," as Mr. Whewell observes, "necessary, in order to give us any knowledge of the external world, any insight into the laws of nature. Different persons, according to their mental habits and constitutions, may be inclined to dwell by preference upon one or other of these two elements. But no knowledge can exist without the practical union of the two, nor any philosophy without their speculative separation." *

From what we have stated, it will be readily perceived, that the philosophical arrangement of scientific knowledge does not necessarily correspond with the order of discoveries; it will be found in many instances to be directly the reverse. The path upon which philosophers actually travelled, in discovering the laws of nature, and the strict rules of philosophizing, by which, according to the Baconian doctrines, they ought to be governed in asserting and demonstrating them, are indeed of very great importance, in a scientific exposition of the principles, upon which those laws, and the truths deduced from those laws, are founded; (and hence it is, that Lord Bacon vehemently complains of the deficiency of general natural history;) yet they do not in any sense constitute this exposition, much less can they be considered as identical with it. It must be remembered, then, that we are not here pointing out, how discoveries were made, or by what rules they ought to be attempted; but we are endeavouring to strike out the exact principle, upon which their truth depends, and the most philosophical manner in which they ought to be arranged: we are engaged, not in instituting axioms, but in determining the position and rank which, when instituted, they, with the results to which they lead, should hold in a

* Vol. I. p. 33.

Philosophy of Science.

We are the more anxious to call attention to this, lest we should be thought to underrate the importance of the Inductive process, or be looked upon as disciples of Plato, when we are, in matters of Induction, close followers of Bacon.

All science, then, may be said to consist of primary or fundamental Ideas, and Truths or Laws which may be deduced from these Ideas, with or without the help of external and material nature. Those truths or laws which can be discovered without this assistance are entirely independent of experience, and may be called necessary truths. They are truths which a mind possessed of the appropriate fundamental Idea must necessarily discover, by simply deducing from that Idea its logical and mathematical consequences; and which when discovered cannot under any circumstances be conceived to be other than what they are. Those Truths or Laws which cannot be deduced from the appropriate fundamental Idea without the aid of external nature, or, in other words, without experience and observation, might properly be called experimental truths or laws, but are generally denominated contingent truths: and are such that the mind may, without absurdity or inconsistency, conceive a natural system governed by laws different from these, or a system in which no laws corresponding to these can be found. On this distinction is founded the common division of general science into the Deductive and the Inductive Sciences; but if the former of these be defined so as to include only Pure Mathematics, while the latter comprehends all the primary and secondary Mechanical and Chemical Sciences, the division is not strictly philosophical; or at least is not sufficiently correct for the purposes of a treatise, in which the Sciences are themselves to be classified and reduced to a Science. A familiar and popular illustration of the difference between Induction and Deduction may be had, by supposing a man shut up alone in a dark room without access to external nature. It is evident that all the truths which he discovers must be necessary truths; and the nature and extent of his discoveries must depend on the Fundamental Ideas of which we suppose him possessed. By carrying out this illustration to a greater length, and supposing him to be possessed of different Ideas at different times, we shall be able to see distinctly on what Fundamental Idea or Ideas a given Science is founded, and what truths or laws of that Science are necessary and what experimental. Let us then suppose a person possessing a mind of unbounded logical and mathematical powers, utterly abstracted from all other minds and from external matter. It is clear that he could not in this position acquire any fundamental Ideas whatever. He could not acquire the

Idea of Space; for as matter to him does not exist, he would not require an Idea which is conceivable only as that in which all objects exist. Nor could he acquire the Idea of Time; since no succession of events, (and upon this the Idea of Time is founded), ever occurred to him. We are therefore at liberty to suppose his mind impressed ab extra with any Fundamental Idea which we may select, and to inquire what deductions he would form from such Ideas.

Let us then first suppose that he is impressed with a correct Idea of Space; which, being infinite itself, is divisible into portions limited by boundaries. This Idea of limited Space at once suggests the conceptions of Figure and Dimensions, which involve the mental acts of Definition and Measurement; and he would immediately begin to exercise his rational powers, by investigating the properties of lines, angles, surfaces, and solid spaces, by means of that partial conception of Magnitude which Space furnishes. Certain simple principles of reasoning, or Axioms, which are involved in and flow directly from the Idea of Space, would immediately occur to him; and by making strictly logical deductions from these in their simple form and as combined with one another, he could deduce without any verbal enunciation, all the Geometrical Properties of bounded Space. Here, then, is a Science composed entirely of necessary Truths, the Science of Geometry; founded upon a single Fundamental Idea, the Idea of Space.

Let us now suppose another Idea impressed upon the Mind; a correct Idea of Time; which, like Space, being infinite itself, is divisible into limited portions. The conception of Dimension and the act of Measurement are now extended to another subject; and the constant recurrence of equal portions of Time, suggests the cognate Idea of Number. Some of the Axioms or principles of reasoning derived from the Idea of Space are seen to flow with equal readiness from that of Number. A connexion is established between Number and Spatial Magnitude. Numbers are found to be a convenient and correct representation of Space, by establishing a referee, or standard, or unit of Space; and the properties of Spatial Magnitudes may be discovered by exercising the logical powers upon the Numbers which represent them. The use of arbitrary symbols to represent numbers in general, and their relations, affords a generalization of these properties of number, and gives to the properties of space thus deduced the same universality as those which were obtained without the intervention of Numbers. And thus another Science is established, also composed entirely of necessary truths, the Science of Algebra and Analytical Geometry; the first part being founded upon the Idea of