On the Philosophy of Discovery, Chapters Historical and Critical

5. Kant considers that Space and Time are conditions of perception, and hence sources of necessary and universal truth. Dr. Whewell agrees with Kant in placing in the mind certain sources of necessary truth; he calls these Fundamental Ideas, and reckons, besides Space and Time, others, as Cause, Likeness, Substance, and several more. Mr. Mill, the most recent and able expounder of the opposite doctrine, derives all truths from Observation, and denies that there is such a separate source of truth as Ideas. Mr. Mansel does not agree either with Mr. Mill or Dr. Whewell; he adheres to the original Kantian thesis, that Space and Time are sources of necessary truths, but denies the office to the other Fundamental Ideas of Dr. Whewell. In reading what has been said by Mr. Mill, Mr. Mansel, and other critics, on the subject of what I have called Fundamental Ideas, I am led to perceive that I have expressed myself incautiously, with regard to the identity of character between the first two of these Fundamental Ideas, namely, Space and Time, and the others, as Force, Composition, and the like. And I am desirous of explaining, to those who take an interest in these speculations, how far I claim for the other Fundamental Ideas the same character and attributes as for Space and Time.

6. The special and characteristic property of all the Fundamental Ideas is what I have already mentioned, that they are the mental sources of necessary and universal scientific truths. I call them Ideas, as being something not derived from sensation, but governing sensation, and consequently giving form to our experience;—Fundamental, as being the foundation of knowledge, or at least of Science. And the way in which those Ideas become the foundations of Science is, that when they are clearly and distinctly entertained in the mind, they give rise to inevitable convictions or intuitions, which may be expressed as Axioms; and these Axioms are the foundations of Sciences respective of each Idea. The Idea of Space, when clearly possessed, gives rise to geometrical Axioms, and is thus the foundation of the Science of Geometry. The Idea of Mechanical Force, (a modification of the Idea of Cause,) when clearly developed in the mind, gives birth to Axioms which are the foundation of the Science of Mechanics. The Idea of Substance gives rise to the Axiom which is universally accepted,—that we cannot, by any process, (for instance, by chemical processes,) create or destroy matter, but can only combine and separate elements;—and thus gives rise to the Science of Chemistry.

7. Now it may be observed, that in giving this account of the foundation of Science, I lay stress on the condition that the Ideas must be clearly and distinctly possessed. The Idea of Space must be quite clear in the mind, or else the Axioms of Geometry will not be seen to be true: there will be no intuition of their truth; and for a mind in such a state, there can be no Science of Geometry. A man may have a confused and perplexed, or a vacant and inert state of mind, in which it is not clearly apparent to him, that two straight lines cannot inclose a space. But this is not a frequent case. The Idea of Space is much more commonly clear in the minds of men than the other Ideas on which science depends, as Force, or Substance. It is much more common to find minds in which these latter Ideas are not so clear and distinct as to make the Axioms of Mechanics or of Chemistry self-evident. Indeed the examples of a state of mind in which the Ideas of Force or of Substance are so clear as to be made the basis of science, are comparatively few. They are the examples of minds scientifically cultivated, at least to some extent. Hence, though the Axioms of Mechanics or of Chemistry may be, in their own nature, as evident as those of Geometry, they are not evident to so many persons, nor at so early a period of intellectual or scientific culture. And this being the case, it is not surprising that some persons should doubt whether these Axioms are evident at all;—should think that it is an error to assert that there exist, in such sciences as Mechanics or Chemistry, Fundamental Ideas, fit to be classed with Space, as being, like it, the origin of Axioms.

In speaking of all the Fundamental Ideas as being alike the source of Axioms when clearly possessed, without dwelling sufficiently upon the amount of mental discipline which is requisite to give the mind this clear possession of most of them; and in not keeping before the reader the different degrees of evidence which, in most minds, the Axioms of different sciences naturally have, I have, as I have said, given occasion to my readers to misunderstand me. I will point out one or two passages which show that this misunderstanding has occurred, and will try to remove it.

8. The character of axiomatic truths seen by intuition is, that they are not only seen to be true, but to be necessary;—that the contrary of them is not only false, but inconceivable. But this inconceivableness depends entirely upon the clearness of the Ideas which the axioms involve. So long as those Ideas are vague and indistinct, the contrary of an Axiom may be assented to, though it cannot be distinctly conceived. It may be assented to, not because it is possible, but because we do not see clearly what is possible. To a person who is only beginning to think geometrically, there may appear nothing absurd in the assertion, that two straight lines may inclose a space. And in the same manner, to a person who is only beginning to think of mechanical truths, it may not appear to be absurd, that in mechanical processes, Reaction should be greater or less than Action; and so, again, to a person who has not thought steadily about Substance, it may not appear inconceivable, that by chemical operations, we should generate new matter, or destroy matter which already exists.

Here then we have a difficulty:—the test of Axioms is that the contrary of them is inconceivable; and yet persons, till they have in some measure studied the subject, do not see this inconceivableness. Hence our Axioms must be evident only to a small number of thinkers; and seem not to deserve the name of self-evident or necessary truths.

This difficulty has been strongly urged by Mr. Mill, as supporting his view, that all knowledge of truth is derived from experience. And in order that the opposite doctrine, which I have advocated, may not labour under any disadvantages which really do not belong to it, I must explain, that I do not by any means assert that those truths which I regard as necessary, are all equally evident to common thinkers, or evident to persons in all stages of intellectual development. I may even say, that some of those truths which I regard as necessary, and the necessity of which I believe the human mind to be capable of seeing, by due preparation and thought, are still such, that this amount of preparation and thought is rare and peculiar; and I will willingly grant, that to attain to and preserve such a clearness and subtlety of mind as this intuition requires, is a task of no ordinary difficulty and labour.

9. This doctrine,—that some truths may be seen by intuition, but yet that the intuition of them may be a rare and difficult attainment,—I have not, it would seem, conveyed with sufficient clearness to obviate misapprehension. Mr. Mill has noticed a passage of my Philosophy on this subject, which he has understood in a sense different from that which I intended. Speaking of the two Principles of Chemical Science,—that combinations are definite in kind, and in quantity,—I had tried to elevate myself to the point of view in which these Principles are seen, not only to be true, but to be necessary. I was aware that even the profoundest chemists had not ventured to do this; yet it appeared to me that there were considerations which seemed to show that any other rule would imply that the world was a world on which the human mind could not employ itself in scientific speculation at all. These considerations I ventured to put forwards, not as views which could at present be generally accepted, but as views to which chemical philosophy appeared to me to tend. Mr. Mill, not unnaturally, I must admit, supposed me to mean that the two Principles of Chemistry just stated, are self-evident, in the same way and in the same degree as the Axioms of Geometry are so. I afterwards explained that what I meant to do was, to throw out an opinion, that if we could conceive the composition of bodies distinctly, we might be able to see that it is necessary that the modes of this composition should be definite. This Mr. Mill does not object to311: but he calls it a great attenuation of my former opinion; which he understood to be that we, (that is, men in general,) already see, or may see, or ought to see, this necessity. Such a general apprehension of the necessity of definite chemical composition I certainly never reckoned upon; and even in my own mind, the thought of such a necessity was rather an anticipation of what the intuitions of philosophical chemists in another generation would be, than an assertion of what they now are or ought to be; much less did I expect that persons, neither chemists nor philosophers, would already, or perhaps ever, see that a proposition, so recently discovered to be true, is not only true, but necessary.

10. Of the bearing of this view on the question at issue between Mr. Mill and me, I may hereafter speak; but I will now notice other persons who have misunderstood me in the same way.

An able writer in the Edinburgh Review312 has, in like manner, said, "Dr. Whewell seems to us to have gone much too far in reducing to necessary truths what assuredly the generality of mankind will not feel to be so." It is a fact which I do not at all contest, that the generality of mankind will not feel the Axioms of Chemistry, or even of Mechanics, to be necessary truths. But I had said, not that the generality of mankind would feel this necessity, but (in a passage just before quoted by the Reviewer) that the mind under certain circumstances attains a point of view from which it can pronounce mechanical (and other) fundamental truths to be necessary in their nature, though disclosed to us by experience and observation.

Both the Edinburgh Reviewer and Mr. Mansel appear to hold a distinction between the fundamental truths of Geometry, and those of the other subjects which I have classed with them. The latter says, that perhaps metaphysicians may hereafter establish the existence of other subjective conditions of intuitions (or, as I should call them, Fundamental Ideas,) besides Space and Time, but that in asserting such to exist in the science of Mechanics, I certainly go too far: and he gives as an instance my Essay,—"Demonstration that all matter is heavy." I certainly did not expect that the Principles asserted in that Essay would be assented to as readily or as generally as the Axioms of Geometry; but I conceive that I have there proved that Chemical Science, using the balance as one of its implements, cannot admit "imponderable bodies" among its elements. This impossibility will, I think, not only be found to exist in fact, but seen to exist necessarily, by chemists, in proportion as they advance towards general propositions of Chemical Science in which the so-called "imponderable fluids" enter. But even if I be right in this opinion, to how few will this necessity be made apparent, and how slowly will the intuition spread! I am as well aware as my critics, that the necessity will probably never be apparent to ordinary thinkers.

11. Though Mr. Mansel does not acknowledge any subjective conditions of intuition besides Space and Time, he does recognize other kinds of necessity, which I should equally refer to Fundamental Ideas; because they are, no less than Space and Time, the foundations of universal and necessary truths in science. Such are313 the Principle of Substance;—All Qualities exist in some subject: and the Principle of Causality;– Every Event has its Cause. To these Principles he ascribes a "metaphysical necessity," the nature and grounds of which he analyses with great acuteness. But what I have to observe is, that whatever differences may be pointed out between the grounds of the necessity, in this case of metaphysical necessity, and in that which Mr. Mansel calls mathematical necessity which belongs to the Conditions or Ideas of Space and of Time; still, it is not the less true that the Ideas of Substance and of Cause, do afford a foundation for necessary truths, and that on these truths are built Sciences. That every Change must have a Cause, with the corresponding Axioms,—that the Cause is known by the Effect, and Measured by it,—is the basis of the Science of Mechanics. That there is a Substance to which qualities belong, with the corresponding Axiom,—that we cannot create or destroy Substance, though we may alter Qualities by combining and separating Substances,—is the basis of the Science of Chemistry. And that this doctrine of the Indestructibility of Substance is a primary axiomatic truth, is certain; both because it has been universally taken for granted by men seeking for general truths; and because it is not and cannot be proved by experience314. So that I have here, even according to Mr. Mansel's own statement, other grounds besides Space and Time, for necessary truths in Science.

12. Besides mathematical and metaphysical necessity, Mr. Mansel recognizes also a logical necessity. I will not pretend to say that this kind of necessity is exactly represented by any of those Fundamental Ideas which are the basis of Science; but yet I think it will be found that this logical necessity mainly operates through the attribution of Names to things; and that a large portion of its cogency arises from these maxims,—that names must be so imposed that General Propositions shall be possible,—and so that Reasoning shall be possible. Now these maxims are really the basis of Natural History, and are so stated in the Philosophy of the Inductive Sciences. The former maxim is the principle of all Classification; and though we have no syllogisms in Natural History, the apparatus of genus, species, differentia, and the like, which was introduced in the analysis of syllogistic reasoning, is really more constantly applied in Natural History than in any other science.

13. Besides the different kinds of necessity which Mr. Mansel thus acknowledges, I do not see why he should not, on his own principles, recognize others; as indeed he appears to me to do. He acknowledges, I think, the distinction of Primary and Secondary qualities; and this must involve him in the doctrine that Secondary Qualities are necessarily perceived by means of a Medium. Again: he would, I think, acknowledge that in organized bodies, the parts exist for a Purpose; and Purpose is an Idea which cannot be inferred by reasoning from facts, without being possessed and applied as an Idea. So that there would, I conceive, exist, in his philosophy, all the grounds of necessary truth which I have termed Fundamental Ideas; only that he would further subdivide, classify, and analyse, the kinds and grounds of this necessity.

In this he would do well; and some of his distinctions and analyses of this kind are, in my judgment, very instructive. But I do not see what objection there can be to my putting together all these kinds of necessity, when my purpose requires it; and, inasmuch as they all are the bases of Science, I may call them by a general name; for instance, Grounds of Scientific Necessity; and these are precisely what I mean by Fundamental Ideas.

That some steady thought, and even some progress in the construction of Science, is needed in order to see the necessity of the Axioms thus introduced, is true, and is repeatedly asserted and illustrated in the History of the Sciences. The necessity of such Axioms is seen, but it is not seen at first. It becomes clearer and clearer to each person, and clear to one person after another, as the human mind dwells more and more steadily on the several subjects of speculation. There are scientific truths which are seen by intuition, but this intuition is progressive. This is the remark which I wish to make in answer to those of my critics who have objected that truths which I have propounded as Axioms, are not evident to all.

14. That the Axioms of Science are not evident to all, is true enough, and too true. Take the Axiom of Substance:—that we may change the condition of a substance in various ways, but cannot destroy it. This has been assumed as evident by philosophers in all ages; but if we ask an ordinary person whether a body can be destroyed by fire, or diminished, will he unhesitatingly reply, that it cannot? It requires some thought to say315, as the philosopher said, that the weight of the smoke is to be found by subtracting the weight of the ashes from that of the fuel; nay, even when this is said, it appears, at first, rather an epigram than a scientific truth. Yet it is by thinking only, not by an experiment, that, from a happy guess it becomes a scientific truth. And the thought is the basis, not the result, of experimental truths; for which reason I ascribe it to a Fundamental Idea. And so, such truths are the genuine growth of the human mind; not innate, as if they needed not to grow; still less, dead twigs plucked from experience and stuck in from without; not universal, as if they grew up everywhere; but not the less, under favourable circumstances, the genuine growth of the scientific intellect.

15. Not only do I hold that the Axioms, on which the truths of science rest, grow from guesses into Axioms in various ways, and often gradually, and at different periods in different minds, and partially, even in the end; but I conceive that this may be shown by the history of science, as having really happened, with regard to all the most conspicuous of such principles. The scientific insight which enabled discoverers to achieve their exploits, implied that they were among the first to acquire an intuitive conviction of the Axioms of their Science: the controversies which form so large a portion of the history of science, arise from the struggles between the clear-sighted and the dimsighted, between those who were forwards and those who were backwards in the progress of ideas; and these controversies have very often ended in diffusing generally a clearness of thought, on the controverted subject, which at first, the few only, or perhaps not even they, possessed. The History of Science consists of the History of Ideas, as well as of the History of Experience and Observation. The latter portion of the subject formed the principal matter of my History of the Inductive Sciences; the former occupied a large portion of the Philosophy of the Inductive Sciences316; which, I may perhaps be allowed to explain, is, for the most part, a Historical Work no less than the other; and was written in a great measure, at the same time, and from the same survey of the works of scientific writers.

16. I am aware that the explanation which I have given, may naturally provoke the opponents of the doctrine of scientific necessity to repeat their ordinary fundamental objections, in a form adapted to the expressions which I have used. They may say, the fact that these so-called Axioms thus become evident only during the progress of experience, proves that they are derived from experience: they may, in reply to our image, say, that truths are stuck into the mind by experience, as seeds are stuck into the ground; and that to maintain that they can grow under any other conditions, is to hold the doctrine of spontaneous generation, which is equally untenable in the intellectual and in the physical world. I shall not however here resume the general discussion; but shall only say briefly in reply, that Axioms,—for instance, this Axiom, that material substances cannot be created or annihilated by any process which we can apply,—though it becomes evident in the progress of experience, cannot be derived from experience; for it is a proposition which never has nor can be proved by experience; but which, nevertheless, has been always assumed by men, seeking for general truths, as necessarily true, and as controlling and correcting all possible experience. And with regard to the image of vegetable development, I may say, that as such development implies both inherent forms in the living seed, and nutritive powers in earth and air; so the development of our scientific ideas implies both a formative power, and materials acted on; and that, though the analogy must be very defective, we conceive that we best follow it by placing the formative power in the living mind, and in the external world the materials acted on: while the doctrine that all truth is derived from experience only, appears to reject altogether one of these elements, or to assert the two to be one.