On the Philosophy of Discovery, Chapters Historical and Critical

by William Whewell

3. It is true, however, that I had adopted some of Kant's views, or at least some of his arguments. The chapters[309] on the Ideas of Space and Time in the Philosophy of the Inductive Sciences, were almost literal translations of chapters in the Kritik der Reinen Vernunft. Yet the author was charged by a reviewer at the time, with explaining these doctrines "in a manner incompatible with the clear views of Emanuel Kant." It appeared to be assumed by the English admirers of the Kantian philosophy, that Kant's views were true and clear in Germany, but became untenable when adopted in England.

4. (Mr. Mansel)—But the most important of my critics on this ground is Mr. Mansel, who has revived the censure of my speculations as not doing justice to the Kantian philosophy. "It is much to be regretted," he says[310], "that Dr. Whewell, who has made good use of Kantian principles in many parts of his Philosophy of the Inductive Sciences," has not more accurately observed Kant's distinction between the necessary laws under which all men think, and the contingent laws under which certain men think of certain things. And further on Mr. Mansel, after giving great praise to the general spirit of the Philosophy of the Inductive Sciences, says, "It is to be regretted that the accuracy of his theory has been in so many instances vitiated by a stumble at the threshold of the Critical Philosophy." Mr. Mansel is, indeed, by much the most zealous English Kantian whose writings I have seen;—among those, I mean, who have brought original powers of philosophical thought to bear upon such subjects; and have not been, as some have been, enslaved by an admiration of German systems, just as bigotted as the contempt of them which others feel. And as Mr. Mansel has stated distinctly some of the points in which he conceives that I have erred in deviating from the doctrines of Kant, I should wish to make a few remarks on those points.

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 to[311]: 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.