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APPENDIX.

NOTE A, p. 84.

It is much to be regretted 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. His neglect of this distinction has given a seeming advantage to the empirical arguments of his antagonist, Mr. Mill, who is thus enabled apparently to decide the question at issue by what is in reality no more than an argumentum ad hominem. Thus Dr. Whewell says, of certain discoveries of physical laws, "So complete has been the victory of truth in most of these instances, that at present we can hardly imagine the struggle to have been necessary. The very essence of these triumphs is that they lead us to regard the views we reject as not only false, but inconceivable." In this relation, it is obvious that the inconceivability is, with reference to the human mind, merely contingent, and relative to the particular studies of particular men. Before the days of Copernicus, men could not conceive the apparent motion of the sun on the heliocentric hypothesis; the progress of science has reversed the difficulty; but the progress of science itself is contingent on the will of certain men to apply themselves to it. By thus endeavoring to exalt inductive laws of matter into à priori laws of mind, Dr. Whewell has unintentionally contributed to give an undue plausibility to the opposite theory, which reduces all laws of mind into the mere associations of this or that material experience.

But, on psychological grounds, it would seem as if the point of separation between à priori principles and empirical generalizations ought not to be very difficult of determination. The difference is not one of degree, but of kind; and the separation between the two classes of truths is such that no conceivable progress of science can ever convert the one into the other.

That which is inconceivable, not accidentally from the peculiar circumstances of certain men, but universally to all, must be so in consequence of an original law of the human mind; that which is universally true within the field of experience indicates an original law of the material world. No transformation of the one into the other is possible, unless the progress of science can change mind to matter or matter to mind. It is therefore incumbent on the philosopher who would extend mathematical certainty to the domain of physical science, to confirm, in every instance, his theory by a psychological deduction of his principles, as Kant has done in the instances of Space and Time.

Dr. Whewell lays much stress on clearness and distinctness of conceptions as the basis of the axiomatic truths of physical science. But the clearness or distinctness of any conception can only enable us more accurately to unfold the virtual contents of the concept itself; it cannot enable us to add à priori any new attribute. In other words, the increased clearness and distinctness of a conception may enable us to multiply to any extent our analytical judgments, but cannot add a single synthetical one. Without something more than this, the philosopher has failed to meet the touchstone of the Kantian question: How are synthetical judgments à priori possible?

The spirit of Dr. Whewell's Philosophy of the Inductive Sciences is beyond all praise. In these days of Positivism and Empiricism it is refreshing to find a writer of such vast attainments in the details of physical science comprising them under such truly philosophical principles. But it is to be regretted that the accuracy of his theory has been in some instances vitiated by a stumble on the threshold of the Critical Philosophy. The distinction laid down by Kant between the synthetical, or, properly, geometrical, and the analytical or general axioms, seems to have been altogether overlooked. Thus, almost at the outset of the Philosophy of the Inductive Sciences, the analytical judgment, "If equals are added to equals, the wholes are equal," is given as a condition of the intuition of magnitudes; and the same oversight runs through the Essay on Mathematical Reasoning, in which he speaks of "self-evident principles, not derived in any immediate manner from experiment, but involved in the very nature of the conceptions which we must possess, in order to reason upon such subjects at all." The very nature of the conceptions, however clearly apprehended, can give rise only to analytical judgments.

And such, I think, may be shown to be the character of all the mechanical axioms derived from the idea of Force. Of force, apart from the conscious exertion of will, we have no positive conception per se; we know

1 Book ii. ch. ix.

it only by its effects. Of equal forces we have no positive conception beyond that of the production of equal effects. To assert, therefore, that equal forces will balance each other at the two extremities of a lever, is to assert no more than that effects universally equal will be equal in any particular case.1

But to establish Mechanics as an à priori science upon the idea of force, it will be necessary to commence with some axioms at least of a synthetical character, analogous to the geometrical principles, "Two straight lines cannot enclose a space;" or, "If a straight line meets two straight lines, so as to make the two interior angles on the same side together less than two right angles, the two straight lines will meet if produced."

As a matter of fact, I do not think that Dr. Whewell has hitherto succeeded in establishing, in the science of Mechanics, a system of à priori synthetical truths derived from the idea of force as distinct from those which are mere applications of the mathematical intuitions of time or space. But as regards mere hypothetical mechanics, such a system is not inconceivable. A more exact psychological analysis of the intuitive fac

1 We must distinguish between the general theoretical statement of this axiom and its practical application to any given object. In Geometry, the axiom, "If equals are added to equals the wholes are equal," is a mere analytical judgment derived from the principle of Identity; but to ascertain whether two given magnitudes are equal, is a question of experiment or observation. So in Mechanics, the axiom that bodies acting with equal forces to turn a lever in opposite directions will retain it in equilibrium, is analytical; and as thus stated, it is unnecessary to add either that the directions of both forces must be perpendicular, or the arms of the lever equal. But in any special application of the axiom there arises at once the question, How can we ascertain that any two given forces are equal as forces acting upon the lever? If the force, for example, be gravity, and two equal weights be suspended, one perpendicularly, the other obliquely, the whole weight of the latter does not act to turn the lever in opposition to the former, and the hypothesis of the axiom is violated; the forces not being in that relation equal. Or if both are suspended perpendicularly, but at unequal distances from the fulcrum, the moments, or forces in relation to the lever, are not equal. The axiom, as stated by Dr. Whewell, "If two equal forces act perpendicularly at the extremities of equal arms of a straight line," has the appearance of a synthetical judgment, by comprehending under one formula the mere analysis of the notion of equal forces, and the empirical determination of equality in any particular instance. If by equal forces is meant forces equal in effect on the lever, the axiom, as stated by Dr. Whewell, is tautological; if the meaning is, forces equal in their effects in some other situation, the axiom is empirical only, and not even universally true. But, except by its effect in some situation or other, what test have we of the magnitude of a force?

ulties may possibly establish the existence of other subjective conditions of intuition besides those of space and time, and, consequently, of other synthetical judgments à priori besides those of Geometry and Arithmetic. But when the same theory comes to be applied, not to hypothetical rigid bodies without weight, but to the actual phenomena of natural agents, as in the "Demonstration that all matter is heavy," and, verbally at least, in speaking of the inconceivability of the pre-Copernican astronomy, we see at once that the boundary is overleaped which separates the necessary laws of thought from the generalized phenomena of matter. This absolute boundary is sufficiently marked. No matter of fact can, in any possible state of human knowledge, be a matter of demonstration. Nay, even supposing such a demonstration possible, it would not add one tittle to the evidence of the fact, as such, in the eyes of any one but an egoist. By him it would be accepted as an additional proof that what are commonly considered as phenomena of the non-ego, are really only modifications of the percipient mind, and governed solely by mental laws. But to the Realist it would at most only suggest the possibility of a preëstablished harmony between the laws of mind and matter, -a suggestion which would require, in every special case, to be verified by the empirical examination of the latter. Mental laws, which alone determine conceivability, are primarily operative only on mental objects, and are applicable to external things only on the hypothesis of their conformity. This hypothesis can only be verified empirically. That every triangle, for example, has its angles equal to two right angles, is strictly true only of the perfect triangle as contemplated by the mind. That this bit of paper lying before me has its angles equal to two right angles, is only true on the supposition of its being a perfect triangle; and the truth of this supposition, in any possible state of perfection of human senses and instruments, can only be determined empirically. It remains always conceivable that there may be an error in the measurement, and that the paper may not have exactly two right angles. The probability of such an error may be diminished to any degree, according to the perfection of our means of measurement; but no approximation of this kind can ever become absolute certainty.

It is not without some hesitation that I have ventured thus far to criticize a work which I believe to be, in its whole spirit and conception, by far the most valuable contribution of modern times to the philosophy of the physical sciences. To those who would survey this branch of knowl

1 Personality may perhaps be specified as another condition of this kind, and the a priori principles of morals as consequent upon it. On this I have remarked at greater length in the Bampton Lectures, Lects. III. and VII.

2 Compare Hume, Essay on the Academical Philosophy, Part ii.

edge in a sound philosophical spirit, alike removed from the idealism of Schelling and from the positivism of Comte, the writings of Dr. Whewell are especially valuable. To those who believe, with the present writer, that the future hopes of speculative philosophy rest on the possibility of a union of the critical principles of Kant with the sober practical spirit which is characteristic of English thinkers, the writings of the same author afford one of the most cheering assurances that the spirit of philosophy, under all its discouragements, is not yet extinct in this country. With this declaration, the spirit that has dictated the preceding criticism will not, I trust, be misunderstood.1

NOTE B, p. 128.

That Berkeley was fully aware of the inconsequence of the conclusions which Hume afterwards attempted to draw from his principles, is manifest from the third Dialogue between Hylas and Philonous, in which he meets by anticipation the argument of the skeptic,2 by maintaining that we are directly conscious of our own being. He is wrong, indeed, in calling this consciousness Reflection; this term being properly applicable only to attention directed to our internal phenomena; - an attention which does not make known, but presupposes, the attending self. But when he asserts, "I know or am conscious of my own being; and that I myself am not my ideas, but somewhat else, a thinking, active principle, that perceives, knows, wills, and operates about ideas," he states the true ground on which we may refute the skeptical conclusions of Hume. Indeed, this part of the Dialogue wants little more than a more complete

1 The preceding note remains nearly as it appeared in the first edition of this work, published in 1851. Since that time, some additional remarks on the matter in question have appeared in Sir William Hamilton's Discussions, p. 323 (second edition, p. 335), in Dr. Whewell's Letter to the Author of Prolegomena Logica, and in the Author's pamphlet in reply, entitled, The Limits of Demonstrative Science considered. Sir W. Hamilton's view is substantially the same as my own; and I cannot help regarding this independent coïncidence as a confirmation of my original criticism. At the same time I feel bound to express my acknowledgments to Dr. Whewell for the instruction which his Letter has afforded me, and for the liberal and courteous tone in which his objections are urged.

2 This part of Berkeley's Dialogue is meant as an answer to Locke, Essay, B. II. ch. 23, § 5, but the same reasoning is also valid against Hume.

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