Bertrand Russell

The Russell Society Page

About Bertrand Russell

A Russell Chronology

A Russell Bibliography

Russell Books & Articles

Other Russell Resources

About the Russell Society

JOIN the Russell Society!

Officers and Organization

Contact the BRS

 Review of Heymans  (1895)*

By Bertrand Russell

Die Gesetze und Elemente des wissenschaftlichen Denkens. Von Dr. G. Heymans, Professor der Philosophie an der Universität zu Groningen. Leiden: S. C. Van Doesburgh; Leipzig: Otto Harrassowitz. Bd. i. 1890, Bd. ii. 1894. Pp. 478

“THE subject of this book,” we are told in the Preface, “is twofold: for non-philosophers it is a text-book of Epistemology, while for philosophers it forms a treatise on method, illustrated by examples. The endeavour to combine the two in a single book springs from my conviction that the empirical method of investigation and proof, which I wish to advocate towards my fellow-philosophers, is precisely the method of presentation best fitted for introducing men of scientific culture to philosophy.”

This two-fold object necessitates a good deal of matter (for example the accounts of the Syllogism and of Mill’s Canons of Induction) which except for the purposes of a text-book would be superfluous; and there is throughout an endeavour to avoid whatever would be too technical for the unphilosophical reader. Our author has, however, allowed himself one exception to this rule, in connection with the relation of Epistemology to Psychology, to which he addresses himself at a very early stage. His position on this question is one which might have been owned by Hume: Epistemology is a “Psychology of Thought,” and is formally defined as “The exact determination and explanation, by means of the empirical investigation of given thought, of the causal relations which condition the occurrence of conviction in consciousness” (p. 3). Whatever may be thought of its philosophical merit, I cannot but think that a position so generally disputed must make the work somewhat unsuitable as a text-book; the more so, as the solutions proposed, at any rate throughout the first volume, are strictly in accordance with this view of the problem – i.e. they are solutions which account psychologically for our beliefs, instead of giving grounds for their validity. Accordingly the ultimate test of certainty is the “Gedankensexperiment”; the laws of Contradiction and Excluded Middle are regarded as “irreducible psychical laws suffering no exception,” and are based on the impossibility which we feel (empfinden) of simultaneously affirming two contradictory propositions (p. 69). Similarly the laws of Arithmetic refer not to things, but to thoughts; they are purely psychological laws. And Geometry is regarded as established by explaining the genesis of space-perception through motor-sensations; these are subjective, and produced by our volitions, and appear to account by this property for the a priori certainty and exactness of the Euclidean system, in relation to which Dr. Heymans adheres to the position of the Transcendental Aesthetic.

In all this there is, it seems to me, a confusion between the psychologically subjective and the logically a priori; the apriority of Logic, Arithmetic and Geometry being proved merely by referring them to subjective psychical processes. But no ground is shewn for regarding the result as less empirical in the case of a “Gedankensexperiment” than in the case of any other kind of experiment. I fail to see how, except by the previous assumption of the whole array of the canons of inductive science, we can have any assurance that two such experiments will give the same result, nor how we can set any limits to the efficiency of the White Queen’s practice in “believing as many as six impossible things before breakfast.” In order to get a theory of knowledge out of psychology, it has been necessary to leave out of account the various emotional and pathological causes of belief, which certainly come under the above definition; it is throughout assumed that no causes of belief are possible except the evidence of the senses, logical reasoning, and certain fundamental a priori laws, i.e. the grounds of correct belief. In short the psychology of belief appears to be rather that which would apply to an intellectually ideal man than to men liable to error; accordingly error is regarded as springing only from deficient analysis, and this is the only answer we obtain to the question how the laws of thought can be at the same time norms for correct thinking and psychological laws for all thinking.

To illustrate this general criticism of the first volume, let us examine more in detail our author’s views on Geometry, to the discussion of which a considerable space is devoted. Here Dr. Heymans maintains a Kantian position, which he supports by Riehl’s hypothesis of the generation of space-perception from motor-sensations. It is somewhat cavalierly assumed, as though no one had ever disputed it, that the propositions of Geometry are exact and of apodeictic certainty, and therefore a priori. The value of metageometry is taken to consist solely in the fact that it has proved the axiom of parallels to be independent of the others and essential to the Euclidean system. The indispensable axioms are regarded as five in number: Every point is determined by three coordinates; these vary continuously; bodies can be moved without distortion; through any two points only one straight line can be drawn; and through any point only one parallel can be drawn to a given straight line (p. 188). These axioms are regarded as all necessarily deriving their evidence in the same way, and are not discussed separately; though the results of non-Euclidean Geometry would seem to necessitate a division into three classes, omitting the second, which is in my opinion involved in the third, since the idea of mobility is only applicable to a continuum. As to the other four, the first deals with a purely sensuous quality of given space, which has no logical importance; the extension to four or n dimensions would not invalidate three-dimensional Geometry any more than the 3rd dimension invalidates Plane Geometry. In fact this axiom might almost be called statistical; the number of dimensions must be a positive integer, so that we are not in the realm of approximations any more than in counting the number of people in a room, and accuracy can therefore hardly be taken as evidence of apriority. The third, the axiom of Congruence or free mobility, on the contrary, has, I think, no sensuous import; for, as Dr. Heymans observes in answer to Helmholtz, any apparent exception to it on the part of actual bodies is always to be regarded as due to physical rather than geometrical causes. But its logical importance is such that without it Geometry in every form would be impossible; no means would exist of discovering how objects changed their shape in moving from place to place, since the change would affect the measure as much as the thing measured. There is also a philosophic absurdity in denying this axiom, for if shapes were changed by mere motion, they must depend on absolute position, and bodies would be determined by their relation to empty space. Between these two extremes come the fourth and fifth of the above axioms, which seem to answer pretty closely to Klein’s definition of axioms in general, that they are postulates by which we rise from the inexactness of sense to the perfect exactness of Mathematics. For, as every one knows, they are equivalent to the assumption that the measure of curvature of our space is zero; and since here it is logically possible, by supposing, the measure of curvature small, to make small departures from such an assumption, (which was not possible with the first axiom), it is difficult to see how sense can give us accuracy beyond the limits of the errors of observation.

These considerations seem to me to necessitate a separate discussion of the different classes, but Dr. Heymans treats them as all alike exact and certain; this certainty, however, must, he thinks, refer to something other than given objects, since mental images suffice to give perfectly correct results, though they can never accurately reproduce those objects. This something, is the motor sense, in terms of which he tries to explain all his five axioms. Motor-sensations are subjective, and they are brought forth by our own volitions; these facts are supposed to establish Geometry on a Kantian a priori basis.

Apart from the psychological validity of Riehl’s hypothesis, this theory of Geometry seems to me very inadequate to Dr. Heymans’ contention; if Geometry really does deal with motor sensations, it must, one would think, be merely a branch of empirical psychology. I fail to see in what sense motor-sensations are less phenomenal or more a priori than any other sensations, and I should have supposed Hume’s difficulties with the minimum sensible would have rendered so sensational an account impossible, unless one were willing to throw to the winds all claim to exactness on the part of Geometry. The entire theory seems to me to rest on the confusion of the a priori with the psychologically subjective, which underlies the whole first volume.

The second volume, which deals with Causation and Mechanics, is for the most part free from this confusion, and consequently appears to me to be of much greater epistemological value than the first. In Logic, Arithmetic and Geometry, we had not yet, in Dr. Heymans’ view, got beyond self-knowledge; our judgments always referred to our own thoughts and feelings. But with the consideration of the real category of cause, we rise to the problem of the knowledge of Not-Self. All Induction rests, directly or indirectly, on Causation, on the definition of which much care is bestowed. After an excellent criticism of the views of Mill and Jevons, Dr. Heymans declares in favour of Hamilton’s hypothesis: causation is equivalent to the axiom that a real creation or destruction is impossible. Having chiefly Mechanics in view, he shews that this axiom accounts for the equivalence of cause and effect, and explains their connection with the logical couple of ground and consequent. The latter being, in accordance with the first volume, taken as a case of psychological causation, our knowledge of the cause is, assuming Hamilton’s principle, the ground of our knowledge of the effect, which essentially is nothing but the perpetuation of the cause (p. 387).

The view of Causation thus gained is now applied with great success to Mechanics. The laws of motion cannot be wholly empirical, for they refer to absolute motion, which is not a possible object of experience. (This is proved by the following argument: If the whole universe were rotating with uniform angular velocity, the laws of motion would require the appearance of centrifugal forces, causing quite a different distribution of matter from that which would otherwise exist; but such a motion could never directly appear to the senses.) The a priori element is Hamilton’s principle. But the laws are not wholly a priori; the first law for example may be thus formulated: The changeless state which, in the absence of any disturbing cause, a body must preserve is not rest, but uniform motion. Hamilton’s principle leaves both these alternatives as possible, in fact the former was taken by the ancients and by the Aristotelians; the function of experience has been to decide in favour of the latter. (It may be observed that the alternative only exists on the assumption that the law refers to absolutemotion: in relative motion there is no difference between rest and uniform velocity.) The other laws are similarly explained by the application of Hamilton’s principle to experience, and this is, in my opinion, much the best section of the book.

As regards Mechanics, Causation in the above sense is probably all that the science requires, being quite superfluous in the sense of efficiency, as is shewn by the superannuation of the idea of force and its supersedence by that of energy. Also it is noteworthy that the mechanical properties of the universe as a whole, its mass, momentum, and energy, are regarded by Mechanics as constant. Of course, the principle is only what Kant would call regulative, not constitutive; we search for as much constancy as possible, but a thorough carrying out of the principle, if applied, as Mechanics requires, to attribute as well as to substance, would involve the task of explaining away all change; the effect cannot be regarded as identical with the cause, or all happening must disappear. The use of the principle in Mechanics involves the abstraction of motion from the moving matter; these two are regarded as separately constant, though the motion is allowed to be transmitted from body to body; in fact, the orthodox mechanical doctrine might be compared to the Transmigration of Souls. Thus the principle is not applied to the real, but to an intellectual and abstract construction of the real, resting on the distinction of substance and attribute. Its efficiency in Mechanics, which depends throughout on this distinction, is thus comprehensible; but it remains a question whether some theory in which cause and effect are less homogeneous, in which there is still some idea of activity, might not be necessary in other sciences, e.g. Psychology; at any rate, Psychology is not yet in the state where its laws can be seen to flow from the indestructibility of existence. Dr. Heymans has not discussed any other sciences than Pure Mathematics and Mechanics; it would have been interesting to see how far it was possible elsewhere to apply the same view.

The chief value of the book seems to me to lie in the analysis of the laws of motion, and in the exposition of the a priori elements contained in them. The whole account is thoroughly self consistent, and shews a distinct superiority to his opponents, Mach and others, who maintain a more empirical position. In the first volume there is some good critical work, for instance in connection with Lange’s geometrical theory of formal logic; but the constructive work is impregnated with his psychological view of Epistemology, and I must therefore regard the discussion of Mechanics as the portion of the book best worthy of attention and of most permanent value.


*  Bertrand Russell, Review of G. Heymans, Die Gesetze und Elemente des wissenschaftlichen Denkens, Mind, n.s. 4 no. 14 (Apr 1895), 245-9