"No conclusions can lay claim to absolute truth, but such as depend upon truths that are themselves absolute. Before there can be exactness in an inference, there must be exactness in the antecedent propositions. A geometrician requires that the straight lines with which he deals shall be veritably straight; and that his circles, and ellipses, and parabolas shall agree with precise definitions—shall perfectly and invariably answer to specified equations. If you put to him a question in which these conditions are not complied with, he tells you that it cannot be answered. So likewise is it with the philosophical moralist. He treats solely of the straight man. He determines the properties of the straight man; describes how the straight man comports himself; shows in what relationship he stands to other straight men; shows how a community of straight men is constituted. Any deviation from strict rectitude he is obliged wholly to ignore. It cannot be admitted into his premises without vitiating all his conclusions. A problem in which a crooked man forms one of the elements is insoluble to him."

Referring to this view, specifically in the first edition of the Methods of Ethics, but more generally in the second edition, Mr. Sidgwick says:

"Those who take this view adduce the analogy of Geometry to show that Ethics ought to deal with ideally perfect human relations, just as Geometry treats of ideally perfect lines and circles. But the most irregular line has definite spatial relations with which Geometry does not refuse to deal: though of course they are more complex than those of a straight line. So in Astronomy, it would be more convenient for purposes of study if the stars moved in circles, as was once believed; but the fact that they move not in circles but in ellipses, and even in imperfect and perturbed ellipses, does not take them out of the sphere of scientific investigation: by patience and industry we have learned how to reduce to principles and calculate even these more complicated motions. It is, no doubt, a convenient artifice for purposes of instruction to assume that the planets move in perfect ellipses (or even—at an earlier stage of study—in circles): we thus allow the individual's knowledge to pass through the same gradations in accuracy as that of the race has done. But what we want, as astronomers, to know is the actual motion of the stars and its causes: and similarly as moralists we naturally inquire what ought to be done in the actual world in which we live." (P. 19, Sec. Ed.)

Beginning with the first of these two statements, which concerns Geometry, I must confess myself surprised to find my propositions called into question; and after full consideration I remain at a loss to understand Mr. Sidgwick's mode of viewing the matter. When, in a sentence preceding those quoted above, I remarked on the impossibility of solving "mathematically a series of problems respecting crooked lines and broken-backed curves," it never occurred to me that I should be met by the direct assertion that "Geometry does not refuse to deal" with "the most irregular line." Mr. Sidgwick states that an irregular line, say such as a child makes in scribbling, has "definite spatial relations." What meaning does he here give to the word "definite?" If he means that its relations to space at large are definite in the sense that by an infinite intelligence they would be definable, the reply is that to an infinite intelligence all spatial relations would be definable: there could be no indefinite spatial relations—the word "definite" thus ceasing to mark any distinction. If, on the other hand, when saying that an irregular line has "definite spatial relations," he means relations knowable definitely by human intelligence, there still comes the question, how is the word "definite" to be understood? Surely anything distinguished as definite admits of being defined; but how can we define an irregular line? And if we cannot define the irregular line itself, how can we know its "spatial relations" definite? And how, in the absence of definition, can Geometry deal with it? If Mr. Sidgwick means that it can be dealt with by the "method of limits," then the reply is that in such case, not the line itself is dealt with geometrically, but certain definite lines artificially put in quasi-definite relations to it, the indefinite becomes cognizable only through the medium of the hypothetically definite.

Turning to the second illustration, the rejoinder to be made is that in so far as it concerns the relations between the ideal and the real, the analogy drawn does not shake but strengthens my argument. For whether considered under its geometrical or under its dynamical aspect, and whether considered in the necessary order of its development or in the order historically displayed, Astronomy shows us throughout that truths respecting simple, theoretically-exact relations, must be ascertained before truths respecting the complex and practically inexact relations that actually exist can be ascertained. As applied to the interpretation of planetary movements, we see that the theory of cycles and epicycles was based on pre-existing knowledge of the circle: the properties of an ideal curve having been learned, a power was acquired of giving some expression to the celestial motions. We see that the Copernican interpretation expressed the facts in terms of circular movements otherwise distributed and combined. We see that Kepler's advance from the conception of circular movements to the conception of elliptic movements was made possible by comparing the facts as they are with the facts as they would be were the movements circular. We see that the subsequently-learned deviations from elliptic movements were learned only through the presupposition that the movements are elliptical. And we see, lastly, that even now predictions concerning the exact positions of planets, after taking account of perturbations, imply constant references to ellipses that are regarded as their normal or average orbits for the time being. Thus, ascertainment of the actual truths has been made possible only by preascertainment of certain ideal truths. To be convinced that by no other course could the actual truths have been ascertained, it needs only to suppose any one saying that it did not concern him, as an astronomer, to know anything about the properties of circles and ellipses, but that he had to deal with the Solar System as it exists, to which end it was his business to observe and tabulate positions and directions and to be guided by the facts as he found them.

So, too, is it if we look at the development of dynamical astronomy. The first proposition in Newton's Principia deals with the movement of a single body round a single center of force; and the phenomena of central motion are first formulated in a case which is not simply ideal, but in which there is no specification of the force concerned: detachment from the real is the greatest possible. Again, postulating a principle of action conforming to an ideal law, the theory of gravitation deals with the several problems of the Solar System in fictitious detachment from the rest; and it makes certain fictitious assumptions, such as that the mass of each body concerned is concentrated in its center of gravity. Only later, after establishing the leading truths by this artifice of disentangling the major factors from the minor factors, is the theory applied to the actual problems in their ascending degrees of complexity; taking in more and more of the minor factors. And if we ask whether the dynamics of the Solar System could have been established in any other way, we see that here, too, simple truths holding under ideal conditions, have to be ascertained before real truths existing under complex conditions can be ascertained.

The alleged necessary precedence of Absolute Ethics over Relative Ethics is thus, I think, further elucidated. One who has followed the general argument thus far, will not deny that an ideal social being may be conceived as so constituted that his spontaneous activities are congruous with the conditions imposed by the social environment formed by other such beings. In many places, and in various ways, I have argued that conformably with the laws of evolution in general, and conformably with the laws of organization in particular, there has been, and is, in progress, an adaptation of humanity to the social state, changing it in the direction of such an ideal congruity. And the corollary before drawn and here repeated, is that the ultimate man is one in whom this process has gone so far as to produce a correspondence between all the promptings of his nature and all the requirements of his life as carried on in society. If so it is a necessary implication that there exists an ideal code of conduct formulating the behavior of the completely adapted man in the completely evolved society. Such a code is that here called Absolute Ethics as distinguished from Relative Ethics—a code the injunctions of which are alone to be considered as absolutely right in contrast with those that are relatively right or least wrong; and which, as a system of ideal conduct, is to serve as a standard for our guidance in solving, as well as we can, the problems of real conduct.

§ 105. A clear conception of this matter is so important that I must be excused for bringing in aid of it a further illustration, more obviously appropriate as being furnished by organic science instead of by inorganic science. The relation between morality proper and morality, as commonly conceived, is analogous to the relation between physiology and pathology; and the course usually pursued by moralists is much like the course of one who studies pathology without previous study of physiology.

Physiology describes the various functions which, as combined, constitute and maintain life; and in treating of them it assumes that they are severally performed in right ways, in due amounts, and in proper order; it recognizes only healthy functions. If it explains digestion, it supposes that the heart is supplying blood and that the visceral nervous system is stimulating the organs immediately concerned. If it gives a theory of the circulation, it assumes that blood has been produced by the combined actions of the structures devoted to its production, and that it is properly ærated. If the relations between respiration and the vital processes at large are interpreted, it is on the presupposition that the heart goes on sending blood, not only to the lungs and to certain nervous centers, but to the diaphragm and intercostal muscles. Physiology ignores failures in the actions of these several organs. It takes no account of imperfections, it neglects derangements, it does not recognize pain, it knows nothing of vital wrong. It simply formulates that which goes on as a result of complete adaptation of all parts to all needs. That is to say, in relation to the inner actions constituting bodily life, physiological theory has a position like that which ethical theory, under its absolute form as above conceived, has to the outer actions constituting conduct. The moment cognizance is taken of excess of function, or arrest of function, or defect of function, with the resulting evil, physiology passes into pathology. We begin now to take account of wrong actions in the inner life analogous to the wrong actions in the outer life taken account of by ordinary theories of morals.

The antithesis thus drawn, however, is but preliminary. After observing the fact that there is a science of vital actions normally carried on, which ignores abnormal actions, we have more especially to observe that the science of abnormal actions can reach such definiteness as is possible to it only on condition that the science of normal actions has previously become definite; or rather, let us say that pathological science depends for its advances on previous advances made by physiological science. The very conception of disordered action implies a preconception of well-ordered action. Before it can be decided that the heart is beating faster or slower than it should its healthy rate of beating must be learned; before the pulse can be recognized as too weak or too strong, its proper strength must be known, and so throughout. Even the rudest and most empirical ideas of diseases, pre-suppose ideas of the healthy states from which they are deviations, and, obviously, the diagnosis of diseases can become scientific only as fast as there arises scientific knowledge of organic actions that are undiseased.