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CHAPTER VIII: Of the Geometrical, or Abstract Method - John Stuart Mill, The Collected Works of John Stuart Mill, Volume VIII - A System of Logic Ratiocinative and Inductive Part II 
The Collected Works of John Stuart Mill, Volume VIII - A System of Logic Ratiocinative and Inductive, Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation (Books IV-VI and Appendices), ed. John M. Robson, Introduction by R.F. McRae (Toronto: University of Toronto Press, London: Routledge and Kegan Paul, 1974).
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Of the Geometrical, or Abstract Method
§ 1. [Characters of this mode of thinking] The misconception discussed in the preceding chapter is, as we said, chiefly committed by persons not much accustomed to scientific investigation: practitioners in politics, who rather employ the commonplaces of philosophy to justify their practice, than seek to guide their practice by aphilosophic principlesa : or imperfectly educated bpersonsb , who, in ignorance of the careful selection and elaborate comparison of instances required for the formation of a sound theory, attempt to found one upon a few coincidences which they have casually noticed.
The erroneous method of which we are now to treat, is, on the contrary, peculiar to thinking and studious minds. It never could have suggested itself but to persons of some familiarity with the nature of scientific research; who,—being aware of the impossibility of establishing, by casual observation or direct experimentation, a true theory of sequences so complex as are those of the social phenomena,—have recourse to the simpler laws which are immediately operative in those phenomena, and which are no other than the laws of the nature of the human beings therein concerned. These thinkers perceive (what the partisans of the chemical or experimental theory do not) that the cscience of society must necessarily be deductivec . But, from an insufficient consideration of the specific nature of the subject matter,—and often because (their own scientific education having stopped short in too early a stage) geometry stands in their minds as the type of all deductive science,—it is to geometry, rather than to astronomy and natural philosophy, that they unconsciously assimilate the deductive science of society.
Among the differences between geometry (a science of coexistent facts, altogether independent of the laws of the succession of phenomena), and those physical Sciences of Causation which have been rendered deductive, the following is one of the most conspicuous: That geometry affords no room for what so constantly occurs in mechanics and its applications, the case of conflicting forces; of causes which counteract or modify one another. In mechanics we continually find two or more moving forces producing, not motion, but rest; or motion in a different direction from that which would have been produced by either of the generating forces. It is true that the effect of the joint forces is the same when they act simultaneously, as if they had acted one after another, or by turns; and it is in this that the difference between mechanical and chemical laws consists. But still the effects, whether produced by successive or by simultaneous action, do, wholly or in part, cancel one another: what the one force does, the other, partly or altogether, undoes. There is no similar state of things in geometry. The result which follows from one geometrical principle has nothing that dconflicts withd the result which follows from another. What is proved true from one geometrical theorem, what would be true if no other geometrical principles existed, cannot be altered and made no longer true by reason of some other egeometricale principle. What is once proved true fisf true in all cases, whatever supposition may be made in regard to any other matter.
Now a conception, similar to this last, would appear to have been formed of the social science, in the minds of the earlier of those who have attempted to cultivate it by a deductive method. Mechanics would be a science very similar to geometry, if every motion resulted from one force alone, and not from a conflict of forces. In the geometrical theory of society, it seems to be supposed that this is really the case with the social phenomena;g that each of them results always from only one force, one single property of human nature.
At the point which we have now reached, it cannot be necessary to say anything either in proof or in illustration of the assertion that such is not the true character of the social phenomena. There is not, among htheseh most complex and (for that reason) most modifiable of all phenomena, any one over which innumerable forces do not exercise influence; which does not depend on a conjunction of very many causes. We have not, therefore, to prove the notion in question to be an error, but to prove that the error has been committed; that so mistaken a conception of the mode in which the phenomena of society are produced, has actually been iascertainedi .
§ 2. [Examples of the Geometrical Method] One numerous division of the reasoners who have treated social facts according to geometrical methods, not admittinga any modification of one law by another, must for the present be left out of consideration; because in them this error is complicated with, and is the effect of, another fundamental misconception, of which we have already taken some notice, and which will be bfurther treated ofb before we conclude. I speak of those who deduce political conclusions not from laws of nature, not from sequences of phenomena, real or imaginary, but from unbending practical maxims. Such, for example, are all who found their ctheoryc of politics on what is called abstract right, that is to say, on universal precepts; a pretension of which we have already noticed the chimerical nature. Such, in like manner, are those who make the assumption of a social contract, or any other kind of original obligation, dand apply itd to particular cases by mere interpretation. But in this the fundamental error is the attempt to treat an art like a science, and to have a deductive art; the irrationality of which will be shown in a future chapter. It will be proper to take our exemplification of the geometrical theory from those thinkers who have avoided this additional error, and who entertain, so far, a juster idea of the nature of political inquiry.
We may cite, in the first instance, those who assume as the principle of their political philosophy that government is founded on fear; that the dread of each other is the one motive by which human beings were originally brought into a state of society, and are still held in it. Some of the earlier scientific inquirers into politics, in particular Hobbes, assumed this proposition, not by implication, but avowedly, as the foundation of their doctrine, and attempted to build a complete philosophy of politics thereupon. It is true that Hobbese did not find this one maxim sufficient to carry him through the whole of his subject, but was obliged to eke it out by the double sophism of an original contract. I call this a double sophism; first, as passing off a fiction for a fact, and, secondly,f assuming a practical principle, or precept, as the basis of a theory; which is a petitio principii, since (as we noticed in treating of that Fallacy) every rule of conduct, even though it be so binding a one as the observance of a promise, must rest its own gfoundationsg on the theory of the subject, and the theory, therefore, cannot rest upon it.
§ 3. [The interest-philosophy of the Bentham School] Passing over less important instances, aIa shall come at once to the most remarkable example afforded by our own times of the geometrical method in politics; emanating from persons who bareb well aware of the distinction between science and art; who cknewc that rules of conduct must follow, not precede, the ascertainment of laws of nature, and that the latter, not the former, is the legitimate field for the application of the deductive method. I allude to the interest-philosophy of the Bentham school.
The profound and original thinkers who are commonly known under this description, founded their general theory of government on one comprehensive premise, namely, that men’s actions are always determined by their interests. There is an ambiguity in this last expression; for, as the same philosophers, despecially Benthamd ,e gave the name of an interest to anything which a person likes, the proposition may be understood to mean only this, that men’s actions are always determined by their wishes. In this sense, however, it would not bear out any of the consequences which these fwritersf drew from it; and the word, therefore, in their political reasonings, must be understood to mean (which is also the explanation they themselves, on such occasions, gave of it) what is commonly termed private, or worldly, interest.
Taking the doctrine, then, in this sense, an objection presents itself in limine which might be deemed a fatal one, namely, that so sweeping a proposition is far from being universally true. gHuman beingsg are not governed in all their actions by their worldly interests. This, however, is by no means so conclusive an objection as it at first appears; because in politics we are for the most part concerned with the conduct, not of individual hpersons, but either of a series of persons (as a succession of kings), or a body or mass of personsh , as a nation, an aristocracy, or a representative assembly. And whatever is true of a large majority of mankind, may without much error be taken for true of any succession of persons, considered as a whole, or of any collection of persons in which the act of the majority becomes the act of the whole body. Although, therefore, the maxim is sometimes expressed in a manner unnecessarily paradoxical, the consequences drawn from it will hold equally good if the assertion be limited as follows—Any succession of ipersons, or the majority of any body of personsi , will be governed in the bulk of their conduct by their personal interests. We are bound to allow to this school of jthinkersj the benefit of this more rational statement of their fundamental maxim, which kis alsok in strict conformity to the explanations which, when considered to be called for, have been given by themselves.
The theory goes on to infer, lquite correctlyl , that if the actions of mankind are determined in the main by their selfish interests, the only rulers who will govern according to the interest of the governed, are those whose selfish interests are in accordance with it. And to this is added a third proposition, namely, that no rulers have their selfish interest identical with that of the governed, unless it be rendered so by accountability, that is, by dependence on the will of the governed. In other words (and as the result of the whole), that the desire of retaining or the fear of losing their power, and whatever is thereon consequent, is the sole motive which can be relied on for producing on the part of rulers a course of conduct in accordance with the general interest.
We have thus a fundamental theorem of political science, consisting of three syllogisms, and depending chiefly on two general premises, in each of which a certain effect is considered as determined only by one cause, not by a concurrence of causes. In the one, it is assumed that the actions of average rulers are determined solely by self-interest; in the other, that the sense of identity of interest with the governed, is produced and producible by no other cause than responsibility.
Neither of these propositions is by any means true; the last is extremely wide of the truth.
It is not true that the actions even of average rulers are wholly, or anything approaching to wholly, determined by their personal interest, or even by their own opinion of their personal interest. I do not speak of the influence of a sense of duty, or feelings of philanthropy, motives never to be mmainlym relied on, though (except in countries or during periods of great moral debasement) they influence almost all rulers in some degree, and some rulers in a very great degree. But I insist only on what is true of all rulers, viz., that the character and course of their actions is largely influenced (independently of personal calculation) by the habitual sentiments and feelings, the general modes of thinking and acting, which prevail throughout the community of which they are members; as well as by the feelings, habits, and modes of thought which characterize the particular class in that community to which they themselves belong. And no one will understand or be able to decipher their system of conduct, who does not take all these things into account. They are also much influenced by the maxims and traditions which have descended to them from other rulers, their predecessors; nwhich maxims and traditions have been known to retain an ascendancy during long periods, even in oppositionn to the private interests of the rulers for the time being. oIo put aside the influence of other less general causes. Although, therefore, the private interest of the rulers or of the ruling class is a very powerful force, constantly in action, and exercising the most important influence upon their conduct; there is also, in what they do, a large portion which that private interest by no means affords a sufficient explanation of: and even the particulars which constitute the goodness or badness of their government, are in some, and no small degree, influenced by those among the circumstances acting upon them, which cannot, with any propriety, be included in the term self-interest.
Turning now to the other proposition, that responsibility to the governed is the only cause capable of producing pin the rulers a sense of identity of interest with the communityp ; this is still less admissible as an universal truth, than even the former. qI am not speaking of perfect identity of interest, which is an impracticable chimera; which, most assuredly, responsibility to the people does not give. Iq speak of identity in essentials; and the essentials are different at different places and times. There are a large number of cases in which those things which it is most for the rgeneral interest that the rulers should do, are also those which they are prompted to do by their strongest personal interest, the consolidation of theirr power. The suppression, for instance, of anarchy and resistance to law,—the complete establishment of the authority of the central government, in a state of society like that of Europe in the middle ages,—is sone of the strongest interestss of the people, and also of tthet rulers simply because they are the rulers: and responsibility on their part could not strengthen, though in many conceivable ways it might weaken, the motives prompting them to pursue this object. During the greater part of the reign of Queen Elizabeth, and of many other monarchs who might be named, the sense of identity of interest between the sovereign and the majority of the people was probably stronger than it usually is in responsible governments: everything that the people had most at heart, the monarch had at heart too. Had Peter the Great, or the rugged savages whom he began to civilize, the truest inclination towards the things which were for the real interest of those savages?
I am not here attempting to establish a theory of government, and am not called upon to determine the proportional weight which ought tobe given to the circumstances which this school of geometrical politicians left out of their system, and those which they took into it. I am only concerned to show that their method was unscientific; not to measure the amount of error which may have affected their practical conclusions.
It is but justice to them, however, to remark, that their mistake was not so much one of substance as of form; and uconsisted in presentingu in a systematic shape, and as the scientific treatment of a great philosophical question, what should have passed for that which it really was, the mere polemics of the day. Although the actions of rulers are by no means wholly determined by their selfish interests, it is vchieflyv as a security against those selfish interests that constitutional checks are required; and for that purpose such checks, in England, and wthe other nations of modern Europew , can in no manner be dispensed with. It is xlikewise true, that in these same nations, and in the present age, responsibility to the governedx is the only means practically available to create a feeling of identity of interest, in the cases, and on the points, where that feeling does not sufficiently exist. To all this, and to the arguments which may be founded on it in favour of measures for the correction of our representative system, I have nothing to object; but I confess my regret, that the small though highly important portion of the philosophy of government, which was wanted for the immediate purpose of serving the cause of parliamentary reform, should have been held forth by ythinkersy of such eminence as a complete theory.
It is not to be imagined possible, nor is it true in point of fact, that these philosophers regarded the few premises of their theory as including all that is required for explaining social phenomena, or for determining the choice of forms of government and measures of legislation and administration. They were too highly instructed, of too comprehensive intellect, and some of them of too sober and practical a character, for such an error. They would have applied, and did apply, their principles with innumerable allowances. But it is not allowances that are wanted. There is little chance of making due amends in the superstructure of a theory for the want of sufficient breadth in its foundations. It is unphilosophical to construct a science out of a few of the agencies by which the phenomena are determined, and leave the rest to the routine of practice or the sagacity of conjecture. We either ought not to pretend to scientific forms, or we ought to study all the determining agencies equally, and endeavour, so far as it can be done, to include all of them within the pale of the science; else we shall infallibly bestow a disproportionate attention upon those which our theory takes zinto accountz , while we misestimate the rest, and probably underrate their importance. That the deductions should be from the whole and not from a part only of the laws of nature that are concerned, would be desirable even if those omitted were so insignificant in comparison with the others, that they might, for most purposes and on most occasions, be left out of the account. But this is far indeed from being true in the social science. The phenomena of society do not depend, in essentials, on asomea one agency or law of human nature, with only inconsiderable modifications from others. The whole of the bqualitiesb of human nature influence those phenomena, and there is not one which influences them in a small degree. There is not one, the removal or any great alteration of which would not materially affect the whole aspect of society, and change more or less cthe sequences of social phenomena generallyc .
The theory which has been the subject of these remarks is in this country at least, the principal dcontemporaryd example of what I have styled the geometrical method of philosophizing in the social science; and our examination of it has, for this reason, been more detailed than ewoulde otherwise have been fsuitable tof a work like the present. Having now sufficiently illustrated the two erroneous methods, we shall pass without further preliminary to the true method; that which proceeds (conformably to the practice of the gmore complex physical sciencesg ) deductively indeed, but by deduction from many, not from one or a very few, original premises; considering each effect as (what it really is) an aggregate result of many causes, operating sometimes through the same, sometimes through different mental agencies, or laws of human nature.
[a-a]MS, 43, 46 any philosophic views
[b-b]MS, 43, 46 men
[c-c]MS, 43, 46 philosophy of society is a deductive science
[d-d]MS, 43, 46, 51, 56, 62, 65 contradicts
[f-f]MS, 43, 46 must be
[g]43, 46 and [printer’s error? cancelled in MS]
[h-h]MS those [printer’s error?]
[i-i]MS, 43, 46, 51, 56, 62 entertained
[a]MS, 43, 46 of
[b-b]MS, 43, 46 treated of more fully
[c-c]MS, 43, 46 theories
[d-d]MS to be applied
[e]MS, 43, 46 (who is so much the most considerable of these, that we need not particularly advert to any of the rest)
[f]MS, 43, 46 as
[b-b]MS, 43, 46, 51, 56, 62, 65, 68 were
[d-d]MS Bentham especially
[e]MS, 43, 46 systematically
[f-f]MS, 43, 46 philosophers
[g-g]MS, 43, 46 Men
[h-h]MS, 43, 46 men, but . . . series of men (as . . . mass of men
[i-i]MS, 43, 46 men, or . . . of men
[j-j]MS, 43, 46 philosophers
[k-k]MS, 43, 46 moreover is
[l-l]MS, 43 correctly enough
[m-m]MS, 43, 46 exclusively
[n-n]MS and which have been known to maintain, during long periods, a successful struggle in a contrary direction] 43, 46 as MS . . . a direction contrary
[p-p]MS a sense in the rulers, of identity of interest with them
[q-q]MS, 43 We are not . . . give. We
[r-r]MS, 43, 46 interest of the people that their ruler should do, are also those which he is prompted to do by his strongest personal interest, the consolidation of his
[s-s]MS, 43, 46 the strongest interest
[u-u]MS arose from their having presented
[v-v]+56, 62, 65, 68, 72
[w-w]MS, 43, 46 in many other countries
[x-x]MS true, moreover, that in the particular stage of civilization through which Europe is now passing, responsibility to the governed, either express or virtual,] 43, 46 as MS . . . passing, either express or virtual responsibility to the governed
[y-y]MS, 43, 46 philosophers
[z-z]MS account of
[a-a]MS, 43, 46 any
[b-b]MS, 43, 46 laws
[c-c]MS, 43, 46 most of the principal sequences of the social phenomena
[d-d]MS, 43, 46 contemporary
[e-e]MS, 43, 46, 51 might
[f-f]MS, 43, 46 deemed necessary in] 51 necessary in
[g-g]MS, 43, 46 higher branches of physical science