Chapter I. The Scientific Approach

1. Human society is the subject of many researches. Some of them constitute specialized disciplines: law, political economy, political history, the history of religions, and the like. Others have not yet been distinguished by special names. To the synthesis of them all, which aims at studying human society in general, we may give the name of sociology.

2. That definition is very inadequate. It may perhaps be improved upon—but not much; for, after all, of none of the sciences, not even of the several mathematical sciences, have we strict definitions. Nor can we have. Only for purposes of convenience do we divide the subject-matter of our knowledge into various parts, and such divisions are artificial and change in course of time. Who can mark the boundaries between chemistry and physics, or between physics and mechanics? And what are we to do with thermodynamics? If we locate that science in physics, it will fit not badly there; if we put it with mechanics, it will not seem out of place; if we prefer to make a separate science of it, no one surely can find fault with us. Instead of wasting time trying to discover the best classification for it, it will be the wiser part to examine the facts with which it deals. Let us put names aside and consider things.

In the same way, we have something better to do than to waste our time deciding whether sociology is or is not an independent science—whether it is anything but the "philosophy of history" under a different name; or to debate at any great length the methods to be followed in the study of sociology. Let us keep to our quest for the relationships between social facts, and people may then give to that inquiry any name they please. And let knowledge of such relationships be obtained by any method that will serve. We are interested in the end, and much less or not at all interested in the means by which we attain it.

3. In considering the definition of sociology just above we found it necessary to hint at one or two norms that we intend to follow in these volumes. We might do the same in other connexions as occasion arises. On the other hand, we might very well set forth our norms once and for all. Each of those procedures has its merits and its defects. Here we prefer to follow the second.¹

4. The principles that a writer chooses to follow may be put forward in two different ways. He may, in the first place, ask that his principles be accepted as demonstrated truths. If they are so accepted, all their logical implications must also be regarded as proved. On the other hand, he may state his principles as mere indications of one course that may be followed among the many possible. In that case any logical implication which they may contain is in no sense demonstrated in the concrete, but is merely hypothetical—hypothetical in the same manner and to the same degree as the premises from which it has been derived. It will therefore often be necessary to abstain from drawing such inferences: the deductive aspects of the subject will be ignored, and relationships be inferred from the facts directly.

Let us consider an example. Suppose Euclid's postulate that a straight line is the shortest distance between two points is set before us as a theorem. We must give battle on the theorem; for if we concede it, the whole system of Euclidean geometry stands demonstrated, and we have nothing left to set against it. But suppose, on the contrary, the postulate be put forward as a hypothesis. We are no longer called upon to contest it. Let the mathematician develop the logical consequences that follow from it. If they are in accord with the concrete, we will accept them; if they seem not to be in such accord, we will reject them. Our freedom of choice has not been fettered by any anticipatory concession. Considering things from that point of view, other geometries—non-Euclidean geometries—are possible, and we may study them without in the least surrendering our freedom of choice in the concrete.

If before proceeding with their researches mathematicians had insisted upon deciding whether or not the postulate of Euclid corresponded to concrete reality, geometry would not exist even today. And that observation is of general bearing. All sciences have advanced when, instead of quarrelling over first principles, people have considered results. The science of celestial mechanics developed as a result of the hypothesis of the law of universal gravitation. Today we suspect that that attraction may be something different from what it was once thought to be; but even if, in the light of new and better observations of fact, our doubts should prove well founded, the results attained by celestial mechanics on the whole would still stand. They would simply have to be retouched and supplemented.

5. Profiting by such experience, we are here setting out to apply to the study of sociology the methods that have proved so useful in the other sciences. We do not posit any dogma as a premise to our research; and our statement of principles serves merely as an indication of that course, among the many courses that might be chosen, which we elect to follow. Therefore anyone who joins us along such a course by no means renounces his right to follow some other. From the first pages of a treatise on geometry it is the part of the mathematician to make clear whether he is expounding the geometry of Euclid, or, let us say, the geometry of Lobachevski. But that is just a hint; and if he goes on and expounds the geometry of Lobachevski, it does not follow that he rejects all other geometries. In that sense and in no other should the statement of principles which we are here making be taken.

6. Hitherto sociology has nearly always been expounded dogmatically. Let us not be deceived by the word "positive" that Comte foisted upon his philosophy. His sociology is as dogmatic as Bossuet's Discourse on Universal History. It is a case of two different religions, but of religions nevertheless; and religions of the same sort are to be seen in the writings of Spencer, De Greef, Letourneau, and numberless other authors.

Faith by its very nature is exclusive. If one believes oneself possessed of the absolute truth, one cannot admit that there are any other truths in the world. So the enthusiastic Christian and the pugnacious free-thinker are, and have to be, equally intolerant. For the believer there is but one good course; all others are bad. The Mohammedan will not take oath upon the Gospels, nor the Christian upon the Koran. But those who have no faith whatever will take their oath upon either Koran or Gospels—or, as a favour to our humanitarians, on the Social Contract of Rousseau; nor even would they scruple to swear on the Decameron of Boccaccio, were it only to see the grimace Senator Berenger would make and the brethren of that gentleman's persuasion.¹ We are by no means asserting that sociologies derived from certain dogmatic principles are useless; just as we in no sense deny utility to the geometries of Lobachevski or Riemann. We simply ask of such sociologies that they use premises and reasonings which are as clear and exact as possible. "Humanitarian" sociologies we have to satiety—they are about the only ones that are being published nowadays. Of metaphysical sociologies (with which are to be classed all positive and humanitarian sociologies) we suffer no dearth. Christian, Catholic, and similar sociologies we have to some small extent. Without disparagement of any of those estimable sociologies, we here venture to expound a sociology that is purely experimental, after the fashion of chemistry, physics, and other such sciences.² In all that follows, therefore, we intend to take only experience³ and observation as our guides. So far as experience is not contrasted with observation, we shall, for love of brevity, refer to experience alone. When we say that a thing is attested "by experience," the reader must add "and by observation." When we speak of "experimental sciences," the reader must supply the adjective "observational," and so on.

7. Current in any given group of people are a number of propositions, descriptive, preceptive, or otherwise. For example: "Youth lacks discretion." "Covet not thy neighbour's goods, nor thy neighbour's wife." "Love thy neighbour as thyself." "Learn to save if you would not one day be in need." Such propositions, combined by logical or pseudo-logical nexuses and amplified with factual narrations¹ of various sorts, constitute theories, theologies, cosmogonies, systems of metaphysics, and so on. Viewed from the outside without regard to any intrinsic merit with which they may be credited by faith, all such propositions and theories are experimental facts, and as experimental facts we are here obliged to consider and examine them.

8. That examination is very useful to sociology; for the image of social activity is stamped on the majority of such propositions and theories, and often it is through them alone that we manage to gain some knowledge of the forces which are at work in society—that is, of the tendencies and inclinations of human beings. For that reason we shall study them at great length in the course of these volumes. Propositions and theories have to be classified at the very outset, for classification is a first step that is almost indispensable if one would have an adequate grasp of any great number of differing objects.¹ To avoid endless repetition of the words "proposition" and "theory," we shall for the moment use only the latter term; but whatever we say of "theories" should be taken as applying also to "propositions," barring specification to the contrary.

9. For the man who lets himself be guided chiefly by sentiment—for the believer, that is—there are usually but two classes of theories: there are theories that are true and theories that are false. The terms "true" and "false" are left vaguely defined. They are felt rather than explained.

10. Oftentimes three further axioms are present:

1. The axiom that every "honest" man, every "intelligent" human being, must accept "true" propositions and reject "false" ones. The person who fails to do so is either not honest or not rational. Theories, it follows, have an absolute character, independent of the minds that produce or accept them.

2. The axiom that every proposition which is "true" is also "beneficial," and vice versa. When, accordingly, a theory has been shown to be true, the study of it is complete, and it is useless to inquire whether it be beneficial or detrimental.

3. At any rate, it is inadmissible that a theory may be beneficial to certain classes of society and detrimental to others—yet that is an axiom of modern currency, and many people deny it without, however, daring to voice that opinion.

11. Were we to meet those assertions with contrary ones, we too would be reasoning a priori; and, experimentally, both sets of assertions would have the same value—zero. If we would remain within the realm of experience, we need simply determine first of all whether the terms used in the assertions correspond to some experimental reality, and then whether the assertions are or are not corroborated by experimental facts. But in order to do that, we are obliged to admit the possibility of both a positive and a negative answer; for it is evident that if we bar one of those two possibilities a priori, we shall be giving a solution likewise a priori to the problem we have set ourselves, instead of leaving the solution of it to experience as we proposed doing.

12. Let us try therefore to classify theories, using the method we would use were we classifying insects, plants, or rocks. We perceive at once that a theory is not a homogeneous entity, such as the "element" known to chemistry. A theory, rather, is like a rock, which is made up of a number of elements. In a theory one may detect descriptive elements, axiomatic assertions, and functionings of certain entities, now concrete, now abstract, now real, now imaginary; and all such things may be said to constitute the matter of the theory. But there are other things in a theory: there are logical or pseudo-logical arguments, appeals to sentiment, "feelings," traces of religious and ethical beliefs, and so on; and such things may be thought of as constituting the instrumentalities whereby the "matter" mentioned above is utilized in order to rear the structure that we call a theory. Here, already, is one aspect under which theories may be considered. It is sufficient for the moment to have called attention to it.¹

13. In the manner just described, the structure has been reared—the theory exists. It is now one of the objects that we are trying to classify. We may consider it under various aspects:

1. Objective aspect. The theory may be considered without reference to the person who has produced it or to the person who assents to it—"objectively," we say, but without attaching any metaphysical sense to the term. In order to take account of all possible combinations that may arise from the character of the matter and the character of the nexus, we must distinguish the following classes and subclasses:

The subclasses Ib and IIb comprise logical sophistries, or specious reasonings calculated to deceive. For the study in which we are engaged they are often far less important than the subclasses Ia or IIa. The subclass Ia comprises all the experimental sciences; we shall call it logico-experimental. Two other varieties may be distinguished in it:

Ia1, comprising the type that is strictly pure, with the matter strictly experimental and the nexus logical. The abstractions and general principles that are used within it are derived exclusively from experience and are subordinated to experience (§ 63).

Ia2, comprising a deviation from the type, which brings us closer to Class II. Explicitly the matter is still experimental, and the nexus logical; but the abstractions, the general principles, acquire (implicitly or explicitly) a significance transcending experience. This variety might be called transitional. Others of like nature might be considered, but they are far less important than this one.

The classification just made, like any other that might be made, is dependent upon the knowledge at our command. A person who regards as experimental certain elements that another person regards as non-experimental will locate in Class I a proposition that the other person will place in Class II. The person who thinks he is using logic and is mistaken will class among logical theories a proposition that a person aware of the error will locate among the nonlogical. The classification above is a classification of types of theories. ln reality, a given theory may be a blend of such types—it may, that is, contain experimental elements and non-experimental elements, logical elements and non-logical elements.¹

2. Subjective aspect. Theories may be considered with reference to the persons who produce them and to the persons who assent to them. We shall therefore have to consider them under the following subjective aspects:

a. Causes in view of which a given theory is devised by a given person. Why does a given person assert that A = B? Conversely, if he makes that assertion, why does he do so?

b. Causes in view of which a given person assents to a given theory. Why does a given person assent to the proposition A = B? Conversely, if he gives such assent, why does he do so?

These inquiries are extensible from individuals to society at large.

3. Aspect of utility. In this connexion, is important to keep the theory distinct from the state of mind, the sentiments, that it reflects. Certain individuals evolve a theory because they have certain sentiments; but then the theory reacts in turn upon them, as well as upon other individuals, to produce, intensify, or modify certain sentiments.

These considerations, too, are extensible to society at large.

We may say, then, that we are to consider propositions and theories under their objective and their subjective aspects, and also from the standpoint of their individual or social utility. However, the meanings of such terms must not be derived from their etymology, or from their usage in common parlance, but exclusively in the manner designated later in § 119.

14. To recapitulate: Given the proposition A = B, we must answer the following questions:

1. Objective aspect. Is the proposition in accord with experience, or is it not?

2. Subjective aspect. Why do certain individuals assert that A = B? And why do other individuals believe that A = B?

3. Aspect of utility. What advantage (or disadvantage) do the sentiments reflected by the proposition A = B have for the person who states it, and for the person who accepts it? What advantage (or disadvantage) does the theory itself have for the person who puts it forward, and for the person who accepts it?

In an extreme case the answer to the first question is yes; and then, as regards the other question, one adds: "People say (people believe) that A = B, because it is true." "The sentiments reflected in the proposition are beneficial¹ because true." "The theory itself is beneficial because true." In this extreme case, we may find that data of logico-experimental science are present, and then "true" means in accord with experience. But also present may be data that by no means belong to logico-experimental science, and in such event "true" signifies not accord with experience but something else—frequently mere accord with the sentiments of the person defending the thesis. We shall see, as we proceed with our experimental research in chapters hereafter, that the following cases are of frequent occurrence in social matters:

a. Propositions in accord with experience that are asserted and accepted because of their accord with sentiments, the latter being now beneficial, now detrimental, to individuals or society

b. Propositions in accord with experience that are rejected because they are not in accord with sentiments, and which, if accepted, would be detrimental to society

c. Propositions not in accord with experience that are asserted and accepted because of their accord with sentiments, the latter being beneficial, oftentimes exceedingly so, to individuals or society

d. Propositions not in accord with experience that are asserted and accepted because of their accord with sentiments, and which are beneficial to certain individuals, detrimental to others, and now beneficial, now detrimental, to society.

On all that we can know nothing a priori. Experience alone can enlighten us.

15. After objects have been classified, they have to be examined, and to that research we shall devote the next chapters. In Chapters IV and V we shall consider theories with special reference to their accord with experience and observation. In Chapters VI, VII, and VIII we shall study the sentiments in which theories originate. In Chapters IX and X we shall consider the ways in which sentiments are reflected in theories. In Chapter XI we shall examine the characteristics of the elements so detected. And finally in Chapters XII and XIII we shall see the social effects of the various elements, and arrive at an approximate concept of variations in the forms of society—the goal at which we shall have been aiming all along and towards which all our successive chapters will have been leading.¹

16. From the objective standpoint (§ 13), we divided propositions or theories into two great classes, the first in no way departing from the realm of experience, the second overstepping it in some respect or other.¹ If one would reason at all exactly, it is essential to keep those two classes distinct, for at bottom they are heterogeneous things that must never be in any way confused, and which cannot, either, be compared.² Each of them has its own manner of reasoning and, in general, its own peculiar standard whereby it falls into two divisions, the one comprising propositions that are in logical accord with the chosen standard and are called true; the other comprising propositions which are not in accord with that standard and are called false. The terms "true" and "false," therefore, stand in strict dependence on the standard chosen. If one should try to give them an absolute meaning, one would be deserting the logico-experimental field for the field of metaphysics.

The standard of truth for propositions of the first class lies in experience and observation only. The standard of truth for the second class lies outside objective experience—in some divine revelation; in concepts that the human mind finds in itself, as some say, without the aid of objective experience; in the universal consensus of mankind, and so on.

There must never be any quarrelling over names. If someone is minded to ascribe a different meaning to the terms "truth" and "science," for our part we shall not raise the slightest objection. We are satisfied if he specifies the sense that he means to give to the terms he uses and especially the standard by which he recognizes a proposition as "true" or "false."

17. If that standard is not specified, it is idle to proceed with a discussion that could only resolve itself into mere talk; just as it would be idle for lawyers to plead their cases in the absence of a judge. If someone asserts that "A has the property B," before going on with the discussion we must know who is to judge the controversy between him and another person who maintains that "A does not have the property B." If it is agreed that the judge shall be objective experience, objective experience will then decide whether A has, or does not have, the property B. Throughout the course of these volumes, we are in the logico-experimental field. I intend to remain absolutely in that field and refuse to depart from it under any inducement whatsoever. If, therefore, the reader desires a judge other than objective experience, he should stop reading this book, just as he would refrain from proceeding with a case before a court to which he objected.

18. If people disposed to argue the propositions mentioned desire a judge other than objective experience, they will do well to declare exactly what their judge is to be, and if possible (it seldom is) to make themselves very clear on the point!. In these volumes we shall refrain from participating in arguments as to the substance of propositions and theories. We are to discuss them strictly from the outside, as social facts with which we have to deal.

19. Metaphysicists generally give the name of "science" to knowledge of the "essences" of things, to knowledge of "principles." If we accept that definition for the moment, it would follow that this" work would be in no way scientific. Not only do we refrain from dealing with essences and principles: we do not even know the meaning of those terms (§ 530).

Vera, Hegel's French translator, says,¹ "The notions of science and absolute science are inseparable. . . . Now if there be an absolute science, it is not and cannot be other than philosophy. So philosophy is the common foundation of all the sciences, and as it were the common intelligence of all intelligences." In this book we refuse to have anything whatever to do with such a science, and with those other pretty things that go with it. "The absolute (in other words, essence) and unity (in other words, the necessary relations of beings) are the two prime conditions of science." Both of them will be found missing in these volumes, and we do not even know what they may be. We seek the relationships obtaining between things within the limits of the space and time known to us, and we ask experience and observation to reveal them to us. "Philosophy is at once an explanation and a creation." We have neither the desire nor the ability to explain, in Vera's sense of the term, much less to create. "The science that knows the absolute and grasps the innermost reason of things knows how and why events come to pass and beings are engendered [That is something we do not know.], and not only knows but in a certain way itself engenders and brings to pass in the very fact of grasping the absolute. And indeed we must either deny science, or else admit that there is a point where knowledge and being, thought and its object, coincide and are identified; and a science of the absolute that arose apart from the absolute, and so failed of achieving its real and innermost nature, would not be a science of the absolute, or more exactly, would not be science at all."

20. Well said! In that we agree with Vera. If science is what Vera's terms describe it as being—terms as inspiring as they are (to us) incomprehensible—we are not here dealing with science. We are, however, dealing with another thing that Vera very well describes in a particular case when he says, p. 214, note: "Generally speaking, mechanics is just a miscellany of experiential data and mathematical formulae." In terms still more general, one might say: "a miscellany of experiential data and logical inferences from such data." Suppose, for a moment, we call that non-science. Both Vera and Hegel are then right in saying that the theories of Newton are not science but non-science; and in these volumes I also intend to deal with non-science, since my wish is to construct a system of sociology on the model of celestial mechanics, physics, chemistry, and other similar non-sciences, and eschew entirely the science or sciences of the metaphysicists (§§ 503, 514).

21. A reader might observe: "That granted, why do you continually harp on science in the course of your book, since you use the term in the sense of non-science? Are you trying in that way to usurp for your non-science a prestige that belongs to science alone?" I answer that if the word "science" ordinarily meant what the metaphysicists say it means, rejecting the thing, I would conscientiously reject the word. But that is not the case. Many people, nay, most people, think of celestial mechanics, physics, chemistry, and so on as sciences; and to call them non-sciences or something else of the sort would, I fear, be ridiculous. All the same, if someone is still not satisfied, let him prefix a "non-" to the words "science" and "scientific" whenever he meets them in these volumes, and he will see that the exposition develops just as smoothly, since we are dealing with things and not with words (§ 119).

22. While metaphysics proceeds from absolute principles to concrete cases, experimental science proceeds from concrete cases, not to absolute principles, which, so far as it is concerned, do not exist, but to general principles, which are brought under principles still more general, and so on indefinitely. That procedure is not readily grasped by minds accustomed to metaphysical thinking, and it gives rise to not a few erroneous interpretations.

23. Let us note, just in passing, the preconception that in order to know a thing its "essence" must be known. To the precise contrary, experimental science starts with knowledge of things, to go on, if not to essences, which are entities unknown to science, at least to general principles (§§ 19-20). Another somewhat similar conception is widely prevalent nowadays in the fields of political economy and sociology. It holds that knowledge of things can be acquired only by tracing their "origins"¹ (§§ 93, 346).

24. In an attenuated form the preconception requiring knowledge of "essences" aims at demonstrating particular facts by means of general principles, instead of deriving the general principle from the fact. Just so proof of the fact is confused with proof of its causes. For example, observation shows the existence of a fact A; and we go on and designate B, C, D . . . as its probable causes. It is later shown that those causes are not operative, and from that the conclusion is drawn that A does not exist. The demonstration would be valid if the existence of B, C, D . . . had been shown by experience and the existence of A inferred from them. It is devoid of the slightest value if observation has yielded A directly.

25. Close kin to the preconception just mentioned is the difficulty some people experience in analyzing a situation and studying its various aspects separately. We shall have frequent occasion to return to this matter. Suffice it here to note that the distinctions drawn above in § 13 will not be recognized by many people; and if others do indeed accept them theoretically, they straightway forget them in actual thinking (§§ 31-32, 817).

26. For people of "living faith" the various characteristics of theories designated in § 13 often come down to one only. What the believer wants to know, and nothing else, is whether the proposition is true or not true. Just what "true" means nobody knows, and the believer less than anybody. In a general way it seems to indicate accord with the believer's sentiments; but that fact is evident only to the person viewing the belief from the outside, as a stranger to it—never to the believer himself. He, as a rule, denies the subjective character of his belief. To tell him that it is subjective is almost to insult him, for he considers it true in an absolute sense. For the same reason he refuses to think of the term "true" apart from the meaning he attaches to it, and readily speaks of a truth different from experimental truth and superior to it.¹

27. It is idle to continue discussions of that type—they can only prove fruitless and inconclusive—unless we know exactly what the terms that are used mean, and unless we have a criterion to refer to, a judge to render judgment in the dispute (§§ 17 f.). Is the criterion, the judge, to be experience and observation, or is it to be something else? That point has to be clearly determined before we can go on. If you are free to choose between two judges, you may pick the one you like best to decide your case. But you cannot choose them both at the same time, unless you are sure in advance that they are both of one mind and one will.

28. Of that agreement metaphysicists enjoy an a priori certitude, for their superexperimental criterion is of such majesty and power that it dominates the experimental criterion, which must of necessity accord with it. For a similar reason theologians too are certain a priori that the two criteria can never fail of accord. We, much more humble, enjoy no such a priori enlightenment. We have no knowledge whatever of what must or ought to be. We are looking strictly for what is. That is why we have to be satisfied with one judge at a time.

29. From our point of view not even logic supplies necessary inferences, except when such inferences are mere tautologies. Logic derives its efficacy from experience and from nothing else (§ 97).¹

30. The human mind is synthetic, and only training in the habit of scientific thinking enables a few individuals to distinguish the parts in a whole by an analytical process (§ 25). Women especially, and the less well-educated among men, often experience an insurmountable difficulty in considering the different aspects of a thing separately, one by one. To be convinced of that one has only to read a newspaper article before a mixed social gathering and then try to discuss one at a time the various aspects under which it may be considered. One will notice that one's listeners do not follow, that they persist in considering all the aspects of the subject all together at one time.

31. The presence of that trait in the human mind makes it very difficult for both the person who is stating a proposition and the person who is listening to keep the two criteria, the experimental and the non-experimental, distinct. An irresistible force seems always to be driving the majority of human beings to confuse them. Many facts of great significance to sociology find their explanation in just that, as will be more clearly apparent from what follows.

32. In the natural sciences people have finally realized the necessity of analysis in studying the various aspects of a concrete phenomenon—the analysis being followed by a synthesis in getting back from theory to the concrete. In the social sciences that necessity is still not grasped by many people.

33. Hence the very common error of denying the truth of a theory because it fails to explain every aspect of a concrete fact; and the same error, under another form, of insisting on embracing under one theory all other similar or even irrelevant theories.

Let O in Figure 1 stand for a concrete situation. By analysis we distinguish within it a number of facts: c, e, g. . . .

The fact c and others like it, a, b . . . are brought together under a certain theory, under a general principle, P. In the same way, e and facts like e (d, f . . .) yield another theory, Q; and the facts g, i, m, n . . . still another theory, R, and so on. These theories are worked out separately; then, to determine the concrete situation O, the results (c, e, g . . .) of the various theories are taken together. After analysis comes synthesis.

People who fail to understand that will say: "The situation O presents not only the fact e but also the fact c; therefore the theory Q has to account for c." That conclusion is erroneous. One should say—and it is the only sound conclusion: ". . . therefore the theory Q accounts for only a part of the situation O."

34. Example: Let Q stand for the theory of political economy. A concrete situation O presents not only an economic aspect, e, but the further aspects c, g . . . of a sociological character. It is a mistake to include, as many have included, the sociological elements c, g . . . under political economy. The only sound conclusion to be drawn from the facts is that the economic theory which accounts for e must be supplemented (supplemented, not replaced) by other theories which account for c, g. . . .

35. In political economy itself, the theories of pure or mathematical economics have to be supplemented—not replaced—by the theories of applied economics. Mathematical economics aims chiefly at emphasizing the interdependence of economic phenomena. So far no other method has been found for attaining that end.¹

36. Straightway one of those numberless unfortunates who are cursed with the mania for talking about things they do not understand comes forward with the discovery—lo the wonders of genius! —that pure economics is not applied economics, and concludes, not that something must be added to pure economics if we are to understand concrete phenomena, but that pure economics must be replaced by his gabble. Alas, good soul, mathematical economics helps, at least, to a rough understanding of the effects of the interdependence of economic phenomena, while your gabble shows absolutely nothing!

37. And lo, another prodigious genius, who holds that because many economic phenomena depend on the human will, economics must be replaced by psychology. But why stop at psychology? Why not geography, or even astronomy? For after all the economic factor is influenced by seas, continents, rivers, and above all by the Sun, fecundator general of "this fair family of flowers and trees and all earthly creatures."¹ Such prattle has been called positive economics, and for that our best gratitude, for it provokes a laugh, and laughter, good digestion!

38. Many economists have been inclined to bring each and every sort of economic theory under the theory of value.¹ True, nearly all economic phenomena express themselves in terms of value; but from that we have a right to conclude that in isolating the various elements in such phenomena we come upon a theory for value—but not that all other elements have to be squeezed into that theory. Nowadays people are going farther still, and value is coming to be the door through which sociology is made to elbow its way into political economy. Perhaps we ought to be thankful that they are stopping at that, for no end of other things might be pushed through the same door: psychology, to explain why and how a thing, real or imaginary, comes to have value; then physiology as handmaiden to psychology; and then—why not?—a little biology to explain the foundations of physiology; and surely a little mathematics, for after all the first member of an equation has the same value as the second and the theory of value would not be complete without the theory of equations; and so on forever. In all of which there is this much truth: that the concrete situation is very complex and may be regarded as a compound of many elements A, B, C. . . . Experience teaches that to understand such a situation it is best to isolate the elements A, B, C . . . and examine them one by one, that we may then bring them together again and so get the theory of the complex as a whole. That is just what logico-experimental science does. But those who are unfamiliar with its methods grope blindly forward, shifting from A to B, from B to C, then every so often turning back, mixing things up, taking refuge in words, thinking of B while studying A, and of something else while studying B. Worse yet, if you are looking into A they interrupt to remind you of B; and if you answer on B, they are off to C, jumping about now here, now there, prattling ever beside the point and demonstrating one thing only: their helpless innocence of any scientific method.

39. Those who deny scientific status to political economy argue, in fact, to show that it is not adequate to explain concrete phenomena; and from that they conclude that it should be ignored in such explanation. The sound conclusion would be that other theories should be added to it. Thinking as such people think we should have to say that chemistry ought to be ignored in agriculture, since chemistry is inadequate to explain everything about a farm. Moreover, engineering schools would have to bar pure mathematics, for it stands to applied mechanics almost as pure economics stands to applied economics.

40. Further, it is difficult, in fact almost impossible, to induce people to keep mere knowledge of the laws (uniformities) of society distinct from action designed to modify them. If someone is keeping strictly to such knowledge, people will insist at all costs that he have some practical purpose in view. They try to find out what it is, and, there being none, one is finally invented for him.

41. In the same way, it is difficult to induce people not to go beyond what an author says and add to the propositions he states others that may seem to be implicit in them but which he never had in mind (§§ 73 f., 311). If you note a defect in a given thing A, it is taken for granted that you are condemning A as a whole; if you note a good point, that you approve of A as a whole. It seems incredibly strange to people that you should be stressing its defects if you are not intending to condemn it as a whole, or its excellences if you are not approving of it as a whole. The inference would be somewhat justified in a case of special pleading, for after all it is not the business of the advocate to accuse his client. But it is not a sound inference from a plain description of fact, or when a scientist is seeking scientific uniformities. The inference would be admissible, further, in the case of an argument not of a logico-experimental character but based on accord of sentiments (§ 514). In fact, when one is trying to win the sympathies of others by such an argument, one may be expected to declare one's own sympathies; and if that is not done explicitly, people may properly assume that it is done implicitly. But when we are reasoning objectively, according to the logico-experimental method, we are not called upon to declare our sentiments either explicitly or by implication.

42. As regards proofs, a person stating a logico-experimental proposition or theory (§ 13, Ia) asks them of observation, experience, and logical inferences from observation and experience. But the person asserting a proposition or theory that is not logico-experimental can rely only on the spontaneous assent of other minds and on the more or less logical inferences he can draw from what is assented to. At bottom he is exhorting rather than proving. However, that is not commonly admitted by people using non-logico-experimental theories. They pretend to be offering proofs of the same nature as the proofs offered for logico-experimental theories; and in such pseudo-experimental arguments they take full advantage of the indefiniteness of common everyday language.

As regards persuasion, proofs are convincing only to minds trained to logico-experimental thinking. Authority plays a great part even in logico-experimental propositions, though it has no status as proof. Passions, accords of sentiment, vagueness of terms, are of great efficacy in everything that is not logico-experimental (§ 514).

43. In the sphere of proof, experience is powerless as against faith, and faith as against experience, with the result that each is confined to its own domain. If John, an unbeliever, denies that God created Heaven and Earth, and you meet him with the authority of the Bible, you have made a nice round hole in the water, for he will deny the authority of the Bible and your argument will crumble. To replace the authority of the Bible with the authority of your "Christian experience" is a childish makeshift, for John will reply that his own experience inclines him not in the least to agree with you; and if you retort that his experience is not Christian, you will have reasoned in a neat circle, for it is certain that if only that experience is Christian which leads to your results, one may conclude without fear of contradiction that Christian experience leads to your results—and by that we have learned exactly nothing.

44. When one asserts a logico-experimental proposition (§ 13, Ia), one can place those who contradict in the dilemma of either accepting the proposition as true or refusing credence to experience and logic. Anyone adopting the latter course would be in the position of John, the unbeliever just mentioned: you would have no way of persuading him.

45. It is therefore evident that, aside as usual from sophistical reasonings made in bad faith, the difference as regards proofs between theories that are logico-experimental (Ia) and theories that are not lies chiefly in the fact that in our day in Western countries it is easier to find disbelievers in the Koran or the Gospels; in types of experience, whether Christian, personal, humanitarian, rational, or of whatever other kind; in the categorical imperative; or in the dogmas of positivism, nationalism, pacifism, and numberless other things of that brand, than it is to find disbelievers in logic and experience. In dealing with other ages and countries the situation maybe different.

46. We are in no sense intending, in company with a certain materialistic metaphysics, to exalt logic and experience to a greater power and majesty than dogmas accepted by sentiment. Our aim is to distinguish, not to compare, and much less to pass judgment on the relative merits and virtues of those two sorts of thinking (§ 69).

47. Again, we have not the remotest intention of bringing back through the window a conviction we have just driven out by the door. We in no wise assert that the logico-experimental proof is superior to the other and is to be preferred. We are saying simply—and it is something quite different—that such proof alone is to be used by a person concerned not to abandon the logico-experimental field.¹

48. The extreme case of a person flatly repudiating all logical discursion, all experience, is rarely met with. Logico-experimental considerations are commonly enough ignored, left unexpressed, crowded aside, by one device or another; but it is difficult to find anyone really combating them as enemies. That is why people almost always try to demonstrate theories that are not objective, not experimental, by pseudo-logical and pseudo-experimental proofs.

49. All religions have proofs of that type, supplemented as a rule by proofs of utility to individual and society. And when one religion replaces another, it is anxious to create the impression that its experimental proofs are of a better quality than any the declining faith can marshal. Christian miracles were held to be more convincing than pagan miracles, and nowadays the "scientific" proofs of "solidarity" and humanitarianism are considered superior to the Christian miracles. All the same, the man who examines such facts without the assistance of faith fails to notice any great difference in them: for him they have exactly the same scientific value, to wit, zero. We are obliged to believe that "when Punic fury thundered from the Thrasimene" the defeat of the Romans was caused by the impious indifference of the consul Flaminius to the portents sent of the gods. The consul had fallen from his horse in front of the statue of Jupiter Stator. The sacred chickens had refused to eat. Finally, the legionary ensign had stuck in the ground and could not be extricated.¹ We shall also be certain (whether more or less certain, I could not say) that the victory of the Crusaders at Antioch was due to the divine protection concretely symbolized in the Holy Lance.² Then again it is certain, in fact the height of certitude, because attested by a better and more modern religion, that Louis XVI of France lost his throne and his life simply because he did not love to the degree required his good, his darling, people. The humanitarian god of democracy never suffers such offences to go unpunished!

50. Experimental science has no dogmas, not even the dogma that experimental facts can be explained only by experience. If the contrary were seen to be the case, experimental science would accept the fact, as it accepts every other fact of observation. And it in truth accepts the proposition that inventions may at times be promoted by non-experimental principles, and does so because that proposition is in accord with the results of experience.¹ But so far as demonstration goes, the history of human knowledge clearly shows that all attempts to explain natural phenomena by means of propositions derived from religious or metaphysical principles have failed. Such attempts have finally been abandoned in astronomy, geology, physiology, and all other similar sciences. If traces of them are still to be found in sociology and its subbranches, law, political economy, ethics, and so on, that is simply because in those fields a strictly scientific status has not yet been attained.²

51. One of the last efforts to subordinate experience to metaphysics was made by Hegel in his Philosophy of Nature, a work which, in all frankness, attains and oversteps the limits of comic absurdity.¹

52. On the other hand, in our day people are beginning to repudiate dogmas that usurp status as experimental science. Sectarians of the humanitarian cult are wont to meet the "fictions" of the religion they are combating with the "certainty" of science. But that "certainty" is just one of their preconceptions. Scientific theories are mere hypotheses, which endure so long as they accord with the facts and which die and vanish from the scene as new investigations destroy that accord. They are then superseded by new ones for which a similar fate is held in store (§ 22).

53. Let us assume that a certain number of facts are given. The problem of discovering their theory may be solved in more than one way. A number of theories may satisfy the data equally well, and the choice between them may sometimes be determined by subjective considerations, such as preference for greater simplicity (§ 64).

54. In both logico-experimental (Ia) and non-logico-experimental theories, one gets certain general propositions called "principles," logically deducible from which are inferences constituting theories. Such principles differ entirely in character in the two kinds of theories mentioned.

55. In logico-experimental theories (Ia) principles are nothing but abstract propositions summarizing the traits common to many different facts. The principles depend on the facts, not the facts on the principles. They are governed by the facts, not the facts by them. They are accepted hypothetically only so long and so far as they are in agreement with the facts; and they are rejected as soon as there is disagreement (§ 63).

56. But scattered through non-logico-experimental theories one finds principles that are accepted a priori, independently of experience, dictating to experience. They do not depend upon the facts; the facts depend upon them. They govern the facts; they are not governed by them. They are accepted without regard to the facts, which must of necessity accord with the inferences deducible from the principles; and if they seem to disagree, one argument after another is tried until one is found that successfully re-establishes the accord, which can never under any circumstances fail.

57. In order of time, the grouping of theories as given in § 13 has in many cases to be reversed. In history, that is, non-logico-experimental theories often come first, the logico-experimental (Ia) afterwards.

58. The subordination of facts to principles in non-logico-experimental theories is manifested in a number of ways:

1. People are so sure of the principles with which they start that they do not even take the trouble to inquire whether their implications are in accord with experience. Accord there must be, and experience as the subordinate cannot, must not, be allowed to talk back to its superior.¹ That is the case especially when logico-experimental theories (Ia) begin to invade a domain that has been pre-empted by non-logico-experimental theories.

2. As that invasion gains headway, progress in the experimental sciences finally rescues them from the servitude to which they were regarded as sternly subject. They are conceded a measure of autonomy; they are permitted to verify the inferences drawn from traditional principles, though people continue to assert that verification always corroborates the principle. If things seem not to turn out that way, casuistry comes to the rescue to re-establish the desired accord.

3. When finally that method of maintaining the sovereignty of the general principles also fails, the experimental sciences are resignedly allowed to enjoy their hard-won independence; but their domain is now represented as of an inferior order envisaging the relative and the particular, whereas philosophical principles contemplate the absolute, the universal.

59. No departure from the experimental field and therefore from the domain of logico-experimental theories (Ia) is involved in the resort to hypotheses, provided they are used strictly as instruments in the quest for consequences that are uniformly subject to verification by experience. The departure arises when hypotheses are used as instruments of proof without reference to experimental verification. The hypothesis of gravitation, for instance, does not carry us outside the experimental field so long as we understand that its implications are at all times subject to experience, as modern physics always assumes. It would carry us outside the experimental field were we to declare gravitation an "essential property" of "matter" and assert that the orbits of the stars must of necessity comply with the Newtonian law. That distinction was not grasped by writers such as Comte, who tried to bar the hypothesis of a luminous ether from science. That hypothesis and others of the kind are to be judged not intrinsically but extrinsicallv, that is, by ascertaining whether and to what extent inferences drawn from them accord with the facts.

60. When any considerable number of inferences from a given hypothesis have been verified by experience, it becomes exceedingly probable that a new implication will likewise be verified; so in that case the two types of hypotheses mentioned in §§ 55 and 56 are inclined to blend, and in practice there is the temptation to accept the new inference without verifying it. That explains the haziness present in many minds as to the distinction between hypotheses subordinate to experience and hypotheses dominating experience. Still, as a matter of practice there are cases where the implications of this or that hypothesis may be accepted without proof. For instance, certain principles of pure mechanics are being questioned nowadays, at least as regards velocities to any considerable degree greater than velocities practically observable. But it is evident that the mechanical engineer may continue to accept them without the slightest fear of going wrong, since the parts of his machines move at speeds which fall far short of any that would require modifications in the principles of dynamics.

61. In pure economics my hypothesis of "ophelimity" (§ 2110) remains experimental so long as inferences from it are held subject to verification on the facts. Were that subordination to cease, the hypothesis could no longer be called experimental. Walras did not think of his "exchange value" in any such manner.¹ If one drops the hypothesis of ophelimity, as is possible by observing curves of indifference (§ 2408¹) or by some other device of the kind, one is excused from verifying experimentally the implications of a hypothesis that is no longer there.

62. Likewise, the hypothesis of value remains experimental so long as value is thought of as something leading to inferences that are experimentally verifiable. It ceases to be experimental when value is taken as a metaphysical entity presumably superior to experimental verification (§ 104).¹

63. In the logico-experimental sciences, if they are to be kept strictly such, so-called general principles are, as we said above (§ 55), nothing but hypotheses designed to formulate syntheses of facts linking facts under theories and epitomizing them. Theories, their principles, their implications, are altogether subordinate to facts and possess no other criterion of truth than their capacity for picturing them. That is an exact reversal of the relations between general principles and experimental facts that obtain in non-logico-experimental theories (§ 13, Class II). But the human mind has such a predilection for theories of that sort that general principles have often been seen to recover sovereignty even over theories aspiring to status as logico-experimental (Ia). It was agreed, that is, that principles had a quasi-independent subsistence, that only one theory was true, while numberless others were false, that experience could indeed determine which theory was true, but that, having done that much, it was called upon to submit to the theory. In a word, general principles, which were lords by divine right in non-logico-experimental theories (§ 16), became lords by election, but lords nevertheless, in logico-experimental theories (Ia). So we get the two subclasses distinguished in § 13; but it is well to note that oftentimes their traits are implicit rather than explicit, that is, general principles are used without explicit declaration as to just how they are regarded.

64. Steady progress in the experimental sciences eventually brought about the downfall of this elective sovereignty as well, and so led to strictly logico-experimental theories (Ia1), in which general principles are mere abstractions devised to picture facts, it being meantime recognized that different theories may be equally true (§ 53), in the sense that they picture the facts equally well and that choice among them is, within certain limits, arbitrary. In a word, one might say that we have reached the extreme of Nominalism, provided that term be stripped of its metaphysical connotations.

65. For the very reason that we intend to remain strictly within logico-experimental bounds, we are not called upon to solve the metaphysical problem of Nominalism and Realism.¹ We do not presume to decide whether only the individuum, or only the species, exists, for the good reason, among others, that we are not sufficiently clear as to the precise meaning of the term "exist." We intend to study things and hence individua, and to consider species as aggregates of more or less similar things on which we determine ourselves for specified purposes. Farther than that we choose not to go just here, though without prejudice to anybody's privilege of going beyond the point at which we stop.

66. The fact that we deal with individua by no means implies that a number of indiuidua taken together are to be considered a simple sum. They form compounds which, like chemical compounds, may have properties that are not the sum of the properties of their components.

67. Whether the principle that replaces experience or observation be theological, metaphysical, or pseudo-experimental may be of great importance from certain points of view; but it is of no importance whatever from the standpoint of the logico-experimental sciences. St. Augustine denies the existence of antipodes because Scripture makes no mention of them.¹ In general, the Church Fathers find all their criteria of truths, even of experimental truths, in Holy Writ. Metaphysicists make fun of them and replace their theological principles with other principles just as remote from experience. Scientists who came after Newton, forgetting that he had wisely halted at the dictum that celestial bodies moved as if by mutual attraction according to a certain law, saw in that law an absolute principle, divined by human intelligence, verified by experience, and presumably governing all creation eternally. But the principles of mechanics have of late been subjected to searching criticism, and the conclusion has been reached that only facts and the equations that picture them can stand. Poincaré judiciously observes that from the very fact that certain phenomena admit of a mechanical explanation, they admit also of an indefinite number of other explanations.

68. All the natural sciences to a greater or lesser extent are approximating the logico-experimental type (Ia1). We intend to study sociology in just that fashion, trying, that is, to reduce it to the same type (§§ 6, 486, 514²).

69. The course we elect to pursue in these volumes is therefore the following:

1. We intend in no way to deal with the intrinsic "truth" of any religion or faith, or of any belief, whether ethical, metaphysical, or otherwise, and we adopt that resolve not in any scorn for such beliefs, but just because they lie beyond the limits within which we have chosen to confine ourselves. Religions, beliefs, and the like we consider strictly from the outside as social facts, and altogether apart from their intrinsic merits. The proposition that "A must¹ be equal to B" in virture of some higher superexperimental principle escapes our examination entirely (§ 46); but we do want to know how that belief arose and developed and in what relationships it stands to other social facts.

2. The field in which we move is therefore the field of experience and observation strictly. We use those terms in the meanings they have in the natural sciences such as astronomy, chemistry, physiology, and so on, and not to mean those other things which it is the fashion to designate by the terms "inner" or "Christian" experience, and which revive, under barely altered names, the "introspection" of the older metaphysicists. Such introspection we consider as a strictly objective fact, as a social fact, and not as otherwise concerning us.

3. Not intruding on the province of others, we cannot grant that others are to intrude on ours.² We deem it inept and idiotic to set up experience against principles transcending experience: but we likewise deny any sovereignty of such principles over experience.³

4. We start with facts to work out theories, and we try at all times to stray from the facts as little as possible. We do not know what the "essences" of things are (§§ 19, 91, 530) and we ignore them, since that investigation oversteps our field (§ 91). We are looking for the uniformities presented by facts,⁴ and those uniformities we may even call laws (§ 99); but the facts are not subject to the laws: the laws are subject to the facts. Laws imply no necessity (§§ 29, 97). They are hypotheses serving to epitomize a more or less extensive number of facts and so serving only until superseded by better ones.

5. Every inquiry of ours, therefore, is contingent, relative, yielding results that are just more or less probable, and at best very highly probable. The space we live in seems actually to be three-dimensional; but if someone says that the Sun and its planets are one day to sweep us into a space of four dimensions, we shall neither agree nor disagree. When experimental proofs of that assertion are brought to us, we shall examine them, but until they are, the problem does not interest us. Every proposition that we state, not excluding propositions in pure logic, must be understood as qualified by the restriction within the limits of the time and experience known to us (§ 97).

6. We argue strictly on things and not on the sentiments that the names of things awaken in us. Those sentiments we study as objective facts strictly. So, for example, we refuse to consider whether an action be "just" or "unjust," "moral" or "immoral," unless the things, to which such terms refer have been clearly specified. Wey shall, however, examine as an objective fact what people of a given social class, in a given country, at a given time, meant when they said that A was a "just" or a "moral" act. We shall see what their motives were, and how oftentimes the more important motives have done their work unbeknown to the very people who were inspired by them; and we shall try to determine the relationships between such facts and other social facts. We shall avoid arguments involving terms lacking in exactness (§ 486), because from inexact premises only inexact conclusions can be drawn.⁵ But such arguments we shall examine as social facts; indeed, we have in mind to solve a very curious problem as to how premises altogether foreign to reality sometimes yield inferences that come fairly close to reality (Chapter XI).

7. Proofs of our propositions we seek strictly in experience and observation, along with the logical inferences they admit of, barring all proof by accord of sentiments, "inner persuasion," "dictate of conscience."

8. For that reason in particular we shall keep strictly to terms corresponding to things, using the utmost care and endeavour to have them as definite as possible in meaning (§ 108).

9. We shall proceed by successive approximations. That is to say, we shall first consider things as wholes, deliberately ignoring details. Of the latter we shall then take account in successive approximations (§ 540).⁶

70. We in no sense mean to imply that the course we follow is better than others, for the reason, if for no other, than the term "better" in this case has no meaning. No comparison is possible between theories altogether contingent and theories recognizing an absolute. They are heterogeneous things and can never be brought together (§ 16). If someone chooses to construct a system of sociology starting with this or that theological or metaphysical principle or, following a contemporary fashion, with the principles of "progressive democracy," we shall pick no quarrel with him, and his work we shall certainly not disparage. The quarrel will not become inevitable until we are asked in the name of those principles to accept some conclusion that falls within the domain of experience and observation. To go back to the case of St. Augustine: When he asserts that the Scriptures are inspired of God, we have no objection to the proposition, which we do not comprehend very clearly to begin with. But when he sets out to prove by the Scriptures that there are no antipodes (§ 485), we have no interest in his arguments, since jurisdiction in the premises belongs to experience and observation.¹

71. We move in a narrow field, the field, namely, of experience and observation. We do not deny that there are other fields, but in these volumes we elect not to enter them. Our purpose is to discover theories that picture facts of experience and observation (§ 486), and in these volumes we refuse to go beyond that. If anyone is minded to do so, if anyone craves an excursion outside the logico-experimental field, he should seek other company and drop ours, for he will find us disappointing.

72. We differ radically from many people following courses similar to ours in that we do not deny the social utility of theories unlike our own. On the contrary we believe that in certain cases they may be very beneficial. Correlation of the social utility of a theory with its experimental truth is, in fact, one of those a priori principles which we reject (§ 14). Do the two things always go hand in hand, or do they not? Observation of facts alone can answer the question; and the pages which follow will furnish proofs that the two things can, in certain cases, be altogether unrelated.

73. I ask the reader to bear in mind, accordingly, that when I call a doctrine absurd, in no sense whatever do I mean to imply that it is detrimental to society: on the contrary, it may be very beneficial. Conversely, when I assert that a theory is beneficial to society, in no wise do I mean to imply that it is experimentally true. In short, a doctrine may be ridiculed on its experimental side and at the same time respected from the standpoint of its social utility. And vice versa.

74. In general, when I call attention to some untoward consequence of a thing A, indeed one very seriously so, in no way do I mean to imply that A on the whole is detrimental to society; for there may be good effects to overbalance the bad. Conversely, when I call attention to a good effect of A, great though it be, I do not at all imply that on the whole A is beneficial to society.

75. The warning I have just given I had to give, for in general people writing on sociology for purposes of propaganda and with ideals to defend speak in unfavourable terms alone of things they consider bad on the whole, and favourably of things they consider good on the whole. Furthermore, since to a greater or lesser extent they use arguments based on accords of sentiment (§§ 41, 514), they are induced to manifest their own sympathies in order to win the sympathies of others. They look at facts with not altogether indifferent eyes. fThey love and they hate, and they disclose their loves and their hates, their likes and dislikes. Accustomed to that manner of doing and saying, a reader very properly concludes that if a writer speaks unfavourably of a thing and stresses one or another of its defects, that means that on the whole he judges it bad and is unfavourably disposed towards it; whereas if he speaks favourably of a thing and stresses one or another of its good points, on the whole he deems it good and is favourably disposed towards it. That rule does not apply to this work; and I shall feel obliged to remind the reader of that fact over and over again (§ 311). In these volumes I am reasoning objectively, analytically, according to the logico-experimental method. In no way am I called upon to make known such sentiments as I may happen to cherish, and the objective judgment I pass upon one aspect of a thing in no sense implies a similar judgment on the thing considered synthetically as a whole.¹

76. If one person would persuade another on matters pertaining to experimental science, he chiefly and, better yet, exclusively, states facts and logical implications of facts (§ 42). But if he would persuade another on matters pertaining to what is still called social science, his chief appeal is to sentiments, with a supplement of facts and logical inferences from facts. And he must proceed in that fashion if his idea is to talk not in vain; for if he were to disregard sentiments, he would persuade very few and in all probability fail to get a hearing at all, whereas if he knows how to play deftly on sentiments, his reputation for eloquence will soar (§ 514).¹

77. Political economy has hitherto been a practical discipline designed to influence human conduct in one direction or another. It could hardly be expected, therefore, to avoid addressing sentiment, and in fact it has not done so. All along economists have given us systems of ethics supplemented in varying degree with narrations of facts and elaborations of the logical implications of facts. That is strikingly apparent in the writings of Bastiat; but it is apparent enough in virtually all writings on economics, not excluding works of the historical school, which are oftentimes more metaphysical and sentimental than the rest. As mere examples of forecasts based on the scientific laws of political economy and sociology (to the exclusion of sentiment), I offer the following. The first volume of my Cours appeared in the year 1896, but had been written in 1895, with statistical tables coming down not later than the year 1894.

1. Contrarily to the views of ethical sociologists, whether of the historical school or otherwise, and of sentimental anti-Malthusians, at that time I wrote with reference to population increase: "We are therefore witnessing rates of increase in our day that cannot have obtained in times past and cannot continue to hold in the future."¹ And I mentioned in that connexion the examples of England and Germany. As for England, there were already signs of a slackening. Not so for Germany, where there were as yet no grounds, empirically, for arriving at any conclusions whatever. But now both countries show a declining curve.²

2. With specific reference to England, after determining the law of population increase for the years 1801-91, I concluded that popu lation could not continue to increase at the same rate. And the rate has in fact fallen.³

3. "The gains made by certain Socialistic ideas in England are probably the result of an increment in the economic obstacles to population increase."⁴ The soundness of that conclusion is even more apparent now. Socialism has progressed in England, while a falling-off has been observable in the other countries in Europe.

4. In Chapter XII we shall see a verification of a sociological law that I used in my Systèmes socialistes.

5. The second volume of my Cours was published in 1897. At that time it was an article of faith with many people that social evolution was in the direction of the rich growing richer and the poor, poorer. Contrarily to that sentimental view, the law of distribution of income led to the proposition⁵ that "if total income increases with respect to population, there must be either an increase in the minimum income, or a decrease in inequality in incomes, or the two things must result simultaneously." Between 1897 and 1911 there was an increase in total income as compared with population, and what in fact resulted was an increase in minimum income and a decrease in inequality in incomes.⁶ A counter-proof, furthermore, is available in the fact that my Cours is defective in those sections into which sentiment was allowed to intrude.⁷

78. A person often accepts a proposition for no other reason than that it accords with his sentiments. Such accord, indeed, usually makes a proposition more "obvious." And from the standpoint of social utility in many cases it is perhaps well that that be so. But from the standpoint of experimental science, such accord has little value and often none whatever. Of that I shall give many examples.

79. Since I intend in these volumes to take my stand strictly within the field of experimental science, I shall try to avoid any appeal to the reader's sentiments whatsoever and keep to facts and implications of facts.¹

80. When a writer is "doing literature" or addressing sentiments in any way at all, he finds it necessary, in deference to them, to choose between the facts he uses. Not all of them rise to the dignity of rhetorical or historical propriety. There is an aristocracy of facts reference to which is always commendable. There is a commonalty of facts reference to which incurs neither praise nor blame. There is a proletariat of facts reference to which is at all times improper and reprehensible. So amateur entomologists may find it pleasant to catch bright-coloured butterflies, just routine to catch flies and wasps, loathsome to lay hand to dung- and carrion-beetles. But the naturalist knows no such distinctions, nor do they arise for us in the field of social science (§§ 85, 896).

81. We keep open house to all facts, whatever their character, provided that directly or indirectly they point the way to discovering a uniformity. Even an absurd, an idiotic argument is a fact, and if accepted by any large number of people, a fact of great importance to sociology. Beliefs, whatever their character, are also facts, and their importance depends not on their intrinsic merits, but on the greater or fewer numbers of individuals who profess them. They serve furthermore to reveal the sentiments of such individuals, and sentiments are among the most important elements with which sociology is called upon to deal (§ 69-6).

82. The reader must bear that in mind, as he encounters in these volumes facts which at first blush might seem insignificant or childish. Tales, legends, the fancies of magic or theology, may often be accounted idle and ridiculous things—and such they are, intrinsically; but then again they may be very helpful as tools for discovering the thoughts and feelings of men. So the psychiatrist studies the ravings of the lunatic not for their intrinsic worth but for their value as symptoms of disease.

83. The road that is to lead us to the uniformities we seek may at times seem a long one. If that is the case, it is simply because I have not succeeded in finding a shorter. If someone manages to do so, all the better; I will straightway leave my road for his. Meantime I deem it the wiser part to push on along the only trail as yet blazed.

84. If one's aim is to inspire or re-enforce certain sentiments in men, one must present facts favourable to that design and keep unfavourable data quiet. But if one is interested strictly in uniformities, one must not ignore any fact that may in any way serve to disclose them. And since my aim in these volumes is no other, I refuse out of hand to consider in a fact anything but its logico-experimental significance.

85. The one concession that I can make—and really it is not so much a concession as a grasp at some method for securing a far greater clearness by removing from the reader's eyes any veil that sentiment may have drawn across them—is to choose from the multitude of facts such as, in my judgment, will exert least influence upon sentiments. So when I have facts of equal experimental value before me from the past and from the present, I choose facts of the past. That accounts for my many quotations from Greek and Latin writers. In the same way, when I have facts of equal experimental value from religions now extinct and religions still extant, I give my preference to the former. But to prefer a thing is not to use it exclusively. In many many cases I am constrained to use facts from the present or from religions still existing, sometimes because I have no other facts of an equivalent experimental value, sometimes in order to show the continuity of certain phenomena from past to present. In such connexions I intend to write with absolute freedom; and the same frankness I maintain against the malevolence of our modern Paladins of Purity, for whom I care not the proverbial fig.¹

86. In propounding this or that theory an author as a rule wants other people to assent to it and adopt it—in him the seeker after experimental truth and the apostle stand combined. In these volumes I keep those attitudes strictly separate, retaining the first and barring the second. I have said, and I repeat, that my sole interest is the quest for social uniformities, social laws. I am here reporting on the results of my quest, since I hold that in view of the restricted number of readers such a study can have and in view of the scientific training that may be taken for granted in them, such a report can do no harm. I should refrain from doing so if I could reasonably imagine that these volumes were to be at all generally read (§§ 14, 1403).¹

87. Long ago in my Manuale, Chap. I, § 1, I wrote: "It is possible for an author to aim exclusively at hunting out and running down uniformities among facts—their laws, in other words—without having any purpose of direct practical utility in mind, any intention of offering remedies and precepts, any ambition, even, to promote the happiness and welfare of mankind in general or of any part of mankind. His purpose in such a case is strictly scientific: he wants to learn, to know, and nothing more. I warn the reader that in this Manual I am trying exclusively to realize this last purpose only. Not that I underrate the others. I am just drawing distinctions between methods, separating them and indicating the one that is to be followed in this book. Anyone differently minded can find plenty of books to his liking. He should feast on them and leave this one alone, for, as Boccaccio said of his tales [Decameron, X, Conclusione], it does not go begging a hearing of anybody."

Such a declaration seems to me clear enpugh, and I confess that I could not express myself in plainer terms. Yet I have been credited with intentions of reforming the world, and even been compared to Fourier!¹

88. In general, this method of studying the social sciences is not grasped by literary economists, the cast of their minds being against any such thing. Then again they often discuss books and other writings that they know only at second hand, and which they have never read, or never read with the care required for understanding them. Finally, the person who has_always had some practical purpose in view can hardly be convinced that anyone can have a purely scientific aim; or if he does understand it for a moment, he immediately forgets. I have therefore little hope that the cautions I have voiced in this chapter will effectually prevent theories which I do not hold from being ascribed to me, similar warnings having failed on past occasions, though endlessly repeated. Yet it seems best to me to follow the maxim "Do what you ought, follow what may." Only I must beg my reader's pardon for certain repetitions that have no other justification, and which may appear superfluous—as they in fact are for anyone consenting to read what I say with moderate attention.

89. This is not the place to add further details touching my manner of regarding economic theories.¹ The reader will find excellent and ample expatiations on that point in the works of Sensini and Boven already referred to.

90. We saw (§§ 13, 63) that our subclass of logico-experimental theories (Ia) was divisible into two varieties, in one of which general principles were mere abstractions from experimental facts, while in the other they aspired more or less explicitly to an existence of their own not strictly dependent on mere abstraction from facts. The two varieties are often distinguished as based on the inductive or the deductive methods. But that is not exact. They differ not in the method they use, but in their respective criteria of truth for propositions and theories. In the strict type, Ia1, whether propositions are obtained by induction or by deduction or by a mixture of the two, they are always subordinate to experience; whereas in the deviation from the type, Ia2, they tend explicitly to dominate experience. When a general principle is corroborated by facts in large numbers as, for instance, the principles of Euclidean geometry or of universal gravitation are, the two varieties are not very sharply distinguished, for after all the experimental verification may often be taken for granted.

91. But if the gap between the two varieties is very marked, a difference appears that is the better seen in a comparison between theories which are logico-experimental (Ia) and theories which are not. In the former procedure is gradual. One starts with facts and reaches this or that abstraction, thence going on to a more general abstraction, becoming more and more circumspect, more and more cautious, the farther one gets from direct experience. In non-logico-experimental theories, a deliberate leap is taken away from direct experience, as broad a leap as possible, and the farther one gets from direct experience, the greater the assurance, the greater the recklessness. One is bent on knowing the "essences" of things, the only kind of knowledge worthy of the name of "science," direct experience and its implications being mere "empiricism," and as such held in poor esteem (§ 530).

92. Working out a chemistry, for example, on that system, the first problem would be to know what "matter" is. Knowing that, we should know its chemical properties. The modern chemist, instead, following the methods and procedures of logico-experimental science, studies chemical properties directly, and gets more and more general properties or abstractions from them.

The ancients thought that in imagining cosmogonies they were studying astronomy. Modern scientists study the movements of the stars directly, and go no farther than required for establishing uniformities in such movements. Newton found that a certain hypothesis, the so-called hypothesis of universal gravitation, was all that was required for discovering the equations governing the movements of the stars. But what is gravitation? Neither he nor his successors in celestial mechanics took the trouble to go too deeply into that question. Not that the problem was not worth considering; but celestial mechanics can dispense with a solution of it. So long as its equations hold, it matters little how they are obtained.

93. Errors that are ancient history for the more advanced sciences recur or have their modern counterparts in the more backward sciences. So the theory of evolution has in some cases played a role in sociology similar to the role once played by cosmogony in astronomy. It was generally held that the only way to determine uniformities in social phenomena was to know the history of the latter and trace them back to their origins (§§ 23, 346).

94. for the theories that are to be elaborated in these volumes we cannot avoid going back to a distinction between the objective and the subjective phenomenon. However, we do not need to go beyond that and solve the problem as to the "reality of the external world" assuming (but not granting) that that problem has some exact meaning (§ 149).

95. Solve it as you will, the two great categories mentioned still stand, even if under different names. It may well be that a sheet of paper with engravings on it and a genuine bank-note of the Bank of England are both mere thoughts of the mind; but if you dine at a London restaurant and try to pay your bill with the first of those thoughts, you will soon notice that just as "one thought is of another born," that thought will present you with a whole litter of offspring: first the thought of a policeman, which, whether objectively real or not, will hale you before the thought of a judge, which will introduce you to the thought of a well-barred jail, where you will meet a thought that the English call "hard labour," and which, according to all reports, is not the pleasantest thought in the world. All that will convince you that the two sheets of paper certainly belong to two sharply distinguished categories, since they give rise to differing facts—or differing thoughts, if you prefer.

Similarly, when we assert that to know the properties of sulphuric anhydride one must appeal to experience and not, as Hegelian metaphysics would have it, to the "concept" of sulphur or even of oxygen, we are not in the least intending to set an external world over against an internal world, an objective reality over against a subjective reality. We can state the same proposition in a jargon that recognizes the "existence" of nothing but thought. We can say, that is, that to get the concept of sulphuric anhydride, it is not enough to have the mere concepts of sulphur and oxygen and meditate upon them. We could do that for century on century without getting concepts of sulphuric anhydride that would gibe with the concepts supplied by chemical experiment. The ancient philosophers thought that they could replace observation and experience in just that way, but they were entirely wrong. Chemistry is learned in laboratories and not by philosophical meditations, even of the Hegelian brand (§ 14). To get the concept, or concepts, of sulphuric anhydride we must first have the many concepts acquired through the concept otherwise known as experience—burning sulphur in oxygen or in air, and collecting the concept of sulphuric anhydride in the concept of a glass container—finally bringing all such concepts together to get the concept of the properties of sulphuric an hydride. But such a jargon would be prolix, tedious, ridiculous; and just to avoid it we use the terms "subjective" and "objective." For the logico-experimental purposes we have in view no other terms are required.

96. In the same way and for the same reason it is enough for us to know that social facts reveal certain uniformities which are connected by ties of interdependence.¹ We are not called upon to go to the trouble of finding out whether and just how that result yielded by observation can be reconciled with what is called free will (if indeed the latter phrase has any meaning). Such problems transcend the limits of our investigations.

97. And we shall also neglect to inquire whether scientific laws have the trait of "necessity" (§ 528). On that point observation and experience can tell us nothing. They can only reveal certain uniformities, and those only within the limits of the time and space to which our observation and experience extend. Every scientific law, therefore, is subject to that qualification; and if, for considerations of brevity, it is omitted, the statement of every scientific law, must nevertheless be taken as prefaced by the restriction: within the limits of time and space known to us (§ 69-5).

In like manner we hold aloof from debates as to the necessity of the conclusion in a syllogism. The syllogism of the text-books on logic, for example, "All men are mortal; Socrates is a man; therefore Socrates is mortal," from the experimental standpoint must be stated thus: "All men of whom we have had any knowledge have died; what we know of Socrates induces us to classify him with such men; therefore it is very probable that Socrates is mortal."

That probability is greatly enhanced by other circumstances which we shall specify farther along (§§ 531, 556); and it is therefore greater, enormously greater, than the plausibility of a syllogism that might have been drawn before the discovery of Australia: "All the swans we have ever known have been white; a bird of unknown colour that has all the characteristics of the swan must be classed with the swans; therefore that bird will probably be white" (§ 526). People reasoning on essences may sometimes substitute certitude for probability, even very great probability. But we know nothing about essences and accordingly lose our certitude.

98. To assert, as some assert, that a miracle is impossible as violating the recognized constancy of natural laws is to reason in a circle and offer an assertion as proof of itself. If a miracle could be proved, the constancy of natural laws would at once go by the board. The kernel of the question therefore lies strictly in the proof of fact. We might add that such a proof has to withstand a scrutiny all the more severe, the farther it carries us outside the circle of known facts. If someone were to assert that the Sun is one day to carry its planetary system to a locality where the laws of chemistry, physics, and mechanics are different from the laws at present known, we could make no objection. We could only remind the prophet that the burden of proof rests upon the person making the assertion. As we have already stated (§ 29), we admit of no exceptions to this rule, even for the laws of logic.

99. Scientific laws are for us, therefore, nothing more than experimental uniformities (§ 69-4). From that point of view there is not the slightest difference between the laws of political economy or sociology and the laws of other sciences. The differences that do exist are of an entirely different character, lying chiefly in the greater or lesser complexity with which effects of the various laws are intertwined (§ 1792). Celestial mechanics has the good fortune to be able to deal with the effects of a single law (uniformity). And that is not all, for the effects might be such as seriously to interfere with the discovery of the uniformity they manifest. But by a most happy circumstance, the mass of the Sun is much greater than the masses of the various planets, so that the uniformity is disclosed under a simple though not strictly exact form by assuming that the planets move around a fixed Sun; whence we can go on to rectify the error involved in the first approximation.¹ Chemistry, physics, mechanics, are likewise able to deal with separate laws, or at least, by one device or another, to isolate effects;² but then again, there are cases where the complex is hard to unravel. Such cases grow more numerous in biology and geology, and most of all in meteorology. It is with these latter that the social sciences are to be classed in this respect.

100. Another difference in scientific laws lies in the possibility or impossibility of isolating their effects by experiment, which is here to be distinguished from observation. Certain sciences, such as chemistry, physics, mechanics, and biology, can and do make extensive use of experiment. Certain others can use it but sparingly; others, such as the social sciences, little if any; still others not at all, as for instance, celestial mechanics—at least as regards the movements of the heavenly bodies.

101. Economic and social laws as well as the laws of the other sciences never suffer any genuine exception.¹ To speak of a uniformity that is not uniform is to say a thing which has no meaning. What is commonly called an exception to a law is really the superposition of the effect of another law upon its own normal effects. From that standpoint all scientific laws, even the laws of mathematics, suffer exceptions. All bodies on the surface of the earth tend to move toward the centre; but a feather caught by the wind moves away from the centre, and a balloon filled with hydrogen rises in the air. The chief difficulty in a great many sciences lies in finding ways to unravel tangles of many different uniformities.

102. To that end, it often helps to consider not the individual phenomena actually observed but average situations where the effects of certain laws are attenuated and those of others are emphasized. We cannot predict, for example, what the temperature on the tentn of June in some future year is going to be; but we can come pretty close to the mean temperature for the month of June, and closer still to the mean temperature over a three months' period for a number of years. No one can tell whether John Doe will live or die next year; but we can tell, approximately, how many people out of a hundred thousand of John Doe's age will die. Who can tell whether a given grain of wheat sown by a farmer will sprout and yield a return? But we can predict with reasonable probability the crop an acre of wheat will yield, and even better the average yield over a specified period of years.

103. We must not forget that such averages are largely arbitrary, that they are formulated by ourselves for purposes of our own, and that therefore we must avoid the error of thinking of them as objective things having an existence independent of the facts. One often finds them going about under different names as metaphysical entities, used by scholars to fix on something at least that is constant in the flux of fact.

104. In political economy, for instance, we find that the wholesale prices of commodities differ in almost every transaction. To get a theory we have to have something less variable, something more constant, than that. Scientifically we consider averages, we strike medium curves (interpolations).¹ Metaphysically, people have used an entity called value taken as a constant cause of variations in price. This second manner of reasoning easily leads astray, since it deprives averages of the status they have scientifically and gives them another that is altogether imaginary (§ 62). This statement, however, implies no criticism of early economists for using the term "value." But it was a notable step in advance when "exchange value" came to be distinguished from "utility value." Further progress derived the far more exact concept of "final utility" from the concept of "utility value"; and going on in that fashion, general theories of the economic equilibrium were finally attained. There is nothing unusual about such a course. It is the course the natural sciences have all followed (§§ 69⁵, 106). But just as it is no longer possible in our day to study celestial mechanics with the tools of Ptolemy or even of Kepler, so political economy can no longer be handled with the indeterminate concept of value.²

105. In a first approximation we may be satisfied with knowing that, roughly, we have discarded certain effects of minor importance as compared with others of major importance. But it is wiser to get at the earliest possible moment a fairly exact picture of what the terms "minor" and "major" imply, and to know approximately what has been discarded and what has been kept. It will be all the better to determine, if we can, the limits of the variations between the situation as it really is—the facts—and the picture which our averages or theories give us of it. In mathematics, it is already something to know that the fraction 22/7 expresses the approximate relationship of the circumference of a circle to the diameter. It is better yet to know that the actual ratio is greater than 22/7; still better to know that the error is less than 0.015, or that the true ratio lies between the fractions 22/7 and 333/106. It is a good thing to know that prices are not numbers varying haphazard. It is better yet to know that there is some relation between them and the tastes of human beings and the difficulties lying in the way of obtaining commodities. It is even better to have some notion of what that relation is, and better still to have the concept more exact and know the relative importance of the situation pictured by the theory, as compared with the real situation, and to know just what aspects it ignores.

106. A concrete situation cannot be known in all its details; there is always a remainder, which is even physically apparent at times.¹ We can have only approximate concepts of concrete phenomena. A theory therefore can never account for all particulars. Divergences are inevitable, and the best we can do is reduce them to a minimum. And in this connexion too we are once more carried back to our successive approximations. Science is a continuous development; that is to say, every theory is supplanted by another which corresponds more closely to the real facts. The theory of yesterday has been perfected today; the theory of today will be improved on tomorrow; that of tomorrow, on the following day; and so on. Such the story that is to be read on every page of the history of the sciences, and no one can suppose that it will not continue to be the story for a long long time to come. Since no theory absolutely commands acceptance, of the theories among which we are free to select we shall prefer the one that diverges least from facts of the past, which best enables us to foresee the facts of the future, and which, in addition, embraces the greatest number of facts.

107. In astronomy the theory of epicycles, which some people are at present trying to rehabilitate on sentimental grounds, satisfies the requirement of adequately picturing facts of the past as such facts are known to us. By multiplying the number of epicycles as often as is required, every movement of the stars that observation reveals can be represented; but we cannot, or cannot so well, foresee future movements, as is possible with the theory of gravitation. The latter theory, furthermore, utilizing the general law of mechanics, embraces a greater number of facts. Hence it is certainly to be preferred, as in fact is customary, to the theory of epicycles. But the choice is made for those reasons, or for others of the kind, not for metaphysical considerations as to the "essence" of things.

108. The facts among which we live have their influence upon us, and as a result our minds acquire certain attitudes which must not be too violently in conflict with those facts. Such attitudes go on to give form and manner to language. Some small amount of information as to external facts we can derive, therefore, from knowledge of the processes of the human mind and from language. But that small amount is small indeed, and once a science is at all advanced, more errors than truths are obtained in that fashion (§§ 113 f.).¹

The terms of common speech are lacking in definiteness, and it cannot be otherwise, for precision goes only with scientific exactitude. Every argument based on sentiment, as all metaphysical arguments are, must of necessity use terms lacking in exactness, since sentiments are indefinite and the name cannot be more definite than the thing. Such arguments, besides, actually rely on the lack of exactness in everyday language to mask their defects in logic and carry conviction (§ 109). Logico-experimental arguments, being based instead on objective observation, tend to use words strictly to designate things and therefore to choose them in such a way as to avoid ambiguities and have terms as exact as possible. Moreover, they eventually equip themselves with a special, technical language and so escape the indefiniteness of common parlance.

As already noted (§ 69-8), our purpose being to use logico-experimental reasoning exclusively, we shall exert every endeavour to use only words that are as far as possible precise and strictly defined and which correspond to things unequivocally and without ambiguities (§ 119), or better, with a minimum of error.

A word designates a concept, and the concept may or may not correspond to a thing. But the correspondence, when it is there, cannot be perfect. Even if the word corresponds to a thing, it can never correspond to it exactly, in an absolute manner. It is always a question of a more or a less. Not only are there no such things, in the concrete, as geometric entities such as the straight line, the circle, and so on, but not even chemical substances that are absolutely pure, not even the species with which zoologists and botanists deal, not even an individual body designated by a name—for it would be further necessary to specify at just what moment it is considered: a piece of iron does not remain identical with itself if it is subject to changes in temperature, in electrical tension, and so on. In a word, the "absolute" has no place in logico-experimental science, and we must always take in a relative sense propositions that in the dress of ordinary parlance seem absolute; and in the same way too, we must make quantitative distinctions where common speech stops at the qualitative (§ 144¹). That much being clearly grasped, any misunderstanding is impossible; whereas to express ourselves always with absolute exactness would be to wallow in lengthy verbosities as useless as they would be pedantic.

We may say, then, that we are carried outside the logico-experimental field entirely whenever we reason in terms which do not lie in that field; and that we are carried partially outside it whenever we reason in indefinite terms which correspond to experimental entities only in part (Chapter X). This last proposition must be taken in the sense that if our terms have that minimum of indefiniteness which corresponds to the present state of knowledge, they take us so little outside the experimental field that we may overlook the extrusion. Though there are no chemical substances that are absolutely pure, the laws of chemistry are valid, in very close approximation, for the substances that our methods of analysis designate as pure.

109. People in the vast majority use common everyday language. A few scientists use scientific language in their specialties, outside of which they reason as badly as the plain man—and often worse. Human beings are prompted to acquire such knowledge as they have from common speech by two sorts of motives: first, because they assume that a word necessarily corresponds to a thing, whereby the name becomes everything and sometimes even acquires mysterious properties; and, second, because of the great ease with which a "science" can be so constituted, each person carrying within himself all that is required for that purpose, without going to the pains of long, difficult, and tedious researches. It is much easier to talk about antipodes than to go out and see if they are really there. To discuss the implication of a "principle of fire" or "damp" is much more expeditious than to prosecute all the field studies that have made up the science of geology. To ruminate on "natural law" is a much more comfortable profession than to dig out the legal codes of the various countries in various periods of history. To prattle about "value" and ask when and under what circumstances it is said that "a thing has value" is much less difficult than to discover and comprehend the laws of the economic equilibrium.

In view of all that, one readily understands how the history of the sciences down to our time is substantially a history of the battles that the experimental method has had to fight and still has to fight against the methods of introspection, etymology, analysis of verbal expression. Defeated and put to rout in one place, the latter method bobs up in another. If it cannot fight in the open it dissembles, flattening out like a snake in the grass, and so succeeds in making its way into the very camp of the adversary under guise of something else.

110. In our day the method has been largely banished from the physical sciences, and the advances they have made are the fruit of that proscription. But it is still strutting about in political economy and more blatantly still in sociology; whereas if those sciences would progress, it is imperative that they should follow the example set by the physical sciences (§ 118).

111. Belief that the facts of the universe and their relationships could be discovered by introspection was general in a day gone by, and it still remains the foundation of metaphysics, which seeks a criterion of truth outside experience. In our day it found its complete expression in the lunacies of Hegel's Philosophy of Nature. One need hardly observe that mankind has never discovered the puniest uniformity in the facts of nature in that fashion (§§ 50, 484).

112. The positivism of Herbert Spencer is nothing but a metaphysics. Though Spencer asserts the relative nature of all knowledge, he still speaks of the relations of knowledge to "absolute reality."¹ He asserts the existence of an Unknowable, but claims, by an amusing contradiction, to know at least something about it.²

113. In all the rustle and bustle of our daily lives we cannot of course speak in the manner or with the severity of the logico-experimental sciences (§§ 108-09), and we are therefore led to ascribe great importance to words. Whenever we are able to give a name to a thing, it succeeds by that sole fact in finding a place in a class of objects of which the properties are known, and its properties therefore also become known. Furthermore—and it is the point that really matters—the thing is viewed in the light of the sentiments the name arouses, and it is to its advantage, therefore, to have a name that awakens favourable sentiments and to its disadvantage to have a name inspiring unfavourable sentiments.¹

In practical life it would be difficult, nay impossible, to do otherwise. We cannot go to the bottom of all the multifarious questions that are at every moment arising—we cannot test everything in the crucible of doubt. Once we admit that a man's hat is his, that is the end of it; he puts it on his head and goes his way; and we could not, before permitting him to take it, debate the real nature of property, nor settle the problem of individual or collective property or other problems of the kind.

In civilized countries civil and penal laws have an exact terminology; and so in order to pass judgment upon an act one must first know the name by which it can be designated. Ordinary speech too has maxims in large numbers, which, save for exactness, in which they are usually wanting, are like the articles in a code of law; so for maxims too the name to be given to an act or a thing is of great importance. The legislator uses terms in the meanings they commonly have among the people for whom he is legislating. He need not wait for scientists to agree upon a definition of the term "religion" before he makes laws governing sacrilege, religious freedom, and the like. We talk of numberless things offhand, never exactly defining their nature and traits. Practical life evolves in the approximate. Science alone aims at the precise.

Within the sphere of that approximate we get theorems that correspond to facts so long as they are not extended beyond the scope, at times very limited, within which they are valid. Ordinary language crystallizes and preserves them, and it is there that we can recover and use them, but always with the reservation that, roughly approximative and true only within certain limits (which as a rule are unknown to us), they become false outside those limits (Chapter XI). Such theorems are theorems of words rather than of things; and we can therefore conclude that in practical life, for purposes of influencing others, and oftentimes in the early beginnings of the sciences, words are of great importance, and that it is by no means a waste of time to quarrel over them.

114. But as regards investigations in experimental science our conclusion must be precisely opposite. Such researches envisage things exclusively, and can therefore derive no advantage from words." They can, however, incur great harm, whether because of the sentiments that words arouse, or because the existence of a word may lead one astray as to the reality of the thing that it is supposed to represent (§§ 366-67), and so introduce into the experimental field imaginary entities such as the fictions of metaphysics or theology; or, finally, because reasonings based on words are as a rule woefully lacking in exactness.

115. So the more advanced sciences develop languages of their own as a result both of coining new terms and of giving special meanings to terms of ordinary parlance. The "water" of chemistry, the "light" of physics, the "velocity" of mechanics, have senses very different from the meanings of those identical words in everyday usage.

116. A simple device often serves to determine whether an argument is of the variety that relies on sentiment or on the assistance of the more or less vague notions stored up in the vernacular, or of the variety peculiar to experimental science. It is sufficient to substitute plain letters of the alphabet, a, b, c . . . for the key-words in it. If the argument loses cogency, it belongs to the first class; if it retains its full vigor, it belongs to the second (§ 642).

117.. Like other sciences, political economy began by using terms from the vernacular, trying merely to give them meanings somewhat more exact; and so it became enriched with the wealth of experience accumulated in everyday language—a capital by no means inconspicuous, for economic operations make up a large fraction of human activity. But then gradually, as political economy progressed, that advantage waned, and the drawbacks involved in the use of such terms became more and more irksome. Jevons in his day very wisely dispensed with the word "value" which from being stretched in this, that, and every direction, and from having countless meanings, ended by having no meaning at all (§ 62 ¹); and he proposed a new term, "rate of exchange," of which he gave an exact definition (§ 387).

118. Literary economists did not follow him along that road; and they are to this day still dilly-dallying with speculations such as "What is value?" "What is capital?" They cannot get it into their heads that things are everything and words nothing, and that they may apply the terms "value" and "capital" to any blessed things they please, so only they be kind enough—they never are—to tell one precisely what those things are. If their arguments partook of experimental science, they would continue to hold even if blanks were used for the terms "value" and "capital"; for the name being taken away, the things still stand, and it is in things alone that experimental science is interested.¹ But since such arguments are primarily rhetorical, they are strictly dependent on words capable of arousing the sentiments that are useful in convincing people; and that is why literary economists very properly are so much concerned about words and much less about things. Anyone asking what value is, what capital is, what income is, and the like, shows by that mere fact that he is concerned primarily with words and secondarily with things. The word "capital" certainly exists for him. What he is in doubt about is what it means, and he sets out to discover that. This procedure might be justifiable on a reasoning developed as follows: "There is something unknown that acts upon language and gives rise to the word 'capital.' Since ordinary words are exact copies of the things they represent, we can understand the thing by studying the word. So by finding out what capital is, we shall come to know the thing unknown." The fallacy in the justification lies in the proposition italicized. It is false. For more convincing proof one need simply substitute for the term "capital" some scientific term such as "water," and see whether the most painstaking inquiry as to what it is that is called water will ever reveal the properties of the chemically pure substance known by that name.

In science the course followed is the exact opposite: first one examines the thing and then hunts up a name to give it. First one considers the substance formed by combining oxygen and hydrogen, and then a term is sought to designate it. Since the substance in question is present in great quantities in the vaguely defined thing that the ordinary vernacular designates as water, we call it water. But it might have been called otherwise—"lavoisier," for instance—and all of chemistry would stand exactly as it is. We would simply say that the liquid present in rivers and in the sea contains great quantities of lavoisier. Literary economists and sociologists do not understand such things, for they are wanting in the mental attitude and the training required for understanding them.

119. In these volumes we intend to keep strictly to the logico-experimental method (§ 108) and deal exclusively with things. Words therefore are of no importance whatever to us; they are mere labels for keeping track of things. So we say, "Such and such a thing we are going to call A"; or, "We suggest calling it A." We do not say—an entirely different matter—"Such and such a thing is A." The first proposition is a definition, and we are free to word it as we choose. The second is a theorem, and requires demonstration; but before we can prove it we have to know exactly what A is (§ 963).

To avoid in these volumes the danger, ever threatening in the social sciences, that meanings of words will be persistently sought not in the objective definitions supplied but in common usage and etymology, we would gladly have replaced word-labels with letters of the alphabet, such as a, b, c . . . or with ordinal numbers; and that we have done for some parts of our exposition (§ 798). We have refrained from doing so more often in fear lest our argument become altogether too tedious and obscure. So here we follow the example of the chemist who continues using the term "water" but gives it an exact meaning.¹

We too shall use terms of ordinary parlance, explaining exactly what they are to represent. We accordingly urge the reader to keep strictly to such definitions and never to try to guess from etymology or common usage the meanings of the technical terms that he finds in these volumes. The reader will shortly be meeting the terms "residues" and "derivations" (§ 868). If he desires to know what they mean, let him refer exclusively to the definitions we furnish. If he were to seek their meaning in etymology or common acceptation, he would be certain to find things very different from the things we label with them. If anyone does not like them, he may feel quite free to replace them with others—we shall never quarrel on that score. And he will see that with his own terms, or better yet, using letters of the alphabet or numerals, all our arguments will stand just the same.

Anyone finding these explanations superfluous must be patient. My excuse is that similar explanations ever and anon repeated for my term "ophelimity" did not prevent literary economists from seeking its meaning in etymology; while others, who must truly have had a deal of time to waste, began wondering whether "desirability" would not have been a better name.² Nor could I silence such idle prattle by showing that we could very well do without "ophelimity" and all other similar terms in developing economic theories.³

120. In these volumes I shall use, for the reasons just stated, a number of terms that are also used in mechanics. I must accordingly make clear the exact senses in which I use them.

121. Let A, B, C . . . stand for certain things that have a capacity for influencing an economic or social situation. We may consider the situation either at a moment when the action of such things is not yet exhausted, or at a moment when it is entirely spent. Let A, for instance, stand for an individual's desire to drink wine, and B for a fear he has that it may injure his health. The man drinks one glass of wine, then a second, and then he stops, because after the second glass the fear effectively curbs the thirst. After the first glass the movement is not complete: the thirst is still effective in spite of the fear. Not even the fear has completed its work, because it has not yet quenched the individual's desire for drinking wine. It is evident that when we are considering a situation we have to specify whether we are considering it at a time when the things A, B have not completed, or at a time when they have completed, their action.

In mechanics there is an analogous situation—analogous, notice, not identical—where two forces are acting upon a physical point. So instead of speaking of two things, A, B, that have a capacity for influencing an economic or a social situation, we may for the sake of brevity speak of two forces, A and B.

122. The intermediate stage in which the individual has drunk the first glass of wine and is about to drink another, in which, that is, the work of A and B is not yet completed, is described in mechanics by saying that an equilibrium has not yet been attained. The stage in which both the thirst and the fear have completed their work, so that the individual ceases drinking, is described in mechanics by saying that an equilibrium has been attained. By analogy, not from identity, we may likewise use the term equilibrium for an economic or a social situation.

123. But an analogy is not a definition; and we should be deliberately exposing ourselves to ready and frequent error were we satisfied with such an analogy to represent the social or economic equilibrium. We are therefore called upon to give an exact definition of the economic or social equilibrium in question; and the reader will find it in Chapter XII.

124. Keeping to the definition of the thing, we can change the term at will and the arguments will stand just the same. For example, instead of calling A and B "forces," we might call them "influences" ("operative things") or even "things I." The state defined above we might call τέλος, or even "state X," instead of "equilibrium." In which cases all the arguments in which we have used the terms "forces" and "equilibrium" would still hold.

125. It is therefore a monumental stupidity to say, as one critic said, that when I speak of a state of equilibrium, I am thinking of a state which I consider better than another state, equilibrium being better than lack of equilibrium!

126. By similar analogy we can use other terms from mechanics in economics and sociology. Suppose we are considering a society in which private property exists. We may propose to study the possible forms of such a society, premising always the condition that private property exist. In the same way other relationships supply other conditions that we may assume or not assume as premises. Similar situations are met with in mechanics, and there the conditions in question are known as ties (vinculo). By analogy, we can use that term in economics and sociology as well.¹ However, if there were no other analogies with mechanics it would be useless to do that, and better in particular not to use the term "tie."

127. Suppose we are considering a system of material points maintained by certain ties, and upon which certain forces A, B, C  . . . are acting. The successive positions of the points will be determined by the resultant of the forces as modified by the ties. Now take a given group of individuals. Certain conditions prevail, such as private property, freedom (or slavery), technical training, wealth, scientific knowledge, religion, and so on. Active also in the group are certain individual desires, interests, prejudices, and the like. The successive states of the group may be assumed as determined by these latter elements working in conjunction with the conditions (the ties) premised.

128. So by analogy—never from identity—we can call the group a social or an economic system and say that certain forces are acting upon it, which determine the position of the points in the system in conjunction with the ties. Considerations of brevity solely and strictly counsel the use of such terms, and as always they may be replaced by others at pleasure.

129.. A transition from one state to another is called a movement in mechanics, and it may be so called in sociology also. In mechanics, if we assume that ties and forces are determined, movements in the system are likewise determined. So in sociology, if we assume conditions and active influences as given, the various successive states of the group are determined. Such movements are called real in mechanics, and may be so called in sociology.

130. If, for theoretical purposes, we assume as suppressed some tie in a mechanical system, some condition in a sociological group, the mechanical system will show movements different from the real, and the sociological group will attain states other than those it really attains. Such movements are called virtual in mechanics, and virtual they may be called in sociology. For example, a person investigating what society would be like if private property were to be abolished is making a study in virtual movements.

131. We can think of the "ties" and "forces" in the social system as summed together; and if we designate the aggregate by the term "conditions," the so-called theory of determinism could be stated by saying that the state of a system is wholly determined by "conditions" and can therefore change only with a change in "conditions."¹

132.. Science has no dogmas, and so cannot and must not accept determinism a priori; and so far as it does accept it, it must, as always, do so strictly within the limits of the time and space that have been investigated. With that premise solidly established, experience indicates that in many cases social situations seem really to be determined by "conditions" and change only with changes in "conditions." In such cases we therefore recognize determinism, but without in the least precluding that there may be other cases where it cannot be granted.¹

133. From the standpoint of the deterministic hypothesis, we are now called upon to solve a problem that is continually arising in one form or another in history and sociology. According to determinism, whatever happens cannot happen otherwise; and so the terms "possible" and "impossible" as used in ordinary language have no meaning, since only that is possible which happens, and what does not happen is impossible. We do not choose to quarrel over words; so if anyone is inclined to throw such terms overboard, let us do so by all means. All the same, after they have been dispensed with we are still confronted with the different things that were designated by them, and for which it will be expedient to find other designations.

John Doe did not have his dinner yesterday, but speaking in ordinary terms, it was "possible" for him to dine. He did not cut off his head; but it was "impossible" for him to cut off his head, then glue it on again and be alive and well today. It may well be that from the standpoint of determinism the two things are equally impossible; but it is also evident that they are different kinds of things, and it would be a grave misfortune if we were unable to designate the different classes to which they belong. Suppose, for the moment, we label the first class (I) and the second (II). It is at once apparent that the difference between (I) and (II) lies in the fact that cases like (I) have been often enough observable, whereas no case like (II) has ever been seen.

134. To be more exact: in both cases we are dealing with "virtual" movements; and in declaring them both impossible, determinism is merely calling them virtual as opposed to real movements. But there is more than one class of virtual movements. There is a class of virtual movements that take place when we assume as absent a certain tie which was not absent at the time the real movement in question was observed, but which has been found absent on other occasions, when real movements equivalent to the virtual movement have been observable. That movement therefore belongs in the class we have called (I) and which, in ordinary langauge, is a class of possible things. There is another class of virtual movements that would take place only if we assumed as absent a tie which has never been found absent, so that real movements equivalent to such virtual movements have never been observed. These belong to the class we have called (II), which in ordinary terms is a class of impossible things. Having so supplied exact definitions of the things that the terms "possible" and "impossible" designate, there can be no objection to using them even with the hypothesis of determinism.

135. Of what conceivable use can the study of virtual movements be if they are things foreign to the domain of reality and only real movements actually occur? The advantages are, in chief, two:

1. If we are considering virtual movements that have not been real because of the presence of ties which have been found absent on other occasions—if, in other words, we are considering movements that are virtual in some cases but are observable as real in others—knowledge of the virtual movements may help to foresee what the real movements are going to be like. Such, for instance, are forecasts as to the effects of a certain piece of legislation or of some other practical measure.

2. Consideration of virtual movements may help towards isolating and determining the character and peculiarities of a given social state.

136. The propositions "A determines B" and "If there were no A there would be no B" state the same fact, in the one case as a function of A, in the other in terms of a virtual movement. The propositions "In such and such a state society has a maximum of A" and "If society departs from that state, there will be a diminution in A" express the same fact, in the first case as a description of the state, in the second in terms of a virtual movement.

137. In the social sciences, virtual movements are to be resorted to with great caution, for very very often we have no means of knowing what the consequences of suppressing some condition, some tie, would be. If a person says, "If the Emperor Julian had continued very long on the throne, the Christian religion would not have survived," he is assuming that the death of Julian was alone responsible for the triumph of Christianity. And if one answers, "If the Emperor Julian had continued longer on the throne, he might have retarded, but could not have prevented, the triumph of Christianity," one is assuming that there were other conditions present which made that triumph certain. In general, propositions of this second variety are more often verifiable than are propositions of the first kind. In many cases, that is, social developments are determined by the concurrent action of large numbers of conditions; so that the removal of any one of them disturbs the course of events but slightly.

138. Conditions, furthermore, are not independent. Many of them influence each other. Nor is that all. The effects of conditions react in turn upon the conditions themselves. In a word, social facts—that is to say, conditions and effects—are interdependent, and modifications in one of them react upon larger or smaller numbers of the others, and with greater or lesser intensities.

139. That is why attempts to remake history by conjecturing what would have happened had a certain event never occurred are altogether fatuous. We have no way of determining all the changes that would have taken place on a given hypothesis if the hypothesis had come true. What would have happened had Napoleon won at Waterloo? Only one answer is possible—"We do not know."

140. We can get something a little better by keeping to effects that are very immediate in a very limited field, and progress in the social sciences will tend gradually to enlarge those very restricted confines. Every time we succeed in discovering some hitherto unknown relation between social facts, we are a little better prepared to know what the effects of certain changes in the social situation will be; and pushing on along that road we make new advances, however slight, towards realizing the purpose of determining the probable course of social developments in the future. Therefore no study that aims at discovering some uniformity in the relations of social facts can be called useless. It may be useless at the present time and continue to be so in any near future; but we cannot be sure that the day will not come when, taken in conjunction with other discoveries, it will contribute towards forecasting probabilities in social evolution.

141. The difficulties in discovering social uniformities are great because of the great complexity of social phenomena. They are immeasurably increased, and in fact become insuperable, when uniformities are sought not with the one and undivided intent of discovering them, but with the purpose, explicitly chosen or tacitly set by sentiment, of justifying a preconception, a doctrine, a faith. Just such impediments account for the present backward state of the social sciences.

142. The man entirely unaffected by sentiments and free from all bias, all faith, does not exist; and to regard that freedom as an essential prerequisite to profitable study of the social sciences would amount to saying that such study is impossible. But experience shows that a person can as it were divide himself in two and, to an extent at least, lay aside his sentiments, preconceptions, and beliefs when engaged in a scientific pursuit, resuming them afterwards. That was the case with Pasteur, who outside his laboratory was a devout Catholic, but inside kept strictly to the experimental method. And before Pasteur one might mention Newton, who certainly used one method in discoursing on the Apocalypse and quite another in his Principia.

143. Such self-detachment is more readily achieved in the natural sciences than in the social sciences. It is an easy matter to look at an ant with the sceptical disinterestedness of experimental science. It is much more difficult to look at human beings that way. But even if complete success in such an effort is impossible, we can at least try, to succeed in part, and reduce the power and influence of sentiments, preconceptions, beliefs, to a minimum. Only at that price can progress in the social sciences be achieved.

144. Social facts are the elements of our study. Our first effort will be to classify them for the purpose of attaining the one and only objective we have in view: the discovery, namely, of uniformities (laws) in the relations between them. When we have so classified kindred facts, a certain number of uniformities will come to the surface by induction; and after going a good distance along that primarily inductive path, we shall turn to another where more ample room will be found for deduction. So we shall verify the uniformities to which induction has carried us, give them a less empirical, more theoretical form, and see just what their implications are, just what picture they give of society.

In general we have to deal with things that vary by imperceptible degrees, and our picture of them approximates reality the more closely in proportion as it is drawn in quantitative terms. That fact if often recognized by saying that as sciences progress, they tend to become more and more quantitative. But that is much more difficult than to study merely qualitative differences. In fact, the first forward step lies always in a rough quantitative approximation.¹

It is no difficult matter to distinguish day from night with tolerable accuracy. Though there is no precise instant at which day ends and night begins, we can after all roughly say that there is a qualitative difference between them. It is more difficult to divide such periods of time into parts. We manage to do so approximately by saying "shortly after sunrise," "towards noon," and the like; and with more or less success—less rather than more—the night used to be divided into "watches." When clocks came to be available, it was possible to get quantitative measurements of time, the exactness increasing with improvements in clocks and becoming very considerable with the modern chronometer.

For a long time people were satisfied with knowing that the death-rate was higher among the aged than among the young, no one as usual knowing very definitely where youth ended and old age began. Then something more was learned; statistics were made available, very imperfect statistics at first, then better ones, now fairly good ones—and they are steadily improving. For a long time there was very little of the quantitative about political economy. Then it became quantitative in pure economics—in theory at least. For sociology we shall try as far as we can to replace qualitative considerations with considerations of quantity. Imperfect, very imperfect, as they may be, they will at any rate be a little better than the qualitative. We shall do what we can, our successors will do better—and so science advances!

In these volumes we shall confine ourselves to a very general picture—something like a sphere offered as a model of the Earth. That is why I call this a general sociology. Details will still be left for future study—much as oceans, continents, and mountains have to be drawn in on the sphere of the Earth. Such studies would make up a special sociology. Incidentally, however, we shall examine not a few special themes in the course of these volumes; for we shall be meeting them all along the path we shall have to traverse in getting our picture of society in general.

1. 3 ¹ In the first chapter of my Manuale I examined with special regard to political economy several subjects that are touched upon here with regard to sociology.

2. 6 ¹ [Senator René Bérenger (1830-1915), a bête noire of Pareto and one of the villains in this long story, was president of the French Fédération des sociétés contre la pornographie, and was the author, among other things, of a Manuel pratique pour la lutte contre la pornographie (Paris, 1907) and of a Rapport (to the French Senate, 1895) . . . sur la prostitution et les outrages aux bonnes mœurs.—A. L.]

3. 6 ² For greater detail on this point, see Sensini, La teoria della rendita, and Boven, Les applications mathématiques à l'économie politique.

4. 6 ³ [In Italian the word esperienza contains the meaning of "experiment" as well as "experience" and the word "experience" is so used in this translation, barring specification to the contrary.—A. L.]

5. 7 ¹ ["Narration," narrazione, is a technical term with Pareto, used for a recital of facts seriatim quite apart from any interpretation, organization or "thought."—A. L.]

6. 8 ¹ The classification that is bartly suggested here will be amply dealt with in later chapters.

7. 12 ¹ We shall discuss it at length in Chapter IV (§ 467).

8. 13 ¹ There are theories that are logico-experimental in appearance but which substantially are not of that character. For an interesting and very important example of such pseudo-logico-experimental theories, see §§ 407 f. Strictly speaking, such theories should be placed in the non-logico-experimental group.

9. 14 ¹ [Pareto's doctrine of utility takes Bentham's utilitarian theory as its point of departure. Bentham used the adjective "useful" as corresponding to "utility," the opposites being "harm" and "harmful." Pareto uses "useful" (utile) quite regularly. In this translation I have found most convenient the terms "utility," "beneficial," "detriment" and "detrimental," alternating, on occasion, with "advantage," "advantageous," "disadvantageous."—A. L.]

10. 15 ¹ In some other book we might carry the investigation begun in this one further and investigate the particular forms of the various social phenomena of which we shall here have found the general forms.

11. 16 ¹ Pareto, Manuale, Chap. I, § 37.

12. 16 ² Ibid., Chap. I, § 41: "Fatuous and silly is the claim of certain individuals that the faith they hold is 'more scientific' than the faiths of other people. Faith and science have nothing in common, and a faith can contain neither more nor less of science."

13. 19 1 Introduction à la philosophie de Hegel, pp. 78-89.

14. 23 ¹ Pareto, Manuale, Chap. I, § 33.

15. 26 ¹ With that state of mind also we shall deal at length in chapters following.

16. 29 ¹ This is not the place to deal with the question. We note the point in passing just to avoid misunderstandings.

17. 35 ¹ Pareto, Manuale, Chap. III, § 228.

18. 37 ¹ [The allusion is to Foscolo, I sepoleri, vv. 4-5.—A. L.]

19. 38 ¹ Pareto, Manuale, Chap. III, § 226; Systêmes socialistes, Vol. I, pp. 338 f.

20. 47 ¹ The remark is really tautological and would hardly be worth making if it were not so frequently forgotten by people who mix experience and faith, reasoning and sentiment.

21. 49 ¹ Cicero, De divinatione, I, 35, 77: "On that occasion the standard-bearer of the First Spears found he could not move his ensign from where it was; and nothing could be done about it, though many came to his assistance. But when the thing was reported to Flaminius he, as was his usual habit, paid no attention; and so, within three hours, his army was cut to pieces and he himself was slain." [The literary allusion in "Punic fury" is to Carducci, "Alle jonti del Clitumno" (Poesie, p. 803).—A. L.]

22. 49 ² Michaud, Histoire des croisades, 1877 ed., Vol. I, p. 94: "Many of the Crusaders attributed the victory they had won over the Saracens to the discovery of the Holy Lance. Raymond d'Agiles avers that the enemy dared not approach battalions in the midst of which the miraculous weapon could be seen glistening." Idem, Bibliothèque des croisades, Vol. I, pp. 33-34: "Raymond d'Agiles adds that none of the men fighting about the Holy Lance suffered any harm. 'If someone objects,' he continues, 'that the Vicomte Héracle, standard-bearer to the Bishop, was wounded, that was because he had handed the banner to another person and had moved some distance away.' "

23. 50 ¹ Pareto, Manuale, Chap. I, §§ 45, 51.

24. 50 ² Experiment is helpful even in mathematics. As is well known, modern analysis has discredited by experimental data a number of theories that were considered certain on the basis of sense-perceptions of space.

25. 51 ¹ Pareto, Systèmes socialistes, Vol. II, pp. 71 f.; Manuel, pp. 35, note 1; 14, note 1.

26. 58 ¹ For example, Zeller well notes of Heraclitus, Philosophie der Griechen, Vol. I, p. 658 (Alleyne, Vol. II, p. 95), that when that philosopher is carried to hypotheses which conflict with the known testimony of the senses, he concludes [Fragmenta, IV ?] not that his hypotheses are false, as an empiricist would do, but that the senses are deceptive, that reason alone gives trustworthy knowledge.

27. 61 ¹ Boven, Les applications mathématiques a l'économie politique, pp. 106 f.: "First a few definitions of Walras. Interesting his definition of 'value': [Éléments d'économie politique pure, p. 44.] 'Exchange value is the property possessed by certain things whereby they are not obtained or disposed of gratuitously, but are bought or sold, received or given, in certain quantitative proportions in exchange for other things.' This 'property possessed by certain things' smacks of the domain of physics or metaphysics. It is not the same thing as price. . . . One gets the impression that Walras finds it hard to explain just what his 'property' is. He goes round and round it, qualifies it, classifies it, suggests the conditions under which it is to be met with, how it behaves; but he never shows it except under a blurred glass."

28. 62 ¹ Pareto, "L'économie et la sociologie," in Scientia, Bologna, 1907, No. 2: "The term [value] has finished by designating some mystical, metaphysical entity or other that may mean anything, since it has come to mean nothing at all. William Stanley Jevons in his day [1882] saw that the term was giving rise to endless misunderstandings and proposed banishing it from science [see Theory of Political Economy, p. 81]. Meantime matters have grown worse, if possible; and use of the term 'value' may in future serve to distinguish economic treatises that are not scientific from treatises that are. [In a note:] In a volume on economics recently published we find that 'price is a concrete manifestation of value.' We are already familiar with the incarnations of Buddha. To them we are now asked to add the incarnations of Value. Using that sort of language we might say that a cat is a concrete manifestation of 'felinity,' water a concrete manifestation of the 'liquid principle.' But what is the liquid principle? Alas, nobody knows!"

29. 65 ¹ Familiar the language in which Boëthius, translating Porphyry, states the problem, Isagogen Porphyrii commenta I, 10 (Vienna, p. 159; Berlin, p. 25): "Mox de generibus et speciebus, illud quidem stve subsistant sive in solis nudis intellectibus posita sint, sive subsistentia corporalia sint an incorporalia, et utrum separata a sensibilius an insensibilibus posita et circa haec consistentia, dicere recusabo." ("Next, as regards genera and species, I must be excused from deciding whether they are real or are mere conceptions of the mind, whether they are corporeal or incorporeal realities, and whether they are real apart from objects or are attributes of objects inseparable from them.")

30. 67 ¹ For his arguments see § 485.

31. 69 ¹ Pareto, Manuale, Chap. I, § § 39-40.

32. 69 ² Ibid., Chap. I, §§ 42-48.

33. 69 ³ These volumes were already in type when an article by Adrien Naville appeared in the Revue de théologie et de philosophie, Sept.-Oct., 1915, excellently urging against the theories of Bergson ideas similar to those above. The conclusions of a thinker of Naville's distinction are well worth noting. Says he, p. 18: "As regards the theory of the two truths and the case made against science, I have come to the conclusion that science is limited, relative, in part conventional, that it is immersed in mystery, and leaves open a whole world of questions partaking of the nature of transcendental speculation; but that meantime in its own domain and in the fields where it pronounces judgment, there is no authority higher than its own." Just previously Naville had said, p. 3: "A strange development has taken place in our day. The sovereignty of science has been brought under fire, and not by backward minds stifled in routine, not by partisans of ignorance and of a dogma concerned to endure for ever unchanged, but by most wide-awake, most open-minded, most active intelligences. Science is being called to the bar by very enlightened and very daring innovators. . . . Not that the cult of science has entirely disappeared. One might even say that it has become wide-spread and that worshippers of science are more numerous today than fifty years ago. The masses at large are professing for science a reverence that seems to be on the increase [§ 2392] and their leaders are encouraging that attitude in them. . . . But if science has maintained all its prestige for those who move on the lower or middle planes of the intellectual world, the case is different with those who dwell on the summits. These latter have grown mistrustful of science—they are talking back, criticizing, drawing up an indictment and demanding an answer." After reviewing a number of such criticisms, Naville continues, p. 16: "M. Bergson . . . is one of the severest critics that science has ever had. Not that he despises the thing, by any means; he vaunts its merits as loudly as anyone, but only on condition that science attend to its own business, which is, one might say, to formulate the truth that is useful and not the truth that is true. The truth that is true can be obtained only by procedures that are altogether different from the procedures of science."

    So by plain observation of facts and without any preconceived theories, Naville is led to note a particular case of a phenomenon of which we shall state the general theory in Chapter XII (§§ 2339 f.); and in the same way he goes on to note other particular cases of the same thing, p. 6: "That there are two truths [Two? There are an infinite number of truths: quot homines tot sententiae!]—the one profound, philosophy, the other less profound and, in a word, less true—is a thesis that has frequently turned up in the course of history."" From the standpoint of logic and experience, this notion of a number of different truths is a vagary without head or tail, a hotchpotch of meaningless words; but from the standpoint of sentiments and the social or individual utility of sentiments (§§ 1678 f.) it expresses, be it only by combating one error with another, the discrepancy between experience, and the dogma that non-logical actions originate exclusively in outworn, absurd, and pernicious prejudices (§ 1679). Says Naville, pp. 7-8: "In Western Europe it [the theory or the two truths] came to the fore with particular aggressiveness in the latter centuries of the Middle Ages. Its appearance marked the decline and heralded the demise of Scholasticism. Scholasticism had been an alliance between Church doctrine and philosophy. There were two Scholasticisms in Europe, the one Christian, the other Judaic. . . . When Greek came to be known and acquaintance with Aristotle to be intimate, the Church had to decide whether to turn her back on Greek science and thought or accept them as auxiliaries and allies. She adopted the latter course, and the alliance was Scholasticism. The Jewish synagogue did likewise. . . . All the same, the alliance between Church doctrine and philosophical speculation had not been struck on a footing of equality. The Church claimed the upper hand—she was mistress: and philosophical research, free within certain limits, was not expected, to overstep them. Towards the close of the Middle Ages the number of emancipated minds progressively increased, and then the theory of the two truths came quite generally to the fore in university circles, notably at Paris and at Padua."

    At that time the theory served as a bridge between the theology of sentiment and the theology of reason, and its indirect consequences were favourable to experimental science. Today the theory is serving as a bridge between the theology of reason and the theology of sentiment; and it may again turn out to be to the benefit of experimental science by demonstrating experimentally the individual and social udlity of non-logical conduct. And see §§ 1567-79.

34. 69 ⁴ Pareto, Manuale, Chap. I, §§ 4 f.

35. 69 ⁵ As always we use the terms "exact," "exactness," in the sense designated in §§ 108 and 119 x. They are applied to terms that designate things with the closest approximation possible. The chemist does not reject the term "water" for pure water—as pure, that is, as can be obtained with the means at present at our command; but he would reject it as a designation for sea-water. The mathematician knows very well that there is no number that, when multiplied by itself, gives 2— which is, in other words, the square root of 2; but he does not scruple to use a number as approximate as is required for the calculation he has in hand, say the number 1.414214; yet he would refuse to use the number 5 for the same computation. Mathematicians have proceeded as though a square root of 2 (in general, an irrational number) existed. They have now come to recognize the necessity of using instead two classes of real numbers, the first containing all rational numbers with squares less than 2, the second, all rational numbers with squares larger than 2. The example is noteworthy on two accounts:

    1. It illustrates the continuous development of science, by showing how in a science as perfect, as exact, as mathematics improvements in the direction of greater perfection and exactness have still been possible. Similar improvements might be mentioned in mathematical series, and in many mathemadcal demonstradons.

    2. It is an example of successive approximation in the sense of gradual progress towards greater and greater exactness. The mathematicians of andquity wisely avoided the risk of losing their way among such nicedes, and modern mathematicians have just as wisely gone into them. The ancients were paving the way for the moderns; the moderns are paving the way for their successors. Hipparchus, Kepler, Newton, Laplace, Gauss, Poincare, represent successive approximations in celestial mechanics. Hegel reached the absolute in one bound; but there is this difference between his speculations and the theories of those scientists: With Hegel's theories one could not locate a star, however indefinitely—he leaves one in the fix of a mathematician taking 100 as the square root of 2; whereas with scientific theories one may determine those locations roughly and with closer and closer approximation, being in the position of the mathematician utilizing some value such as 1.414214 as the square root of 2. We arc trying to follow in sociology the path trodden before us by astronomers, physicists, chemists, geologists, botanists, zoologists, physiologists, in short, by all natural scientists of modern times; and to avoid, so far as within us lies, the road that led the Church Fathers to denying the existence of antipodes, and Hegel to prattling about mechanics, chemistry, and other similar sciences—and which is generally followed by metaphysicists, theologians, and men of letters in studies that they pretend deal with facts of nature but which in reality are a mere hotchpotch of sentiments.

36. 69 ⁶ Pareto, Manuale, Chap. I, § 14. I have given many illustrations of the method of successive approximations in my Cours and Manuale. For sociology a good example is available in Marie Kolabinska's La circulation des élites en France. The writer wisely centred on the main elements in her problem, disregarding the secondary. That method is the only one that can be followed if one is to construct a scientific theory and steer clear of the divagations of that ethical literature which is still passed off as sociology. Many further examples of successive approximations will be found in these volumes.

37. 70 ¹ Hence also we refrain from passing any judgment on the conflict now raging on the matter of divine inspiration between Catholic orthodoxy and the Modernists. The subject lies outside the field in which we choose to remain. We must, however, remark that the interpretation of the Modernists has really nothing to do with the positive sciences.

38. 75 ¹ I am going to register just one exception at this point, and after all it is more apparent than real, since it aims at clearer explanation, by an example, of the objective fact here in point. I shall have occasion hereafter to speak unfavourably, very much so, of certain acts by Athenian demagogues. Now I do not imagine the reader is especially concerned to know my global personal attitude towards the ancient Athenian republic. However, if I may be allowed to state it, I will say that I do not think anyone admires or loves the Greek mind more than I do. I shall poke fun at the "goddess Science," yet the fact stands that I have devoted my life to experimental sciences. One may ridicule the democratic humanitarianism of this or that French politician and still hold the scientists of that country in highest esteem, and even regard the republican form of government as perhaps the best for France. One may note the licentiousness of certain emancipated women in the United States and still cherish the deepest reverence for the many admirable wives and mothers who are to be found in that country. Finally, to point the finger of scorn at the hypocrisies of German sex-reformers is not inconsistent with admiration for their mighty nation and reverence for German scholarship. I deem it superfluous to note similar contrasts in the case of my own country, Italy. That is my whole confession. I urgently beg the reader to be convinced that this exception will have no counterparts. These volumes should be read not for something that is not there—a statement, namely, of my personal sentiments—but exclusively for reports on objective relationships between things, between facts, and between experimental uniformities.

39. 76 ¹ This topic is touched upon just incidentally here. It belongs to our study of the objective aspect of theories (§ 13) and will be amply developed in due course.

40. 77 ¹ Cours, § 198.

41. 77 ² Ibid., § 196: "It is therefore quite evident that the population of the three countries considered cannot continue to increase indefinitely at the present rate." The three countries were Norway, England-Wales, and Germany. As regards Norway, the annual rate of geometric increase, which was 13.9 per cent for the period 1861-80, fell to 5.7 per cent for the period 1905-10. For England-Wales and Germany the figures are as follows:

    	Percentage of Increase
    Years	England-Wales	Germany
    1880-85	11.1	7.1
    1885-90	13.4	10.7
    1890-95	11.5	11.3
    1895-1900	11.5	15.2
    1900-05	10.6	14.7
    1905-10	10.4	13.7

    "It is evident that after reaching a maximum in the years 1895-1900, the rate of population increase in Germany is now [1910] on a descending curve. The falling-off in rate is more clearly apparent still from the annual statistics of births per thousand:

    	Percentage of Increase
    Years	Norway	England-Wales	Germany
    1875	31.2	35.4	40.6
    1885	31.3	32.9	37.0
    1895	30.5	30.3	36.1
    1900	29.9	28.7	35.6
    1905	27.4	27.3	33.0
    1910	26.1	25.1	31.1 (for 1909)

    "The falling-off in the rate of population increase in Germany is especially notable in the large cities, where wealth has appreciably increased:

    	Number of Births per 1000 Inhabitants
    Germany	1902	1912
    Munich	35.1	21.9
    Leipzig	31.5	22.1
    Dresden	31.5	20.3
    Cologne	37.8	26.7
    Magdeburg	29.2	22.8
    Stettin	35.3	22.7
    Danzig	34.7	27.6"

    That substantiates what I wrote in my Cours, § 198: "It is therefore evident that forces limiting increment in population must have interfered with the genetic tendency in times past, or will do so in the future."

42. 77 ³ Ibid., § 211 ¹. If P is the population in the year t, reckoning from the year 1801, we get:

    log P = 6.96324 + 0.005637t.

    That yields the theoretical law of population for the years 1801-91. The following figures are given in my Cours:

    	Population (in Millions)
    Years	Real	Estimated	Difference
    1801	8.892	9.188	+0.296
    1811	10.164	10.294	+0.130
    1821	12.000	11.912	-0.088
    1831	13.897	13.563	-0.334
    1841	15.914	15.443	-0.471
    1851	17.928	17.583	-0.345
    1861	20.066	20.020	-0.046
    1871	22.712	22.795	+0.083
    1881	25.975	25.953	-0.022
    1891	29.001	29.551	+0.550

    The greatest difference, in other words the maximum error, arising in the application of the formula is 0.550. Using the formula to estimate population for the year 1910, we get 37.816, while the actual population was 35.796. The difference is +2.020, a figure much greater than the maximum error. That proves that population is no longer following the law observable for the years 1801-91, and that it is increasing at a slower rate.

43. 77 ⁴ Ibid., § 211 ². The remark has to be taken in connexion with matter preceding, §§ 179-80: "Movements in the transformation of personal capital are in part dependent on the economic movement. It must not be forgotten that we have not shown their explicit dependence on the economic situation, but merely their dependence on variations in it. [In a note:] If the economic situation is characterized by a function F of any number of variables that are functions of the time t, then we have shown that the numbers of marriages, births, and to a certain extent also deaths, are a function of $\frac{dF}{dt}$; but we have not shown that such numbers are explicit functions of F."

44. 77 ⁵ Ibid., § 965.

45. 77 ⁶ A definition of "decrease in inequality in incomes" is given in Ibid., § 965 ¹. See also my Manuel, pp. 389 f., and Sensini, La teoria della rendita, pp. 342-53, and especially p. 350, § 185.⁴

46. 77 ⁷ A criticism of the passages may be found in the introduction to my Manuale, where the various errors are duly noted.

47. 79 ¹ That is why there will be so many notes with quotations. Their design is to keep the body of facts vividly present before the reader's mind.

48. 85 ¹ See in this connexion, Pareto, Le mythe vertuiste.

49. 86 ¹ Running, as it does, counter to the general trend in the social sciences, this work will be severely criticized by all individuals whose minds are closed to innovations from a habit of drifting with that current. They state the problem of judging a theory in the terms: "Is it in accord with the theories I consider good?" If the answer is yes, they classify it with the good theories, if no, with the bad. It is obvious enough that being at variance with all such theories, this one of mine will certainly be bad. It may find a warmer welcome among young people whose minds are not yet clogged with the preconceptions of orthodox science and among people who state the problem of judging a theory in the terms: "Is it in accord with the facts?" I must have made it sufficiently clear by this time that that is the only accord I seek, and that I have no interest whatsoever in anything else.

50. 87 ¹ In the year 1909 and with the Manuale, which had appeared in 1906, before his eyes, Professor Gide, Histoire des doctrines économiques, p. 623, was able to write: "The Hedonists [Among whom Gide counts V. Pareto—on what grounds, he only knows] are very reticent as regards the possibilities of realizing their economic world. On the other hand they are very positive, in fact a little too much so, as regards the virtues of their method, not being exempt on that score from a dogmatic conceit that reminds one of the utopian Socialists. One seems to be listening to Fourier when one reads that 'what has already been discovered in political economy is nothing as compared with what may be discovered hereafter'—by the mathematical method, of course." Gide ascribes his quotation to one "V. Pareto, ["Le nuove teorie economiche"], Giornale degli economisti, September, 1901." Even if the quotation were exact, M. Gide might at least have noted that V. Pareto had changed his views, as is apparent enough from his Manuale. But it is not exact, for M. Gide is thinking of practice, whereas I was thinking strictly of pure theory! A good guess would be that M. Gide had not read the article from which he quoted. My article says, p. 239: ". . . Now the outstanding trait in the new economic theories is that they are the only ones so far to have given us a general picture of the economic phenomenon as a whole. The picture is just approximative, much like a sphere offered as a model of the Earth. All the same we know of nothing better." On p. 241, as to "the equations of pure economics," I clearly state that they are of service only as instruments for study, much as it is of service to know, for instance, the dimensions of the terrestrial ellipsoid. On p. 242: "Pure economics, one may say, has indeed found the tool for its researches, but it has hardly begun to use it. Practically everything along that line is still to be done; and economists really devoted to the progress of their science ought to set about doing it." I was speaking of science, pure science, and not of practical applications, as Gide's allusion to Fourier would insinuate. I conclude, p. 252, with the quotation that Gide detached from its context—with a remodelling to boot: "We are in the first stages of the new science, and what it has already achieved is nothing as compared with the results it may achieve hereafter. The present state of pure economics is not even comparable to the state of astronomy after the appearance of Newton's Principia." The parallel I drew was with an abstract science, astronomy, not with a concrete science. In the rest of his article Professor Gide continues to ascribe to me opinions and theories that I have never held and which I have even disputed as directly opposite to theories actually mine. For further details see my article, Économie mathématique, in the Encyclopédie des sciences mathématiques [Meyer, Vol. I, pp. 1094-1120, s. v. Anwendungen der Mathematik auf Nationalökonomie; Molk, Vol. I, pp. 591-640] and in Giornale degli economisti, Nov., 1906, p. 424.

51. 89 ¹ An altogether estimable person once asked whether my science were "democratic"! It has been said, in black and white, that it was "socialistic"; and then again that it was "reactionary." The science interested strictly in uniformities (laws) among facts is nothing of any of those sorts and can in no way be so labelled. It is just a quest for uniformities, and that is the end of it. Personally, I was a free-trader in my Cours; but in my Manuale I dropped that cloak, and I remain divested of it when dealing with science.

52. 96 ¹ ["Interdependence" is a technical term with Pareto—see our Index. The same concept is expressed in English by the words "correlation," "interrelation."—A. L.]

53. 99 ¹ We shall see something remotely similar in the case of sociology (Chapter XII).

54. 99 ² Pareto, Manuale, Chap. I, § 20.

55. 101 ¹ Pareto, Manuale, Chap. 1, § 7. There are still professors of political economy who keep repeating parrot-like that economic laws have exceptions, while physical laws do not. Such "the ignorance that tormenteth them"! Not even with a spyglass could one find a physicist to class among unexceptionable physical laws the law that bodies diminish in volume as they cool.

56. 104 ¹ One of the many forms of the method of successive approximations (§§ 69-9, 540).

57. 104 ² Pareto, Manuale, Chap. III, §§ 29-30, 35.

58. 106 ¹ Pareto, Manuel, p. 10. To humour the Hegelians we might say: "It has been observable that the concept of a thing which people have at a given moment is supplemented, as time goes by, with new concepts, and the series of additions, so far as we can tell, must be infinite."

59. 108 ¹ That influence—nothing very definite, to tell the truth—of the facts upon our minds makes up such truth, experimentally speaking, as there is in theories ascribing a scientific status to intuition. Intuition serves about as much towards knowledge of reality as a poor, sometimes a very poor, photograph of a place serves towards knowledge of that place. Sometimes intuition supplies just a fanciful illusion, and not even a poor photograph, of reality.

60. 112 ¹ First Principles, § 46. "Thought being possible only under relation, the relative reality can be conceived as such only in connexion with an absolute reality; and the connexion between the two being absolutely persistent in our consciousness, is real in the same sense as the terms it unites are real." All of Spencer's writing is packed with such concepts.

61. 112 ² Here is an example selected at random: Ibid., § 48: "Such being our cognition of the relative reality, what are we to say of the absolute reality? We can only say that it is some mode of the Unknowable, related to the Matter we know as cause to effect." There are people who will tell you they understand that.

62. 113 ¹ Of that we shall give many examples in the pages that follow.

63. 118 ¹ In my Manuale I showed that economic theories can just as well be elaborated without mention of the terms "value," "price," "capital," and the like. Literary economists cannot see it that way; and to an extent they are right, since for them the term "capital," let us say, designates not a thing but a sum of sentiments, and naturally enough they want to keep a term to designate that sum. To humour them, the thing might be called "objective capital," and the complex of sentiments "subjective capital." Then one could say: "Economic theories concerned exclusively with investigating relationships between economic facts have nothing to do with the concept 'subjective capital.' They may or may not, as they choose, utilize the concept 'objective capital.' " And going on: "Economic theories that aim at making converts and thereby at achieving some practical result can turn the concept of 'subjective capital' to good account, converts being made by appeals to sentiment. For that reason it is the wiser part for them to create a confusion between the notions of 'objective capital' and 'subjective capital,' so that the scientific argument will not avail against the sentimental argument." At some few points such theories approximate the concrete more closely than the theories of pure economics, for they inject into the concept of "subjective capital" sociological notions that have no place in scientific economics. But they still have the fatal defect of being entirely devoid of exactness. If one would get closer to the concrete, instead of introducing sociological concepts implicitly and as it were by stealth, it would be better to advance them openly: that would make at least a certain amount of definiteness unavoidable. All such things can be better seen from Sensini's La teoria della rendita.

    The concept "subjective capital" becomes of prime importance to sociology, which is in fact directly concerned with the sentiments expressed in such terms; and since the concrete phenomenon is both economic and sociological, anyone studying it in applied economics inevitably encounters notions analogous to "subjective capital." That is why, in my Manuale, I examined concrete phenomena not only from the strictly economic standpoint, but also as regards the manners in which they are conceived by the individuals involved in them (see the caption Veduta soggettiva in the index to the Manuale).

64. 119 ¹ One should here recall the points alluded to in § 108. There is nothing absolute in logico-experimental science. Here the term "exact" means "with the least possible margin of error." Science tries to bring theory as close to the facts as possible, knowing very well that absolute coincidence cannot be attained. If, in view of that impossibility, anyone refuses to be satisfied with approximate exactness, he had better emigrate from this concrete world, for it has nothing better to offer.

65. 119 ² Pareto, Manuel, p. 556, note 1.

66. 119 ³ For other misconceptions arising from lack of exactness in language and from the prattle of literary economics, see my Manuel, pp. 219, note 1; 246, 329, note 1; 333, note 1; 391, note 1; 414, 439, note 1; 544, note 1; 636, note 1; 638, note 1; but especially, Sensini, La teoria della rendita, and Boven, Les applications mathématiques à l'économie politique.

67. 126 ¹ [Pareto's word was vincolo, "bond." The vincolo is a force that conditions the operation of another force. The term vinculum itself has a certain currency in technical sociologies. In most connexions it can well be translated as "condition," or "check," and more generally as "correlation," or even as "premise." In deference to the baroque quality of Pareto's own term, I render it regularly as "tie."—A. L.]

68. 131 ¹ Here, accordingly, the term "conditions" has a different and more comprehensive meaning than it had in § 126.

69. 132 ¹ Naville, review of Bergson, Op. cit., p. 11: "I am well aware that determinism has its fascination for the scholar and affords great satisfaction to the scientific mind. [More exactly, "to the theology of Reason."] Determinism is the belief [That word alone should serve to give warning that we are overstepping the boundaries of experimental science.] that everything can be explained, and what the scientist wants is explanations. Determinism is the conviction that all phenomena can be understood, associated, that is, with other phenomena that envelop and produce them. . . . But however natural the inclination [to determinism] may be, it proves nothing, and not all scientists succumb to it."

70. 144 ¹ The terms "quality," "quantity," "qualitative," "quantitative," will at all times be used in these volumes not in any metaphysical sense but in the sense commonly used in chemistry in contrasting qualitative with quantitative analysis. The one shows, for instance, that a given substance is an alloy of gold and copper; the other shows the weight of gold and the weight of copper present in a given weight of the alloy. Whenever we note the presence of a certain element in a sociological complex, we are stating a qualitative proposition. When we are in a position to designate, however roughly, the intensity of that element, our proposition becomes quantitative. Unfortunately no scales are available for weighing the things that are dealt with in sociology, and we shall generally have to be satisfied with designating quantities by certain indices that increase or diminish with the thing itself. An interesting example of that method applied to political economy is provided in my use of indices of ophelimity (see my Manuale, Appendix).