Chapter III: Evidence and Reasoning (2)

34. Reasoning from Analogy. Analogy in its most tenuous form is weak as a basis for an actual inference, though it is often effective as a means of expressing an intuitive judgment where the reasons are too subtle and diffused for formal explanation. When Lincoln in the middle of the Civil War said that men do not swap horses while they are crossing a stream, the analog, though subtle, was felt to be real. Popular adages and proverbs are common modes of expressing such deep-lying analogies: for example, "Where there is smoke there is fire"; "The slothful man saith, There is a lion in the way." Poetry too is full of these subtle, pregnant similarities which link things in some one aspect, but fail for all others.

To die; to sleep;
No more; and by a sleep to say we end
The heart-ache and the thousand natural shocks
That flesh is heir to. 'Tis a consummation
Devoutly to be wish'd. To die; to sleep;--
To sleep? Perchance to dream! Ay, there's the rub;
For in that sleep of death what dreams may come,
When we have shuffl'd off this mortal coil,
Must give us pause.

But, as in this case of Hamlet's, poetical analogies will not bear much strain; the aspect in which the similarity holds is usually the only aspect the two cases have in common, and to take poetry as a precise formulation of fact is to sin against both humor and sound reasoning.

In daily life we are constantly reasoning by analogy. If you argue that a certain man who has been successful at the head of a railroad will therefore make a good president for a college because that also is a complex institution, or that because self-government has worked well in a certain school it will probably work well in a college, or that because a friend has been cured of sleeplessness by taking a walk just before going to bed therefore everybody who sleeps badly can be cured in the same way,--in all these cases you are reasoning by analogy. In each case it will be noticed you would pass from a similarity which exists in a single case or in a small number of cases to the conclusion. The reasoning is sound, however, only in so far as the similarity bears on the actual purpose in hand: in the first example, if the success of the railroad president arises from the power of understanding men and of philosophic insight into large problems, the reasoning will probably be valid; in the last example, if applied to insomnia due to overwork, it might be bad.

In practical affairs it is easy to find examples of reasoning from analogy, especially in arguments of policy. The first trial of city government by commission depended on such reasoning: when Galveston, Texas, was devastated by a storm it was reasoned that in business matters a small body of picked men with absolute powers are most efficient in an emergency, and that since the reconstruction of the city was essentially a matter of business, such a body would best meet the emergency. So the extension of commission government in other states at first followed reasoning by analogy: government by commission worked well in Galveston; it would probably work well in Des Moines. In the same way with the arguments for a parcels post: they proceed from the analogy of the present postal service, which has been successful so far as it goes, and from the success of the parcels post in almost all the countries of Europe. If you were arguing that "Association" (or "soccer") football should be made one of the major sports at your college, you would reason from the analogy of its great popularity with Englishmen all over the world that it would also probably be popular in America.

When you use the argument from analogy, however, you must make sure that the similarity between the two cases runs to the point you wish to establish. In the following extract from an argument in favor of commission government for all cities, the author explicitly limits his reasoning from the analogy of Washington to the point of the extension of the system to large cities.

If we look for successful governments by commission in this country, it is not difficult to find them in our largest cities. The city of Washington is governed by a small commission, and is acknowledged to be one of our best-governed cities. While this commission originated in an entirely different way from that of the commission form of government, successful administration under its rule is a valid answer to the argument that small commissions are suited only to the administration of small cities.[26]

Whenever you use this type of reasoning, it is wise thus to limit its bearing. If in an argument in favor of allowing secret societies in a high school you rely on the analogy of college life, take pains to show that the resemblance covers the social life of a school. If you were arguing that your city should establish a municipal gymnasium, and relied on the reasoning from the analogy of a family, in which all the members have a direct interest in the health of the others, show that this interest has practical grounds of welfare, and does not rest wholly on affection. In every case, unless the limits of the analogy are obvious, specify them in order to carry your readers safely with you.

35. False Analogy. A peculiar danger of the argument from analogy is the fallacy which is known as false analogy, or reasoning to a conclusion which the similarity does not support. Arguments in which there are many figures of speech, especially when the style is at all florid, are apt to slop over into this fallacy. To liken education to the unfolding of a flower is all very well, if you do not go on to argue that because the lily of the field neither toils nor spins, therefore a child should do no work in school. It is said that M. Stolypin, the late premier of Russia, once half apologized In the Duma for the slowness of his reforms, saying that he Was like a man shooting with a flintlock musket; to which one of the Liberal members replied that it was not a question of weapons, but of aim, and that if his Excellency was to go on shooting at the people, it would be better if he went on using flintlocks. Under the auspices of the Carnegie Institution an expert in business administration made an inquiry into the methods of teaching and research in physics at various American universities, and made recommendations based on the conduct of business establishments. A professor of physics in answer showed in how many ways the analogy between a business concern, whose end is profit, and a physical laboratory, whose end is the advancement of knowledge, is false and misleading. The expert had suggested a general research board to correlate researches; the professor cited the cases of Airy, the astronomer royal of England, who by his dominating position held back astronomical research in England for a generation, and of Sir Humphry Davy, who discouraged the work of Faraday, when the latter was his assistant.

The expert suggested that apparatus could be passed on from one investigator to another: the professor replied that few men can use apparatus designed for some one else's purpose, and that the cost of reconstruction would exceed the cost of new machines. In short, he completely riddled the argument from analogy set up by the expert.[27]

A notable example of conclusive refutation of an argument based on a false analogy is to be found in William James's Ingersoll Lecture on Immortality. He took up the ordinary argument against the immortality of the soul, which, starting from the accepted physiological and psychological formula, "Thought is a function of the brain," reasons that therefore when the brain dies and decays, thought and consciousness die, too.

This, then, is the objection to immortality; and the next thing in order for me is to try to make plain to you why I believe that it has in strict logic no deterrent power. I must show you that the fatal consequence is not coercive, as is commonly imagined; and that, even though our soul's life (as here below it is revealed to us) may be in literal strictness the function of a brain that perishes, yet it is not at all impossible, but on the contrary quite possible, that the life may still continue when the brain itself is dead.

The supposed impossibility of its continuing comes from too superficial a look at the admitted fact of functional dependence. The moment we inquire more closely into the notion of functional dependence, and ask ourselves, for example, how many kinds of functional dependence there may be, we immediately perceive that there is one kind at least that does not exclude a life hereafter at all. The fatal conclusion of the physiologist flows from his assuming offhand another kind of functional dependence, and treating it as the only imaginable kind.

When the physiologist who thinks that his science cuts off all hope of immortality pronounces the phrase, "Thought is a function of the brain," he thinks of the matter just as he thinks when he says, "Steam is a function of the teakettle," "Light is a function of the electric circuit," "Power is a function of the moving waterfall." In these latter cases the several material objects have the function of inwardly creating or engendering their effects, and their function must be called _productive_ function. Just so, he thinks, it must be with the brain. Engendering consciousness in its interior, much as it engenders cholesterin and creatin and carbonic acid, its relation to our soul's life must also be called productive function. Of course, if such production be the function, then when the organ perishes, since the production can no longer continue, the soul must surely die. Such a conclusion as this is indeed inevitable from that particular conception of the facts.

Rut in the world of physical nature productive function of this sort is not the only kind of function with which we are familiar. We have also releasing or permissive function; and we have transmissive function.

The trigger of a crossbow has a releasing function: it removes the obstacle that holds the string, and lets the bow fly back to its natural shape. So when the hammer falls upon a detonating compound. By knocking out the inner molecular obstructions, it lets the constituent gases resume their normal bulk, and so permits the explosion to take place.

In the case of a colored glass, a prism, or a refracting lens, we have transmissive function. The energy of the light, no matter how produced, is by the glass sifted and limited in color, and by the lens or prism determined to a certain path and shape. Similarly, the keys of an organ have only a transmissive function. They open successively the various pipes and let the wind in the air chest escape in various ways. The voices of the various pipes are constituted by the columns of air trembling as they emerge. But the air is not engendered in the organ. The organ proper, as distinguished from its air chest, is only an apparatus for letting portions of It loose upon the world in these peculiarly limited shapes.

My thesis now is this: that, when we think of the law that thought is a function of the brain, we are not required to think of productive function only; _we are entitled also to consider permissive or transmissive function_. And this the ordinary psychophysiologist leaves out of account.[28]

The question of the validity of an analogy in reasoning is always, as here, whether the similarity on which the reasoning rests really runs between the two cases in hand, or is not merely a general resemblance expressed by some phrase or word which seems to mean more than it does. In other words, when you are testing an analogy, whether your own or an opponent's, make sure that the similarity is real for the present case. A picturesque figure of speech may add life to an argument, but it may also cover a gap in the reasoning.

36. Reasoning by Classification or Generalization. Obviously the strength of reasoning from analogy increases with the number of cases which you can point to as showing the similarity on which you rely, for you can then begin to generalize and classify.

Analogy expresses our natural tendency to assimilate the new to the old, to interpret what is strange and unfamiliar in the light of what we already know. It may therefore be described as classification in the making. The resemblances which guide us are called analogies so long as they are newly seen, rare, or doubtful; but as the number of cases increases, analogy passes by insensible stages into established classification.[29]

An excellent example of this transition may be seen in the present state of the argument in favor of commission government: at first, as we have seen, it depended chiefly on reasoning from analogy; by this time enough cities have adopted the plan to make it possible to classify them, and so reason by generalization.

Generalization and classification, it may be noted in passing, are two aspects of the same process of thought. When one passes from the individual facts to the larger fact which brings them together, as in the assertion, _Members of the Phi Beta Kappa are good scholars_, one makes a generalization; when one asserts of an individual the larger fact, as in the assertion, My _brother is a good scholar_ (My _brother belongs to the class Good Scholars_), one makes a classification.

When a classification or generalization is constant and familiar, it brings forth, by the natural economy of language, a name for the class or the principle; "federation," "deciduous trees," "emotion," "terminal moraine," are all names of classes; "attraction of gravity," "erosion," "degeneration," "natural selection," are names of principles which sum up acts of generalization. Almost always these names begin as figures of speech, but where they are used accurately they have a perfectly exact meaning. Darwin has given some account of this process of language:

"It has been said that I speak of natural selection as an active power or deity, but who objects to an author speaking of the attraction of gravity as ruling the movements of planets? Every one knows what is meant by such metaphorical expressions, and they are almost necessary for brevity: so, again, it is difficult to avoid personifying the word 'Nature.' But I mean by Nature the aggregate action and product of many laws, and by laws the sequence of events as ascertained by us."[30]

When the facts intended to be meant by a phrase are thus carefully specified and delimited, the phrase ceases to be a figure of speech, and becomes the name of a class or of a principle.

Generalization and classification always take place for purposes of reasoning;[31] and reasoning which is dependent on them rests on the assumption that things are uniformly correlated in nature; when we throw things together into classes we assume that what is true for one member of a class, so far as it is a member of that class, is true to the same extent and for the purpose for which the class is made for all other members of that class.

In practice a large part of our reasoning is through generalization and classification; and as we have seen, it has a more substantial basis than when we rest on an analogy. If you hear that your brother has been elected to the Phi Beta Kappa, you reason from the generalization that all members of the Phi Beta Kappa are high scholars to the inference that your brother must have taken high rank. When I see a gang of carpenters knocking off work at four o'clock in the afternoon, I infer that they must belong to the union, because I know that unions as a class have established an eight-hour day. If you were arguing that the standards for graduation from your college should be raised, you would try to show that each year enough men are graduated with low intellectual attainments to make a class large enough to generalize from. If you were arguing that your city should establish a municipal gymnasium, you would try to show that of the boys and young men brought before the police courts for petty mischief and more serious offenses almost all have lacked the chance to work off their animal spirits in a healthy way. Wherever you can thus establish your special case in a class which has known characteristics or consequences, you can then apply the characteristics and consequences of the class to your special case.

Where the class is recognized as having definite characteristics or consequences, you can make your inference by showing that your case falls within the class. Sometimes the stress of your reasoning will come on making it clear that the consequence or characteristic on which your reasoning depends really belongs to the class. If, for example, you were arguing, as did the Class of '85 at Amherst College, that your college should return to something like the old-fashioned classical education, you would try to establish the fact that men who have had the old-fashioned classical education are as a rule characterized by intelligence, liberal culture, and open-mindedness. In such cases it is the generalization on which the class is based which is the difficult part of your task.

In general, however, if you can show your readers that the present case belongs in a class of cases which can be recognized as belonging together by virtue of definable characteristics, you have established an excellent foundation for an inference based on those characteristics.

37. Reasoning by Causal Relation. Reasoning by generalization rises greatly in certainty, however, whenever you can show the workings of cause and effect. If a college receives every year from a certain school a number of boys who are slack and lazy students, the dean of that college may come to generalize and expect most of the boys from that school to be poor timber. If, however, he finds that the master of the school will take and keep any boy who lives in the town, he is able to argue from this as a cause to the conclusion that the standards of the school are low, and then from these low standards as a cause to the poor quality of the graduates of the school.

Here is another example, from Professor James:

I am sitting in a railroad car, waiting for the train to start. It
is winter, and the stove fills the car with pungent smoke. The
brakeman enters, and my neighbor asks him to "stop that stove
smoking." He replies that it will stop entirely as soon as the car
begins to move. "Why so?" asks the passenger. "It _always_ does,"
replies the brakeman. It is evident from this "always" that the
connection between car moving and smoke stopping was a purely
empirical one in the brakeman's mind, bred of habit. But if the
passenger had been an acute reasoner ... [and had] singled out of
all the numerous points involved in a stove's not smoking the one
special point of smoke pouring freely out of the stove-pipe's mouth,
he would probably ... have been immediately reminded of the law that
a fluid passes more rapidly out of a pipe's mouth if another fluid
be at the same time streaming over that mouth.[32]

Here the passenger's certainty that the smoking would stop would have been much increased if he had, as Professor James suggests, reasoned to the cause, instead of trusting to the brakeman's generalization from experience.

In scientific matters search for cause and effect the chief mode of progress. General Sternberg's article "Yellow Fever and Mosquitoes" (p. 251) is an admirable account of this advance from probability to certainty, which comes from demonstrating the necessary sequence which we call cause and effect. When Major Reed and his associates had shown that in cases where mosquitoes were kept away there was no yellow fever, but that in cases where infected mosquitoes were allowed to bite patients yellow fever followed, they turned the probability that mosquitoes were the transmitting agent of the fever into a certainty. Likewise with the glacial theory: it had already in the time of the elder Professor Agassiz been established that certain regions of northern Europe and America could be classed together by the occurrence of certain phenomena--rounded hills, ledges of rock smoothed off and marked with scratches running more or less north and south, deposits of clean gravel and sand, boulders of various foreign kinds of rock scattered over the surface of the country; when he showed that glaciers in their movements produce all these phenomena, he laid bare the cause of the phenomena, and so demonstrated with practical certainty the theory of the former existence of a huge glacial sheet in the northern hemisphere. Wherever you can show that your case not only belongs to a recognized class of cases, with recognized characteristics, but also that in those characteristics there is a necessary sequence of cause and effect, you have proved your point.

In the example above, of an argument for the establishment of a municipal gymnasium, if after showing that all the boys and young men who get into the courts have no normal and healthy way of working off their natural animal spirits, you can show that in places where through settlements or municipal action gymnasiums have been provided, the number of arrests of boys and young men has greatly fallen off, you have established the grounds for an inference of cause and effect which gives your argument a wholly new strength. In the case of the argument for a return to a classical course in a college, this sequence of cause and effect would be very difficult to establish, for here you would be deep down in the most complex and subtle region of human nature. Wherever it is possible, however, lead the inference from a classification or generalization on to an inference of cause and effect.

38. Induction and Deduction. Our next step is to consider how we get the generalizations on which we base so much of our reasoning. As we have seen, the science which deals with the making of them, with their basis, and with the rules which govern inferences made from them is logic.

Logicians generally distinguish between two branches of their science, inductive and deductive reasoning. In inductive reasoning we pass from individual facts to general principles; in deductive reasoning we pass from general principles to conclusions about individual facts. The distinction, however, draws less interest in recent times than formerly, and logicians of the present generation tend to doubt whether it has any vital significance.[33] They point out that in practice we intermingle the two kinds almost inextricably, that the distinction between facts and principles is temporary and shifting, and that we cannot fit some of the common forms of inference into these categories without difficult and complicated restatement.

Nevertheless, as deductive logic and inductive logic are ancient and time-honored terms which have become a part of the vocabulary of educated men, it is worth while to take some note of the distinction between them, I shall not attempt here to do more than to explain a few of the more important principles. I shall begin with inductive logic, since that is the branch which deals with the making of generalizations from individual fact, and therefore that which has most concern in the arguments of the average man in his passage through life.

39. Inductive Reasoning. In inductive reasoning we put individual facts and cases together into a class on the basis of some definable similarity, and then infer from them a general principle. The types of inductive reasoning have been reduced by logicians to certain canons, but these reduce themselves to two main methods, which depend on whether in a given piece of reasoning we start from the likeness between the instances or the differences between them. On these two methods, the method of agreement and the method of difference, hang all the processes of modern science, and most of our everyday arguments.

The method of agreement has been defined as follows:

If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree is the cause (or effect) of the given phenomenon.[34]

A few examples, which might easily be multiplied, will show how constantly we use this method in everyday life. Suppose that a teacher is annoyed at somewhat irregular intervals by whispering and laughing in the back of the schoolroom, for which he can find no cause, but that presently he notices that whenever a certain pair of boys sit together there the trouble begins; he infers that these two boys are the cause of the trouble.

In the old days before it had been discovered that the germs of malaria are carried by mosquitoes, the disease was ascribed to a miasma which floated over low ground at night; and the innkeepers of the Roman Campagna, where malaria had almost driven out the population, urged their guests never to leave their windows open at night, for fear of letting in the miasma. In the lights of those days this was good reasoning by the method of agreement, for it was common observation that of all the many kinds of people who slept with their windows open most had malaria. We are constantly using this method in cases of this sort, where from observation we are sure that a single cause is at work under diverse circumstances. If the cases are numerous enough and diverse enough, we arrive at a safe degree of certainty for practical purposes. As the case just cited shows, however, the method does not establish a cause with great certainty. No matter how many cases we gather, if a whole new field related to the subject happens to be opened up, the agreement may be shattered.

The method of difference, which in some cases does establish causes with as great certainty as is possible for human fallibility, works in the opposite way: instead of collecting a large number of cases and noting the single point of agreement, it takes a single case and varies a single one of its elements. The method has been stated as follows:

If an instance in which the phenomenon occurs, and an instance in which it does not occur, have every circumstance in common save one, that one occurring only in the former; the circumstance in which alone the two instances differ, is the effect, or the cause, or an indispensable part of the cause, of the phenomenon.[35]

The principle is clearer and more apprehensible in the concrete example than in the abstract statement; as a matter of fact it is applied in every experimental search for a cause. The Agricultural College of New York, for example, in the course of certain experiments on apple orchards, bought an orchard which had not been yielding well, and divided it into halves; one half was then kept plowed and cultivated, the other half was left in grass; otherwise the treatment was the same. When the half which was kept cultivated gave a much larger yield than the other, it was safe to infer that the cultivation was the cause of the heavier yield. Dr. Ehrlich, the great German pathologist, is said to have tried six hundred and five different substances before he found one which would kill the germ of a certain disease; in each experiment he was using the method of difference, keeping the conditions the same in all except a single point, which was the addition of the substance used in that particular experiment. Wherever the conditions of an experiment can be thus controlled, the method of difference gives a very accurate way of discovering causes. With advancing knowledge a supposed cause may be in turn analyzed in such a way that each of its parts can be separately varied, in order to come more closely to the actual sequence involved.

It has been pointed out[36] that the two methods are really statements of what is required for the verification of a theory at two stages of its growth: when we are first getting a glimpse of a causal connection between two facts we collect all the cases in which they occur in as much variety as possible, to see if the connection is really universal; then, having established the universal sequence, we come to close quarters with it in a single critical instance, varying the conditions singly until we run down the one without which the effect cannot take place.

No neater and more illuminating example of this relation between the two methods and the successful working of them can be found than that in the article by General Steinberg, "Yellow Fever and Mosquitoes" (p. 251). In that case first Dr. Carlos Finlay of Havana, and then Dr. Sternberg himself, had become convinced by comparing many cases of yellow fever that there was some intermediate host for the bacillus that caused the disease. This conclusion they reached through the method of agreement. Dr. Finlay's experiments by the method of difference had failed, however, indisputably to establish the cause, since he did not see that it was necessary to allow the bacillus at least twelve days for incubation in the body of the mosquito. The final and definitive proof, which came through the splendid self-devotion of the surgeons in charge of the experiment and of certain enlisted men who volunteered to be made the subject of the experiment, was by the method of difference. These brave men allowed themselves to be exposed to mosquitoes which had already bitten patients suffering from the fever, and they promptly came down with the disease; one of them, Dr. Lazear, gave his life for his devotion to the cause of his fellow men. Then other men were exposed in a mosquito-proof room to clothes and other articles brought directly from yellow-fever patients, and showed no ill effects. Thus it was absolutely proved, though the bacillus itself had not been found, that yellow fever is carried by mosquitoes, and is not carried by ordinary contagion.

The unsuccessful experiments of Dr. Finlay and the later success of Major Reed show how science advances by refinement of analysis in the use of the method. The hypothesis on which the former worked was that all mosquitoes who had bitten a yellow-fever patient can carry the disease. Dr. Reed and his associates analyzed the phenomenon more closely and tried their experiments on the hypothesis that only mosquitoes who have lived twelve days after biting the patient are capable of passing on the disease. This refinement of analysis and observation is the chief mode of advance in the sciences which depend on experiment.

Scientific arguments, therefore, make constant use of both methods. Medical research frequently begins with the gathering of statistics from reported cases, and the theory or theories suggested by the method of agreement working on these facts leads to the application of the method of difference through some series of critical experiments. In general the conclusions of science where experiment cannot be used depend on the method of agreement, especially in the larger theories in biology and geology, where the lapse of unnumbered centuries is necessary to bring about changes. In physics, in chemistry, in medicine, on the other hand, critical experiments are generally possible, and so progress is by the method of difference. In such subjects as political science and government, where experiment is out of the question, one must depend chiefly on the method of agreement, except in such cases as will be mentioned below where a change in policy has the same effect as an experiment. Here, however, one must not forget that in all matters human the incalculable clement of human nature enters to complicate all results, and that emotion and feeling are always irrational.

It is by the same processes that we get most of our explanations of the world as we go through it, and most of the facts on which we base judgment and action. When the same sort of thing happens in a number of fairly different cases, we begin to suspect that there is a reason; and if we are going to make an argument on the subject, we take note of the cases and try in some way to arrange and tabulate them. The supporters of a protective tariff collect instances of prosperity under such a tariff, the supporters of free trade cases of prosperity under free trade, the believers in the classical education cases of men trained in that way who have attained to eminence, believers in the elective system cases of men who are the products of that system who have attained equal eminence. In most cases such collection of instances does not carry you far toward a coercive argument; the cases are too complex for you to assert that any one factor is the cause of the result.

In another kind of case you can come a little nearer. In an argument for the establishment of a commission form of government in a given city or town there are now enough cases of this type of government in practice to make possible a good argument by the method of agreement; the places are scattered over the country, north and south, east and west, and range greatly in size and environments; and all of them so far (1911) report improvement in efficiency and honesty of government. Accordingly it is a fair presumption that the improvement is due to the introduction of the new form of government, since in all other respects the places which have tried it have little in common.

A more important result of the inquiry is to lead us on to an application of the method of difference. Starting with this strong probability that the improvement is due to the new form of government, we can go a step further and examine a single case, in order to establish more clearly the sequence of events which we call a cause. In the case of any given town which has adopted the commission government the material for the application of the method of difference is ready to our hands, if nothing else has been changed in the town but the form of government. The inhabitants and the voters are the same, the physical conditions are the same. If now we seek for the cause of an admitted improvement in the administration of the city affairs, we are driven to ascribe it to the only factor in the case which has been changed, and this is the form of government. Such an argument, if supported by figures and specific facts, is obviously strong.

The same kind of argument is constantly used in the discussion of prohibition and local option as a means of reducing the amount of liquor consumed in a community, for the frequent changes both in states and in smaller communities provide material for the application of the same method of difference. Here, however, the factors are more complex, on account of differences in the character of the population in different places, and their inherited habits as concerns the use of wine, beer, and other liquors.

40. Faulty Generalization. Both generalization through the method of agreement, and the assignment of causes through the method of difference, however, have their dangers, like all forms of reasoning. A discussion of these dangers will throw light on the processes themselves.

The chief danger when you reason through the method of agreement is of jumping to a conclusion too soon, and before you have collected enough cases for a safe conclusion. This is to commit the fallacy known as hasty generalization. It is the error committed by the dogmatic sort of globetrotter, who after six weeks spent in Swiss-managed hotels in Italy will supply you with a full set of opinions on the government, morals, and customs of the country. In a less crass form it affects the judgment of most Englishmen who write books about this country, for they come over with letters of introduction to New York, Boston, Chicago, and San Francisco, and then generalize about the rest of the country and its population.

We are all in danger from the fallacy, however, for it is a necessary law of the mind that we shall begin to make opinions and judgments on a subject as soon as we become acquainted with it. The only safeguards are, in the first place, to keep these preliminary judgments tentative and fluid, and in the second, to keep them to one's self until there is some need of expressing them. The path to wisdom in action is through open-mindedness and caution.

When one has to refute an argument in which there is faulty generalization, it is often easy to point out that its author had no sufficient time or chance to make observations, or to point out that the instances on which he relied are not fair examples of their class. In practice the strength of an argument in which this error is to be found lies largely in the positiveness with which it is pronounced; for it is human nature to accept opinions which have an outward appearance of certainty.

A not uncommon form of faulty generalization is to base an argument on a mere enumeration of similar cases. This is a poor foundation for an argument, especially for a probability in the future, unless the enumeration approaches an exhaustive list of all possible cases. To have reasoned a few years ago that because Yale had beaten Harvard at rowing almost every year for fifteen years it had a permanent superiority in the strength and skill of its oarsmen would have been dangerous, for when the years before the given period were looked up they would have shown results the other way. And an enumeration may run through a very long period of time, and still in the end be upset.

To an inhabitant of Central Africa fifty years ago, no fact probably appeared to rest on more uniform experience than this, that all human beings are black. To Europeans not many years ago, the proposition, 'All swans are white,' appeared an equally unequivocal instance of uniformity in the course of nature. Further experience has proved to both that they were mistaken; but they had to wait fifty centuries for this experience. During that long time, mankind believed in an uniformity of the course of nature where no such uniformity really existed.[37]

Unless you have so wide and complete a view of your subject that you can practically insure your enumeration as exhaustive, it is not safe to reason that because a thing has always happened so in the past, it will always happen so in the future. The notorious difficulty of proving a negative goes back to this principle.

So closely like hasty generalization that it cannot be clearly separated from it is faulty reasoning that arises from neglecting exceptions to a general principle. All our generalizations, except those that are so near truisms as to be barren of interest, are more or less rough and ready, and the process of refining them is a process of finding exceptions and restating the principle so that it will meet the case of the exceptions.

Darwin is said to have had "the power of never letting exceptions pass unnoticed. Every one notices a fact as an exception when it is striking or frequent, but he had a special instinct for arresting an exception."[38] It was this instinct which made him so cautious and therefore so sure in the statement of his hypotheses: after the idea of natural selection as an explanation of the origin of the species of the natural world had occurred to him, he spent twenty years collecting further facts and verifying observations to test the theory before he gave it to the world. A generalization that the republican form of government produces greater peace and prosperity than the monarchical would neglect the obvious exceptions in the Central American republics; and to make it at all tenable the generalization would have to have some such proviso as, "among peoples of Germanic race." Even then the exceptions would be more numerous than the cases which would fall within the rule.[39] One must cultivate respect for facts in making theories: a theory should always be held so tentatively that any new or unnoticed facts can have their due influence in altering it.

Of the errors in reasoning about a cause none is more common than that known by the older logic as _post hoc, ergo propter hoc_ (after this, therefore on account of it), or more briefly, the _post hoc_ fallacy. All of us who have a pet remedy for a cold probably commit this fallacy two times out of three when we declare that our quinine or rhinitis or camphor pill has cured us; for as a wise old doctor of two generations ago declared, and as the new doctrines of medical research are making clear, in nine cases out of ten nature cures.

Of the same character are the common superstitions of daily life, for example, that if thirteen sit at table together one will die within the year, or that crossing a funeral procession brings misfortune. Where such superstitions are more than playfully held, they are gross cases of calling that a cause which has no relation to the event. Here is another example, from a letter to _The Nation:_[40]

In the last volume of the Shakespeare controversy, the argument presented "To the Reader" seems fairly to be summarized as follows: The plays are recognized as wonderful; scholars are amazed at the knowledge of the classes in them, lawyers at the law, travelers at the minute accuracy of the descriptions of foreign cities; they show a keen critic of court etiquette and French soldiery; the only possible man of the time with this encyclopedic outlook was Francis Bacon. Both in the original and in the summary there seems a _casual_ connection implied, namely, that the plays are wonderful because of the knowledge, and because of the knowledge Bacon is the author. But, stated thus baldly, the fallacy is obvious. It is not because the author "had by study obtained nearly all the learning that could be gained from books" that the Elizabethans went to see the plays, or that we to-day read them; but it is because there is to be found in them wonderful characterization expressed dramatically, namely, before an audience. And this audience is what the scholars seem to forget. For by it is the dramatist limited, since profundity of thought or skill in allusion is good or bad, artistically, exactly in proportion as the thought is comprehended or the allusion understood.

Sometimes this fallacy is caused by assuming that because a certain result followed an event in the only case known, therefore there was a causal connection. In a hearing before a committee of the Massachusetts legislature on a bill to establish closer relations between Boston and its suburbs, the question was asked of a witness whether he believed that in the case of London "the London police would have been as efficient as they are now if there had been no annexation" of the surrounding towns; he very properly replied: "That's a hard question to answer, because we have only the existing side to look at. We don't know what it would have been as separate communities." Wherever multiple causes are possible for a phenomenon it is unsafe to argue from a single case.

Another form of error in reasoning to a cause is to assume that a fact is simple, when it is really complex, as in the following example:

I do not think I am overstepping the bounds when I say that the headship of no corporation, or state, or even the headship of the United States, requires greater general ability, force of character, or knowledge of administration than the head of administration of a great city like New York or Berlin. The latter we know to be well administered, the former--well, let us say, less so. The whole difference is in the systems. Apply the Berlin system to New York, and you will get Berlin results.

Here the writer wholly ignores all sorts of active causes for this difference: Berlin has a tolerably homogeneous population, New York the most heterogeneous in the world; Germans by nature respect law and authority, and hanker for centralization; Americans make and break laws light-heartedly, and are restive under authority; and one might easily go further.

Arguments that national prosperity has followed a higher or a lower tariff are especially apt to be vitiated by this error. It is not that the tariff has no relation to the prosperity, but that there are other causes intermingled with it which may have had more immediate effect. A bad grain crop or a season of reckless speculation may obliterate all the traceable causes of a change in the tariff. Arguments from motive, too, are apt to fall into this error. It is notorious that human motives are mixed. If you argue that a whole class of business organizations are evil because they have been formed solely for the purpose of making inordinate and oppressive profits, you leave out of sight a motive which is strong among American business men--the interest in seeing a great business more efficiently managed, and the desire to exercise power beneficently; and your argument suffers from its illegitimate assumption of a simple cause. So in the same way if you are arguing for or against the advantages of the elective system in a school or a college, or of a classical education, or of athletics, it would be folly to assume that any one cause or effect covered the whole case. Whenever in an argument you are trying to establish any such large and complex fact, you must be wary lest you thus assume a single cause where in reality there are a legion of causes.

41. Deductive Logic--the Syllogism. Deductive logic, as we have seen, deals with reasoning which passes from general principles to individual cases. Its typical form is the syllogism, in which we pass from two propositions which are given to a third, the conclusion. Of the two former one is a general principle, the other an assertion of a particular case. The classic example of the syllogism, which started with Aristotle and has grown hoary with repetition, and so venerable that it is one of the commonplaces of educated speech, runs as follows: _All men are mortal, Socrates is a man, Therefore Socrates is mortal_. Here there is the general principle, _All men are mortal_, and the assertion about the particular case, _Socrates is a man_. The two have one term in common, _men_ (or more strictly, the class Man), which is known as the middle term, through which we reach the conclusion that the characteristic of mortality in which all men are similar is true also of Socrates, by virtue of his being a man. Of the other terms, _mortal_, which is the more inclusive, is known as the major term, and _Socrates_, the less inclusive, as the minor term. The first two propositions are the premises, that which contains the major term being known as the major premise, and the other as the minor premise.

The validity of the syllogism lies, as I have said, in the assertion of a general principle, and the bringing of the particular case in hand under that principle: if the principle is granted as incontrovertible, and the special case as really coming under it, the conclusion is inevitable.

On the syllogism in its various forms deductive logic has built up an imposing structure of rules and conclusions. In practice the value of the syllogism is largely indirect. The trouble with it in itself as a mode of progress in reasoning is twofold: in the first place there are very few general principles which, if you are cautious, you will accept without reservations; and in the second place the crucial question in another set of cases is whether the given case really falls under the general principle. The syllogism, _All great statesmen are farsighted, Daniel Webster was a great statesman, Therefore Daniel Webster was farsighted_, sounds simple; but two generations have disagreed on the question whether Webster was a great statesman; and both _great statesman_ and _farsighted_ are such vague and inclusive terms that one would either accept a general principle of which they are terms as a harmless truism, or else balk at being asked to grant a proposition which might have unexpected meanings thrust into it. This double difficulty pursues the syllogism as a device for forwarding knowledge: either it sets forth a truth so large and vague that you cannot say whether you accept it for all cases or not, or else the disagreement comes on one of the premises, and unless both the premises are granted, strictly syllogistic reasoning does not get under way.

Nevertheless, the syllogism has great practical value for the reasoning and arguments of everyday life: in the first place it affords a means of expanding and scrutinizing the condensed forms of reasoning which are so common and so useful; and in the second place it can be used to sum up and state the results of a course of reasoning in incontrovertible form. I shall examine and illustrate both these uses of the syllogism; but first I shall give certain rules which govern all sound reasoning through syllogisms. They were invented by Aristotle, the great Greek philosopher.

42. The Rules of the Syllogism. (A term is said to be distributed, or taken universally, when the proposition of which it is a part makes a statement about all the objects included in the term. In the proposition _All men are mortal_, the term _men_ is obviously distributed, but _mortals_ is not; for no assertion is made about all mortals but only about those that are included under all men. In the proposition _No hens are intelligent_, both terms are distributed; for the assertion covers all hens, and also the whole class of intelligent beings, since it is asserted of the class as a whole that it contains no hens.)

I. A syllogism must contain three terms, and not more than three terms.

This rule is to be understood as guarding against ambiguity, especially in the middle term; if the middle term, or either of the others, can be understood in two ways, the syllogism will not hold water.

II. A syllogism must consist of three and only three propositions. The reasons for this rule are sufficiently obvious.

III. The middle term of the syllogism must be distributed at least once in the premises.

If it were not thus distributed or taken universally, the two premises might refer to separate parts of the middle term, and so there would be no meeting ground on which to form the conclusion. In the syllogism, All good athletes lend a clean life, These men lead a clean life, Therefore these men are good athletes, the fallacy lies in the fact that in neither premise is any assertion made about all men who lead a clean life. This fallacy, which is not uncommon in practice where the terms are complicated, is known as the fallacy of the undistributed middle.

IV. No term must be distributed in the conclusion unless it was distributed in at least one of the premises.

In other words, if you have premises which deal with part of a class only, you cannot reach a conclusion about the whole class. In the syllogism, All newspaper editors know how to write, All newspaper editors are paid, Therefore all men who know how to write are paid, the fallacy is obvious. But in the following, _All bitter partisans are dangerous citizens, This man is not a bitter partisan, Therefore this man is not a dangerous citizen_, one may have to scrutinize the reasoning a little to see that the fallacy lies in the fact that _dangerous citizen_ is taken universally in the conclusion, since a proposition with a negative predicate makes an assertion about the whole of its predicate, but that it is not taken universally in the premise in which it occurs. A fallacy which thus arises from not noticing that a negative predicate distributes its term is apt to be insidious.

V. No conclusion can be drawn from two negative premises.

In other words, if both the major term and the minor term lie outside the middle term, the syllogism gives us no means of knowing what their relation is to each other. The following example will make the reason clear: _No amateur athlete has a salary for playing, John Gorman is not an amateur athlete, Therefore John Gorman has a salary for playing_.

VI. If one of the premises is negative, the conclusion must be negative.

If of the major and minor premise one is negative, then either the major or the minor term does not agree with the middle term, and the other does; therefore the major and minor term cannot agree with each other.