Chapter 5

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, Mybrother is a good scholar(Mybrother 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;31and 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.

"The whole object of any class name is to group together (for the purpose of making general assertions) individual members which are not only alike but different; and so to give unity in spite of difference."—A. Sidgwick, The Use of Words in Reasoning, London, 1901, p. 165.]

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. "Italwaysdoes," 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 is 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.33They 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 out36that 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."38It 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.39One 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 aspost hoc, ergo propter hoc(after this, therefore on account of it), or more briefly, thepost hocfallacy. 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 toThe 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 acasualconnection 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, andSocrates, 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 bothgreat statesmanandfarsightedare 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 propositionAll men are mortal, the termmenis obviously distributed, butmortalsis not; for no assertion is made about all mortals but only about those that are included under all men. In the propositionNo 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.

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 thatdangerous citizenis 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.

43. The Syllogism in Practical Use.The practical value of the syllogism and its rules comes in the first place, as I have said, when we expand a condensed form of reasoning into its full grounds in the form of a syllogism. Our reasoned judgments ordinarily take the shortened form,Socrates is mortal, because he is a man; The Corporation Tax Bill is constitutional, because it is a tax on a way of doing business.In each of these cases we are reasoning from a general principle, which is previously established, and from a particular way of conceiving the special fact before us, but we assume the general principle as understood. In the cases above the meaning is clear without declaring at length,All men are mortal,orAll taxes on a way of doing business are constitutional.

At any time, however, when you find a piece of reasoning in this condensed form, whether your own or some one else's, which seems to you suspicious, if you expand it into a full syllogism you will have all its parts laid bare for scrutiny. Take, for example, the assertion,"Robinson Crusoe" must be a true story, for everything in it is so minutely described: if you expand it into the full syllogism,All books in which the description is minute are true, "Robinson Crusoe" is a book in which the description is minute, Therefore "Robinson Crusoe" is true, you would at once stick at the major premise. So where you suspect an ambiguity in the use of terms, you can bring it to the surface, if it is there, by the same sort of expansion. In the argument,Bachelors should be punished, because they break a law of nature, the ambiguity becomes obvious when you expand:All law breakers should be punished, Bachelors break a law of nature, Therefore bachelors should be punished; at once you see thatlawis used in two senses, one thelaw of the land, the other the statement of a uniformity in nature. In the argument,These men are good citizens, for they take an interest in politics, the expansion toAll good citizens are interested in politics, These men are interested in politics, Therefore these men are good citizens,41shows that the reasoning contains a breach of the third rule of the syllogism (see p. 148) and is therefore a case of the fallacy of the undistributed middle.

Whenever you make or find an assertion with a reason attached by such a word as "since," "for," or "because," or an assertion with a consequence attached by a word like "therefore," "hence," or "accordingly," you have a case of this condensed reasoning, which, theoretically at any rate, you can expand into a full syllogism, and so go over the reasoning link by link.

Sometimes, however, the expansion is far from easy, for in many of the practical exigencies of everyday life our judgments are intuitive, and not reasoned. In such judgments we jump to a conclusion by an inarticulate, unreasoned feeling of what is true or expedient, and the grounds of the feeling may be so shadowy and complex that they can never be adequately displayed.

"Over immense departments of our thought we are still, all of us, in the savage state. Similarity operates in us, but abstraction has not taken place. We know what the present case is like, we know what it reminds us of, we have an intuition of the right course to take, if it be a practical matter. But analytic thought has made no tracks, and we cannot justify ourselves to others. In ethical, psychological, and aesthetic matters, to give a clear reason for one's judgment is universally recognized as a mark of rare genius. The helplessness of uneducated people to account for their likes and dislikes is often ludicrous. Ask the first Irish girl why she likes this country better or worse than her home, and see how much she can tell you. But if you ask your most educated friend why he prefers Titian to Paul Veronese, you will hardly get more of a reply; and you will probably get absolutely none if you inquire why Beethoven reminds him of Michael Angelo, or how it comes that a bare figure with unduly flexed joints, by the latter, can so suggest the moral tragedy of life.... The well-known story of the old judge advising the new one never to give reasons for his decisions, 'the decisions will probably be right, the reasons will surely be wrong,' illustrates this. The doctor will feel that the patient is doomed, the dentist will have a premonition that the tooth will break, though neither can articulate a reason for his foreboding. The reason lies embedded, but not yet laid bare, in all the previous cases dimly suggested by the actual one, all calling up the same conclusion, which the adept thus finds himself swept on to, he knows not how or why."42

The small boy who said that he could not keep step because he had a cold in his head was relying on a sound general truth,Colds in the head make one stupid, for his major premise, but his condition prevented his disentangling it; and all of us every day use minor premises for which we should be incapable of stating the major.

A second practical use of the syllogism is to set forth a chain of reasoning in incontrovertible form. If you have a general principle which is granted, and have established the fact that your case certainly falls under it, you can make an effective summing up by throwing the reasoning into the form of a syllogism.

Conversely, you can use a syllogism to bring out some essential part of the reasoning of an opponent which you know will not commend itself to the audience, as did Lincoln in his debate with Douglas at Galesburg. Douglas had defended the Dred Scott decision of the United States Supreme Court, which decided that the right of property in a slave is affirmed by the United States Constitution. Lincoln wished to make the consequences of this doctrine as glaringly evident as possible. He did so as follows:

I think it follows, and I submit to the consideration of men capable of arguing, whether as I state it, in syllogistic form, the argument has any fault in it.Nothing in the Constitution or laws of any State can destroy a right distinctly and expressly affirmed in the Constitution of the United States.The right of property in a slave is distinctly and expressly affirmed in the Constitution of the United States.Therefore, nothing in the Constitution or laws of any State can destroy the right of property in a slave.I believe that no fault can be pointed out in that argument; assuming the truth of the premises, the conclusion, so far as I have capacity at all to understand it, follows inevitably.43

I think it follows, and I submit to the consideration of men capable of arguing, whether as I state it, in syllogistic form, the argument has any fault in it.

Nothing in the Constitution or laws of any State can destroy a right distinctly and expressly affirmed in the Constitution of the United States.

The right of property in a slave is distinctly and expressly affirmed in the Constitution of the United States.

Therefore, nothing in the Constitution or laws of any State can destroy the right of property in a slave.

I believe that no fault can be pointed out in that argument; assuming the truth of the premises, the conclusion, so far as I have capacity at all to understand it, follows inevitably.43

Lincoln knew that this doctrine that no state could interfere with slavery would be intolerable to the people of Illinois, before whom he was carrying on his campaign; and this syllogism made clear to them the consequences of the decision of the Supreme Court.

Or you can use a syllogism to make obvious a flaw in the reasoning of your opponent, as in the following example:

In view of the history of commission government in this country so far as it has been made, the burden of proof rests with those who attempt to show that a government which has been so successful in cities of moderate size will not be successful in our largest cities. The syllogism they are required to prove runs briefly thus:Commission government is acknowledged to have been successful in cities as large as one hundred and thirty thousand inhabitants, butIt has not been tried in cities containing more than one hundred and thirty thousand inhabitants;Therefore, it will not be successful in cities of four hundred thousand or larger, which is areductio ad absurdum.The folly of the attempt is shown by the very statement of the conclusion.44

Commission government is acknowledged to have been successful in cities as large as one hundred and thirty thousand inhabitants, but

It has not been tried in cities containing more than one hundred and thirty thousand inhabitants;

Therefore, it will not be successful in cities of four hundred thousand or larger, which is areductio ad absurdum.

The folly of the attempt is shown by the very statement of the conclusion.44

44. The Dilemma.One special form of the syllogism is at times so strong an argument that it deserves special mention here, namely, the dilemma. This is a syllogism in which the major premise consists of two or more hypothetical propositions (that is, propositions with an "if" clause) and the minor of a disjunctive proposition (a proposition with two or more clauses connected by "or").

In the course of the Lincoln-Douglas debate a question was put by Lincoln to Douglas, as follows: "Can the people of a United States territory in any lawful way, against the wish of any citizens of the United States, exclude slavery from its limits, prior to the formation of a state constitution?" The question may be viewed as the source of a dilemma, both in the practical and in the syllogistic sense of the term.

In fact it involved a situation which, syllogistically, comprised more than one dilemma. They may be stated as follows:

I. If Douglas answers yes, he offends the South, and if he answers no, he offends the North;But he must answer either yes or no;Therefore he will offend either the South or the North.II. If Douglas offends the South, he loses the nomination for the Presidency in the next convention; and if he offends the North, he loses the election to the United States Senatorship (and his chances for the Presidency);But he must offend either the South or the North;Therefore he loses either the Presidency or the Senatorship.Or, III. If Douglas offends the South, he cannot become President; and if he offends the North, he cannot become President;But he must offend either the South or the North;Therefore he cannot become President.45

I. If Douglas answers yes, he offends the South, and if he answers no, he offends the North;

But he must answer either yes or no;Therefore he will offend either the South or the North.

But he must answer either yes or no;

Therefore he will offend either the South or the North.

II. If Douglas offends the South, he loses the nomination for the Presidency in the next convention; and if he offends the North, he loses the election to the United States Senatorship (and his chances for the Presidency);

But he must offend either the South or the North;Therefore he loses either the Presidency or the Senatorship.

But he must offend either the South or the North;

Therefore he loses either the Presidency or the Senatorship.

Or, III. If Douglas offends the South, he cannot become President; and if he offends the North, he cannot become President;

But he must offend either the South or the North;Therefore he cannot become President.45

But he must offend either the South or the North;

Therefore he cannot become President.45

The dilemma, if it leaves no hole for the other side to creep through, is an extremely effective argument in politics and in competitive debate. If you can thus get your adversary between the devil and the deep sea on a point that in the eyes of your audience is interesting and critical, you have crippled his case. But if the point is not momentous, though your audience may find the dilemma amusing, you run the risk of the reproach of "smartness" if you crow very loudly over it.

On the other hand, a dilemma that is not exhaustive will hold no one. Many of the arguments against the imposition of a federal tax on corporations assumed that if the tax were imposed it would soon be made unreasonable in amount. Most arguments that the other side will abuse any power that is given to them may be regarded as falling into the class of incomplete dilemma. A speaker who uses a leaky dilemma must have great confidence in the unintelligence of his audience, but it is surprising to see how often such dilemmas occur in political debates.

45. Reasoning from Circumstantial Evidence.The third type of reasoning from similarity named on page 120 is reasoning from circumstantial evidence. The term is familiar to every one from murder trials and detective stories. Webster's argument in the White Murder Case, from which I print a short extract on page 157, is a famous example of an argument on circumstantial evidence; and in fiction Sir Conan Doyle has created for our delectation many notable and ingenious cases of it. But reasoning from circumstantial evidence is far from being confined to criminal cases and fiction; as Huxley points out (see p. 241), it is also the basis of some of the broadest and most illuminating generalizations of science; and the example below from Macaulay is only one of innumerable cases of its use in history.

Reasoning from circumstantial evidence differs from reasoning from analogy or generalization in that it rests on similarities reaching out in a number of separate directions, all of which, however, converge on the case in hand. This convergence is pointed out by Macaulay in the following admirable little argument on the authorship of theJunius Letters, which were a series of pseudonymous and malignant attacks on the British government about 1770:

Was he [Francis] the author of the Letters of Junius? Our own firm belief is that he was. The evidence is, we think, such as would support a verdict in a civil, nay, in a criminal proceeding. The handwriting of Junius is the very peculiar handwriting of Francis, slightly disguised. As to the position, pursuits, and connections of Junius, the following are the most important facts which can be considered as clearly proved: first, that he was acquainted with the technical forms of the secretary of state's office; secondly, that he was intimately acquainted with the business of the war office; thirdly, that he, during the year 1770, attended debates in the House of Lords, and look notes of speeches, particularly of the speeches of Lord Chatham; fourthly, that he bitterly resented the appointment of Mr. Chamier to the place of deputy secretary-at-war; fifthly, that he was bound by some strong tie to the first Lord Holland. Now, Francis passed some years in the secretary of state's office. He was subsequently chief clerk of the war office. He repeatedly mentioned that he had himself, in 1770, heard speeches of Lord Chatham; and some of these speeches were actually printed from his notes. He resigned his clerkship at the war office from resentment at the appointment of Mr. Chamier. It was by Lord Holland that he was first introduced into the public service. Now, here are five marks all of which ought to be found in Junius. They are all five found in Francis. We do not believe that more than two of them can be found in any other person whatever. If this agreement does not settle the question, there is an end of all reasoning on circumstantial evidence.46

Here the five points or marks of similarity between the writer of the letters and Philip Francis are of such diversity that it would be an extraordinary coincidence if there had happened to be two men whom they would fit: where so many lines converge so closely at a single point it would hardly be possible for them to meet on more than one person.

The following brief extract from Webster's argument in the White Murder Case shows the same sort of convergence of similarities: each circumstance in itself is hardly strong enough to furnish ground for an argument on analogy, but taken all together they point irresistibly in one direction, namely, to the fact of a conspiracy.

Let me ask your attention, then, in the first place, to those appearances, on the morning after the murder, which have a tendency to show that it was done in pursuance of a preconcerted plan of operation. What are they? A man was found murdered in his bed. No stranger had done the deed, no one unacquainted with the house had done it. It was apparent that somebody within had opened, and that somebody without had entered. There had obviously and certainly been concert and cooperation. The inmates of the house were not alarmed when the murder was perpetrated. The assassin had entered without any riot or any violence. He had found the way prepared before him. The house had been previously opened. The window was unbarred from within, and its fastening unscrewed. There was a lock on the door of the chamber in which Mr. White slept, but the key was gone. It had been taken away and secreted. The footsteps of the murderer were visible, outdoors, tending toward the window. The plank by which he entered the window still remained. The road he pursued had thus been prepared for him. The victim was slain, and the murderer had escaped. Everything indicated that somebody within had cooperated with somebody without. Everything proclaimed that some of the inmates, or somebody having access to the house, had had a hand in the murder. On the face of the circumstances, it was apparent, therefore, that this was a premeditated, concerted murder; that there had been a conspiracy to commit it.47

The strength of reasoning from circumstantial evidence lies in the number and the diversity of the points of similarity to the point in hand. If there are few of them, the possibility of coincidence increases, as it also does when the points of similarity come from the same source or are of the same nature. This possibility of coincidence is a good rough test of the value of reasoning from circumstantial evidence: where the theory of a coincidence would stretch all probabilities one may safely leave it out of account.

In practice the argument from circumstantial evidence is more frequent in the experience of lawyers than in that of other men; but sooner or later everybody has to pass on such reasoning, for wherever direct evidence is out of the question it may be necessary to piece the situation together by circumstantial evidence. There is some prejudice against such evidence, springing from reported cases of miscarriage of justice in convictions based on it. Such cases, however, are very rare in reality, and probably do not equal in number the cases in which mistaken or false direct testimony has caused injustice.

46. Some Pitfalls of Reasoning—Ambiguity.I have already spoken of some of the dangers to which reasoning is subject—false analogy, faulty generalization of various kinds, and various sins against the rules of the syllogism. There are still a few general dangers to speak about. It should be noted that the various kinds of fallacies run into each other, and not infrequently a given piece of bad reasoning can be described under more than one of them.

Of all the sources of faulty and misleading reasoning, ambiguity is the most fruitful and the most inclusive.

It springs from the facts that words, except those which are almost technically specific, are constantly used in more than one sense, and that a great many of the words which we use in everyday life are essentially vague in meaning. Such common words as "liberty," "right," "gentleman," "better," "classic," "honor," and innumerable others each need a treatise for any thorough definition; and then the definition, if complete, would be largely a tabulation of perfectly proper senses in which the words can be used, or a list of the ways in which different people have used them. Besides this notorious vagueness of many common words, a good many words, as I have already shown (p. 54), have two or more distinct and definable meanings.

Strictly speaking, the ambiguity does not inhere in the word itself, but rather in its use in an assertion, since ambiguity can arise only when we are making an assertion. It has been defined as "the neglect of distinctions in the meaning of terms, when these distinctions are important for the given occasion."48Suppose, for example, you are arguing against a certain improvement in a college dormitory, on the ground that it makes for luxury: clearly "luxury" is a word that may mean one thing to you, and another to half of your audience. By itself it is an indefinite word, except in its emotional implication; and its meaning varies with the people concerning whom it is used, since what would be luxury for a boy brought up on a farm would be bare comfort to the son of wealthy parents in the city. Indeed the advances of plumbing in the last generation have completely changed the relative meanings of the words "comfort" and "luxury" so far as they concern bathrooms and bathtubs. In the case of such a word, then, the weight of the definition above falls on the last clause, "when these distinctions are important for the given occasion"; here is a case where the occasion on which the word "luxury" is used determines nearly the whole of its meaning. In practice, if you have a suspicion that a word may be taken in another sense than that you intend, the first thing to do is to define it—to lay down as exactly as possible the cases which it is intended to cover on the present occasion, and the meaning it is to have in those cases. For good examples of this enlightened caution, see the definitions on pages 54-65, especially that from Bagchot.

A similar difficulty arises with the words which, in the somewhat slipshod use of everyday life, have come to have as it were a sliding value.

We may raise no difficulty about understanding the assertions that Brown, and Jones, and Robinson are "honest," but when we come to the case of Smith we discover a difficulty in placing him clearly on either side of the line. That difficulty is nothing less than the difficulty of knowing the meaning given to the word in this particular assertion. We might, for instance, agree to mean by Smith's "honesty" that no shady transactions could be legally proved against him, or that he is "honest according to his lights," or again that he is about as honest as the majority of his neighbors or the average of his trade or profession.49

That this is not a fanciful case can be shown by noticing how often we speak of "transparent" honesty, or of "absolute" honesty: this is notably one of the words for which we have a sliding scale of values, which vary considerably with the age and the community. "Political honesty" has a very different meaning in the England of to-day from that which it had in the eighteenth century. To get at the exact meaning of honesty, then, either for Mr. Sidgwick's Brown, Jones, Robinson, and Smith, or for Mr. Asquith and Mr. Balfour as compared with Walpole or Pitt, we need a good deal more than a dictionary definition. What has already been said (p. 65) on the use of the history of the case to get a preliminary understanding of the question which is to be argued, and the terms to be used in it, applies all through the reasoning involved in the argument. Scrutinize all the terms you use yourself, as well as those used in arguments on the other side.

I have already pointed out the ambiguity there is in the emotional implications of words; but the danger from it is so subtle and so besetting that it will be worth while to dwell on it again. There are many cases in which there is no doubt as to the denotation of the word,—the cases which it is intended to name,—but in which the two sides to a controversy use the word with a totally different effect on their own and other people's feelings. Before the Civil War pretty much the whole South had come to use the word "slavery" as implying one of the settled institutions of the country, more or less sanctified by divine ordinance; at the same time a large portion of the North had come to look on it as an abomination to the Lord. Here there was no doubt as to the denotation of the word; but in a highly important respect it was ambiguous, because it implied a totally different reaction among the people who used it. In a case where the contrast is so glaring there is little danger of confusion; but there are a good many cases where a word may have very different effects on the feelings of an audience without the fact coming very clearly to the surface. "Liberal" is to most Americans a term implying praise, so far as it goes; to Cardinal Newman it implied what were to him the irreverent and dangerous heresies of free thought, and therefore in his mouth it was a word of condemnation.50"Aesthetic" to many good people has an implication of effeminacy and of trifling which is far from praiseworthy; to artists and critics it may sum up what is most admirable in civilization. If in an argument on abolishing football as an intercollegiate sport you described a

certain game as played "with spirit and fierceness," football players would think of it as a good game, but opponents of football would hold that such a description justified them in classing the game with prize fighting. When one of the terms you use may thus stir one part of your audience in one way, and the other part in just the opposite way, you are dealing with an uncomfortable kind of ambiguity.

It is easy to get into the way of thinking that the denotation of a word—the things which it names—is the only part of its meaning that counts; but with many words the connotation—I use the word in the rhetorical rather than in the logical sense, to include its implications, associations, and general emotional coloring—has more effect on human nature. There is a good deal of difference between telling a man that his assertion is "incorrect," "untrue," or "false"; if you use the last and he is at all choleric you may bring on an explosion. In argument, where you are aiming to persuade as well as to convince, the question of the feelings of your audience and how they will be affected by the terms you use is obviously of great importance. And if you are using such terms as "gentleman," "political honesty," "socialist," "coeducation," you must not forget that such words have a definite emotional connotation, which will vary largely with the reader.

47. Begging the Question.The fallacy of "begging the question" consists of assuming as true something that the other side would not admit. It is especially insidious in the condensed arguments of which I spoke a few pages back. A common form of the fallacy consists of slipping in an epithet which quietly takes for granted one's own view of the question, or of using some expression that assumes one's own view as correct. For example, in an argument for a change in a city government, to declare that all intelligent citizens favor it would be begging the question. In an argument for the protection of crows, to begin, "Few people know how many of these useful birds are killed each year," would be to beg the question, since the argument turns on whether crows are useful or not. A gross and uncivil form of this fallacy is to use opprobrious epithets in describing persons who take the other view, as in the following sentence from an article in a magazine on the question of examinations for entrance to college:

As for interest and variety, what could destroy and taboo both more effectually than the rigid and rigorous demands of a formal set of examinations prepared, as a rule, by pedantic specialists who know practically nothing of the fundamental problems and needs of the high school.

Begging the question is often committed in the course of defining terms, as in the following passage from Cardinal Newman's "Idea of a University":

It is the fashion just now, as you very well know, to erect so-called Universities, without making any provision in them at all for Theological chairs. Institutions of this kind exist both here [Ireland] and in England. Such a procedure, though defended by writers of the generation just passed with much plausible argument and not a little wit, seems to me an intellectual absurdity; and my reason For saying so runs, with whatever abruptness, into the form of a syllogism:—A University, I should lay down, by its very name professes to teach universal knowledge; Theology is surely a branch of knowledge; how then is it possible for it to profess all branches of knowledge, and yet to exclude from the subjects of its teaching one which, to say the least, is as important and as large as any of them? I do not see that either premise of this argument is open to exception.51

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