40. Faulty Generalization. Both generalization through the method of agreement, and the a.s.signment 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 cra.s.s 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 cla.s.s. In practice the strength of an argument in which this error is to be found lies largely in the positiveness with which it is p.r.o.nounced; 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 pa.s.s 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 superst.i.tions 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 superst.i.tions 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 cla.s.ses 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 a.s.suming 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 Ma.s.sachusetts 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 a.s.sume 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 h.o.m.ogeneous 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 cla.s.s 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 a.s.sumption 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 cla.s.sical education, or of athletics, it would be folly to a.s.sume 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 a.s.sume 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 pa.s.ses from general principles to individual cases. Its typical form is the syllogism, in which we pa.s.s from two propositions which are given to a third, the conclusion. Of the two former one is a general principle, the other an a.s.sertion of a particular case. The cla.s.sic example of the syllogism, which started with Aristotle and has grown h.o.a.ry with repet.i.tion, 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 a.s.sertion about the particular case, _Socrates is a man_. The two have one term in common, _men_ (or more strictly, the cla.s.s 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 a.s.sertion 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 ill.u.s.trate 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 a.s.sertion 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 a.s.sertion covers all hens, and also the whole cla.s.s of intelligent beings, since it is a.s.serted of the cla.s.s 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 a.s.sertion 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 cla.s.s only, you cannot reach a conclusion about the whole cla.s.s. 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 a.s.sertion 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 const.i.tutional, 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 a.s.sume the general principle as understood. In the cases above the meaning is clear without declaring at length, _All men are mortal,_ or _All taxes on a way of doing business are const.i.tutional._

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 a.s.sertion, _"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 that _law_ is used in two senses, one the _law 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 to _All good citizens are interested in politics, These men are interested in politics, Therefore these men are good citizens,_[41] shows 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 a.s.sertion with a reason attached by such a word as "since," "for," or "because," or an a.s.sertion 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 a.n.a.lytic 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 t.i.tian 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,' ill.u.s.trates 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 Const.i.tution. 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 Const.i.tution or laws of any State can destroy a right distinctly and expressly affirmed in the Const.i.tution of the United States.

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

Therefore, nothing in the Const.i.tution 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; a.s.suming the truth of the premises, the conclusion, so far as I have capacity at all to understand it, follows inevitably.[43]