Here the writer wholly ignores all sorts of active causes for this difference: Berlin has a tolerably homogeneous population, New York the most heterogeneous in the world; Germans by nature respect law and authority, and hanker for centralization; Americans make and break laws light-heartedly, and are restive under authority; and one might easily go further.
Arguments that national prosperity has followed a higher or a lower tariff are especially apt to be vitiated by this error. It is not that the tariff has no relation to the prosperity, but that there are other causes intermingled with it which may have had more immediate effect. A bad grain crop or a season of reckless speculation may obliterate all the traceable causes of a change in the tariff. Arguments from motive, too, are apt to fall into this error. It is notorious that human motives are mixed. If you argue that a whole class of business organizations are evil because they have been formed solely for the purpose of making inordinate and oppressive profits, you leave out of sight a motive which is strong among American business men—the interest in seeing a great business more efficiently managed, and the desire to exercise power beneficently; and your argument suffers from its illegitimate assumption of a simple cause. So in the same way if you are arguing for or against the advantages of the elective system in a school or a college, or of a classical education, or of athletics, it would be folly to assume that any one cause or effect covered the whole case. Whenever in an argument you are trying to establish any such large and complex fact, you must be wary lest you thus assume a single cause where in reality there are a legion of causes.
41. Deductive Logic—the Syllogism. Deductive logic, as we have seen, deals with reasoning which passes from general principles to individual cases. Its typical form is the syllogism, in which we pass from two propositions which are given to a third, the conclusion. Of the two former one is a general principle, the other an assertion of a particular case. The classic example of the syllogism, which started with Aristotle and has grown hoary with repetition, and so venerable that it is one of the commonplaces of educated speech, runs as follows: All men are mortal, Socrates is a man, Therefore Socrates is mortal. Here there is the general principle, All men are mortal, and the assertion about the particular case, Socrates is a man. The two have one term in common, men (or more strictly, the class Man), which is known as the middle term, through which we reach the conclusion that the characteristic of mortality in which all men are similar is true also of Socrates, by virtue of his being a man. Of the other terms, mortal, which is the more inclusive, is known as the major term, and Socrates, the less inclusive, as the minor term. The first two propositions are the premises, that which contains the major term being known as the major premise, and the other as the minor premise.
The validity of the syllogism lies, as I have said, in the assertion of a general principle, and the bringing of the particular case in hand under that principle: if the principle is granted as incontrovertible, and the special case as really coming under it, the conclusion is inevitable.
On the syllogism in its various forms deductive logic has built up an imposing structure of rules and conclusions. In practice the value of the syllogism is largely indirect. The trouble with it in itself as a mode of progress in reasoning is twofold: in the first place there are very few general principles which, if you are cautious, you will accept without reservations; and in the second place the crucial question in another set of cases is whether the given case really falls under the general principle. The syllogism, All great statesmen are farsighted, Daniel Webster was a great statesman, Therefore Daniel Webster was farsighted, sounds simple; but two generations have disagreed on the question whether Webster was a great statesman; and both great statesman and farsighted are such vague and inclusive terms that one would either accept a general principle of which they are terms as a harmless truism, or else balk at being asked to grant a proposition which might have unexpected meanings thrust into it. This double difficulty pursues the syllogism as a device for forwarding knowledge: either it sets forth a truth so large and vague that you cannot say whether you accept it for all cases or not, or else the disagreement comes on one of the premises, and unless both the premises are granted, strictly syllogistic reasoning does not get under way.
Nevertheless, the syllogism has great practical value for the reasoning and arguments of everyday life: in the first place it affords a means of expanding and scrutinizing the condensed forms of reasoning which are so common and so useful; and in the second place it can be used to sum up and state the results of a course of reasoning in incontrovertible form. I shall examine and illustrate both these uses of the syllogism; but first I shall give certain rules which govern all sound reasoning through syllogisms. They were invented by Aristotle, the great Greek philosopher.
42. The Rules of the Syllogism. (A term is said to be distributed, or taken universally, when the proposition of which it is a part makes a statement about all the objects included in the term. In the proposition All men are mortal, the term men is obviously distributed, but mortals is not; for no assertion is made about all mortals but only about those that are included under all men. In the proposition No hens are intelligent, both terms are distributed; for the assertion covers all hens, and also the whole class of intelligent beings, since it is asserted of the class as a whole that it contains no hens.)
I. A syllogism must contain three terms, and not more than three terms.
This rule is to be understood as guarding against ambiguity, especially in the middle term; if the middle term, or either of the others, can be understood in two ways, the syllogism will not hold water.
II. A syllogism must consist of three and only three propositions. The reasons for this rule are sufficiently obvious.
III. The middle term of the syllogism must be distributed at least once in the premises.