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.