malian animals are viviparous." It would follow that "whales are viviparous;" and so far as the inference is concerned it does not matter what is the meaning we attribute to the words viviparous and mammalian. In this case "mammalian animal" is the middle term.

The name Syllogism means the joining together in thought of two propositions, and is derived from the Greek words oúv, with, and λóyos, thought or reason. It is thus exactly the equivalent of the word Computation, which means thinking together (Latin con, together, puto, to think), or reckoning. In a syllogism we so unite in thought two premises, or propositions put forward, that we are enabled to draw from them or infer, by means of the middle term they contain, a third proposition called the conclusion. Syllogism may thus be defined as the act of thought by which from two given propositions we proceed to a third proposition, the truth of which necessarily follows from the truth of these given propositions. When the argument is fully expressed in language it is usual to call it concretely a syllogism.

The special rules of the syllogism are founded upon the Laws of Thought and the Canons considered in the previous Lesson. They serve to inform us exactly under what circumstances one proposition can be inferred from two other propositions, and are eight in number, as follows:

1. Every syllogism has three and only three terms. These terms are called the major term, the minor term, and the middle term.

2. Every syllogism contains three, and only three propositions.

These propositions are called the major premise, the minor premise, and the conclusion.

3. The middle term must be distributed once at least, and must not be ambiguous.

4. No term must be distributed in the conclusion which was not distributed in one of the premises.

5. From negative premises nothing can be inferred.

6. If one premise be negative, the conclusion must be negative; and vice versâ, to prove a negative conclusion one of the premises must be negative.

From the above rules may be deduced two subordinate rules, which it will nevertheless be convenient to state at once.

7. From two particular premises no conclusion can be drawn.

8. If one premise be particular, the conclusion must be particular.

All these rules are of such extreme importance that it will be desirable for the student not only to acquire a perfect comprehension of their meaning and truth, but to commit them to memory. During the remainder of this lesson we shall consider their meaning and force.

As the syllogism consists in comparing two terms by means of a middle term, there cannot of course be less than three terms, nor can there be more; for if there were four terms, say A, B, C, D, and we compared A with B and C with D, we should either have no common medium at all between A and D, or we should require a second syllogism, so as first to compare A and C with B, and then A and D with C.

The middle term may always be known by the fact that it does not occur in the conclusion. The major term is always the predicate of the conclusion, and the minor term the subject. These terms are thus called because in the universal affirmative proposition (A) the predicate is necessarily a wider or greater or major term than the subject; thus in "all men are mortals," the predicate includes all other animals as well as men, and is obviously a major term or wider term than men,

Again, the syllogism necessarily consists of a premise called the major premise, in which the major and middle terms are compared together; of a minor premise which similarly compares the minor and middle terms; and of a conclusion, which contains the major and minor terms only. In a strictly correct syllogism the major premise always stands before the minor premise, but in ordinary writing and speaking this rule is seldom observed; and that premise which contains the major term still continues to be the major premise, whatever may be its position.

The third rule is a very important one, because many fallacies arise from its neglect. By the middle term being distributed once at least, we mean (see p. 74) that the whole of it must be referred to universally in one premise, if not both. The two propositions—

All Frenchmen are Europeans,

All Russians are Europeans,

do not distribute the middle term at all, because they are both affirmative propositions, which have (p. 75) undistributed predicates. It is apparent that Frenchmen are one part of Europeans, and Russians another part, as shown in Euler's method in Fig. 6, so that

there is no real middle term. Those propositions would equally allow of Russians being or not being Frenchmen; for whether the two interior circles overlap or not they are equally within the larger circle of Europeans. Again, the two propositions

All Frenchmen are Europeans,

All Parisians are Europeans,

do not enable us to infer that all Parisians are FrenchFor though we know of course that all Parisians

men.

Fig. 7.

Europeans

Parisians

French

are included among Frenchmen, the premises would allow of their being placed anywhere within the circle of Europeans. We see in this instance that the premises and conclusion of an apparent argument may all be true and yet the argument may be fallacious.

The part of the third rule which refers to an ambiguous middle term hardly requires explanation. It has been stated (Lesson IV.) that an ambiguous term is one which has two different meanings, implying different connotations, and it is really equivalent to two different terms which happen to have the same form of spelling, so that they are readily mistaken for each other. Thus if we were to argue that because "all metals are elements and

brass is metal, therefore it is an element," we should be committing a fallacy by using the middle term metal in two different senses, in one of which it means the pure simple substances known to chemists as metals, and in the other a mixture of metals commonly called metal in the arts, but known to chemists by the name alloy. In many examples which may be found in logical books the ambiguity of the middle term is exceedingly obvious, but the reader should always be prepared to meet with cases where exceedingly subtle and difficult cases of ambiguity occur. Thus it might be argued that "what is right should be enforced by law, and that charity is right and should therefore be enforced by the law." Here it is evident that right is applied in one case to what the conscience approves, and in another case to what public opinion holds to be necessary for the good of society.

The fourth rule forbids us to distribute a term in the conclusion unless it was distributed in the premises. As the sole object of the syllogism is to prove the conclusion by the premises, it is obvious that we must not make a statement concerning anything unless that thing was mentioned in the premises, in a way warranting the statement. Thus if we were to argue that "because many nations are capable of self-government and that nations capable of self-government should not receive laws from a despotic government, therefore no nation should receive laws from a despotic government," we should be clearly exceeding the contents of our premises. The minor term, many nations, was particular in the minor premise, and must not be made universal in the conclusion. The pre

mises do not warrant a statement concerning anything but the many nations capable of self-government. The above argument would therefore be fallacious and would be technically called an illicit process of the minor term, meaning that we have improperly treated the minor term.