THE FOURTH FIGURE

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were the products of genius." It will be seen that the minor premise, "All works of genius, etc.," will give a valid conclusion, but that none of the others will. (2) If the major premise be affirmative and particular, the minor premise must be universal and affirmative. With the minor premise "No products of genius are inimitable," no conclusion can be drawn; since only some great poems have been included in works of genius, it may well be that some inimitable things may be found among those not so included. (3) The major premise may be negative. "No great statesmen are selfish politicians; some (or all) selfish politicians amass great fortunes; therefore, some persons who amass great fortunes are not great statesmen." Some such persons might be great statesmen, so far as our premises are concerned; hence we have no right to conclude that no persons who amassed great fortunes were great statesmen.

EXERCISES

State the Figure and point out the errors in reasoning in the following cyllogisms:

(1) All wisdom is desirable, but a knowledge of slang is not wisdom, and is, therefore, not desirable.

(2) Logic and mathematics furnish good mental training, and consequently the latter may be regarded as a branch of the former.

(3) Some athletes are susceptible to pneumonia, and as all these men are athletes some of them must be susceptible to pneumonia.

(4) Some industrious people are also bright, for there are both bright and industrious students in that group.

(5) Some statues are very lifelike, and no lifelike things are contrary to the laws of nature; hence, nothing contrary to the laws of nature is a statue.

(6) Some gymnastic exercises are good for increasing strength, but swimming is not, and hence is not a gymnastic exercise.

(7) All Democrats voted against the bill, and as most of our Congressmen are Democrats, they must all have voted against the bill.

(8) All M is P;

No M is S;

..No S is P.

(9) Europeans cannot endure that climate; neither can Americans; hence, Americans may be regarded as a species of European.

(10) All ballads are interesting, and some interesting things are very old; hence, some very old things are ballads.

(11) All text-books are to be had at this store, but some novels are not to be had here, which proves that novels are not text-books.

For further examples see page 150 and page 177f.

CHAPTER IX

TRADITIONAL TREATMENT OF THE SYLLOGISM

THE traditional treatment of the syllogism is simple though very formal. The syllogism is regarded as a form of reasoning in which each of two terms is compared with a third and as a result the two terms are found to be related to each other. Each of the two is compared with the third in a premise. The result of the comparison is stated in the conclusion.

P and S are found to stand in certain relations to M. In this case and in many others we are justified in asserting a relation between S and P: S and P are found to be related through M as a medium. For this reason M is called the Middle Term and the syllogism is said to embody Mediate Reasoning.

The validity of the reasoning is tested by the application of a number of rules. These rules have to do with the relation and distribution of the several terms in the syllogism. They are as follows:

1. Every syllogism contains three propositions and only three.

2. Every syllogism has three terms and only three. (If any term is ambiguous this rule is violated.)

3. The middle term must be distributed at least

once.

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

5. From two negative premises nothing can be inferred.

6. If one premise be negative, the conclusion must be negative; if both premises be affirmative, the conclusion must be affirmative.

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

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

Let us examine these rules in the order given.

1. With more than three propositions, we should have more than a syllogism, though our reasoning might be valid.

2. The violation of rule two gives rise to the Fallacy of Four Terms. Unless two of the terms are confused this fallacy is not likely to arise. No one would try to draw a conclusion from the propositions, "Socrates was a philosopher," and "The earth revolves about the sun." But one might be tempted to draw a conclusion from the premises, "Steel is made from iron; iron is dug from the ground." Still, it would be wrong to conclude that steel is dug from the ground. The terms here are, "steel," "(something) made from iron," "iron," and "(something) dug from the ground."

3. The violation of rule three gives rise to the Fallacy of Undistributed Middle. Thus, the premises, "Some men are brave; and some men are strong," do not prove anything; nor do these: "All brave men

THE UNDISTRIBUTED MIDDLE

139

should be respected; and, all just men should be respected."

Let us represent the middle term by M, the minor term (subject of the conclusion) by S, and the major term (predicate of conclusion) by P. We are not justified by the premises in making any statement about the relation of S and P, for they may be wholly or partially identical or they may be mutually exclusive. But if the middle term were distributed we might be able to draw a conclusion. If all M is P and all S is M, we may conclude that all S is P.

SMP

Or if no M is P and all S is M, then no S is P.

SMP

An invalid syllogism is one in which it is not possible to determine fully the relation of the circles to each other, since there are conflicting possibilities. In the case of Undistributed Middle cited above, all, some, or none of S may be included in P.