E and O by Rule 1, II. We shall resort to indirect proof to show that the possible combinations of premises must give a particular conclusion. Suppose the conclusion universal, then it would be either A or E. If A, there would have to be one distribution in the premises besides that providing for the middle term, for the A conclusion distributes its minor term. If E, there would have to be two distributions in the premises besides that providing for the middle term, for the E conclusion distributes both its minor and major terms. In all, then, the premises would have to make two distributions were the conclusion A and three were it E. Now the combination of A and I as premises provides only one distribution (the subject of the A), and hence would be impossible. The other combination, A and O, would provide two distributions, but the only universal conclusion permissible would be E (A would violate Rule 1, III), which would require three distributions. Hence A in combination with any particular as premises could not give a universal conclusion. The only combination not yet tested is E and I. The conclusion could not be A, for this violates Rule 1, III. If it were E, which distributes both terms, the premises would have to provide three distributions (two for the major and minor, and one for the middle). But I and E in combination provide only two distributions. Hence we could not have a universal conclusion from I and E.

IV. (1) The reason for requiring the distribution of the middle term once at least is apparent, when one considers that if not distributed in either premise, there is

no means of instituting an intelligent comparison of the major and minor terms. The major term might allude to things lying in one part of the denotation signified by the middle term, while the minor term might allude to things lying in an entirely different part of its denotation. This condition of things would give no ground for bringing the minor and major terms into positive or negative relation in the conclusion. Violation of this rule occasions the fallacy of Undistributed Middle. The following fallacious syllogism illustrates how absurd would be a conclusion reached from premises providing no distribution of the middle term:

All eagles are birds (undistributed middle);

All finches are birds (undistributed middle);
Therefore all finches are eagles.

IV. (2) The rule prohibiting the distribution of terms in the conclusion unless they were distributed in the premises is merely an extension of the principle already explained (p. 101) as conditioning conversion. Just as in conversion the convertend is to be regarded as an empirically derived general truth, stating all the knowledge regarding the relation of the terms that experience warrants; so in the syllogism the premises are the ground, guaranteed by experience, of the judgment expressing the conclusion. This once admitted, it is immediately apparent that the terms as used in the conclusion must keep within the denotation signified by the terms as employed in the premises. Violation of this rule involving the minor term issues in the fallacy of illicit process of the minor term (illicit minor), involving

the major term, in the fallacy of illicit process of the major term (illicit major).

It should here be noted that the rules under headings II and III condition the moods, and those under IV the figures of the syllogism. The meaning of these terms will be made clear in the ensuing explanation.

REFERENCES

Creighton, An Introductory Logic, Ch. VIII.

Welton, Manual of Logic, Vol. I, Bk. IV, Ch. I and Ch. II, (§§ 109-111.

Welton, The Logical Bases of Education, Ch. IX, §§ 1-3.
Hyslop, Elements of Logic, Ch. XI.

Hibben, Logic, Deductive and Inductive, Pt. I, Ch. XV.
Sigwart, Logic, Vol. I, Pt. II, Ch. III, § 55.

REVIEW QUESTIONS

1. What is the derivation of the word syllogism? 2. How did Aristotle use it?

3. How may the deductive syllogism be defined?

4. What relation has the syllogism to the common form of reasoning?

5. Why is deductive reasoning called mediate?

6. How many terms can there be to a true reasoning process? 7. What is the conclusion when both premises state an agreement? 8. What is the conclusion when one premise states a disagreement?

9. Under what circumstances can no conclusion be reached? 10. How many propositions in the syllogism?

11. How many times is each term used in the syllogism?

12. What term appears only in the premises?

13. Where else would you look for the subject-term of the conclusion? for its predicate-term?

14. What is the major term? the minor term? the middle term? 15. Where is the minor term fixed in its position? where free to change its position? Answer the same questions about the major

term.

16. Name some common verbal signs of a conclusion? of the grounds of inference?

17. What is the formal or standard order of the syllogism? Does ordinary reasoning follow this order?

18. Upon what does the position of the middle term depend? To what does this position give rise?

19. Memorize and be prepared to state all the rules of the syllogism (just as stated in the text).

20. Be prepared to show the reason for or to prove each of the rules.

21. What occasions undistributed middle?

minor?

illicit major and

22. Which rules condition the moods? which the figures?

EXERCISES ON CHAPTER X

1. Select and name the various propositions and terms of the syllogism in the following informally stated arguments. Then reconstruct them so as to make formally correct syllogisms:

(1.) All leeches must be true worms; for all annelids are and leeches are annelids.

worms,

(2.) Caterpillars have true legs; worms do not; and so caterpillars are not worms.

(3.) Amphibians are not reptiles, since they breathe by gills in the larval stage, and reptiles do not.

2. Using dogs as the middle term, construct a formally correct syllogism proving that all hounds are flesh-eaters. Name each term and proposition as used in the syllogism.

3. With insects are invertebrates as a major premise, supply a minor premise to prove that butterflies are invertebrates.

4. With some political bosses do not seek to appropriate property without labor as a minor premise, supply a major premise that would bring the conclusion that some political bosses are not dishonest.

5. Construct a syllogism with eagles as the minor term, birds of prey as the middle term, and capable of sustained flight as the major term, leading to an A conclusion.

6. Construct a syllogism with fish as the major term, mammals as the middle term, and whales as the minor term, giving an E conclusion.

CHAPTER XI.-MOODS, FIGURES, AND RE

DUCTION

66. PERMUTATION OF PROPOSITIONS IN THE SYLLOGISM.—There are four kinds of propositions (A, E, I, and O) and three places for them in the syllogism. Ignoring for the moment the conflict of certain combinations with the rules of the syllogism, and assuming that they may combine in any way and order, these four propositions in the three places which the syllogism offers to them would present sixty-four permutations or changes of combination before there would be a repetition of form. That is, the possible permutations without repetition would be mathematically represented by four raised to the third power (43). To these permutations is given the technical name of moods. By mood, then, is meant the kind of propositions entering into the construction of the syllogism and the order in which they are used. It is purely a mechanical procedure to write out all possible permutations. To do so one has simply to begin with the A proposition as a major premise, A as a minor premise, and A as a conclusion (A A A). Giving heed to the order of the letters A E I O in the alphabet, change the conclusion four times (until all possible conclusions have been written with A A as premises). Next change the minor premise to E, writing the four conclusions with A E as premises. Continue changing the minor premise, with A still the major