to any and every man. But THE PREDICATE "mortal" IS ONLY

TAKEN PARTICULARLY AND IS NOT DISTRIBUTED.

Therefore, we see that a UNIVERSAL AFFIRMATIVE DISTRIBUTES ITS SUBJECT BUT NOT ITS PREDICATE.

As a universal negative proposition take, "No sea-weed is a flowering plant." The subject "sea-weed" is distributed. If there could be found a single flowering plant which is a seaweed, then the proposition would not be true. Hence the prediIcate is also distributed.

Hence, THE UNIVERSAL NEGATIVE PROPOSITION DISTRIBUTES ITS SUBJECT AND ITS PREDICATE.

No difficulty is experienced in seeing that the particular affirmative distributes neither its subject nor its predicate, and that the

PARTICULAR NEGATIVE DISTRIBUTES ITS PREDICATE BUT NOT ITS SUBJECT.

In the absence of any knowledge to the contrary, the word "some," in the particular affirmative and particular negative, must be taken to mean "SOME AND IT MAY BE ALL."

17. The Law of Converse. Two propositions are the converse of each other when the subject of one is the predicate of the other. Thus,

"Equilateral triangles are equiangular, “(direct).

Equiangular triangles are equilateral, (converse).

It does not follow that because a proposition is true its converse will also be true. Thus, "All regular polygons are equilateral (direct); all equilateral (polygons) are regular, (converse). This last is not true. The converse of all definitions are true.

Whenever three theorems have the following relations, their

converses are true:

1. If it is known that when A> B, then x >y, and 2. If it is known that when A = B, then x = y, and 3. If it is known that when A < B, then x <y, then the converse of each of these is true.

For

1. If x>y, then A cannot equal B and A cannot be less than B without violating 2 or 3; .. A> B. (Converse of 1.) 21. If x = y, then A cannot be greater than B and A cannot be less than B without violating 1 or 3; .. A=B. (Converse of 2.)

1.

31. If x <y, then A cannot be greater than B and A cannot be equal to B without violating 1 or 2; .. A< B. (Converse of 3.)

18. The opposite of a proposition is formed by stating the negative of its hypothesis and conclusions. Thus,

If AB, then CD (Direct.)

If A is not equal B, then C is not equal D. (Opposite.)

19. If the direct proposition and its converse are true, the opposite proposition is true; and if a direct proposition and its opposite are true, the converse proposition is true. Thus,

I.

i. If AB, CD. If C = D, A = B.

(Direct.)
(Converse.)

If A is not equal to B, C is not equal to D

2.

If A=B, CD.

(Direct.)

(Converse.)

(Opposite.)

If A is not equal to B, C is not equal to D. (Opposite.)
Then, if CD, A= B.

20. Methods of Reasoning. There are two methods of reasoning, viz., the Inductive and the Deductive.

The Inductive Method is used in reaching a general truth or principle by an examination and comparison of particular facts. Thus, This apple is equal to the sum of all its parts, this piece of crayon is equal to the sum of all its parts, this orange is equal to the sum of all its parts, and so with peaches, pears, balls, pebbles, slates, knives, and chairs.

Therefore, the whole of any object is equal to the sum of all its parts, or the whole is equal to the sum of all its parts. This is inductive reasoning.

The Deductive Method is used in reaching a particular truth or principle from general truths or principles. Thus.

All animals suffer pain.

Flies are animals.

Therefore, flies suffer pain.

21. The Syllogism. When we compare propositions we reason. Deriving a third proposition from two given propositions is called syllogistic reasoning, or Deductive Reasoning. Thus,

I.

All English silver coins are coined at Tower
Hill.

2. All sixpences are coined at Tower Hill.

Therefore, All sixpences are English silver coins.

The last proposition is called the conclusion, the other two propositions are called premises, and the three together the syllogism.

Again,

From the examples given, we see that there are only three terms or classes of things reasoned about; in the first example the three terms are "All English silver coins," "Tower Hill," and "all sixpences." Of these, the class, "English silver coins," does not occur in the conclusion. It is used to enable us to compare together the other two classes of things. It is called

the middle term. (Things) "coined at Tower Hill," is called the major term for the reason that it has the larger extension, and "sixpences," the subject of the conclusion, is called the minor term of the syllogism, for the reason that it has a lesser extension than the subject of the conclusion.

The premise in which the "major term" is found is called the major premise, and the one in which the minor term is found is called the minor premise.

Hence, the middle term is always the term not found in the conclusion; the major term is the predicate of the conclusion; and the minor term is the subject of the conclusion.

Suppose that the two premises and the conclusion of the last syllogism be varied in every possible way from affirmative to negative, from universal to particular and vice versa.

Each proposition can be converted into four different propositions and each one of these four may be compounded with any one of the other two. Hence the number of changes (called moods) is 4 X 4 X 4 = 64. These moods may be still further varied, if instead of the middle term being the subject of the first and the predicate of the second, this order may be reversed, or if the middle term the subject of both, or the predicate of both. In this way we see that for each of the sixty-four moods we get four syllogisms called figures.

Of the sixty-four moods, there are altogether nineteen moods of the syllogism that are admissible.

22. Rules of the Syllogism. To find out whether an argument is valid or not, we must examine it carefully to ascertain whether it agrees with certain rules discovered by Aristotle. Modern logicians have to some extent broken away from these rules. Without going into the matter in detail we state these rules.

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

II. Every syllogism contains three and only three propositions.

III. The middle term must be distributed once at least in the premises and must not be ambiguous.

Some animals are flesh-eating.
Some animals have two stomachs.

No conclusion can be drawn.

But if we say,

Some animals are flesh-eating,

Animal

All animals consume oxygen, we

can say

Therefore, some animals consuming oxygen are flesh-eating.