The Syllogism

( Originally Published 1912 )

THE purpose of logic is to test the validity of reasoning. The syllogism is used as a formula, consisting of three propositions, two called the premises —major and minor—which together prove the third, or the conclusion. The name syllogism literally means a reckoning all together, or the joining together in thought of two propositions. This exercise is a particularly useful one for mental discipline, and may be employed in simple forms like these :

Every man has his price.
Blank is a man.
Blank has his price.

All men are fallible.
All kings are men.
All kings are fallible.

Iron is a metal.
All metals are elements.
Iron is an element.

When the syllogism is formally stated, there must be three propositions, the conclusion coming' last. Every term in the syllogism occurs twice, and must be used precisely in the same sense. In other words, there must not be the slightest ambiguity or equivocation in the use of terms, lest the correctness of the conclusion be seriously impaired.

The forms of the syllogism may be exprest, for convenience sake, in letters or syllables, thus :

B is C. A is B.

Therefore A is C.

All A is B. All B is C.

Therefore all C is A.

All A is B.

No A is C.

Therefore no C is B

The names of the three terms corn-prizing the syllogism are illustrated by Alexander Bain, thus :

Men are fallible.
Kings are men.
Kings are fallible.

Fallible is the major term.
Men is the middle term.
Kings is the minor term.

In dealing, therefore, with an uncertain or complex argument, Bain says :

1. Ascertain what is the conclusion, or the point to be proved. State this distinctly in a proposition so as to distinguish the minor term of the syllogism and the major term.

2. Find out the middle term of the argument. In a valid syllogism there must be a middle term, and only one; and it must be something that does not occur in the conclusion.

3. Find out some proposition connecting the middle term with the major term; also some proposition connecting the middle term with the minor term.

It is not the intention to present here an exhaustive treatment of the syllogism and its numerous forms, as an abundance of such material may readily be found in standard works of logic. The following examples are offered, however, for preliminary study and analysis. The student should examine each of these care-fully, and endeavor to point out any fallacious reasoning.

You are not what I am.
I am a man.
Therefore you are not a man.

The wise are good.
Some Ignorant people are good.
Therefore some ignorant people are wise.

A question neither affirms nor denies.
A judgment must affirm or deny.
All planets are round.
A wheel is round.
Therefore a wheel is a planet.

Whoever kills another is a murderer.
A soldier kills another.
Therefore a soldier is a murderer.

Improbable events happen daily.
What happens daily is probable.
Therefore improbable events are probable.

White is a good fellow.
Linen is white.
Therefore linen is a good fellow.

John is taller than William.
William is taller than Charles.
Therefore John is taller than Charles.

Who is the most hungry eats most.
Who eats least is most hungry.
herefore who eats least eats most.

Stone is a body.
Man is a body.
Therefore man is a stone.

Nothing is better than wisdom.
Dry bread is better than nothing.
No cat has nine lives.
One cat has one more life than no cat.
Therefore a cat has ten lives.

Every light can be extinguished.
The intellect is a light.
Therefore the intellect can be extinguished.

All A is B or C.
This A is not B.
Therefore this A is C

No A is 0.
All B is C.
Therefore no B is A.

All C is A.
Some B is C.
Therefore some B is A.

It will be seen that the syllogism simply amounts to this : When one says that all men are fallible and that A is a man, it is only necessary that the truth of these two statements be admitted in order to make one believe that A is fallible.

The student should not be over-anxious to attempt difficult and intricate problems at the beginning of this work. A certain man once dipped into the last few chapters of a new book of geometry and mensuration. Pyramids, conic sections, and the rest so confused him that he shut the book in despair. But persuaded to be-gin at the beginning with lines and angles, he found pleasure in his work and at length became one of the foremost geometers of his age.

What is most needed is a mastery of plain facts, or the logic of common sense.

But this common sense is disciplined by the study and application of the syllogism, by which one learns to draw correct inferences and conclusions from stated propositions. Logic not only recognizes the truth, but tests it. As Mill says:

If there be rules to which every mind conforms in every instance in which it judges rightly, there seems little necessity for discussing whether a person is more likely to observe those rules when he knows the rules than when he is unacquainted with them."

The student is therefore urged to study logic from a standard text-book, of which there are several, and learn the simple rules of accurate reasoning. Logic will not furnish him with knowledge, but it will teach him how best to use what he has, and whether he speak in private or in public, he will learn how to state his reasons so clearly that others can not fail to understand them.

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