The Syllogism and its Kinds

Chapter II — Reasoning Expressed

Just as the idea is expressed in the term, and the judgment in the proposition, so the reasoning process is expressed in argumentation. Argumentation (or argument) may be defined as a process of speech in which one proposition is explicitly inferred from other propositions in which it is implicitly contained.

The most perfect form of argumentation is the syllogism. This Chapter deals with the syllogism.

The Chapter treats of the nature and classification of the syllogism, the laws by which it is governed, the moods and figures in which it may be constructed, and the imperfect, but valid, forms in which the syllogism may be found.

The Chapter is therefore divided into the following Articles:

• Article 1. The Syllogism and its Kinds
• Article 2. Laws of the Syllogism
• Article 3. Figures and Moods of the Syllogism
• Article 4. Imperfect Syllogisms

Article 1. The Syllogism and its Kinds

a) The Syllogism    b) Correctness and Truth of the Syllogism    c) Kinds of Syllogisms

a) The Syllogism

The syllogism is an argument consisting of three propositions so related that when the first two are posited the third necessarily follows.

Example:

Every man is mortal
John Smith is a man
Therefore John Smith is mortal

The first two propositions of the syllogism are called the premisses. The third proposition (which is implied in the premisses) is the conclusion or consequent. The logical connection existing between the premisses and the conclusion is called consequence; and if a conclusion is not legitimately drawn from given premisses, the syllogism is said to lack consequence.

The terms used in the simple syllogism are three in number. These are called the major term, the middle term, and the minor term, according as they express respectively the major, the middle, and the minor idea of the reasoning process. A practical rule for distinguishing the terms is the following: the major term is the predicate of the conclusion; the minor term is the subject of the conclusion; the middle term occurs in each premiss but not in the conclusion. This rule is not a scientific one for the Dialectician, for it presupposes a perfect syllogism to begin with; but it is a good handy rule in practice. The reason for it will appear upon recollection or review of what we have learned about the major, middle, and minor ideas of the reasoning process, and the place of these ideas and their function in that process. In the syllogism given above, the major term is mortal; the minor term is John Smith, and the middle term is man. The major and minor terms are called extremes as contrasted with the mean, or middle term.

The premisses are called the major premiss and the minor premiss. This distinction of premisses was originally based upon the distinction of terms, so that the major premiss was that premiss which contained the major term, and the minor premiss was that which contained the minor term. But usage has brought a change, and now the distinction of premisses as major and minor amounts simply to first and second premiss respectively.

The three propositions and the three terms that enter into the construction of the syllogism constitute its matter or material element. The logical structure, which makes clear the connection of the premisses and the consequence of the syllogism, is the form or formal element of the syllogism.

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b) Correctness and Truth of the Syllogism

The syllogism is correct when its material and formal elements are both present in integrity; in other words, it is correct when the conclusion follows necessarily from the premisses as given. The syllogism is true when its conclusion states a true fact, regardless of the truth of the premisses, and regardless of the consequence, that is, the necessary inference of the conclusion from the premisses as given.

The following syllogism is correct but not true:

Every tree is a spirit
The oak is a tree
Therefore the oak is a spirit

The following syllogism is true but not correct:

Every spiritual being is immortal
The soul is immortal
Therefore the soul is a spiritual being

Notice in the latter example that the conclusion expresses a truth, viz., “the soul is a spiritual being.” But this conclusion is not legitimately drawn from the premisses; the syllogism lacks consequence; therefore the syllogism is incorrect.

Now Dialectics looks only to correctness in syllogisms. While it is evident that the syllogism can serve no worthy or valuable purpose unless it is both correct and true, we must learn first how to make it correct. The science of Dialectics has correctness of reasoning as its Formal Object, and in all that follows we look to correctness of syllogisms and not to their truth. Nevertheless, Dialectics finds a stable relation existing between truth and correctness in syllogisms, and the following practical principles are discerned:

1. The correctness of the syllogism being supposed, it follows that if the premisses are true the conclusion will be true; but if the premisses are false, the conclusion may be false or true.
2. The correctness of the syllogism being supposed, it follows that if the conclusion is false, one or both of the premisses must be false; but if the conclusion is true, the premisses may be true or false.

To state the principles in a somewhat more direct form:

True premisses — true conclusion
True conclusion — false or true premisses
False premisses — false or true conclusion
False conclusion — false premisses (one or both)

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c) Kinds of Syllogisms

Here we speak only of the perfect syllogism, that is, the syllogism which squares precisely with the definition of syllogism given above. Of imperfect syllogisms we shall speak in Article 4 of this Chapter.

The perfect syllogism is:

1. Categorical when all three of its propositions are categorical, that is absolute and unconditioned propositions. The categorical syllogism is simple or compound, according as its propositions are simple or compound propositions.
2. Hypothetical when the major (first) premiss is a hypothetical proposition. This syllogism is connective (or simply conditional), conjunctive, or disjunctive, according as its major proposition is a connective, conjunctive, or disjunctive proposition.

Examples:

1. Simple categorical syllogism:

Every man is mortal
John Smith is a man
Therefore, John Smith is mortal

2. Compound categorical syllogism:

Whatever is infinitely perfect is necessarily eternal
God is infinitely perfect
Therefore, God is necessarily eternal

3. Conditional syllogism:

If it rains, there will be no game
It rains
Therefore, there will be no game

4. Conjunctive syllogism:

The milk cannot be at once sweet and sour
It is sweet
Therefore, it is not sour

5. Disjunctive syllogism:

Either Smith won, or he was defeated
He was defeated
Therefore, he did not win.

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Summary of the Article

In this Article we have learned that the syllogism is the most perfect form of argumentation, which is the expression in speech of the reasoning process. We have also defined it, have studied its elements, and have learned the names of its terms and propositions. We have investigated the matter of truth and correctness in syllogisms, and, while asserting the aim of Dialectics as the achieving of correctness, we have indicated certain basic principles for judging of the truth of correct syllogisms. We have distinguished syllogisms as categorical and hypothetical, and have illustrated the classes by examples.