The Syllogism and Its Kinds
The syllogism defined, its terms and propositions named, correctness distinguished from truth, and the kinds of syllogism (categorical and hypothetical) enumerated and illustrated.
The syllogism is a formal argument in which a conclusion follows necessarily from two premises by means of a middle term that appears in both premises but not in the conclusion. It has three terms (major: in the major premise and conclusion; minor: in the minor premise and conclusion; middle: in both premises only) and three propositions (major premise, minor premise, conclusion). A syllogism may be formally correct (the conclusion necessarily follows from the premises given) without being materially true (the premises being actually true). The categorical syllogism has categorical propositions throughout; the hypothetical syllogism has a hypothetical (conditional, conjunctive, or disjunctive) major premise and takes correspondingly different valid forms of inference.
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) is 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.
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 are called the premisses. The third proposition (implied in the premisses) is the conclusion or consequent. The logical connection existing between the premisses and the conclusion is called consequence; if a conclusion is not legitimately drawn from given premisses, the syllogism is said to lack consequence.
Terms of the Syllogism
The simple syllogism uses exactly three terms:
- Major term: the predicate of the conclusion.
- Minor term: the subject of the conclusion.
- Middle term: occurs in each premiss but not in the conclusion.
The major and minor terms are called the extremes, contrasted with the middle term or mean. In the example above: mortal is the major term; John Smith is the minor term; man is the middle term.
A handy practical rule (not a scientific definition): 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.
Propositions of the Syllogism
- Major premiss (first premiss): contains the major term.
- Minor premiss (second premiss): contains the minor term.
(Note: usage has simplified this — major and minor premiss now simply mean first and second premiss respectively.)
The three propositions and three terms constitute the matter or material element of the syllogism. The logical structure making clear the connection of the premisses and the consequence is the form or formal element.
b) Correctness and Truth of the Syllogism
The syllogism is correct when its material and formal elements are both present in integrity — 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 consequence.
Correct but not true:
Every tree is a spirit. The oak is a tree. Therefore the oak is a spirit. (The conclusion follows necessarily from the premisses as given — the syllogism is correct. But the premiss and conclusion are false.)
True but not correct:
Every spiritual being is immortal. The soul is immortal. Therefore the soul is a spiritual being. (The conclusion expresses a truth, but it is not legitimately drawn from the premisses — the syllogism lacks consequence and is incorrect.)
Dialectics looks only to correctness. Nevertheless, certain practical principles emerge from the relation between truth and correctness in correct syllogisms:
| Premisses | Conclusion |
|---|---|
| True premisses | True conclusion |
| True conclusion | Premisses may be true or false |
| False premisses | Conclusion may be false or true |
| False conclusion | Premisses false (one or both) |
c) Kinds of Syllogisms
Here we speak only of the perfect syllogism (that which exactly squares with the definition above). Imperfect syllogisms are treated in Article 4.
1. Categorical: all three propositions are categorical (absolute and unconditioned). May be simple or compound.
2. Hypothetical: the major (first) premiss is a hypothetical proposition. Three sub-types according as the major is connective, conjunctive, or disjunctive.
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.
Summary of the Article
We have learned that the syllogism is the most perfect form of argumentation. We have defined it, studied its elements, and learned the names of its terms (major, minor, middle) and propositions (major premiss, minor premiss, conclusion). We have investigated truth and correctness in syllogisms, asserted Dialectics’ aim as correctness, and indicated basic principles for judging the truth of correct syllogisms. We have distinguished syllogisms as categorical and hypothetical and illustrated the classes by examples.