Categorical Syllogisms
A categorical syllogism is composed of three, simple, categorical statements. The first two are called the premises, and the third is the conclusion.
The subject and predicate of a categorical statement are each called the "terms." All categorical statements have two and only two terms. Neither the quantifier nor the copula are part of either the subject or predicate terms. The quantifier and copula are used to determine the statement type (A, E, I, O).
All categorical syllogisms have three statements: two premises and a conclusion. Each statement is written on a separate line with the conclusion written last. The conclusion usually starts with "so", "therefore", "hence" or a similar designation. Often a line is drawn between the second premise and the conclusion.
When working with categorical syllogisms in any way whatsoever always start with the conclusion. This is much easier.
| Premise 1
All grass eaters are herbivores Premise 2 All cows are grass eaters Conclusion Therefore, all cows are herbivores |
Example of a categorical syllogism
Since each statement must have two terms and there must be three statements then there must be six "slots" in a categorical syllogism for terms: a subject and predicate term in each statement.
The subject term of the conclusion is called the minor term. The predicate term of the conclusion is called the major term. This is by definition. The conclusion is commonly abbreviated "minor / major".
Of the two premises, only one will have the major term, the other only the minor term. The premise with the major term is called the major premise. The premise with the minor term is called the minor premise. The wording of the major and minor terms in the premises should be identical with their wording in the conclusion. Attempting to use synonymous terms will often result in faulty conclusions since different wordings of a term are very seldom exactly synonymous.
The empty slot in each of the premises is filled with what is called the middle term. The wording of the middle term in each premise should be identical for the reasons given above.
For clarity, the premise containing the major term should be give first, then the premise with the minor term, followed by the conclusion. This results in the four standard figures.
|
Figure 1 |
Figure 2 |
Figure 3 |
Figure 4 |
Major premise |
middle / major |
major / middle |
middle / major |
major / middle |
Minor premise |
minor / middle |
minor / middle |
middle / minor |
middle / minor |
Conclusion |
minor / major |
minor / major |
minor / major |
minor / major |
This table is sometimes displayed as follows. It is also possible to omit the last row since it is always the same. But N.B., the subject of the conclusion ALWAYS comes from the minor premise! A very common mistake is to try to take one of the terms of the major premise to be the subject of the conclusion.
|
Figure 1 |
Figure 2 |
Figure 3 |
Figure 4 |
|
Major premise |
M / P |
P / M |
M / P |
P / M |
Minor premise |
S / M |
S / M |
M / S |
M / S |
Conclusion |
S / P |
S / P |
S / P |
S / P |
Here M is the middle term. S is the subject term of the conclusion. P is the predicate term of the conclusion.
Now, when we combine the four figures with the four types of statements were get the 256 different "moods" of the categorical syllogism.
