Syllogisms
A syllogism is a type of argument formed by using categorical sentences as premises and a categorical proposition as conclusion. A syllogism has exactly two premises. Exactly three terms occur in the three categorical sentences which make up the syllogism. The subject term of the conclusion is called the minor term. It must occur as the subject term of the conclusion and also in one of the premises. The premise containing the subject term is called the minor premise. The predicate term of the conclusion is called the major term. Besides occurring in the conclusion, it occurs in one premise, called the major premise. The third term, called the middle term, occurs in each of the premises. When a syllogism is in the order:
| major premise |
| minor premise |
| conclusion |
it is said t be in standard form.
Let's look at the following syllogism:
| All bass are fish. | <-- NOT IN STANDARD FORM |
| All fish are swimmers. | |
| All bass are swimmers. |
major term: swimmers
minor term: bass
middle term: fish
major premises: All fish are swimmers
minor premise: All bass are fish.
Notice that the syllogism above is not in standard form. To be in standard form the major premise must be first. In standard form the above syllogism is:
| All fish are swimmers. |
| All bass are fish. |
| All bass are swimmers. |
We can characterize standard form syllogisms completely by specifying their mood and their figure. The mood of a standard form syllogism is an ordered triple of the letter names of the major premise, minor premise, and conclusion, in that order. The above syllogism has the mood AAA. The following standard form syllogism:
| Some dogs are happy |
| Some dogs are not brown. |
| No brown things are happy. |
has the mood: IOE.
The figure of a standard form syllogism is determined by the relative position of the middle term in the premises. There are four different figures, each with a number-name:
| M | P | P | M | M | P | P | M | |||
| S | M | S | M | M | S | M | S | |||
| Figure 1 | Figure 2 | Figure 3 | Figure 4 | |||||||
In our last syllogism (the "dog" syllogism) the figure is 3. Thus we specify the mood and figure together as I)E?3. In our "fish" syllogism, the figure was 1. Hence the mood and figure are AAA-1. Note that mood and figure apply only to standard form syllogisms.
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