Standard Form

Categorical Syllogism :

- is an argument where both the two premises and conclusion are categorical propositions.
- contains exactly three different terms. Each used exactly twice, but never twice in the same proposition.
  - major term: the predicate term of the conclusion.
  - minor term: the subject term of the conclusion.
  - middle term: the remaining third term. It occurs once in each premise.
  - major premise: one that contains the major term.
  - minor premise: one that contains the minor premise.
- A categorical syllogism is in standard form when:
  - major premise is listed first.
  - minor premise is listed second.
  - conclusion is listed third.

Syllogism's Mood:

- is defined by a list of three letters, designating the categorical type of each proposition. (A, E, I, or O)
  - The first letter designates the major premise.
  - The second letter designates the minor premise.
  - The third designates the conclusion.

Syllogism's Figure:

- is a number from 1 to 4 which specifies the arrangement of the middle term in the premises.

Figure 1 | Figure 2 | Figure 2 | Figure 3
...M...P ...S...M ...S...P | ...P...M ...S...M ...S...P | ...M...P ...M...S ...S...P | ...P...M ...M...S ...S...P

Example:

Some Democrats are rich.
All Democrats are courteous.
Some courteous people are rich.

Old form:

Some D are R
All D are C
Some C are R

- The syllogism is in standard form .
  - The major term is, "rich people". This term is found in the major premise which is placed first.
  - The minor term is, "courteous people". This term is found in the minor premise which is placed second.
  - The conclusion is placed third.
- Mood.
  - The first premise is an I categorical type.
  - The second premise is an A categorical type,
  - The conclusion is an I categorical type.
  - So the mood is: IAI.
- Figure.
  - The middle term is in the subject position of both premises. So it is a figure 3.