In mediate inference conclusion draw from two and more than two premises. Both premises jointly imply the conclusion.

**Syllogism: **A syllogism is a form of mediate deductive inference, in which the conclusion is drawn from two premises take jointly. There are three major types of syllogism:

- Conditional syllogism
- Categorical syllogism
- Disjunctive syllogism

**Categorical Syllogism: **

A categorical syllogism is a deductive argument consisting of exactly three categorical propositions (two premises and a conclusion) in which there appear a total of exactly three categorical terms, each of which is used exactly twice.

In a standard form categorical syllogism, major premise comes first, then the minor premise occurs and conclusion comes in the end. Standard form order of a syllogism is the following format:

*Major premise*: A general statement.

*Minor premise*: A specific statement.

*Conclusion*: based on the two premises.

Consider, for example, the categorical syllogism:

No geese are felines.

Some birds are geese.

Therefore, Some birds are not felines.

** **

**Terms Used in Categorical Syllogism**

A syllogism contains exactly three terms or class names:

**Major Term/Major Premise:** The major term is the term that occurs as the predicate of the conclusion in a standard-form syllogism.

The major premise is the premise that contains the major term.

**Minor Term/Miner Premise:** The minor term is the term that occurs as the subject of the conclusion in a standard form syllogism.** **

The minor premise is the premise that contains the minor term.

**Middle term:** The term that occurs in both premises, but not in the conclusion, of a standard form syllogism.

**Syllogistic Moods:**

Logicians also speak of syllogistic moods. Moods are defined as the arrangement of the premises according to quantity (universal or particular) and quality (affirmative or negative). In other words, we can say that mood is determined by the type of standard form categorical propositions of the syllogism contains. Example:

A- All M is P.

A- All S is M.

A- All S is P.

So , AAA is the mood of this syllogism.

Now we will see what rules govern each figure and how these rules affect the validity of the single moods.

**Figure in Syllogism:**

The figure of a syllogism, determined by the positions of the middle term in its premises; there are four possible figures. When we use the term “syllogistic figure” we understand **the disposition of the middle term (M) with respect to the major (P) and minor terms (S) in the premises of a syllogism**.

The minor term **(S)** is always the subject and the major term **(P)** is always the predicate of the conclusion. Whatever variations that can take place in the relative position of the terms among themselves must occur in the premises.

In the major premise the middle term is compared with the major extreme. In the minor premise the middle term is compared with the minor extreme. This gives four different syllogistic figures:

Figure 1 | Figure 2 | Figure 3 | Figure 4 | |||

M — P | P — M | M– P | P — M | |||

S — M | S — M | M– S | M — S | |||

S — P | S — P | S — P | S — P |

**First Figure**

M P | All animals (M) are a nuisance (P). |

S M | All dogs (S) are animals (M). |

S P | Therefore, All dogs (S) are a nuisance (P). |

The middle term is the subject of the major premise and the predicate of the minor premise.

**Second Figure**

P M | No statesmen are good politicians. |

S M | Some journalists are good politicians. |

S P | Therefore, Some journalists are not statesmen. |

The middle term is the predicate of both premises.

**Third Figure**

M P | All writers are intelligent. |

M S | Some writers are American citizens. |

S P | Therefore, Some American citizens are intelligent. |

The middle term is the subject of both premises.

**Fourth Figure**

P M | All Americans are happy people. |

M S | All happy people are fun-loving |

S P | Therefore, Some fun-loving people are Americans. |

The middle term is the predicate of the major premise and the subject of the minor premise.

The First Figure has been considered to be the perfect syllogism because it is the way we tend to make statements normally and naturally. The other three figures, however, are correct forms of syllogistic reasoning, even if they seem to be somewhat stilted and unnatural.

**Rule of remind figures:** **SP**IRIT O**PP**RE**SS**ED THE **PS**ALMIST.

Meaning: SP- First figure, PP- Second figure, SS –Third figure and PS- Fourth figure.