# Syllogism

In traditional logic, a**syllogism**is an inference in which one proposition (the

**conclusion**) follows of necessity from two others (known as premises).

The definition is traditional, but is derived loosely from Aristotle's *Prior Analytics*, Book I, c. 1. The Greek sullogismos means "deduction".

Forms of syllogism:

- Categorical syllogism
- Disjunctive syllogism
- Hypothetical syllogism
- Polysyllogism
- Quasi-syllogism
- Statistical syllogism
*add list of other syllogism forms here*

- If all humans (B's) are mortal (A),
- and all Greeks (C's) are humans (B's),
- then all Greeks (C's) are mortal (A).

- Men die.
- Socrates is a man.
- Socrates will die.

- Grass dies.
- Men die.
- Men are grass.

Syllogisms may also be invalid if they have four terms or the middle term is not distributed.

**Epagoge** are weak syllogisms that rely on inductive reasoning.

By the definition of conditional and biconditional the consequences of the principle of the syllogism may be stated in the following formulas:

**See also:** Venn diagram