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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:

The Aristotle wrote the classic "Barbara" syllogism:

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).

That is,

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

Metaphor, in contrast, resembles a form of syllogism called “Affirming the Consequent”:

Grass dies.
Men die.
Men are grass.

A Barbara syllogism involves grammar and logical types; it has a subject and a predicate. Affirming the Consequent, the basis of metaphor, is grammatically symmetrical: it equates two predicates. This form of syllogism is logically invalid.

Epagoge are weak syllogisms that rely on inductive reasoning.

See also: Venn diagram