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A syllogism (Greek: συλλογισμός – syllogismos – “conclusion,” “inference”) is a kind of logical argument in which deductive reasoning is used to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true.
In its earliest form, defined by Aristotle, from the combination of a general statement (the major premise) and a specific statement (the minor premise), a conclusion is deduced . For example, knowing that all men are mortal (major premise) and that Socrates is a man (minor premise), we may validly conclude that Socrates is mortal. Syllogistic arguments are usually represented in a three-line form (without sentence-terminating periods):
All men are mortal
Socrates is a man
Therefore, Socrates is mortal
The word “therefore” is usually either omitted or replaced by the symbol “∴”