## The Law of Syllogism

In logic, the law of syllogism is the second of the three classic laws of thought (along with the law of identity and the law of non-contradiction). It states that: “For all propositions P and Q, if P is true and Q is true, then P∧Q is true”.

### All men are mortal.

The law of syllogism is a logical rule that states that if two statements are true, then a third statement can be inferred from them. In other words, if all men are mortal and Socrates is a man, then it must be true that Socrates is mortal. This rule is also known as the law of deduction.

### Socrates is a man.

The law of syllogism is a formal principle of logic. It states that if two propositions are true, then a third proposition that is logically related to them must also be true. For example, the propositions “All men are mortal” and “Socrates is a man” are both true. Therefore, the proposition “Socrates is mortal” must also be true.

### Therefore, Socrates is mortal.

A syllogism is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. Syllogisms are usually represented in a three-line form: All men are mortal; Socrates is a man; therefore, Socrates is mortal.

The first two statements, known as the premises, must be true in order for the conclusion to be valid. In this example, the premises are “All men are mortal” and “Socrates is a man.” These two premises provide the evidence or support for the conclusion “Socrates is mortal.”

The syllogism takes its name from the Greek word syllogismos, which means “conclusion, inference.” The term was first used by Aristotle in his work Prior Analytics, where he developed the concept of deductive reasoning.