# What is Syllogism definition/concept/elaboration

Etymologically, the word syllogism comes from the Latin syllogismus which, in turn, comes from the Greek syllogismós. According to its semantic meaning, it refers to the union of two concepts: syn and logos, which can be translated as a union or combination of expressions.

The syllogism is a **structure consisting of two premises and a conclusion**. This term contains three (a major and a minor and an average) that present themselves as a deductive reasoning that goes from the general to the particular. An example of the classic syllogism would be the following: all men are mortal (major premise); Aristotle is a man (smallest premise); therefore, Aristotle is mortal (**conclusion**).

It should be noted that not every syllogism due to the fact of being is necessarily true, but that in order to be valid it must respect certain rules, but specifically eight.

Syllogisms were created 2500 years ago by Aristotle as a part of logic. Its fundamental idea is to extract or derive a conclusion from two premises, for which it must follow a series of rules of inference.

### Syllogism inference rules

- – the first rule refers to the number of terms, which must always be three. Any variation to this rule would create a fallacy, that is, false reasoning with the appearance of truth;
- – the second rule indicates that the middle term should not be part of the conclusion;
- – the third states that the middle term must be distributed in one of the premises as a minimum;
- – according to the fourth rule, the middle term can be found in its universal extension in at least one of its premises;
- – the fifth rule states that two negative premises is impossible to reach any conclusion;
- – the sixth says that through two affirmative premises it is not possible to draw a negative conclusion;
- – according to the seventh rule, if a premise is particular it means that the conclusion will also be, on the other hand, if a premise is negative, the conclusion will be equally negative;
- – the eighth and last rule states that through two particular premises it is impossible to reach a conclusion.

### The syllogism is present in our mentality and in mathematics

In everyday life we use this logical structure consciously or not. Syllogisms help to think with a logical criterion. However, it is in mathematics where they are employed. In this sense, reasoning and mathematical proofs are based on the rules of the syllogism.