Etymologically it comes from the Latin syllogismus which, in turn, comes from the Greek syllogismós. According to its semantic sense, it is the union of two cocepts, syn and logos, which could be translated as a union or combination of expressions. A syllogism is a structure that consists of two premises and a conclusion. In it there are three terms (major, minor and middle) that are presented as a deductive reasoning that goes from the general to the particular.
An example of a classical syllogism would be the following:
1) all men are mortal,
2) Aristotle is a man and
3) then Aristotle is mortal (in this example the major term will be mortal, the minor term will be Aristotle and the middle term will be man).
It must be said that not all syllogism by virtue of being one is necessarily true, but that in order for it to be valid it must respect certain rules, specifically eight.
Syllogisms were created 2500 ago by Aristotle as a part of logic. Its fundamental idea consists of extracting or deriving a conclusion from two premises and for this a series of inference rules must be followed.
Rules of inference of the syllogism
- 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 affirms that the middle term has to be distributed in at least one of the premises.
- According to the fourth rule, the middle term must be found in its universal extension at least in one of the premises.
- The fifth rule states that from two negative premises it is impossible to obtain any kind of conclusion.
- The sixth says that from two affirmative premises it is not possible to draw a negative conclusion.
- According to the seventh rule, if a premise is particular, this implies that the conclusion will also be particular and, on the other hand, if a premise is negative, the conclusion will be equally negative.
- The eighth and last rule holds that from two particular premises it is impossible to reach a conclusion.
The syllogism is present in our mental schemes and in mathematics
In everyday life we use, consciously or not, this logical structure. The syllogisms help to think with a logical criterion. However, it is in mathematics where they are most used. In this sense, reasoning and mathematical proofs are based on the rules of syllogisms.
