Syllogism (Meaning and Explanation)

We explain what a syllogism is in logic, its structure, relationship between premises, types, rules and examples. Also, what is a fallacy.

What is a syllogism?

In logic, a syllogism It is a method of reasoning, both inductive and deductive.. Its name comes from Greek syllogismos and it was studied by ancient Greek philosophy, especially by Aristotle (384-322 BC), who was the first to formulate it.

It is a fixed method of logical reasoning that It consists of three parts: two premises and a conclusionthe latter obtained as a result of the first two.

All syllogism connects two parts through judgmentsthat is, of their comparison. The first, Aristotle called major premiseto the second minor premise and to the conclusion consequent. These parts are usually understood as propositions, capable of having a true (T) or false (F) value.

Syllogistic logic or syllogisms is abundantly practiced in propositional logic, within mathematical or computer science studies, and also within the study of philosophy.

Structure of the syllogism

As we said before, the structure of the syllogism is fixed, regardless of the issue they address or the nature of their premises, and consists of three elements:

A major premiseequivalent to a predicate of the conclusion (P).
A minor premiseequivalent to a subject of the conclusion (S).
A middle groundwith which P and S are compared.
A consequent or conclusionwhich is arrived at by affirming or denying the relationship between P and S.

You may be interested: Theory of Knowledge

These terms are related to each other by judgments, which can be of a specific nature, depending on the type of affirmations or denials they make:

Universal: they maintain that a property concerns all the elements, that is: all S is P.
Individuals: on the contrary, they extend a property over some elements of a greater whole, that is: some S are P.
Affirmatives: also called union, they propose an equivalence relationship between the terms: S is P.
Negatives: also called separation, they propose the complete opposite of the previous ones: S is not P.

Thus, there are four possible argument types from a syllogism:

(A) Affirmative universals: All S is P (where S is universal and P is particular). For example: “All humans must breathe.”
(E) Negative universals: No S is P (where S is universal and P is universal). “No human breathes underwater.”
(I) Affirmative particulars: Some S is P (where S is particular and P is particular). “Some humans are born in Egypt.”
(O) Negative particulars: Some S is not P (where S is particular and P is universal). “Some humans are not born in Egypt.”

Types of syllogism

Depending on how the premises of a syllogism are related, we can distinguish some of its classes, such as:

Categorical or classical syllogism. This is the usual and simple type of syllogism, in which the premises and conclusion are simple propositions. For example:

Every week starts on a Monday.
Today is Monday.
So today begins a week.

conditional syllogism. In this type, the major premise establishes a relationship of dependence with respect to two categorical propositions. Therefore, the minor premise either affirms or denies one of the terms, and the conclusion affirms or denies the opposite term. For example:

If it is daytime, then the sun is shining.
Now it's not daytime.
So the sun doesn't shine.

You may be interested: Research Techniques

disjunctive syllogism. In it, the major premise proposes a disjunction, that is, the choice between two terms that are opposed, so that they cannot be simultaneously true or false. For example:

An animal is born as a male or as a female.
An animal is born male.
So it's not female.

Rules of syllogisms

Syllogisms are governed by a set of unbreakable rules, such as:

No syllogism consists of more than three terms.
The conclusion It cannot be longer than the premises.
The middle ground It cannot be in the conclusion.

On the other hand, the premises also have their rules:

No conclusion can be obtained from two negative premises.
A negative conclusion cannot be obtained from two affirmative premises.
A valid conclusion cannot be obtained from two particular premises.

Examples of syllogisms

Here are some simple examples of syllogisms:

Those who are born in Spain are Spanish. My mother was born in Spain. Then, my mother is Spanish.
I'm only late when it rains. It didn't rain today. Then, I'll arrive on time.
Some people don't know how to swim. To save yourself you have to swim. Therefore, some people will not be saved.
All my friends speak Spanish. Rodrigo does not speak Spanish. Then, Rodrigo is not my friend.

Fallacies

The fallacies are those arguments that formally seem valid, but are not. This does not imply that its premises and conclusions are false or true, but rather that the relationship established between them is invalid.

In their Sophistical refutationsAristotle identified up to thirteen types of fallacy, but there are hundreds of them in modern classifications. A simple example of a fallacy is the following syllogism: