What is a syllogism?

What Does Syllogism Mean

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

Syllogisms are studied in propositional logic, mathematics, computer science, and philosophy.

What is a syllogism?

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

It is a fixed method of logical reasoning that consists of three parts: two premises and a conclusion , the latter obtained from the first two. Every syllogism relates two parts through judgments , that is, their comparison. Aristotle called the first major premise , the second minor premise, and the consequent conclusion . These parts are usually understood as propositions , capable of having a true (V) or false (F) value. The syllogistic or syllogistic logic is abundantly practiced in propositional logic, within mathematical or computer studies, and also within the study of philosophy.

It can help you: Deductive and inductive arguments

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 its premises, and consists of three elements:

  • A major premise , equivalent to a predicate of the conclusion (P).
  • A minor premise , equivalent to a subject of the conclusion (S).
  • A middle term , with which P and S are compared.
  • A consequent or conclusion , which is reached by affirming or denying the relationship between P and S.

These terms are related to each other by judgments, which can be of a certain 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.
  • Particulars : on the contrary, they extend a property over some elements of a larger totality, that is: some S are P.
  • Affirmative : also called union, they propose an equivalence relation between the terms: S is P.
  • Negative : also called separation, they propose the opposite of the previous ones: S is not P.

Thus, there are four types of possible arguments 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 . It is the usual and simple type of syllogism, in which the premises and the conclusion are simple propositions. For example:

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

Conditional syllogism . In this type, the major premise establishes a dependency relationship with respect to two categorical propositions. Hence, 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.
  • It is not daylight now.
  • So the sun doesn't shine.

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

  • An animal is born male or female.
  • An animal is born male.
  • So it is 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 cannot be longer than the premises.
  • The middle ground cannot be in the conclusion.

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

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

Examples of syllogisms

Here are some simple examples of syllogisms:

  • Those born in Spain are Spanish. My mother was born in Spain. Then my mother is Spanish.
  • I'm only late when it rains. Today it did not rain. Then I'll be on time.
  • Some people cannot swim. To save yourself you have to swim. Then 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 that the relationship established between them is invalid. In his Sophistic Refutations , Aristotle 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:

  • All my colleagues are English. Boris is English. Then Boris is my partner.

As will be seen, a conclusion is reached that is not necessarily drawn from the premises , since being English does not condition being a partner, but the other way around. From this initial premise, we could only conclude that Boris is English if we were told that he is a partner. More in: Fallacy

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