Structure syllogisms, rules and examples

The syllogism It is a term created by Aristotle (384-322 BC), a philosopher considered the father of logic and one of the founders of Western philosophy. It is a form of deductive argumentation that starts from a global approach to arrive at a specific and conclusive one..

It is considered the logical reasoning par excellence for obtaining totally new judgments, having as the origin of the analysis two known premises. For example: All cats are felines> Some felines are tigers> Therefore, some tigers are cats. 

The syllogism would become the main notion of Aristotelian logic, considered in turn as one of the columns of scientific thought.

A more accepted and clearer definition of this term is that it is a deductive reasoning in which a conclusion is reached from two premises or propositions, a third premise that must be deduced from the relationship of the first two.

There are several types of syllogisms -categorical, conditional, disjunctive, etc.-, but the basic model is the Aristotelian, which corresponds to the categorical.

Article index

• 1 Elements of the syllogism (structure)
  • 1.1 Major premise
  • 1.2 Minor premise
  • 1.3 conclusion
• 2 Rules of syllogisms
  • 2.1 Three terms
  • 2.2 Universal middle term
  • 2.3 Conclusion drawn
  • 2.4 Affirmative and negative rules
• 3 Examples of syllogisms
• 4 References

Elements of the syllogism (structure)

A syllogism is made up of three judgments or propositions: a major or universal premise, a minor or particular premise, and the conclusion.

Propositions in turn consist of three terms: a minor or subject term, a major or predicate term, and a middle or common term (which share the two premises)..

A classic example to display the elements:

• Major premise: All men are mortal.
• Minor premise: Socrates is a man.
• Conclusion: Socrates is deadly.

Major premise

"All men are mortal".

In the major premise the subject would be "all men", the predicate "are mortal" and the middle term "men", which in the minor premise would be found in the predicate. The relationship between the major and minor premises is known as the argument.

Minor premise

"Socrates is a man".

Here we can see that the minor premise is included in the syllogism, the middle of which is in predicate form. It is always the second premise. From the combination of both, the conclusion will emerge.

Conclution

"Socrates is mortal".

If we follow Aristotelian reasoning, saying that all men are mortal and stating that Socrates is a man, the irrefutable conclusion will be that, evidently, Socrates is mortal as a man..

The premises are statements or judgments that can be classified according to their quantity or extension (universal or particular), and their quality (affirmative or negative).

From the combination of these two criteria, four classes of judgments emerge: affirmative universal, negative universal, affirmative particular and negative particular..

"All men are mortal" could be an example of a universal affirmative judgment; "Men are not birds", a negative universal judgment; "Socrates is a man", a particular affirmative judgment, and "Carlos is not a bird", a particular negative judgment..

Rules of syllogisms

For a syllogism to be valid and not be considered a false statement (that is, a fallacy), it must comply with a series of rules:

Three terms

Every syllogism must consist of three terms: a subject, a predicate, and a middle term. Adding another subject, for example, would make it a false statement.

Universal middle term

The middle term, at least in one of the premises, must be universal ("men", in Socrates' syllogism).

This means that from two particular premises, without universal middle terms, a valid conclusion cannot be drawn.

Conclusion deduced

The conclusion must follow from the premises. A conclusion other than the terms included in the premises would be a false statement.

Affirmative and negative rules

Two affirmative premises cannot give a negative conclusion (for example, "all horses are quadruped; Lucero is a horse; Lucero is not quadruped").

Two negative premises cannot have a valid conclusion. A negative and a positive premise will have a negative conclusion.

Examples of syllogisms

Although Aristotle was the first to theorize this way of thinking, it is probable that syllogistic reasoning has been present long before in the human being and his way of knowing and understanding the world.

Here are some simple examples of syllogisms with which we can illustrate this way of thinking.

Example 1

1. All women can be mothers
2. Marcela is a woman
3. Marcela can be a mother

Example 2

1. Liquid water is essential for life
2. Earth has liquid water
3. The Earth is fit for life

Example 3

1. Mammals cannot breathe underwater
2. The fox is mammal
3. The fox cannot breathe underwater

Example 4

1. Smokers can die from cancer
2. Francisco smokes
3. Francisco may die of cancer

Example 5

1. All human beings grow old
2. Daniela is a human being
3. Daniela is going to grow old

Example 6

1. Susana likes music
2. José plays guitar
3. Susana might like José

Example 7

1. Some snakes are not poisonous
2. There is a snake in my house
3. Maybe not a poisonous snake

Example 8

1. Covid19 is very contagious
2. Leon has Covid 19
3. Leon can infect others

Example 9

1. All people are the same
2. Maria and Carlos are people
3. Maria and Carlos are the same

Example 10

1. Every night is dark
2. Manuel is afraid of the dark
3. Manuel fears the night

Example 11

1. All birds have feathers
2. The rhea is a bird
3. The rhea has feathers

Example 12

1. No human being has feathers
2. Rolando is a human being
3. Rolando has no feathers

Example 13

1. Plastic is a not very rigid material
2. The chair is plastic
3. The chair is not very rigid

Example 14

1. All four wheel drive cars are rustic
2. My car does not have 4WD
3. My car is not rustic

Example 15

1. All Madrilenians are Spanish
2. Paco is from Madrid
3. Paco is Spanish

Example 16

1. Everything that has a screen has electronic components
2. My phone has a screen
3. My phone has electronic components

Example 17

1. All metals rust over time
2. Aluminum is a metal
3. Aluminum rusts over time

Example 18

1. All comets have ice
2. The Halley is a comet
3. The Halley has ice

Example 19

1. Cows are herbivorous
2. Butterfly is a cow
3. Butterfly is herbivorous

Example 20

1. Even numbers are multiples of two
2. Eight is an even number
3. Eight is a multiple of two

References

1. Valiña, M. D. and De Vega, M. (1988). An experimental study of everyday reasoning in syllogism tasks: a pragmatic approach. Taken from dialnet.unirioja.es.
2. Santamaría, C. (1989). Mental models and semantic reasoning. Taken from dialnet.unirioja.es.
3. Suárez, R. and Villamizar, C. (2002). Syllogisms and elements that compose it. Taken from metabase.uaem.mx.
4. Carnero, S. (2005). The syllogism: history and development. Taken from serbal.pntic.mec.es.
5. Berríos, F. (2016). Syllogism. Structure and types. Taken from logicautem.wordpress.com.
6. Syllogism (2020). Taken from es.wikipedia.org.