SYLLOGISM: STRUCTURE, RULES, MODES AND EXAMPLES - PHILOSOPHY - 2025

A syllogism is a form of deductive argumentation that starts from a global categorical approach to arrive at a specific and conclusive one. It is considered the logical reasoning par excellence to obtain 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. By means of the comparative analysis of the judgments (the close, the palpable), the syllogism seeks to conceptualize what is within the reach of man, what makes up his reality. This deductive resource seeks to give defining notions of the observable through the relationship between a subject and a predicate.

Aristotle of Estagira, father of the syllogism

The concept of syllogism was first introduced by the Greek philosopher Aristotle in his book First Analytical. This book personifies one of the most important contributions of the Hellenic thinker to the world of logic and is taken as a global point of reference for the argumentative-deductive study.

Aristotle, considered the father of logic for having been the first philosopher to systematize reasoning, laid the foundations for formal scientific studies. The syllogism for him meant the perfect and refined rational link, capable of connecting harmoniously and conclusively the elements of an environment.

Formulation of a syllogism

In order to fully understand the universe of the syllogism, it is necessary to be clear about the elements that make it up:

Composition of the premises

The premises can be composed of two of the following three aspects:

- A subject, whom we will call "S". For example: men, women, Maria, Pedro.

- A predicate, which we will call "P". For example: they are smart, they are not fierce, they are fantastic, they are friendly.

- A middle ground, which we will call "M". This in particular is the constant between the two premises, which allows linking them. It does not appear in the consequent, as it is what causes the conclusions.

To find out how to identify the middle term, the following example can be used:

PM = "All French are Latino."

Pm = "Francois is French."

PC = "Therefore, Francois is Latino."

In this example it is clearly denoted that the middle term ”or“ M ”is: French, French.

For its part, the consequent or “conclusion will always be made up of the following elements:

- A subject, whom we will call "S".

- A predicate, which we will call "P".

This can be seen in the following sentence: “Some cups (S) do not have handles (P)”.

Extensions of premises

The relationships between these terms that make up the premises and the conclusions will give them different types of connotations depending on their extension. These connotations typical of their extension (also understood as the space they cover) are of two types:

Connotations of universal extension

It refers to when the statement of the premise includes or excludes all individuals of a race or element, whatever their quality.

They are easy to identify because they use the words "all" or "none" in their propositions. For example: "all horses are equines" or "no politician is honest".

Connotations of particular extension

It is when the statement of the premise covers only a part of the total number of individuals of a race or element, whatever their quality.

They are also easy to identify since they use the words “some” or “few”. For example: "some cats eat fish" or "few dogs bark loudly."

Qualities of the premises

This refers to the relationships that exist between the subjects, predicates and the middle terms that make up a premise. These qualities can be of two types:

Affirmative quality

It is also called the quality of union ”. It is a premise that is affirmative when the subject (S) is predicated (P). For example: "all men are born pure."

Negative quality

It is also called the quality of separation. It is a premise that is negative when the subject (S) is not predicated (P). For example: “some fish are not from the river”.

Structure

The syllogism is structured in judgments, two of these so-called premises and a final one, the product of the deduction between the two premises, called consequent or conclusion.

Now, having clear the aspects that concern the premises and consequents, we will now talk about how syllogisms are structured:

Major premise (PM)

It is so called because it is the statement that occupies the first place in the syllogism. This judgment has the predicate (P) of the conclusion; it is accompanied by the middle term (M), which we know will disappear in the consequence.

Minor premise (Pm)

It is so called because it is the sentence that occupies the second place in the syllogism. It has the subject (S) of the conclusion and is accompanied by the middle term (M), which will also disappear in the consequence.

Consequent (PC)

It is so called because it is the judgment that is reached. It is also called a conclusion and in this the qualities of S and P are joined or disunited.

It is necessary to be clear that from the interaction of the judgments of the major premise and the minor premise, the arguments that give way to the conception of the conclusions are built.

Having understood what is stated in the previous paragraph, the syllogism can be seen as an entity that allows to obtain a conclusion product of the comparison of two judgments regarding a third term, which is known as the middle term or "M".

Rules

Syllogisms, to be considered such, must respond to a series of well demarcated statutes. There are eight statutes in total; four of the statutes respond or condition the terms, and the other four condition the premises.

No syllogism can have more than three terms

It is a clear statute that seeks to respect the formal structure of the syllogism. That is to say: two terms that are compared with a third term in two different premises to give rise to a third conclusive premise where S and P converge, in denial or belonging, and the comparative term disappears.

Sometimes there are cases of pseudo-syllogisms, in which a fourth term is incorporated due to ignorance, violating its structure. Obviously, not complying with the norm is not taken into account. This type of false syllogism is known as a four-legged syllogism.

Here is an example of a pseudo-syllogism:

PM) Men by nature are unfaithful.

Pm) The woman is not a man.

PC) The woman is not unfaithful.

This is a typical four-legged syllogism error, made when making deductive argumentation. Why is it a mistake? In this case the word "man" is used to denote the human race, it includes both sexes; therefore, introducing the word "man" in the minor premise is including the "fourth leg", breaking the first rule.

Terms of the premises cannot be longer in the conclusions

The conclusion cannot exceed the size of the premises from which it was drawn. The consequent must have, at most, an extension proportional to the size of the union of the (S) and the (P) that preceded it.

Example

PM) Men by nature are unfaithful.

Pm) Pedro is a man.

PC) Pedro is honestly an unfaithful individual, you can tell by…

Here we see how the elegance of a structure designed for summary and synthesis can be ended, adding irrelevant aspects.

The middle term cannot be included in the conclusion

The main function of the middle term is to serve as a link between propositions, between premises. Because it is a common factor, it cannot be included in the conclusions. In the conclusions there are only one S and one P.

Below is a flawed argument for inclusion of the "M":

PM) Men by nature are unfaithful.

Pm) Pedro is a man.

PC) Pedro is an unfaithful man.

The middle term must be universal in one of the trials

If an "M" does not appear with the condition of universality, the syllogism would allow for individual comparisons typical of a four-legged syllogism.

Example

PM) All cats are felines.

Pm) Some cats are tigers.

PC) Therefore, some tigers are cats.

Here it can be denoted that it is not a valid proposition, because the major premise -being affirmative- denotes a “particular” predicate, giving way to a false generalization.

Rules of premises

If there are two negative premises, no conclusions can be drawn

This explanation is very simple. The function that "M" fulfills is to relate the "S" to the "P". If we deny the relationship of "P" with "M" and of "S" with "M", there is no point of connection that is worth, there is no analogy that can be made.

Example

PM) All ships do not sink.

Pm) The wandering sailor is not a ship.

PC)?

A negative conclusion cannot be drawn from two affirmative premises

This is as logical as what is stated in the previous rule. If “S” is related to “M” and “P” is also related to “M”, then there is no way that “S” and “P” are not positively related in the conclusions.

Example

PM) All dogs are faithful.

Pm) August is a dog.

PC) August is unfaithful. (?!)

Two premises of a particular character cannot generate a conclusion

This would break the entire conceptual logic of the syllogism. The syllogism proposes going from the universal to the specific to reveal a conclusion that relates the macro to the micro. If the two premises we have are micro (they are specific), then they are not related to each other and, therefore, there is no valid conclusion.

Example

PM) Some monkeys are hairy.

Pm) Some cat meows.

PC)?

Conclusions will always go after weak particles

By weak we mean the particular versus the universal and the negative versus the positive. As manifested in the statement, the conclusions are conditioned by the negative and the particular at the time of being carried out.

Example

PM) All dogs are canines.

Pm) August is not a dog.

PC) August is not a canine.

Modes

When we speak of "modes" we speak of the number of possible combinations of judgments according to their classification; that is, of types A, E, I, O.

The classifications will be explained below and then the four simplest combinations that can be made within the universe of 256 possible mixtures will be exemplified.

Classification of trials

After having clear the qualities of the premises and their extensions, it is time to determine the types of judgments that they can contain or issue. We have the following four classes:

A: universal affirmative

It specifies that all "S" is "P". For example: "all cats are felines" (S: universal-P: particular).

E: negative universal

It specifies that no "S" is "P". For example: "no cat is feline" (S: universal-P: universal).

I: particular affirmative

It specifies that some "S" is "P". For example: "some cat is feline" (S: particular-P: particular).

O: Negative particular

It specifies that some "S" is not "P". For example: "some cat is not feline" (S: particular-P: universal).

Now, the premises, regardless of their position (this was seen in the structure of the syllogisms) may be composed and superimposed with the following combinations (Let's remember the assignments subject: "S"; predicate: "P"; and middle term: " M ”):

First mode

(PM) / (SM) = (SP)

Example

PM) Cats are felines.

Pm) August is a feline.

PC) August is a cat.

Second mode

(MP) / (SM) = (SP)

Example

PM) Some cats meow.

Pm) August is a feline.

PC) August meows.

Third way

(PM) / (MS) = (SP)

Example

PM) Cats are felines.

Pm) The felines meow.

PC) The meow is from cats.

Fourth way

(MP) / (MS) = (SP)

Example

PM) Some cats meow.

Pm) Some felines are cats.

PC) Cats meow.

It is necessary to bear in mind that in these examples the content of the first parentheses is the upper premise, the content of the second is the lower premise and the third represents the conclusion.

It was clearly seen how logic prevailed in each case and how the syllogisms gave us irrefutable conclusions.

Importance

Despite the time that this philosophical resource has been founded (more than 2300 years), it does not lose its essence and importance. It has resisted time and has given way to great schools of reason and thought, immortalizing Aristotle.

The syllogisms allow man to understand the environment fully, simply and effectively, justifying and relating each of the events that arise close to him.

The syllogisms show that only through observation, practice, and trial error can a real understanding of physical, social, psychological and natural phenomena be reached.

Every global event is related to some particle, and if the appropriate connective is found, the syllogism will allow the appearance of a conclusion that amalgamates the universe with the concrete event, leaving an apprenticeship.

The syllogism represents a unique tool of logical development, both in the pedagogical and in the andragogical fields. It is a resource for the empowerment of reasoning and deductive logic.

References

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3. Gallegos, E. (S. f.). The God of the syllogism. Mexico: Focus. Recovered from: focus.com
4. Galisteo Gómez, E. (2013). What is a syllogism? (n / a): The Guide. Recovered from: philosophia.laguia2000.com
5. Belandria, M. (2014). Venezuela: Journal of Master of Philosophy ULA. Recovered from: erevistas.saber.ula.ve