HYPOTHETICAL SYLLOGISM: CHARACTERISTICS AND EXAMPLES - PHILOSOPHY - 2025

A hypothetical syllogism is one that starts from several hypothesis-based judgments and ends up drawing a valid conclusion by relating them to each other. It is a tool used in logic that is very present in any type of experience, since it allows extrapolating relationships between interconnected events.

In general, syllogisms are defined as part of deductive reasoning. There are several types and all are formed by three premises: a first considered major, a second minor and, finally, a third that would be in which the conclusion generated by relating the previous ones is established.

Aristotle, the first philosopher to formulate a theory about syllogisms

The first thinker to formulate a theory about syllogisms was Aristotle. This philosopher is considered the father of logic. Syllogisms remain one of the main modes of human reasoning and are often represented using a kind of mathematical formula to help better understand them.

There are different types of syllogisms, classified into four figures. All have the three terms mentioned, and up to 256 different syllogism modes can be found. Among those, only 19 are considered legitimate. The syllogisms have led to the appearance of fallacies, which are produced by misusing the logical elements established in them.

Aristotelian logic and syllogisms

As noted above, it is Aristotle who first begins to theorize about the concept of syllogism. The Greek philosopher uses this term when dealing with the so-called Aristotelian judgments.

To do so, he begins to study the relationship between various terms, putting them together and drawing conclusions: logic was born, long called Aristotelian in honor of its creator.

In his book First analytics and in the compilation The organon is where the thinker expresses all his contributions on the subject.

Hypothetical syllogism

Definition

The classical definition states that hypothetical syllogisms are a class or rule of inference with which to draw conclusions. In this case, and hence its hypothetical name, what it raises is a conditional case, and valid or invalid terms may appear.

According to propositional logic, which uses logical connectors to join concepts, the hypothetical is a type of syllogism from which an inference can be drawn.

In the realm of the history of logic, it has been established that these syllogisms are the predecessors of the theory of consequences.

In any case, the arguments presented by these syllogisms make them very frequent in all areas of life. It is enough for someone to reflect to make a decision so that, unconsciously, they are using them. For example:

If I don't pay the taxes, I will be committing a crime.

If I commit a crime, I could go to jail.

So if I don't pay my taxes, I could go to jail.

Formulation

When speaking of logic, the formulations or notations are those formulas that are used to facilitate its use. They are very common in schools, since they work to remember the structure of the syllogism.

As a general rule, the hypothetical notation is as follows:

1st premise: P -–> Q

2nd premise: Q -> R

Conclusion: P -> R.

To make the formula more understandable, it can be summarized as follows:

If A is, B is.

If B is, C is.

Then if A is, C is.

The 3 main types of hypothetical syllogisms

Within the hypothetical syllogisms there are several different types that, although they share the same structure and characteristics, have small differences.

1- Pure hypothetical syllogism

It is the one that has been explained previously, in which the logical structure is maintained without any change with respect to the rule.

In this way, knowing both the first premise (A and B) and the second (B and C), a logical conclusion can be inferred.

Example

If I fall asleep in the morning, I'll be late for work.

If I'm late for work, they'll get my attention.

So if I fall asleep in the morning, they'll get my attention at work. "

2- Mixed hypothetical syllogism

The mixed mixes the hypothesis of the first premise with a second and third categorical. They can be negative or positive, with different structures.

Example of affirmative mixed syllogism

The affirmative, called modus ponens, would translate into a syllogism like this:

If it's sunny, then it's daytime.

It is sunny.

Therefore, it is daytime.

Example of negative mixed syllogism

The negative modus tollens would be as follows:

If the moon rises, then it is night.

It is not night.

Therefore, we do not see the moon.

3- Disjunctive hypothetical syllogism

Mix in its major premise the hypothesis and the dilemma. If this occurs, a hypothetical disjunctive syllogism is generated. Like the mixed ones, these have a positive and a negative form, with the same names that were pointed out.

Example

If A is, B is or C is.

This is how B is.

Therefore, C is not ».

Examples of syllogisms

Sometimes it is not easy to understand the concept of syllogism, so the best way to answer any questions is to see some examples:

First example

“If my sister is at home, then she can't look for work.

If you're not looking for a job, then no one is going to hire you.

Later, if my sister is at home, no one will hire her.

Second example

If men are nice, then everyone likes them.

If everyone likes you, then you will have a lot of friends.

Then if men are kind, then they will have many friends.

Third example

If I don't wake up, I can't go to the party.

If I don't go to the party, I won't have fun.

So if I don't wake up I won't have fun.

Fourth example

«If you study logic, you will know ways to deduce valid arguments.

If you know ways to deduce valid arguments, then you can learn to raise valid arguments.

Therefore, if you study logic, then you can learn to make valid arguments.

References

1. abc. Law of the hypothetical syllogism. Obtained from abc.com.py
2. Delira Bautista, José. The hypothetical syllogism in human thought. Recovered from uaa.mx
3. Beuchot, Mauritius. Introduction to logic. Recovered from books.google.es
4. Philosophy-index. Hypothetical syllogism. Retrieved from philosophy-index.com
5. Dr. Naugle. Hypothetical Syllogisms. Recovered from dbu.edu
6. Crucible concept. Lessons in logic hypothetical syllogism. Retrieved from conceptcrucible.com
7. Lear, Jonathan. Aristotle and Logical Theory. Recovered from books.google.es
8. Harris, Robert. Deduction. Retrieved from virtualsalt.com